Finite Group Databasebeta

← C101×#14112 #38796263

Subgroups — C101×#14112 #38796263

Order 25856.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C101C211yesmaximal, characteristic, complemented
2C2×#388×C101C211yesmaximal, characteristic
3C2×#388×C101C211yesmaximal, characteristic
4C2×#385×C101C211yesmaximal, characteristic
5C2×#385×C101C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C101C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C101C211yesmaximal, characteristic
8C101×#1444C211yesmaximal, characteristic, complemented
9C101×#1441C211yesmaximal, characteristic, complemented
10C101×#1439C211yesmaximal, characteristic
11C101×#1439C211yesmaximal, characteristic
12C101×#1436C211yesmaximal, characteristic, complemented
13C101×#1436C211yesmaximal, characteristic, complemented
14C101×#1436C211yesmaximal, characteristic, complemented
15C101×C4⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C101C2211yescharacteristic
17C22×C4⋊C4×C101C2211yescharacteristic
18C22×C4⋊C4×C101C2211yescharacteristic
19C22×C4⋊C4×C101C2211yescharacteristic
20C22×C4⋊C4×C101C2211yescharacteristic
21C22×C4⋊C4×C101C2211yescharacteristic
22C22×C4⋊C4×C101C2211yescharacteristic
23C22×C4⋊C4×C101C2211yescharacteristic
24C22×C4⋊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×C42×C101C2211yescharacteristic
32C22×C42×C101C2211yescharacteristic
33C22×C42×C101C2211yescharacteristic
34C22×C42×C101C2211yescharacteristic
35#389×C101—24no—
36#388×C101—24no—
37#388×C101C418yescomplemented
38#385×C101—24no—
39#385×C101—24no—
40C4×C4⋊C4×C101—24no—
41C4×C22⋊C4×C101—24no—
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
59C23×C4×C101—22no—
60C23×C4×C101—22no—
61C23×C4×C101—22no—
62C23×C4×C101—22no—
63C23×C4×C101—22no—
64C23×C4×C101—41no—
65C23×C4×C101—41no—
66C23×C4×C101C2311yescharacteristic
67C23×C4×C101C2311yescharacteristic
68C23×C4×C101C2311yescharacteristic
69C23×C4×C101C2311yescharacteristic
70C23×C4×C101C2311yescharacteristic
71C23×C4×C101C2311yescharacteristic
72C23×C4×C101C2311yescharacteristic
73C23×C4×C101C2311yescharacteristic
74C23×C4×C101C2311yescharacteristic
75C23×C4×C101C2311yescharacteristic
76C23×C4×C101C2311yescharacteristic
77C23×C4×C101C2311yescharacteristic
78C23×C4×C101C2311yescharacteristic
79C23×C4×C101C2311yescharacteristic
80C2×C4⋊C4×C101—22no—
81C2×C4⋊C4×C101—22no—
82C2×C4⋊C4×C101—22no—
83C2×C4⋊C4×C101—22no—
84C2×C4⋊C4×C101—22no—
85C2×C4⋊C4×C101—22no—
86C2×C4⋊C4×C101—22no—
87C2×C4⋊C4×C101—22no—
88C2×C4⋊C4×C101—22no—
89C2×C4⋊C4×C101—22no—
90C2×C4⋊C4×C101—22no—
91C2×C4⋊C4×C101—22no—
92C2×C4⋊C4×C101—22no—
93C2×C4⋊C4×C101—22no—
94C2×C4⋊C4×C101—22no—
95C2×C4⋊C4×C101—22no—
96C2×C4⋊C4×C101—22no—
97C2×C4⋊C4×C101—22no—
98C2×C4⋊C4×C101—41no—
99C2×C4⋊C4×C101—41no—
100C2×C4⋊C4×C101—41no—
101C2×C4⋊C4×C101—41no—
102C2×C4⋊C4×C101C2×C414yescomplemented
103C2×C4⋊C4×C101D414yes—
104C2×C22⋊C4×C101—22no—
105C2×C22⋊C4×C101—22no—
106C2×C22⋊C4×C101—22no—
107C2×C22⋊C4×C101—22no—
108C2×C22⋊C4×C101—22no—
109C2×C22⋊C4×C101—22no—
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—41no—
116C2×C22⋊C4×C101—41no—
117C2×C22⋊C4×C101C2×C414yes—
118C2×C22⋊C4×C101C2×C414yes—
119C2×C22⋊C4×C101C2×C414yes—
120C2×C22⋊C4×C101D414yes—
121C2×C22⋊C4×C101Q814yes—
122C2×C42×C101—22no—
123C2×C42×C101—22no—
124C2×C42×C101—22no—
125C2×C42×C101—22no—
126C2×C42×C101—22no—
127C2×C42×C101—22no—
128C2×C42×C101—22no—
129C2×C42×C101—22no—
130C2×C42×C101—41no—
131C2×C42×C101—41no—
132C2×C42×C101—41no—
133C2×C42×C101C2×C414yescomplemented
134#95×C101—22no—
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—41no—
147#95×C101C2×C414yescomplemented
148#95×C101C2×C414yescomplemented
149#95×C101D414yes—
150C24×C101—21no—
151C24×C101—21no—
152C24×C101—21no—
153C24×C101—21no—
154C24×C101—21no—
155C24×C101—21no—
156C24×C101—21no—
157C24×C101—21no—
158C24×C101—21no—
159C24×C101—21no—
160C24×C101—21no—
161C24×C101—21no—
162C24×C101C22×C412yes—
163C24×C101C2×D412yes—
164C24×C101C2×Q812yes—
165C24×C101C2411yescharacteristic
166C22×C4×C101—21no—
167C22×C4×C101—21no—
168C22×C4×C101—21no—
169C22×C4×C101—21no—
170C22×C4×C101—21no—
171C22×C4×C101—21no—
172C22×C4×C101—21no—
173C22×C4×C101—21no—
174C22×C4×C101—21no—
175C22×C4×C101—21no—
176C22×C4×C101—21no—
177C22×C4×C101—21no—
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—28no—
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—21no—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
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—44no—
244C22×C4×C101—44no—
245C22×C4×C101—44no—
246C22×C4×C101—44no—
247C22×C4×C101—44no—
248C22×C4×C101—44no—
249C22×C4×C101C22×C412yes—
250C22×C4×C101C22×C412yes—
251C22×C4×C101C22×C412yes—
252C22×C4×C101C22×C412yes—
253C22×C4×C101C22×C412yes—
254C22×C4×C101C22×C412yes—
255C22×C4×C101C2×D412yes—
256C22×C4×C101C2×D412yes—
257C22×C4×C101C2×D412yes—
258C22×C4×C101C2×D412yes—
259C22×C4×C101C2×D412yes—
260C22×C4×C101C2×D412yes—
261C22×C4×C101C2×D412yes—
262C22×C4×C101C2×D412yes—
263C22×C4×C101C2×Q812yes—
264C22×C4×C101C2×Q812yes—
265C22×C4×C101#4112yes—
266C22×C4×C101#4112yes—
267C22×C4×C101#4112yes—
268C22×C4×C101#4112yes—
269C22×C4×C101#4112yes—
270C22×C4×C101#4112yes—
271C4⋊C4×C101—28no—
272C4⋊C4×C101—28no—
273C4⋊C4×C101—28no—
274C4⋊C4×C101—44no—
275C4⋊C4×C101—44no—
276C4⋊C4×C101—44no—
277C4⋊C4×C101—44no—
278C4⋊C4×C101—44no—
279C22⋊C4×C101—28no—
280C22⋊C4×C101—28no—
281C22⋊C4×C101—28no—
282C22⋊C4×C101—44no—
283C22⋊C4×C101—44no—
284C22⋊C4×C101C4⋊C4116yescomplemented
285C42×C101—28no—
286C42×C101—44no—
287C42×C101—44no—
288C42×C101—44no—
289C23×C101—22no—
290C23×C101—22no—
291C23×C101—22no—
292C23×C101—22no—
293C23×C101—22no—
294C23×C101—22no—
295C23×C101—22no—
296C23×C101—22no—
297C23×C101—22no—
298C23×C101—22no—
299C23×C101—22no—
300C23×C101—22no—
301C23×C101—22no—
302C23×C101—22no—
303C23×C101—22no—
304C23×C101—22no—
305C23×C101—22no—
306C23×C101—22no—
307C23×C101—41no—
308C23×C101—41no—
309C23×C101—41no—
310C23×C101—41no—
311C23×C101—41no—
312C23×C101—41no—
313C23×C101—41no—
314C23×C101—41no—
315C23×C101—41no—
316C23×C101—41no—
317C23×C101—41no—
318C23×C101—41no—
319C23×C101—41no—
320C23×C101—41no—
321C23×C101—41no—
322C23×C101—41no—
323C23×C101C2×C4⋊C414yes—
324C23×C101C23×C411yescharacteristic
325C23×C101C22×D411yescharacteristic
326C23×C101C22×D411yescharacteristic
327C23×C101C22×D411yescharacteristic
328C23×C101C22×Q811yescharacteristic
329C23×C101C2×#4111yescharacteristic
330C23×C101C2×#4111yescharacteristic
331C23×C101C2×#4111yescharacteristic
332C23×C101C2×#4111yescharacteristic
333C23×C101C2×#4111yescharacteristic
334C23×C101C2×#4111yescharacteristic
335C23×C101H(5,𝔽2)11yescharacteristic
336C23×C101H(5,𝔽2)11yescharacteristic
337C23×C1012−1+411yescharacteristic
338C23×C1012−1+411yescharacteristic
339C2×C4×C101—22no—
340C2×C4×C101—22no—
341C2×C4×C101—22no—
342C2×C4×C101—22no—
343C2×C4×C101—22no—
344C2×C4×C101—22no—
345C2×C4×C101—22no—
346C2×C4×C101—22no—
347C2×C4×C101—22no—
348C2×C4×C101—22no—
349C2×C4×C101—22no—
350C2×C4×C101—22no—
351C2×C4×C101—22no—
352C2×C4×C101—22no—
353C2×C4×C101—22no—
354C2×C4×C101—22no—
355C2×C4×C101—22no—
356C2×C4×C101—22no—
357C2×C4×C101—22no—
358C2×C4×C101—22no—
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—416no—
391C2×C4×C101—41no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—41no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101—41no—
399C2×C4×C101—41no—
400C2×C4×C101—41no—
401C2×C4×C101—41no—
402C2×C4×C101—41no—
403C2×C4×C101—41no—
404C2×C4×C101—41no—
405C2×C4×C101—41no—
406C2×C4×C101—41no—
407C2×C4×C101—41no—
408C2×C4×C101—41no—
409C2×C4×C101—41no—
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×C101C2×C4⋊C414yes—
434C2×C4×C101C2×C4⋊C414yes—
435C2×C4×C101C4×D414yes—
436C2×C4×C101C4×D414yes—
437C2×C4×C101#12114yes—
438C22×C101—24no—
439C22×C101—24no—
440C22×C101—24no—
441C22×C101—42no—
442C22×C101—42no—
443C22×C101—42no—
444C22×C101—42no—
445C22×C101—42no—
446C22×C101—42no—
447C22×C101—42no—
448C22×C101—42no—
449C22×C101—42no—
450C22×C101—42no—
451C22×C101—42no—
452C22×C101—42no—
453C22×C101C22×C4⋊C411yescharacteristic
454C22×C101C2×C4×D411yescharacteristic
455C22×C101C2×C4×D411yescharacteristic
456C22×C101C4×#4111yescharacteristic
457C22×C101C4×#4111yescharacteristic
458C22×C101#52011yescharacteristic
459C22×C101#52011yescharacteristic
460C22×C101C2×#12111yescharacteristic
461C22×C101#52511yescharacteristic
462C22×C101#52511yescharacteristic
463C22×C101#52511yescharacteristic
464C22×C101#52911yescharacteristic
465C22×C101#53211yescharacteristic
466C22×C101#53311yescharacteristic
467C22×C101#53311yescharacteristic
468C22×C101#53811yescharacteristic
469C22×C101#53911yescharacteristic
470C22×C101#54111yescharacteristic
471C22×C101#54211yescharacteristic
472C22×C101D4211yescharacteristic
473C22×C101D4211yescharacteristic
474C22×C101#54611yescharacteristic
475C22×C101#54611yescharacteristic
476C22×C101#54711yescharacteristic
477C22×C101#54711yescharacteristic
478C22×C101#54711yescharacteristic
479C22×C101#54811yescharacteristic
480C22×C101D4×Q811yescharacteristic
481C22×C101D4×Q811yescharacteristic
482C22×C101#55111yescharacteristic
483C22×C101#55211yescharacteristic
484C22×C101#55411yescharacteristic
485C22×C101#55411yescharacteristic
486C22×C101#55611yescharacteristic
487C22×C101#55911yescharacteristic
488C4×C101—24no—
489C4×C101—24no—
490C4×C101—24no—
491C4×C101—24no—
492C4×C101—24no—
493C4×C101—42no—
494C4×C101—42no—
495C4×C101—42no—
496C4×C101—42no—
497C4×C101—42no—
498C4×C101—42no—
499C4×C101—42no—
500C4×C101—81no—
501C4×C101—81no—
502#14112C10111yesmaximal, characteristic, direct product factor, Sylow
503C2×C101—44no—
504C2×C101#229611yescharacteristic
505C2×C101C4×#12111yescharacteristic
506C2×C101#233411yescharacteristic
507C2×C101D4×C4⋊C411yescharacteristic
508C2×C101D4×C4⋊C411yescharacteristic
509C2×C101#235911yescharacteristic
510C2×C101#236711yescharacteristic
511C2×C101#242411yescharacteristic
512C2×C101#242911yescharacteristic
513C2×C101#245511yescharacteristic
514C2×C101#246111yescharacteristic
515C2×C101#246511yescharacteristic
516C2×C101#247811yescharacteristic
517C2×C101#255611yescharacteristic
518C2×C101#258911yescharacteristic
519C2×#389C2×C10111yescharacteristic, complemented
520C2×#388C2×C10111yescharacteristic
521C2×#388C2×C10111yescharacteristic
522C2×#385C2×C10111yescharacteristic
523C2×#385C2×C10111yescharacteristic
524C2×C4×C4⋊C4C2×C10111yescharacteristic, complemented
525C2×C4×C22⋊C4C2×C10111yescharacteristic
526#1444C2×C10111yescharacteristic, complemented
527#1441C2×C10111yescharacteristic, complemented
528#1439C2×C10111yescharacteristic
529#1439C2×C10111yescharacteristic
530#1436C2×C10111yescharacteristic, complemented
531#1436C2×C10111yescharacteristic, complemented
532#1436C2×C10111yescharacteristic, complemented
533C4⋊#95C2×C10111yescharacteristic, complemented
534C101#1411211yescharacteristic, direct product factor, Sylow
535C24×C4C22×C10111yescharacteristic
536C22×C4⋊C4C22×C10111yescharacteristic
537C22×C4⋊C4C22×C10111yescharacteristic
538C22×C4⋊C4C22×C10111yescharacteristic
539C22×C4⋊C4C22×C10111yescharacteristic
540C22×C4⋊C4C22×C10111yescharacteristic
541C22×C4⋊C4C22×C10111yescharacteristic
542C22×C4⋊C4C22×C10111yescharacteristic
543C22×C4⋊C4C22×C10111yescharacteristic
544C22×C22⋊C4C22×C10111yescharacteristic
545C22×C22⋊C4C22×C10111yescharacteristic
546C22×C22⋊C4C22×C10111yescharacteristic
547C22×C22⋊C4C22×C10111yescharacteristic
548C22×C22⋊C4C22×C10111yescharacteristic
549C22×C22⋊C4C22×C10111yescharacteristic
550C22×C42C22×C10111yescharacteristic
551C22×C42C22×C10111yescharacteristic
552C22×C42C22×C10111yescharacteristic
553C22×C42C22×C10111yescharacteristic
554#389—24no—
555#388—24no—
556#388C4×C10118yescomplemented
557#385—24no—
558#385—24no—
559C4×C4⋊C4—24no—
560C4×C22⋊C4—24no—
561C2×#95C22×C10111yescharacteristic
562C2×#95C22×C10111yescharacteristic
563C2×#95C22×C10111yescharacteristic
564C2×#95C22×C10111yescharacteristic
565C2×#95C22×C10111yescharacteristic
566C2×#95C22×C10111yescharacteristic
567C2×#95C22×C10111yescharacteristic
568C2×#95C22×C10111yescharacteristic
569C2×#95C22×C10111yescharacteristic
570C2×#95C22×C10111yescharacteristic
571C2×#95C22×C10111yescharacteristic
572C2×#95C22×C10111yescharacteristic
573C2×#95C22×C10111yescharacteristic
574C2×#95C22×C10111yescharacteristic
575C2×#95C22×C10111yescharacteristic
576C2×#95C22×C10111yescharacteristic
577C25C23×C10111yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C10111yescharacteristic
586C23×C4C23×C10111yescharacteristic
587C23×C4C23×C10111yescharacteristic
588C23×C4C23×C10111yescharacteristic
589C23×C4C23×C10111yescharacteristic
590C23×C4C23×C10111yescharacteristic
591C23×C4C23×C10111yescharacteristic
592C23×C4C23×C10111yescharacteristic
593C23×C4C23×C10111yescharacteristic
594C23×C4C23×C10111yescharacteristic
595C23×C4C23×C10111yescharacteristic
596C23×C4C23×C10111yescharacteristic
597C23×C4C23×C10111yescharacteristic
598C23×C4C23×C10111yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4C2×C4×C10114yescomplemented
622C2×C4⋊C4D4×C10114yes—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4C2×C4×C10114yes—
637C2×C22⋊C4C2×C4×C10114yes—
638C2×C22⋊C4C2×C4×C10114yes—
639C2×C22⋊C4D4×C10114yes—
640C2×C22⋊C4Q8×C10114yes—
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—22no—
644C2×C42—22no—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—41no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42C2×C4×C10114yescomplemented
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—41no—
666#95C2×C4×C10114yescomplemented
667#95C2×C4×C10114yescomplemented
668#95D4×C10114yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C10112yes—
682C24C2×D4×C10112yes—
683C24C2×Q8×C10112yes—
684C24C24×C10111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—28no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
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—21no—
736C22×C4—21no—
737C22×C4—21no—
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—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4C22×C4×C10112yes—
769C22×C4C22×C4×C10112yes—
770C22×C4C22×C4×C10112yes—
771C22×C4C22×C4×C10112yes—
772C22×C4C22×C4×C10112yes—
773C22×C4C22×C4×C10112yes—
774C22×C4C2×D4×C10112yes—
775C22×C4C2×D4×C10112yes—
776C22×C4C2×D4×C10112yes—
777C22×C4C2×D4×C10112yes—
778C22×C4C2×D4×C10112yes—
779C22×C4C2×D4×C10112yes—
780C22×C4C2×D4×C10112yes—
781C22×C4C2×D4×C10112yes—
782C22×C4C2×Q8×C10112yes—
783C22×C4C2×Q8×C10112yes—
784C22×C4#41×C10112yes—
785C22×C4#41×C10112yes—
786C22×C4#41×C10112yes—
787C22×C4#41×C10112yes—
788C22×C4#41×C10112yes—
789C22×C4#41×C10112yes—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4C4⋊C4×C101116yescomplemented
804C42—28no—
805C42—44no—
806C42—44no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊C4×C10114yes—
843C23C23×C4×C10111yescharacteristic
844C23C22×D4×C10111yescharacteristic
845C23C22×D4×C10111yescharacteristic
846C23C22×D4×C10111yescharacteristic
847C23C22×Q8×C10111yescharacteristic
848C23C2×#41×C10111yescharacteristic
849C23C2×#41×C10111yescharacteristic
850C23C2×#41×C10111yescharacteristic
851C23C2×#41×C10111yescharacteristic
852C23C2×#41×C10111yescharacteristic
853C23C2×#41×C10111yescharacteristic
854C23H(5,𝔽2)×C10111yescharacteristic
855C23H(5,𝔽2)×C10111yescharacteristic
856C232−1+4×C10111yescharacteristic
857C232−1+4×C10111yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
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—416no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4C2×C4⋊C4×C10114yes—
953C2×C4C2×C4⋊C4×C10114yes—
954C2×C4C4×D4×C10114yes—
955C2×C4C4×D4×C10114yes—
956C2×C4#121×C10114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊C4×C10111yescharacteristic
973C22C2×C4×D4×C10111yescharacteristic
974C22C2×C4×D4×C10111yescharacteristic
975C22C4×#41×C10111yescharacteristic
976C22C4×#41×C10111yescharacteristic
977C22#520×C10111yescharacteristic
978C22#520×C10111yescharacteristic
979C22C2×#121×C10111yescharacteristic
980C22#525×C10111yescharacteristic
981C22#525×C10111yescharacteristic
982C22#525×C10111yescharacteristic
983C22#529×C10111yescharacteristic
984C22#532×C10111yescharacteristic
985C22#533×C10111yescharacteristic
986C22#533×C10111yescharacteristic
987C22#538×C10111yescharacteristic
988C22#539×C10111yescharacteristic
989C22#541×C10111yescharacteristic
990C22#542×C10111yescharacteristic
991C22D42×C10111yescharacteristic
992C22D42×C10111yescharacteristic
993C22#546×C10111yescharacteristic
994C22#546×C10111yescharacteristic
995C22#547×C10111yescharacteristic
996C22#547×C10111yescharacteristic
997C22#547×C10111yescharacteristic
998C22#548×C10111yescharacteristic
999C22D4×Q8×C10111yescharacteristic
1000C22D4×Q8×C10111yescharacteristic
1001C22#551×C10111yescharacteristic
1002C22#552×C10111yescharacteristic
1003C22#554×C10111yescharacteristic
1004C22#554×C10111yescharacteristic
1005C22#556×C10111yescharacteristic
1006C22#559×C10111yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C101×#229611yescharacteristic
1023C2C4×#121×C10111yescharacteristic
1024C2C101×#233411yescharacteristic
1025C2D4×C4⋊C4×C10111yescharacteristic
1026C2D4×C4⋊C4×C10111yescharacteristic
1027C2C101×#235911yescharacteristic
1028C2C101×#236711yescharacteristic
1029C2C101×#242411yescharacteristic
1030C2C101×#242911yescharacteristic
1031C2C101×#245511yescharacteristic
1032C2C101×#246111yescharacteristic
1033C2C101×#246511yescharacteristic
1034C2C101×#247811yescharacteristic
1035C2C101×#255611yescharacteristic
1036C2C101×#258911yescharacteristic
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
1. C2×#389×C101C2semidirect
6. C2×C4×C4⋊C4×C101C2semidirect
8. C101×#1444C2semidirect
9. C101×#1441C2semidirect
12. C101×#1436C2semidirect
13. C101×#1436C2semidirect
14. C101×#1436C2semidirect
15. C101×C4⋊#95C2semidirect
37. #388×C101C4semidirect
102. C2×C4⋊C4×C101C2×C4semidirect
133. C2×C42×C101C2×C4semidirect
147. #95×C101C2×C4semidirect
148. #95×C101C2×C4semidirect
284. C22⋊C4×C101C4⋊C4semidirect
502. #14112C101direct (N × H)
519. C2×#389C2×C101semidirect
524. C2×C4×C4⋊C4C2×C101semidirect
526. #1444C2×C101semidirect
527. #1441C2×C101semidirect
530. #1436C2×C101semidirect
531. #1436C2×C101semidirect
532. #1436C2×C101semidirect
533. C4⋊#95C2×C101semidirect
534. C101#14112direct (N × H)
556. #388C4×C101semidirect
621. C2×C4⋊C4C2×C4×C101semidirect
652. C2×C42C2×C4×C101semidirect
666. #95C2×C4×C101semidirect
667. #95C2×C4×C101semidirect
803. C22⋊C4C4⋊C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1012
C2×#388×C1012
C2×#385×C1012
C2×C4×C4⋊C4×C1012
C2×C4×C22⋊C4×C1012
C101×#14442
C101×#14412
C101×#14392
C101×#14362
C101×C4⋊#952
#14112101