Finite Group Databasebeta

← C101×#15776 #38797927

Subgroups — C101×#15776 #38797927

Order 25856.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C101C211yesmaximal, characteristic, complemented
2C2×#396×C101C211yesmaximal, characteristic, complemented
3C2×#394×C101C211yesmaximal, characteristic, complemented
4C2×#392×C101C211yesmaximal, characteristic
5C2×#390×C101C211yesmaximal, characteristic, complemented
6C2×#390×C101C211yesmaximal, characteristic, complemented
7C2×#388×C101C211yesmaximal, characteristic, complemented
8C2×#387×C101C211yesmaximal, characteristic, complemented
9C101×#1439C211yesmaximal, characteristic, complemented
10C101×#1439C211yesmaximal, characteristic, complemented
11C101×#1438C211yesmaximal, characteristic, complemented
12C101×#1438C211yesmaximal, characteristic, complemented
13C101×#1438C211yesmaximal, characteristic, complemented
14C101×#1437C211yesmaximal, characteristic, complemented
15C101×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C23×D4×C101C2211yescharacteristic
19C22×C4⋊C4×C101C2211yescharacteristic
20C22×C4⋊C4×C101C2211yescharacteristic
21C22×C4⋊C4×C101C2211yescharacteristic
22C22×C4⋊C4×C101C2211yescharacteristic
23C22×C4⋊C4×C101C2211yescharacteristic
24C22×C22⋊C4×C101C2211yescharacteristic
25C22×C22⋊C4×C101C2211yescharacteristic
26C22×C22⋊C4×C101C2211yescharacteristic
27C22×C22⋊C4×C101C2211yescharacteristic
28C22×C22⋊C4×C101C2211yescharacteristic
29C22×C22⋊C4×C101C2211yescharacteristic
30C22×C22⋊C4×C101C2211yescharacteristic
31C22×C22⋊C4×C101C2211yescharacteristic
32C22×C22⋊C4×C101C2211yescharacteristic
33C22×C22⋊C4×C101C2211yescharacteristic
34C22×C22⋊C4×C101C2211yescharacteristic
35C22×C22⋊C4×C101C2211yescharacteristic
36C22×C22⋊C4×C101C2211yescharacteristic
37C22×C22⋊C4×C101C2211yescharacteristic
38C22×C22⋊C4×C101C2211yescharacteristic
39C22×C42×C101C2211yescharacteristic
40C22×C42×C101C2211yescharacteristic
41#399×C101—24no—
42#396×C101—24no—
43#394×C101—24no—
44#392×C101—24no—
45#390×C101—24no—
46#390×C101—24no—
47#388×C101—24no—
48#387×C101—24no—
49C2×#95×C101C2211yescharacteristic
50C2×#95×C101C2211yescharacteristic
51C2×#95×C101C2211yescharacteristic
52C2×#95×C101C2211yescharacteristic
53C2×#95×C101C2211yescharacteristic
54C2×#95×C101C2211yescharacteristic
55C2×#95×C101C2211yescharacteristic
56C2×#95×C101C2211yescharacteristic
57C2×#95×C101C2211yescharacteristic
58C2×#95×C101C2211yescharacteristic
59C25×C101C2311yescharacteristic
60C25×C101C2311yescharacteristic
61C25×C101C2311yescharacteristic
62C22×D4×C101—22no—
63C22×D4×C101—22no—
64C22×D4×C101—22no—
65C22×D4×C101—22no—
66C22×D4×C101—22no—
67C22×D4×C101—22no—
68C22×D4×C101—22no—
69C22×D4×C101—22no—
70C22×D4×C101—22no—
71C22×D4×C101—22no—
72C22×D4×C101—22no—
73C22×D4×C101—22no—
74C22×D4×C101—22no—
75C22×D4×C101—41no—
76C22×D4×C101—41no—
77C22×D4×C101—41no—
78C22×D4×C101—41no—
79C22×D4×C101—41no—
80C22×D4×C101—41no—
81C22×D4×C101—41no—
82C22×D4×C101—41no—
83C23×C4×C101C2311yescharacteristic
84C23×C4×C101C2311yescharacteristic
85C23×C4×C101C2311yescharacteristic
86C23×C4×C101C2311yescharacteristic
87C23×C4×C101C2311yescharacteristic
88C23×C4×C101C2311yescharacteristic
89C23×C4×C101C2311yescharacteristic
90C23×C4×C101C2311yescharacteristic
91C23×C4×C101C2311yescharacteristic
92C23×C4×C101C2311yescharacteristic
93C23×C4×C101C2311yescharacteristic
94C23×C4×C101C2311yescharacteristic
95C2×C4⋊C4×C101—22no—
96C2×C4⋊C4×C101—22no—
97C2×C4⋊C4×C101—22no—
98C2×C4⋊C4×C101—22no—
99C2×C4⋊C4×C101—22no—
100C2×C4⋊C4×C101—22no—
101C2×C4⋊C4×C101—22no—
102C2×C4⋊C4×C101—22no—
103C2×C4⋊C4×C101—22no—
104C2×C4⋊C4×C101—41no—
105C2×C4⋊C4×C101—41no—
106C2×C4⋊C4×C101—41no—
107C2×C4⋊C4×C101—41no—
108C2×C4⋊C4×C101D414yescomplemented
109C2×C4⋊C4×C101D414yescomplemented
110C2×C22⋊C4×C101—22no—
111C2×C22⋊C4×C101—22no—
112C2×C22⋊C4×C101—22no—
113C2×C22⋊C4×C101—22no—
114C2×C22⋊C4×C101—22no—
115C2×C22⋊C4×C101—22no—
116C2×C22⋊C4×C101—22no—
117C2×C22⋊C4×C101—22no—
118C2×C22⋊C4×C101—22no—
119C2×C22⋊C4×C101—22no—
120C2×C22⋊C4×C101—22no—
121C2×C22⋊C4×C101—22no—
122C2×C22⋊C4×C101—22no—
123C2×C22⋊C4×C101—22no—
124C2×C22⋊C4×C101—22no—
125C2×C22⋊C4×C101—22no—
126C2×C22⋊C4×C101—22no—
127C2×C22⋊C4×C101—22no—
128C2×C22⋊C4×C101—22no—
129C2×C22⋊C4×C101—22no—
130C2×C22⋊C4×C101—22no—
131C2×C22⋊C4×C101—22no—
132C2×C22⋊C4×C101—22no—
133C2×C22⋊C4×C101—22no—
134C2×C22⋊C4×C101—22no—
135C2×C22⋊C4×C101—22no—
136C2×C22⋊C4×C101—22no—
137C2×C22⋊C4×C101—22no—
138C2×C22⋊C4×C101—22no—
139C2×C22⋊C4×C101—22no—
140C2×C22⋊C4×C101—22no—
141C2×C22⋊C4×C101—41no—
142C2×C22⋊C4×C101—41no—
143C2×C22⋊C4×C101—41no—
144C2×C22⋊C4×C101—41no—
145C2×C22⋊C4×C101—41no—
146C2×C22⋊C4×C101—41no—
147C2×C22⋊C4×C101—41no—
148C2×C22⋊C4×C101—41no—
149C2×C22⋊C4×C101—41no—
150C2×C22⋊C4×C101—41no—
151C2×C22⋊C4×C101—41no—
152C2×C22⋊C4×C101—41no—
153C2×C22⋊C4×C101—41no—
154C2×C22⋊C4×C101—41no—
155C2×C42×C101—22no—
156C2×C42×C101—22no—
157C2×C42×C101—22no—
158C2×C42×C101—22no—
159C2×C42×C101—41no—
160C2×C42×C101—41no—
161#95×C101—22no—
162#95×C101—22no—
163#95×C101—22no—
164#95×C101—22no—
165#95×C101—22no—
166#95×C101—22no—
167#95×C101—41no—
168#95×C101—41no—
169#95×C101D414yes—
170#95×C101D414yescomplemented
171C24×C101—21no—
172C24×C101—21no—
173C24×C101—21no—
174C24×C101—21no—
175C24×C101—21no—
176C24×C101—21no—
177C24×C101—21no—
178C24×C101—21no—
179C24×C101—21no—
180C24×C101—21no—
181C24×C101—21no—
182C24×C101—21no—
183C24×C101—21no—
184C24×C101—21no—
185C24×C101—21no—
186C24×C101—21no—
187C24×C101—21no—
188C24×C101—21no—
189C24×C101—21no—
190C24×C101—21no—
191C24×C101—21no—
192C24×C101—21no—
193C24×C101—21no—
194C24×C101—21no—
195C24×C101—21no—
196C24×C101—21no—
197C24×C101—21no—
198C24×C101—21no—
199C24×C101—21no—
200C24×C101—21no—
201C24×C101—21no—
202C24×C101—21no—
203C24×C101—21no—
204C24×C101—21no—
205C24×C101—21no—
206C24×C101—21no—
207C24×C101—21no—
208C24×C101—21no—
209C24×C101—21no—
210C24×C101—21no—
211C24×C101—21no—
212C24×C101—21no—
213C24×C101#4112yes—
214C24×C101#4112yes—
215C24×C101#4112yes—
216C24×C101C2411yescharacteristic
217C2×D4×C101—28no—
218C2×D4×C101—28no—
219C2×D4×C101—44no—
220C2×D4×C101—44no—
221C2×D4×C101—44no—
222C2×D4×C101—44no—
223C2×D4×C101—44no—
224C2×D4×C101—44no—
225C2×D4×C101—44no—
226C2×D4×C101—44no—
227C2×D4×C101—44no—
228C2×D4×C101—44no—
229C2×D4×C101—44no—
230C2×D4×C101—44no—
231C2×D4×C101—44no—
232C2×D4×C101—44no—
233C2×D4×C101—44no—
234C2×D4×C101—44no—
235C2×D4×C101—44no—
236C2×D4×C101—44no—
237C2×D4×C101—44no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—21no—
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—21no—
245C22×C4×C101—21no—
246C22×C4×C101—21no—
247C22×C4×C101—21no—
248C22×C4×C101—21no—
249C22×C4×C101—21no—
250C22×C4×C101—21no—
251C22×C4×C101—21no—
252C22×C4×C101—21no—
253C22×C4×C101—21no—
254C22×C4×C101—21no—
255C22×C4×C101—21no—
256C22×C4×C101—21no—
257C22×C4×C101—21no—
258C22×C4×C101—21no—
259C22×C4×C101—21no—
260C22×C4×C101—21no—
261C22×C4×C101—21no—
262C22×C4×C101—21no—
263C22×C4×C101—21no—
264C22×C4×C101—21no—
265C22×C4×C101—21no—
266C22×C4×C101—21no—
267C22×C4×C101—21no—
268C22×C4×C101—21no—
269C22×C4×C101—21no—
270C22×C4×C101—21no—
271C22×C4×C101—21no—
272C22×C4×C101—21no—
273C22×C4×C101—21no—
274C22×C4×C101—21no—
275C22×C4×C101—21no—
276C22×C4×C101—21no—
277C22×C4×C101—21no—
278C22×C4×C101—21no—
279C22×C4×C101—21no—
280C22×C4×C101—21no—
281C22×C4×C101—21no—
282C22×C4×C101—21no—
283C22×C4×C101—21no—
284C22×C4×C101—21no—
285C22×C4×C101—21no—
286C22×C4×C101—21no—
287C22×C4×C101—21no—
288C22×C4×C101—21no—
289C22×C4×C101—21no—
290C22×C4×C101—21no—
291C22×C4×C101—21no—
292C22×C4×C101—21no—
293C22×C4×C101—21no—
294C22×C4×C101—21no—
295C22×C4×C101—21no—
296C22×C4×C101—21no—
297C22×C4×C101—21no—
298C22×C4×C101—21no—
299C22×C4×C101—21no—
300C22×C4×C101—21no—
301C22×C4×C101—21no—
302C22×C4×C101—21no—
303C22×C4×C101—21no—
304C22×C4×C101—21no—
305C22×C4×C101—21no—
306C22×C4×C101—21no—
307C22×C4×C101—21no—
308C22×C4×C101C2×D412yes—
309C22×C4×C101C2×D412yes—
310C22×C4×C101C2×D412yes—
311C22×C4×C101C2×D412yes—
312C22×C4×C101C2×D412yes—
313C22×C4×C101C2×D412yes—
314C22×C4×C101C2×D412yes—
315C22×C4×C101C2×D412yes—
316C22×C4×C101C2×D412yes—
317C22×C4×C101C2×D412yes—
318C22×C4×C101C2×D412yes—
319C22×C4×C101C2×D412yes—
320C22×C4×C101#4112yes—
321C22×C4×C101#4112yes—
322C4⋊C4×C101—28no—
323C4⋊C4×C101—44no—
324C4⋊C4×C101—44no—
325C4⋊C4×C101—44no—
326C4⋊C4×C101—44no—
327C22⋊C4×C101—28no—
328C22⋊C4×C101—44no—
329C22⋊C4×C101—44no—
330C22⋊C4×C101—44no—
331C22⋊C4×C101—44no—
332C22⋊C4×C101—44no—
333C22⋊C4×C101—44no—
334C22⋊C4×C101—44no—
335C22⋊C4×C101—44no—
336C22⋊C4×C101—44no—
337C22⋊C4×C101—44no—
338C22⋊C4×C101—44no—
339C22⋊C4×C101—44no—
340C22⋊C4×C101—44no—
341C22⋊C4×C101—44no—
342C42×C101—44no—
343C42×C101—44no—
344C23×C101—22no—
345C23×C101—22no—
346C23×C101—22no—
347C23×C101—22no—
348C23×C101—22no—
349C23×C101—22no—
350C23×C101—22no—
351C23×C101—22no—
352C23×C101—22no—
353C23×C101—22no—
354C23×C101—22no—
355C23×C101—22no—
356C23×C101—22no—
357C23×C101—22no—
358C23×C101—22no—
359C23×C101—22no—
360C23×C101—22no—
361C23×C101—22no—
362C23×C101—22no—
363C23×C101—22no—
364C23×C101—22no—
365C23×C101—41no—
366C23×C101—41no—
367C23×C101—41no—
368C23×C101—41no—
369C23×C101—41no—
370C23×C101—41no—
371C23×C101—41no—
372C23×C101—41no—
373C23×C101—41no—
374C23×C101—41no—
375C23×C101—41no—
376C23×C101—41no—
377C23×C101—41no—
378C23×C101—41no—
379C23×C101—41no—
380C23×C101—41no—
381C23×C101—41no—
382C23×C101—41no—
383C23×C101—41no—
384C23×C101—41no—
385C23×C101—41no—
386C23×C101—41no—
387C23×C101—41no—
388C23×C101—41no—
389C23×C101—41no—
390C23×C101—41no—
391C23×C101—41no—
392C23×C101—41no—
393C23×C101—41no—
394C23×C101—41no—
395C23×C101—41no—
396C23×C101—41no—
397C23×C101—41no—
398C23×C101—41no—
399C23×C101—41no—
400C23×C101—41no—
401C23×C101—41no—
402C23×C101—41no—
403C23×C101—41no—
404C23×C101—41no—
405C23×C101—41no—
406C23×C101—41no—
407C23×C101—41no—
408C23×C101—41no—
409C23×C101—41no—
410C23×C101—41no—
411C23×C101—41no—
412C23×C101—41no—
413C23×C101—41no—
414C23×C101—41no—
415C23×C101—41no—
416C23×C101—41no—
417C23×C101—41no—
418C23×C101—41no—
419C23×C101—41no—
420C23×C101—41no—
421C23×C101—41no—
422C23×C101—41no—
423C23×C101—41no—
424C23×C101—41no—
425C23×C101—41no—
426C23×C101—41no—
427C23×C101—41no—
428C23×C101—41no—
429C23×C101—41no—
430C23×C101—41no—
431C23×C101—41no—
432C23×C101—41no—
433C23×C101—41no—
434C23×C101—41no—
435C23×C101—41no—
436C23×C101—41no—
437C23×C101—41no—
438C23×C101—41no—
439C23×C101—41no—
440C23×C101—41no—
441C23×C101—41no—
442C23×C101—41no—
443C23×C101—41no—
444C23×C101—41no—
445C23×C101—41no—
446C23×C101—41no—
447C23×C101—41no—
448C23×C101—41no—
449C23×C101C22×D411yescharacteristic
450C23×C101C22×D411yescharacteristic
451C23×C101C22×D411yescharacteristic
452C23×C101C22×D411yescharacteristic
453C23×C101C2×#4111yescharacteristic
454C23×C101C2×#4111yescharacteristic
455C23×C101C2×#4111yescharacteristic
456C23×C101C2×#4111yescharacteristic
457C23×C101C2×#4111yescharacteristic
458C23×C101H(5,𝔽2)11yescharacteristic
459C23×C101H(5,𝔽2)11yescharacteristic
460C23×C101H(5,𝔽2)11yescharacteristic
461C23×C101H(5,𝔽2)11yescharacteristic
462C23×C101H(5,𝔽2)11yescharacteristic
463C23×C1012−1+411yescharacteristic
464D4×C101—416no—
465D4×C101—416no—
466D4×C101—416no—
467C2×C4×C101—22no—
468C2×C4×C101—22no—
469C2×C4×C101—22no—
470C2×C4×C101—22no—
471C2×C4×C101—22no—
472C2×C4×C101—22no—
473C2×C4×C101—22no—
474C2×C4×C101—22no—
475C2×C4×C101—22no—
476C2×C4×C101—22no—
477C2×C4×C101—22no—
478C2×C4×C101—22no—
479C2×C4×C101—22no—
480C2×C4×C101—22no—
481C2×C4×C101—22no—
482C2×C4×C101—22no—
483C2×C4×C101—22no—
484C2×C4×C101—22no—
485C2×C4×C101—22no—
486C2×C4×C101—22no—
487C2×C4×C101—22no—
488C2×C4×C101—22no—
489C2×C4×C101—22no—
490C2×C4×C101—22no—
491C2×C4×C101—22no—
492C2×C4×C101—22no—
493C2×C4×C101—22no—
494C2×C4×C101—22no—
495C2×C4×C101—22no—
496C2×C4×C101—22no—
497C2×C4×C101—22no—
498C2×C4×C101—22no—
499C2×C4×C101—22no—
500C2×C4×C101—22no—
501C2×C4×C101—22no—
502C2×C4×C101—22no—
503C2×C4×C101—41no—
504C2×C4×C101—41no—
505C2×C4×C101—41no—
506C2×C4×C101—41no—
507C2×C4×C101—41no—
508C2×C4×C101—41no—
509C2×C4×C101—41no—
510C2×C4×C101—41no—
511C2×C4×C101—41no—
512C2×C4×C101—41no—
513C2×C4×C101—41no—
514C2×C4×C101—41no—
515C2×C4×C101—41no—
516C2×C4×C101—41no—
517C2×C4×C101—41no—
518C2×C4×C101—41no—
519C2×C4×C101—41no—
520C2×C4×C101—41no—
521C2×C4×C101—41no—
522C2×C4×C101—41no—
523C2×C4×C101—41no—
524C2×C4×C101—41no—
525C2×C4×C101—41no—
526C2×C4×C101—41no—
527C2×C4×C101—41no—
528C2×C4×C101—41no—
529C2×C4×C101—41no—
530C2×C4×C101—41no—
531C2×C4×C101—41no—
532C2×C4×C101—41no—
533C2×C4×C101—41no—
534C2×C4×C101—41no—
535C2×C4×C101—41no—
536C2×C4×C101—41no—
537C2×C4×C101—41no—
538C2×C4×C101—41no—
539C2×C4×C101—41no—
540C2×C4×C101—41no—
541C2×C4×C101—41no—
542C2×C4×C101—41no—
543C2×C4×C101—41no—
544C2×C4×C101—41no—
545C2×C4×C101—41no—
546C2×C4×C101—41no—
547C2×C4×C101—41no—
548C2×C4×C101—41no—
549C2×C4×C101#12114yes—
550C2×C4×C101#12714yes—
551C22×C101—42no—
552C22×C101—42no—
553C22×C101—42no—
554C22×C101—42no—
555C22×C101—42no—
556C22×C101—42no—
557C22×C101—42no—
558C22×C101—42no—
559C22×C101—42no—
560C22×C101—42no—
561C22×C101—42no—
562C22×C101—42no—
563C22×C101—42no—
564C22×C101—42no—
565C22×C101—42no—
566C22×C101—42no—
567C22×C101—42no—
568C22×C101—42no—
569C22×C101—42no—
570C22×C101—42no—
571C22×C101—42no—
572C22×C101—81no—
573C22×C101—81no—
574C22×C101—81no—
575C22×C101—81no—
576C22×C101—81no—
577C22×C101—81no—
578C22×C101—81no—
579C22×C101—81no—
580C22×C101—81no—
581C22×C101—81no—
582C22×C101—81no—
583C22×C101—81no—
584C22×C101—81no—
585C22×C101—81no—
586C22×C101—81no—
587C22×C101—81no—
588C22×C101—81no—
589C22×C101—81no—
590C22×C101—81no—
591C22×C101—81no—
592C22×C101—81no—
593C22×C101—81no—
594C22×C101—81no—
595C22×C101—81no—
596C22×C101C2×#12111yescharacteristic
597C22×C101#52511yescharacteristic
598C22×C101#52511yescharacteristic
599C22×C101#52511yescharacteristic
600C22×C101#52911yescharacteristic
601C22×C101C2×#12711yescharacteristic
602C22×C101#53411yescharacteristic
603C22×C101#53511yescharacteristic
604C22×C101#53511yescharacteristic
605C22×C101#53711yescharacteristic
606C22×C101#53811yescharacteristic
607C22×C101#53811yescharacteristic
608C22×C101#53911yescharacteristic
609C22×C101#54011yescharacteristic
610C22×C101#54211yescharacteristic
611C22×C101D4211yescharacteristic
612C22×C101D4211yescharacteristic
613C22×C101#54611yescharacteristic
614C22×C101#54611yescharacteristic
615C22×C101#54611yescharacteristic
616C22×C101#54611yescharacteristic
617C22×C101#54611yescharacteristic
618C22×C101#54611yescharacteristic
619C22×C101#54811yescharacteristic
620C22×C101#54811yescharacteristic
621C22×C101#54811yescharacteristic
622C22×C101#55011yescharacteristic
623C22×C101#55011yescharacteristic
624C22×C101#55011yescharacteristic
625C22×C101#55111yescharacteristic
626C22×C101#55111yescharacteristic
627C22×C101#55111yescharacteristic
628C22×C101#55311yescharacteristic
629C22×C101#56011yescharacteristic
630C22×C101#56211yescharacteristic
631C4×C101—24no—
632C4×C101—24no—
633C4×C101—42no—
634C4×C101—42no—
635C4×C101—42no—
636C4×C101—42no—
637C4×C101—42no—
638C4×C101—42no—
639C4×C101—42no—
640C4×C101—42no—
641C4×C101—81no—
642C4×C101—81no—
643#15776C10111yesmaximal, characteristic, direct product factor, Sylow
644C2×C101—82no—
645C2×C101—82no—
646C2×C101—82no—
647C2×C101#241111yescharacteristic
648C2×C101#242611yescharacteristic
649C2×C101#245611yescharacteristic
650C2×C101#246311yescharacteristic
651C2×C101#246711yescharacteristic
652C2×C101#247111yescharacteristic
653C2×C101#253911yescharacteristic
654C2×C101#254011yescharacteristic
655C2×C101#254111yescharacteristic
656C2×C101#267311yescharacteristic
657C2×C101#267611yescharacteristic
658C2×C101#268511yescharacteristic
659C2×C101#270511yescharacteristic
660C2×C101#271111yescharacteristic
661C2×C101#273011yescharacteristic
662C2×#399C2×C10111yescharacteristic, complemented
663C2×#396C2×C10111yescharacteristic, complemented
664C2×#394C2×C10111yescharacteristic, complemented
665C2×#392C2×C10111yescharacteristic
666C2×#390C2×C10111yescharacteristic, complemented
667C2×#390C2×C10111yescharacteristic, complemented
668C2×#388C2×C10111yescharacteristic, complemented
669C2×#387C2×C10111yescharacteristic, complemented
670#1439C2×C10111yescharacteristic, complemented
671#1439C2×C10111yescharacteristic, complemented
672#1438C2×C10111yescharacteristic, complemented
673#1438C2×C10111yescharacteristic, complemented
674#1438C2×C10111yescharacteristic, complemented
675#1437C2×C10111yescharacteristic, complemented
676#1436C2×C10111yescharacteristic, complemented
677C101#1577611yescharacteristic, direct product factor, Sylow
678C23×D4C22×C10111yescharacteristic
679C23×D4C22×C10111yescharacteristic
680C23×D4C22×C10111yescharacteristic
681C22×C4⋊C4C22×C10111yescharacteristic
682C22×C4⋊C4C22×C10111yescharacteristic
683C22×C4⋊C4C22×C10111yescharacteristic
684C22×C4⋊C4C22×C10111yescharacteristic
685C22×C4⋊C4C22×C10111yescharacteristic
686C22×C22⋊C4C22×C10111yescharacteristic
687C22×C22⋊C4C22×C10111yescharacteristic
688C22×C22⋊C4C22×C10111yescharacteristic
689C22×C22⋊C4C22×C10111yescharacteristic
690C22×C22⋊C4C22×C10111yescharacteristic
691C22×C22⋊C4C22×C10111yescharacteristic
692C22×C22⋊C4C22×C10111yescharacteristic
693C22×C22⋊C4C22×C10111yescharacteristic
694C22×C22⋊C4C22×C10111yescharacteristic
695C22×C22⋊C4C22×C10111yescharacteristic
696C22×C22⋊C4C22×C10111yescharacteristic
697C22×C22⋊C4C22×C10111yescharacteristic
698C22×C22⋊C4C22×C10111yescharacteristic
699C22×C22⋊C4C22×C10111yescharacteristic
700C22×C22⋊C4C22×C10111yescharacteristic
701C22×C42C22×C10111yescharacteristic
702C22×C42C22×C10111yescharacteristic
703#399—24no—
704#396—24no—
705#394—24no—
706#392—24no—
707#390—24no—
708#390—24no—
709#388—24no—
710#387—24no—
711C2×#95C22×C10111yescharacteristic
712C2×#95C22×C10111yescharacteristic
713C2×#95C22×C10111yescharacteristic
714C2×#95C22×C10111yescharacteristic
715C2×#95C22×C10111yescharacteristic
716C2×#95C22×C10111yescharacteristic
717C2×#95C22×C10111yescharacteristic
718C2×#95C22×C10111yescharacteristic
719C2×#95C22×C10111yescharacteristic
720C2×#95C22×C10111yescharacteristic
721C25C23×C10111yescharacteristic
722C25C23×C10111yescharacteristic
723C25C23×C10111yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C23×C4C23×C10111yescharacteristic
746C23×C4C23×C10111yescharacteristic
747C23×C4C23×C10111yescharacteristic
748C23×C4C23×C10111yescharacteristic
749C23×C4C23×C10111yescharacteristic
750C23×C4C23×C10111yescharacteristic
751C23×C4C23×C10111yescharacteristic
752C23×C4C23×C10111yescharacteristic
753C23×C4C23×C10111yescharacteristic
754C23×C4C23×C10111yescharacteristic
755C23×C4C23×C10111yescharacteristic
756C23×C4C23×C10111yescharacteristic
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—41no—
767C2×C4⋊C4—41no—
768C2×C4⋊C4—41no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4D4×C10114yescomplemented
771C2×C4⋊C4D4×C10114yescomplemented
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C42—22no—
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—41no—
822C2×C42—41no—
823#95—22no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—41no—
830#95—41no—
831#95D4×C10114yes—
832#95D4×C10114yescomplemented
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24#41×C10112yes—
876C24#41×C10112yes—
877C24#41×C10112yes—
878C24C24×C10111yescharacteristic
879C2×D4—28no—
880C2×D4—28no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4C2×D4×C10112yes—
971C22×C4C2×D4×C10112yes—
972C22×C4C2×D4×C10112yes—
973C22×C4C2×D4×C10112yes—
974C22×C4C2×D4×C10112yes—
975C22×C4C2×D4×C10112yes—
976C22×C4C2×D4×C10112yes—
977C22×C4C2×D4×C10112yes—
978C22×C4C2×D4×C10112yes—
979C22×C4C2×D4×C10112yes—
980C22×C4C2×D4×C10112yes—
981C22×C4C2×D4×C10112yes—
982C22×C4#41×C10112yes—
983C22×C4#41×C10112yes—
984C4⋊C4—28no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C22⋊C4—28no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C42—44no—
1005C42—44no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23C22×D4×C10111yescharacteristic
1112C23C22×D4×C10111yescharacteristic
1113C23C22×D4×C10111yescharacteristic
1114C23C22×D4×C10111yescharacteristic
1115C23C2×#41×C10111yescharacteristic
1116C23C2×#41×C10111yescharacteristic
1117C23C2×#41×C10111yescharacteristic
1118C23C2×#41×C10111yescharacteristic
1119C23C2×#41×C10111yescharacteristic
1120C23H(5,𝔽2)×C10111yescharacteristic
1121C23H(5,𝔽2)×C10111yescharacteristic
1122C23H(5,𝔽2)×C10111yescharacteristic
1123C23H(5,𝔽2)×C10111yescharacteristic
1124C23H(5,𝔽2)×C10111yescharacteristic
1125C232−1+4×C10111yescharacteristic
1126D4—416no—
1127D4—416no—
1128D4—416no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4#121×C10114yes—
1212C2×C4#127×C10114yes—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22C2×#121×C10111yescharacteristic
1259C22#525×C10111yescharacteristic
1260C22#525×C10111yescharacteristic
1261C22#525×C10111yescharacteristic
1262C22#529×C10111yescharacteristic
1263C22C2×#127×C10111yescharacteristic
1264C22#534×C10111yescharacteristic
1265C22#535×C10111yescharacteristic
1266C22#535×C10111yescharacteristic
1267C22#537×C10111yescharacteristic
1268C22#538×C10111yescharacteristic
1269C22#538×C10111yescharacteristic
1270C22#539×C10111yescharacteristic
1271C22#540×C10111yescharacteristic
1272C22#542×C10111yescharacteristic
1273C22D42×C10111yescharacteristic
1274C22D42×C10111yescharacteristic
1275C22#546×C10111yescharacteristic
1276C22#546×C10111yescharacteristic
1277C22#546×C10111yescharacteristic
1278C22#546×C10111yescharacteristic
1279C22#546×C10111yescharacteristic
1280C22#546×C10111yescharacteristic
1281C22#548×C10111yescharacteristic
1282C22#548×C10111yescharacteristic
1283C22#548×C10111yescharacteristic
1284C22#550×C10111yescharacteristic
1285C22#550×C10111yescharacteristic
1286C22#550×C10111yescharacteristic
1287C22#551×C10111yescharacteristic
1288C22#551×C10111yescharacteristic
1289C22#551×C10111yescharacteristic
1290C22#553×C10111yescharacteristic
1291C22#560×C10111yescharacteristic
1292C22#562×C10111yescharacteristic
1293C4—24no—
1294C4—24no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—81no—
1304C4—81no—
1305C2—82no—
1306C2—82no—
1307C2—82no—
1308C2C101×#241111yescharacteristic
1309C2C101×#242611yescharacteristic
1310C2C101×#245611yescharacteristic
1311C2C101×#246311yescharacteristic
1312C2C101×#246711yescharacteristic
1313C2C101×#247111yescharacteristic
1314C2C101×#253911yescharacteristic
1315C2C101×#254011yescharacteristic
1316C2C101×#254111yescharacteristic
1317C2C101×#267311yescharacteristic
1318C2C101×#267611yescharacteristic
1319C2C101×#268511yescharacteristic
1320C2C101×#270511yescharacteristic
1321C2C101×#271111yescharacteristic
1322C2C101×#273011yescharacteristic
subgroupG/H
center, socleC24×C101C24
commutator, Frattini, cosocleC24C24×C101
prime radicalC2×#392×C101C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#399×C101C2semidirect
2. C2×#396×C101C2semidirect
3. C2×#394×C101C2semidirect
5. C2×#390×C101C2semidirect
6. C2×#390×C101C2semidirect
7. C2×#388×C101C2semidirect
8. C2×#387×C101C2semidirect
9. C101×#1439C2semidirect
10. C101×#1439C2semidirect
11. C101×#1438C2semidirect
12. C101×#1438C2semidirect
13. C101×#1438C2semidirect
14. C101×#1437C2semidirect
15. C101×#1436C2semidirect
108. C2×C4⋊C4×C101D4semidirect
109. C2×C4⋊C4×C101D4semidirect
170. #95×C101D4semidirect
643. #15776C101direct (N × H)
662. C2×#399C2×C101semidirect
663. C2×#396C2×C101semidirect
664. C2×#394C2×C101semidirect
666. C2×#390C2×C101semidirect
667. C2×#390C2×C101semidirect
668. C2×#388C2×C101semidirect
669. C2×#387C2×C101semidirect
670. #1439C2×C101semidirect
671. #1439C2×C101semidirect
672. #1438C2×C101semidirect
673. #1438C2×C101semidirect
674. #1438C2×C101semidirect
675. #1437C2×C101semidirect
676. #1436C2×C101semidirect
677. C101#15776direct (N × H)
770. C2×C4⋊C4D4×C101semidirect
771. C2×C4⋊C4D4×C101semidirect
832. #95D4×C101semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#399×C1012
C2×#396×C1012
C2×#394×C1012
C2×#392×C1012
C2×#390×C1012
C2×#388×C1012
C2×#387×C1012
C101×#14392
C101×#14382
C101×#14372
C101×#14362
#15776101