Finite Group Databasebeta

← C101×#14052 #38796203

Subgroups — C101×#14052 #38796203

Order 25856.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C101C211yesmaximal, characteristic
2C2×#391×C101C211yesmaximal, characteristic, complemented
3C2×#385×C101C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C101C211yesmaximal, characteristic
5C22×#95×C101C211yesmaximal, characteristic
6C101×#1446C211yesmaximal, characteristic, complemented
7C101×#1445C211yesmaximal, characteristic, complemented
8C101×#1441C211yesmaximal, characteristic, complemented
9C101×#1441C211yesmaximal, characteristic, complemented
10C101×#1436C211yesmaximal, characteristic, complemented
11C101×#1436C211yesmaximal, characteristic, complemented
12C101×C4⋊#95C211yesmaximal, characteristic, complemented
13C101×C22⋊#95C211yesmaximal, characteristic
14C101×C22⋊#95C211yesmaximal, characteristic
15C101×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C101C2211yescharacteristic
17C24×C4×C101C2211yescharacteristic
18C24×C4×C101C2211yescharacteristic
19C24×C4×C101C2211yescharacteristic
20C2×C22⋊Q8×C101—24no—
21C2×C22⋊Q8×C101—24no—
22C2×C22⋊Q8×C101C418yescomplemented
23C22×C4⋊C4×C101C2211yescharacteristic
24C22×C4⋊C4×C101C2211yescharacteristic
25C22×C4⋊C4×C101C2211yescharacteristic
26C22×C4⋊C4×C101C2211yescharacteristic
27C22×C4⋊C4×C101C2211yescharacteristic
28C22×C22⋊C4×C101C2211yescharacteristic
29C22×C22⋊C4×C101C2211yescharacteristic
30C22×C22⋊C4×C101C2211yescharacteristic
31C22×C22⋊C4×C101C2211yescharacteristic
32C22×C42×C101C2211yescharacteristic
33C22×C42×C101C2211yescharacteristic
34#391×C101—24no—
35#385×C101—24no—
36C4×C22⋊C4×C101—24no—
37C2×#95×C101—24no—
38C2×#95×C101C2211yescharacteristic
39C2×#95×C101C2211yescharacteristic
40C2×#95×C101C2211yescharacteristic
41C2×#95×C101C2211yescharacteristic
42C2×#95×C101C2211yescharacteristic
43C2×#95×C101C2211yescharacteristic
44C2×#95×C101C2211yescharacteristic
45C2×#95×C101C2211yescharacteristic
46C2×#95×C101C2211yescharacteristic
47C2×#95×C101C2211yescharacteristic
48C2×#95×C101C2211yescharacteristic
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
58C25×C101C2311yescharacteristic
59C22×Q8×C101—22no—
60C22×Q8×C101—22no—
61C22×Q8×C101—22no—
62C22×Q8×C101—22no—
63C22×Q8×C101—41no—
64C22×Q8×C101—41no—
65C22×Q8×C101C2×C414yescomplemented
66C23×C4×C101—22no—
67C23×C4×C101—22no—
68C23×C4×C101—22no—
69C23×C4×C101—22no—
70C23×C4×C101—22no—
71C23×C4×C101—22no—
72C23×C4×C101—22no—
73C23×C4×C101—22no—
74C23×C4×C101—22no—
75C23×C4×C101—22no—
76C23×C4×C101—22no—
77C23×C4×C101—22no—
78C23×C4×C101—22no—
79C23×C4×C101—41no—
80C23×C4×C101—41no—
81C23×C4×C101—41no—
82C23×C4×C101—41no—
83C23×C4×C101—41no—
84C23×C4×C101—41no—
85C23×C4×C101C2×C414yes—
86C23×C4×C101Q814yescomplemented
87C23×C4×C101C2311yescharacteristic
88C23×C4×C101C2311yescharacteristic
89C23×C4×C101C2311yescharacteristic
90C23×C4×C101C2311yescharacteristic
91C23×C4×C101C2311yescharacteristic
92C23×C4×C101C2311yescharacteristic
93C23×C4×C101C2311yescharacteristic
94C23×C4×C101C2311yescharacteristic
95C23×C4×C101C2311yescharacteristic
96C23×C4×C101C2311yescharacteristic
97C23×C4×C101C2311yescharacteristic
98C23×C4×C101C2311yescharacteristic
99C23×C4×C101C2311yescharacteristic
100C23×C4×C101C2311yescharacteristic
101C22⋊Q8×C101—232no—
102C2×C4⋊C4×C101—22no—
103C2×C4⋊C4×C101—22no—
104C2×C4⋊C4×C101—22no—
105C2×C4⋊C4×C101—22no—
106C2×C4⋊C4×C101—22no—
107C2×C4⋊C4×C101—22no—
108C2×C4⋊C4×C101—22no—
109C2×C4⋊C4×C101—22no—
110C2×C4⋊C4×C101—22no—
111C2×C4⋊C4×C101—22no—
112C2×C4⋊C4×C101—41no—
113C2×C4⋊C4×C101—41no—
114C2×C4⋊C4×C101C2×C414yescomplemented
115C2×C4⋊C4×C101C2×C414yescomplemented
116C2×C4⋊C4×C101C2×C414yescomplemented
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×C101C2×C414yes—
125C2×C22⋊C4×C101C2×C414yes—
126C2×C22⋊C4×C101D414yes—
127C2×C22⋊C4×C101D414yes—
128C2×C22⋊C4×C101Q814yescomplemented
129C2×C42×C101—22no—
130C2×C42×C101—22no—
131C2×C42×C101—22no—
132C2×C42×C101—22no—
133C2×C42×C101—41no—
134C2×C42×C101—41no—
135#95×C101—22no—
136#95×C101—22no—
137#95×C101—22no—
138#95×C101—22no—
139#95×C101—22no—
140#95×C101—22no—
141#95×C101—22no—
142#95×C101—22no—
143#95×C101—22no—
144#95×C101—22no—
145#95×C101—22no—
146#95×C101—22no—
147#95×C101—22no—
148#95×C101—41no—
149#95×C101—41no—
150#95×C101—41no—
151#95×C101—41no—
152#95×C101—41no—
153#95×C101—41no—
154#95×C101D414yes—
155C24×C101—21no—
156C24×C101—21no—
157C24×C101—21no—
158C24×C101—21no—
159C24×C101—21no—
160C24×C101—21no—
161C24×C101—21no—
162C24×C101—21no—
163C24×C101C22×C412yes—
164C24×C101C2×D412yes—
165C24×C101C2×D412yes—
166C24×C101C2×Q812yes—
167C24×C101C2×Q812yes—
168C24×C101#4112yes—
169C24×C101#4112yes—
170C24×C101C2411yescharacteristic
171C2×Q8×C101—28no—
172C2×Q8×C101—28no—
173C2×Q8×C101—44no—
174C2×Q8×C101—44no—
175C2×Q8×C101—44no—
176C2×Q8×C101—44no—
177C2×Q8×C101—44no—
178C22×C4×C101—21no—
179C22×C4×C101—21no—
180C22×C4×C101—21no—
181C22×C4×C101—21no—
182C22×C4×C101—21no—
183C22×C4×C101—21no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—21no—
187C22×C4×C101—21no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—28no—
195C22×C4×C101—28no—
196C22×C4×C101—28no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—21no—
206C22×C4×C101—21no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—21no—
218C22×C4×C101—21no—
219C22×C4×C101—21no—
220C22×C4×C101—21no—
221C22×C4×C101—21no—
222C22×C4×C101—21no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—21no—
229C22×C4×C101—21no—
230C22×C4×C101—21no—
231C22×C4×C101—21no—
232C22×C4×C101—21no—
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—21no—
237C22×C4×C101—21no—
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—28no—
246C22×C4×C101—28no—
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—44no—
262C22×C4×C101—44no—
263C22×C4×C101—44no—
264C22×C4×C101—44no—
265C22×C4×C101—44no—
266C22×C4×C101—44no—
267C22×C4×C101—44no—
268C22×C4×C101—44no—
269C22×C4×C101—44no—
270C22×C4×C101—44no—
271C22×C4×C101—44no—
272C22×C4×C101—44no—
273C22×C4×C101—44no—
274C22×C4×C101—44no—
275C22×C4×C101—44no—
276C22×C4×C101—44no—
277C22×C4×C101C22×C412yes—
278C22×C4×C101C22×C412yes—
279C22×C4×C101C22×C412yes—
280C22×C4×C101C22×C412yes—
281C22×C4×C101C22×C412yes—
282C22×C4×C101C22×C412yes—
283C22×C4×C101C2×D412yes—
284C22×C4×C101C2×D412yes—
285C22×C4×C101C2×D412yes—
286C22×C4×C101C2×D412yes—
287C22×C4×C101C2×D412yes—
288C22×C4×C101C2×D412yes—
289C22×C4×C101C2×D412yes—
290C22×C4×C101C2×Q812yes—
291C22×C4×C101C2×Q812yes—
292C22×C4×C101C2×Q812yes—
293C22×C4×C101C2×Q812yes—
294C22×C4×C101#4112yes—
295C22×C4×C101#4112yes—
296C22×C4×C101#4112yes—
297C4⋊C4×C101—28no—
298C4⋊C4×C101—28no—
299C4⋊C4×C101—28no—
300C4⋊C4×C101—44no—
301C4⋊C4×C101—44no—
302C22⋊C4×C101—28no—
303C22⋊C4×C101—28no—
304C22⋊C4×C101—44no—
305C22⋊C4×C101C22⋊C4116yes—
306C42×C101—44no—
307C42×C101—44no—
308C23×C101—22no—
309C23×C101—22no—
310C23×C101—22no—
311C23×C101—22no—
312C23×C101—22no—
313C23×C101—22no—
314C23×C101—22no—
315C23×C101—22no—
316C23×C101—22no—
317C23×C101—22no—
318C23×C101—22no—
319C23×C101—22no—
320C23×C101—22no—
321C23×C101—22no—
322C23×C101—22no—
323C23×C101—22no—
324C23×C101—22no—
325C23×C101—22no—
326C23×C101—22no—
327C23×C101—22no—
328C23×C101—22no—
329C23×C101—22no—
330C23×C101—22no—
331C23×C101—22no—
332C23×C101—22no—
333C23×C101—22no—
334C23×C101—22no—
335C23×C101—22no—
336C23×C101C2×C22⋊C414yes—
337C23×C101C4×Q814yes—
338C23×C101C4×Q814yes—
339C23×C101C22⋊Q814yes—
340C23×C101C22⋊Q814yes—
341C23×C101#12414yes—
342C23×C101C4⋊Q814yes—
343C23×C101C23×C411yescharacteristic
344C23×C101C22×D411yescharacteristic
345C23×C101C22×D411yescharacteristic
346C23×C101C22×D411yescharacteristic
347C23×C101C22×Q811yescharacteristic
348C23×C101C22×Q811yescharacteristic
349C23×C101C2×#4111yescharacteristic
350C23×C101C2×#4111yescharacteristic
351C23×C101C2×#4111yescharacteristic
352C23×C101C2×#4111yescharacteristic
353C23×C101C2×#4111yescharacteristic
354C23×C101H(5,𝔽2)11yescharacteristic
355C23×C101H(5,𝔽2)11yescharacteristic
356C23×C101H(5,𝔽2)11yescharacteristic
357C23×C1012−1+411yescharacteristic
358Q8×C101—416no—
359C2×C4×C101—22no—
360C2×C4×C101—22no—
361C2×C4×C101—22no—
362C2×C4×C101—22no—
363C2×C4×C101—22no—
364C2×C4×C101—22no—
365C2×C4×C101—22no—
366C2×C4×C101—22no—
367C2×C4×C101—22no—
368C2×C4×C101—22no—
369C2×C4×C101—22no—
370C2×C4×C101—22no—
371C2×C4×C101—22no—
372C2×C4×C101—22no—
373C2×C4×C101—22no—
374C2×C4×C101—22no—
375C2×C4×C101—22no—
376C2×C4×C101—22no—
377C2×C4×C101—22no—
378C2×C4×C101—22no—
379C2×C4×C101—22no—
380C2×C4×C101—22no—
381C2×C4×C101—22no—
382C2×C4×C101—22no—
383C2×C4×C101—22no—
384C2×C4×C101—22no—
385C2×C4×C101—22no—
386C2×C4×C101—22no—
387C2×C4×C101—22no—
388C2×C4×C101—22no—
389C2×C4×C101—22no—
390C2×C4×C101—22no—
391C2×C4×C101—22no—
392C2×C4×C101—22no—
393C2×C4×C101—22no—
394C2×C4×C101—22no—
395C2×C4×C101—22no—
396C2×C4×C101—22no—
397C2×C4×C101—22no—
398C2×C4×C101—22no—
399C2×C4×C101—22no—
400C2×C4×C101—22no—
401C2×C4×C101—22no—
402C2×C4×C101—22no—
403C2×C4×C101—22no—
404C2×C4×C101—22no—
405C2×C4×C101—22no—
406C2×C4×C101—22no—
407C2×C4×C101—416no—
408C2×C4×C101—416no—
409C2×C4×C101—416no—
410C2×C4×C101—41no—
411C2×C4×C101—41no—
412C2×C4×C101—41no—
413C2×C4×C101—41no—
414C2×C4×C101—41no—
415C2×C4×C101—41no—
416C2×C4×C101—41no—
417C2×C4×C101—41no—
418C2×C4×C101—41no—
419C2×C4×C101—41no—
420C2×C4×C101—41no—
421C2×C4×C101—41no—
422C2×C4×C101—41no—
423C2×C4×C101—41no—
424C2×C4×C101—41no—
425C2×C4×C101—41no—
426C2×C4×C101—41no—
427C2×C4×C101—41no—
428C2×C4×C101—41no—
429C2×C4×C101—41no—
430C2×C4×C101—41no—
431C2×C4×C101—41no—
432C2×C4×C101—41no—
433C2×C4×C101—41no—
434C2×C4×C101—41no—
435C2×C4×C101—41no—
436C2×C4×C101—41no—
437C2×C4×C101—41no—
438C2×C4×C101—41no—
439C2×C4×C101—41no—
440C2×C4×C101—41no—
441C2×C4×C101—41no—
442C2×C4×C101—41no—
443C2×C4×C101—41no—
444C2×C4×C101—41no—
445C2×C4×C101—41no—
446C2×C4×C101—41no—
447C2×C4×C101—41no—
448C2×C4×C101—41no—
449C2×C4×C101—41no—
450C2×C4×C101—41no—
451C2×C4×C101—41no—
452C2×C4×C101—41no—
453C2×C4×C101—41no—
454C2×C4×C101—41no—
455C2×C4×C101—41no—
456C2×C4×C101C2×C22⋊C414yes—
457C2×C4×C101C2×C22⋊C414yes—
458C2×C4×C101C4×D414yes—
459C2×C4×C101C22⋊Q814yescomplemented
460C22×C101—24no—
461C22×C101—24no—
462C22×C101—24no—
463C22×C101—24no—
464C22×C101—24no—
465C22×C101—24no—
466C22×C101—24no—
467C22×C101—24no—
468C22×C101—24no—
469C22×C101—24no—
470C22×C101—24no—
471C22×C101—24no—
472C22×C101—24no—
473C22×C101—24no—
474C22×C101#39118yescomplemented
475C22×C101C22×C22⋊C411yescharacteristic
476C22×C101C2×C4×D411yescharacteristic
477C22×C101C2×C4×Q811yescharacteristic
478C22×C101C2×C4×Q811yescharacteristic
479C22×C101C4×#4111yescharacteristic
480C22×C101#51811yescharacteristic
481C22×C101#52011yescharacteristic
482C22×C101C2×C22⋊Q811yescharacteristic
483C22×C101C2×C22⋊Q811yescharacteristic
484C22×C101C2×C22⋊Q811yescharacteristic
485C22×C101#52511yescharacteristic
486C22×C101C2×#12411yescharacteristic
487C22×C101#52911yescharacteristic
488C22×C101C2×C4⋊Q811yescharacteristic
489C22×C101#53311yescharacteristic
490C22×C101#53811yescharacteristic
491C22×C101#53911yescharacteristic
492C22×C101#54311yescharacteristic
493C22×C101#54411yescharacteristic
494C22×C101D4211yescharacteristic
495C22×C101D4211yescharacteristic
496C22×C101#54611yescharacteristic
497C22×C101#54611yescharacteristic
498C22×C101#54611yescharacteristic
499C22×C101#54611yescharacteristic
500C22×C101#54611yescharacteristic
501C22×C101#54711yescharacteristic
502C22×C101#54711yescharacteristic
503C22×C101D4×Q811yescharacteristic
504C22×C101#55111yescharacteristic
505C22×C101#55111yescharacteristic
506C22×C101#55211yescharacteristic
507C22×C101#55411yescharacteristic
508C22×C101#55411yescharacteristic
509C22×C101#55411yescharacteristic
510C4×C101—24no—
511C4×C101—24no—
512C4×C101—24no—
513C4×C101—24no—
514C4×C101—42no—
515C4×C101—42no—
516C4×C101—42no—
517C4×C101—42no—
518C4×C101—42no—
519C4×C101—42no—
520C4×C101—42no—
521C4×C101—42no—
522C4×C101—81no—
523C4×C101—81no—
524#14052C10111yesmaximal, characteristic, direct product factor, Sylow
525C2×C101—28no—
526C2×C101C2×#39111yescharacteristic
527C2×C101C4×C22⋊Q811yescharacteristic
528C2×C101#232911yescharacteristic
529C2×C101D4×C22⋊C411yescharacteristic
530C2×C101#233911yescharacteristic
531C2×C101#236011yescharacteristic
532C2×C101#236811yescharacteristic
533C2×C101#243711yescharacteristic
534C2×C101#243811yescharacteristic
535C2×C101#244011yescharacteristic
536C2×C101#244911yescharacteristic
537C2×C101#245011yescharacteristic
538C2×C101#247211yescharacteristic
539C2×C101#248811yescharacteristic
540C2×C101#254911yescharacteristic
541C22×C22⋊Q8C2×C10111yescharacteristic
542C2×#391C2×C10111yescharacteristic, complemented
543C2×#385C2×C10111yescharacteristic
544C2×C4×C22⋊C4C2×C10111yescharacteristic
545C22×#95C2×C10111yescharacteristic
546#1446C2×C10111yescharacteristic, complemented
547#1445C2×C10111yescharacteristic, complemented
548#1441C2×C10111yescharacteristic, complemented
549#1441C2×C10111yescharacteristic, complemented
550#1436C2×C10111yescharacteristic, complemented
551#1436C2×C10111yescharacteristic, complemented
552C4⋊#95C2×C10111yescharacteristic, complemented
553C22⋊#95C2×C10111yescharacteristic
554C22⋊#95C2×C10111yescharacteristic
555C22⋊#95C2×C10111yescharacteristic
556C101#1405211yescharacteristic, direct product factor, Sylow
557C23×Q8C22×C10111yescharacteristic
558C24×C4C22×C10111yescharacteristic
559C24×C4C22×C10111yescharacteristic
560C24×C4C22×C10111yescharacteristic
561C2×C22⋊Q8—24no—
562C2×C22⋊Q8—24no—
563C2×C22⋊Q8C4×C10118yescomplemented
564C22×C4⋊C4C22×C10111yescharacteristic
565C22×C4⋊C4C22×C10111yescharacteristic
566C22×C4⋊C4C22×C10111yescharacteristic
567C22×C4⋊C4C22×C10111yescharacteristic
568C22×C4⋊C4C22×C10111yescharacteristic
569C22×C22⋊C4C22×C10111yescharacteristic
570C22×C22⋊C4C22×C10111yescharacteristic
571C22×C22⋊C4C22×C10111yescharacteristic
572C22×C22⋊C4C22×C10111yescharacteristic
573C22×C42C22×C10111yescharacteristic
574C22×C42C22×C10111yescharacteristic
575#391—24no—
576#385—24no—
577C4×C22⋊C4—24no—
578C2×#95—24no—
579C2×#95C22×C10111yescharacteristic
580C2×#95C22×C10111yescharacteristic
581C2×#95C22×C10111yescharacteristic
582C2×#95C22×C10111yescharacteristic
583C2×#95C22×C10111yescharacteristic
584C2×#95C22×C10111yescharacteristic
585C2×#95C22×C10111yescharacteristic
586C2×#95C22×C10111yescharacteristic
587C2×#95C22×C10111yescharacteristic
588C2×#95C22×C10111yescharacteristic
589C2×#95C22×C10111yescharacteristic
590C2×#95C22×C10111yescharacteristic
591C2×#95C22×C10111yescharacteristic
592C2×#95C22×C10111yescharacteristic
593C2×#95C22×C10111yescharacteristic
594C2×#95C22×C10111yescharacteristic
595C2×#95C22×C10111yescharacteristic
596C2×#95C22×C10111yescharacteristic
597C2×#95C22×C10111yescharacteristic
598C2×#95C22×C10111yescharacteristic
599C25C23×C10111yescharacteristic
600C22×Q8—22no—
601C22×Q8—22no—
602C22×Q8—22no—
603C22×Q8—22no—
604C22×Q8—41no—
605C22×Q8—41no—
606C22×Q8C2×C4×C10114yescomplemented
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—22no—
616C23×C4—22no—
617C23×C4—22no—
618C23×C4—22no—
619C23×C4—22no—
620C23×C4—41no—
621C23×C4—41no—
622C23×C4—41no—
623C23×C4—41no—
624C23×C4—41no—
625C23×C4—41no—
626C23×C4C2×C4×C10114yes—
627C23×C4Q8×C10114yescomplemented
628C23×C4C23×C10111yescharacteristic
629C23×C4C23×C10111yescharacteristic
630C23×C4C23×C10111yescharacteristic
631C23×C4C23×C10111yescharacteristic
632C23×C4C23×C10111yescharacteristic
633C23×C4C23×C10111yescharacteristic
634C23×C4C23×C10111yescharacteristic
635C23×C4C23×C10111yescharacteristic
636C23×C4C23×C10111yescharacteristic
637C23×C4C23×C10111yescharacteristic
638C23×C4C23×C10111yescharacteristic
639C23×C4C23×C10111yescharacteristic
640C23×C4C23×C10111yescharacteristic
641C23×C4C23×C10111yescharacteristic
642C22⋊Q8—232no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4C2×C4×C10114yescomplemented
656C2×C4⋊C4C2×C4×C10114yescomplemented
657C2×C4⋊C4C2×C4×C10114yescomplemented
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4C2×C4×C10114yes—
666C2×C22⋊C4C2×C4×C10114yes—
667C2×C22⋊C4D4×C10114yes—
668C2×C22⋊C4D4×C10114yes—
669C2×C22⋊C4Q8×C10114yescomplemented
670C2×C42—22no—
671C2×C42—22no—
672C2×C42—22no—
673C2×C42—22no—
674C2×C42—41no—
675C2×C42—41no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—22no—
688#95—22no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95—41no—
693#95—41no—
694#95—41no—
695#95D4×C10114yes—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24C22×C4×C10112yes—
705C24C2×D4×C10112yes—
706C24C2×D4×C10112yes—
707C24C2×Q8×C10112yes—
708C24C2×Q8×C10112yes—
709C24#41×C10112yes—
710C24#41×C10112yes—
711C24C24×C10111yescharacteristic
712C2×Q8—28no—
713C2×Q8—28no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—44no—
718C2×Q8—44no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4C22×C4×C10112yes—
819C22×C4C22×C4×C10112yes—
820C22×C4C22×C4×C10112yes—
821C22×C4C22×C4×C10112yes—
822C22×C4C22×C4×C10112yes—
823C22×C4C22×C4×C10112yes—
824C22×C4C2×D4×C10112yes—
825C22×C4C2×D4×C10112yes—
826C22×C4C2×D4×C10112yes—
827C22×C4C2×D4×C10112yes—
828C22×C4C2×D4×C10112yes—
829C22×C4C2×D4×C10112yes—
830C22×C4C2×D4×C10112yes—
831C22×C4C2×Q8×C10112yes—
832C22×C4C2×Q8×C10112yes—
833C22×C4C2×Q8×C10112yes—
834C22×C4C2×Q8×C10112yes—
835C22×C4#41×C10112yes—
836C22×C4#41×C10112yes—
837C22×C4#41×C10112yes—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—44no—
846C22⋊C4C22⋊C4×C101116yes—
847C42—44no—
848C42—44no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23C2×C22⋊C4×C10114yes—
878C23C4×Q8×C10114yes—
879C23C4×Q8×C10114yes—
880C23C22⋊Q8×C10114yes—
881C23C22⋊Q8×C10114yes—
882C23#124×C10114yes—
883C23C4⋊Q8×C10114yes—
884C23C23×C4×C10111yescharacteristic
885C23C22×D4×C10111yescharacteristic
886C23C22×D4×C10111yescharacteristic
887C23C22×D4×C10111yescharacteristic
888C23C22×Q8×C10111yescharacteristic
889C23C22×Q8×C10111yescharacteristic
890C23C2×#41×C10111yescharacteristic
891C23C2×#41×C10111yescharacteristic
892C23C2×#41×C10111yescharacteristic
893C23C2×#41×C10111yescharacteristic
894C23C2×#41×C10111yescharacteristic
895C23H(5,𝔽2)×C10111yescharacteristic
896C23H(5,𝔽2)×C10111yescharacteristic
897C23H(5,𝔽2)×C10111yescharacteristic
898C232−1+4×C10111yescharacteristic
899Q8—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—416no—
949C2×C4—416no—
950C2×C4—416no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4C2×C22⋊C4×C10114yes—
998C2×C4C2×C22⋊C4×C10114yes—
999C2×C4C4×D4×C10114yes—
1000C2×C4C22⋊Q8×C10114yescomplemented
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22#391×C10118yescomplemented
1016C22C22×C22⋊C4×C10111yescharacteristic
1017C22C2×C4×D4×C10111yescharacteristic
1018C22C2×C4×Q8×C10111yescharacteristic
1019C22C2×C4×Q8×C10111yescharacteristic
1020C22C4×#41×C10111yescharacteristic
1021C22#518×C10111yescharacteristic
1022C22#520×C10111yescharacteristic
1023C22C2×C22⋊Q8×C10111yescharacteristic
1024C22C2×C22⋊Q8×C10111yescharacteristic
1025C22C2×C22⋊Q8×C10111yescharacteristic
1026C22#525×C10111yescharacteristic
1027C22C2×#124×C10111yescharacteristic
1028C22#529×C10111yescharacteristic
1029C22C2×C4⋊Q8×C10111yescharacteristic
1030C22#533×C10111yescharacteristic
1031C22#538×C10111yescharacteristic
1032C22#539×C10111yescharacteristic
1033C22#543×C10111yescharacteristic
1034C22#544×C10111yescharacteristic
1035C22D42×C10111yescharacteristic
1036C22D42×C10111yescharacteristic
1037C22#546×C10111yescharacteristic
1038C22#546×C10111yescharacteristic
1039C22#546×C10111yescharacteristic
1040C22#546×C10111yescharacteristic
1041C22#546×C10111yescharacteristic
1042C22#547×C10111yescharacteristic
1043C22#547×C10111yescharacteristic
1044C22D4×Q8×C10111yescharacteristic
1045C22#551×C10111yescharacteristic
1046C22#551×C10111yescharacteristic
1047C22#552×C10111yescharacteristic
1048C22#554×C10111yescharacteristic
1049C22#554×C10111yescharacteristic
1050C22#554×C10111yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—24no—
1054C4—24no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—81no—
1065C2—28no—
1066C2C2×#391×C10111yescharacteristic
1067C2C4×C22⋊Q8×C10111yescharacteristic
1068C2C101×#232911yescharacteristic
1069C2D4×C22⋊C4×C10111yescharacteristic
1070C2C101×#233911yescharacteristic
1071C2C101×#236011yescharacteristic
1072C2C101×#236811yescharacteristic
1073C2C101×#243711yescharacteristic
1074C2C101×#243811yescharacteristic
1075C2C101×#244011yescharacteristic
1076C2C101×#244911yescharacteristic
1077C2C101×#245011yescharacteristic
1078C2C101×#247211yescharacteristic
1079C2C101×#248811yescharacteristic
1080C2C101×#254911yescharacteristic
subgroupG/H
center, socleC24×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC24C24×C101
prime radicalC25×C101C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#391×C101C2semidirect
6. C101×#1446C2semidirect
7. C101×#1445C2semidirect
8. C101×#1441C2semidirect
9. C101×#1441C2semidirect
10. C101×#1436C2semidirect
11. C101×#1436C2semidirect
12. C101×C4⋊#95C2semidirect
22. C2×C22⋊Q8×C101C4semidirect
65. C22×Q8×C101C2×C4semidirect
86. C23×C4×C101Q8semidirect
114. C2×C4⋊C4×C101C2×C4semidirect
115. C2×C4⋊C4×C101C2×C4semidirect
116. C2×C4⋊C4×C101C2×C4semidirect
128. C2×C22⋊C4×C101Q8semidirect
459. C2×C4×C101C22⋊Q8semidirect
474. C22×C101#391semidirect
524. #14052C101direct (N × H)
542. C2×#391C2×C101semidirect
546. #1446C2×C101semidirect
547. #1445C2×C101semidirect
548. #1441C2×C101semidirect
549. #1441C2×C101semidirect
550. #1436C2×C101semidirect
551. #1436C2×C101semidirect
552. C4⋊#95C2×C101semidirect
556. C101#14052direct (N × H)
563. C2×C22⋊Q8C4×C101semidirect
606. C22×Q8C2×C4×C101semidirect
627. C23×C4Q8×C101semidirect
655. C2×C4⋊C4C2×C4×C101semidirect
656. C2×C4⋊C4C2×C4×C101semidirect
657. C2×C4⋊C4C2×C4×C101semidirect
669. C2×C22⋊C4Q8×C101semidirect
1000. C2×C4C22⋊Q8×C101semidirect
1015. C22#391×C101semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1012
C2×#391×C1012
C2×#385×C1012
C2×C4×C22⋊C4×C1012
C22×#95×C1012
C101×#14462
C101×#14452
C101×#14412
C101×#14362
C101×C4⋊#952
C101×C22⋊#952
#14052101