Finite Group Databasebeta

← C101×#24142 #38806293

Subgroups — C101×#24142 #38806293

Order 25856.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3505C211yesmaximal, characteristic, complemented
2C101×#2626C211yesmaximal, characteristic, complemented
3C101×#2617C211yesmaximal, characteristic, complemented
4C101×#2321C211yesmaximal, characteristic, complemented
5C101×#2044C212yesmaximal, complemented
6C101×#2021C212yesmaximal, complemented
7C101×#1996C211yesmaximal, characteristic, complemented
8C101×#1964C211yesmaximal, characteristic, complemented
9C101×#1889C212yesmaximal, complemented
10C101×#1867C212yesmaximal, complemented
11C101×#1799C211yesmaximal, characteristic, complemented
12#553×C101—22no—
13#553×C101—21no—
14#552×C101—21no—
15#551×C101—22no—
16#548×C101—21no—
17#546×C101—21no—
18#539×C101—21no—
19#538×C101—21no—
20#534×C101C2212yes—
21#529×C101—21no—
22#525×C101—21no—
23C2×C22⋊Q8×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic
25C2×#120×C101C2211yescharacteristic
26C2×#120×C101C2212yes—
27#518×C101C2212yes—
28C2×C4×D4×C101C2211yescharacteristic
29C22×C22⋊C4×C101C2211yescharacteristic
30C2×#99×C101C2212yes—
31C2×#99×C101C2212yes—
32C2×#99×C101C2212yes—
33#399×C101—21no—
34#397×C101—21no—
35#396×C101—22no—
36#394×C101—22no—
37#393×C101—21no—
38#392×C101—21no—
39#390×C101—21no—
40#388×C101—21no—
41#388×C101—21no—
42#386×C101—21no—
43#386×C101C2211yescharacteristic
44#386×C101C2212yes—
45#385×C101C2212yes—
46#385×C101C2211yescharacteristic
47#380×C101C2211yescharacteristic
48#380×C101C2211yescharacteristic
49#379×C101C2211yescharacteristic
50#379×C101C2212yes—
51C4×C22⋊C4×C101C2211yescharacteristic
52#342×C101C2212yes—
53#342×C101C2212yes—
54#342×C101C2212yes—
55C25×C101C2311yescharacteristic
56C2×#41×C101—21no—
57C22×Q8×C101D411yescharacteristic, complemented
58C22×D4×C101—21no—
59C22×D4×C101—22no—
60C22×D4×C101D411yescharacteristic, complemented
61C22×D4×C101C2311yescharacteristic
62C22×D4×C101C2312yes—
63C23×C4×C101D411yescharacteristic, complemented
64C23×C4×C101C2311yescharacteristic
65C23×C4×C101C2311yescharacteristic
66#126×C101—22no—
67#126×C101—22no—
68#126×C101—22no—
69#125×C101—21no—
70#125×C101—22no—
71#124×C101—21no—
72#124×C101—22no—
73#123×C101—22no—
74#123×C101—22no—
75#123×C101—22no—
76#123×C101—22no—
77#123×C101—22no—
78C22⋊Q8×C101—21no—
79C22⋊Q8×C101—22no—
80C22⋊Q8×C101—21no—
81C22⋊Q8×C101—21no—
82C22⋊Q8×C101—21no—
83C22⋊Q8×C101—21no—
84#121×C101—21no—
85#121×C101—22no—
86#121×C101—21no—
87#121×C101—21no—
88#121×C101—21no—
89#121×C101—21no—
90#121×C101—22no—
91#121×C101—22no—
92#120×C101—22no—
93#120×C101—22no—
94#120×C101—22no—
95#120×C101—22no—
96#120×C101—24no—
97#120×C101—42no—
98C4×Q8×C101—21no—
99C4×D4×C101—22no—
100C4×D4×C101—21no—
101C4×D4×C101—21no—
102C4×D4×C101—21no—
103C4×D4×C101—21no—
104C4×D4×C101—21no—
105C4×D4×C101—22no—
106C4×D4×C101—22no—
107C4×D4×C101—22no—
108C4×D4×C101—22no—
109#117×C101—21no—
110#117×C101—22no—
111#117×C101—22no—
112C2×C4⋊C4×C101—21no—
113C2×C4⋊C4×C101—22no—
114C2×C4⋊C4×C101—21no—
115C2×C4⋊C4×C101—21no—
116C2×C4⋊C4×C101D412yescomplemented
117C2×C4⋊C4×C101D411yescharacteristic, complemented
118C2×C4⋊C4×C101D411yescharacteristic, complemented
119C2×C4⋊C4×C101D411yescharacteristic, complemented
120C2×C22⋊C4×C101—22no—
121C2×C22⋊C4×C101—21no—
122C2×C22⋊C4×C101—21no—
123C2×C22⋊C4×C101—21no—
124C2×C22⋊C4×C101—22no—
125C2×C22⋊C4×C101—21no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101—22no—
131C2×C22⋊C4×C101—22no—
132C2×C22⋊C4×C101—22no—
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101D411yescharacteristic, complemented
136C2×C22⋊C4×C101D412yescomplemented
137C2×C22⋊C4×C101C2312yes—
138C2×C22⋊C4×C101C2311yescharacteristic
139C2×C22⋊C4×C101C2312yes—
140C2×C22⋊C4×C101C2311yescharacteristic
141C2×C22⋊C4×C101C2312yes—
142C2×C22⋊C4×C101C2311yescharacteristic
143C2×C42×C101—21no—
144C2×C42×C101D411yescharacteristic, complemented
145#99×C101—24no—
146#99×C101—42no—
147#99×C101—42no—
148#95×C101—22no—
149#95×C101—21no—
150#95×C101—22no—
151#95×C101—21no—
152#95×C101—21no—
153#95×C101—21no—
154#95×C101—21no—
155C24×C101—21no—
156C24×C101—21no—
157C24×C101—21no—
158C24×C101—21no—
159C24×C101—21no—
160C24×C101—21no—
161C24×C101—81no—
162C24×C101—81no—
163C24×C101C2×D412yes—
164C24×C101C2×D411yescharacteristic
165C24×C101#4112yescomplemented
166C24×C101C2411yescharacteristic
167#41×C101—82no—
168C2×Q8×C101—21no—
169C2×Q8×C101—21no—
170C2×Q8×C101—81no—
171C2×D4×C101—21no—
172C2×D4×C101—22no—
173C2×D4×C101—21no—
174C2×D4×C101—22no—
175C2×D4×C101—22no—
176C2×D4×C101—21no—
177C2×D4×C101—21no—
178C2×D4×C101—22no—
179C2×D4×C101—21no—
180C2×D4×C101—22no—
181C2×D4×C101—21no—
182C2×D4×C101—22no—
183C2×D4×C101—22no—
184C2×D4×C101—22no—
185C2×D4×C101—24no—
186C2×D4×C101—21no—
187C2×D4×C101—21no—
188C2×D4×C101—44no—
189C2×D4×C101—81no—
190C2×D4×C101—81no—
191C2×D4×C101—81no—
192C2×D4×C101—82no—
193C2×D4×C101—82no—
194C22×C4×C101—21no—
195C22×C4×C101—22no—
196C22×C4×C101—22no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—22no—
203C22×C4×C101—22no—
204C22×C4×C101—21no—
205C22×C4×C101—81no—
206C22×C4×C101—81no—
207C22×C4×C101—81no—
208C22×C4×C101C2×D411yescharacteristic
209C22×C4×C101C2×D412yes—
210C22×C4×C101C2×D411yescharacteristic
211C22×C4×C101C2×D412yes—
212C22×C4×C101C2×D411yescharacteristic
213C22×C4×C101C2×D412yes—
214C22×C4×C101C2×D411yescharacteristic
215C22×C4×C101C2×D411yescharacteristic
216C22×C4×C101C2×D411yescharacteristic
217C22×C4×C101C2×D411yescharacteristic
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101C2×D411yescharacteristic
220C4⋊C4×C101—22no—
221C4⋊C4×C101—22no—
222C4⋊C4×C101—22no—
223C4⋊C4×C101—22no—
224C4⋊C4×C101—21no—
225C4⋊C4×C101—22no—
226C4⋊C4×C101—21no—
227C4⋊C4×C101—21no—
228C4⋊C4×C101—21no—
229C4⋊C4×C101—21no—
230C4⋊C4×C101—22no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—81no—
233C4⋊C4×C101—81no—
234C4⋊C4×C101—81no—
235C4⋊C4×C101—82no—
236C22⋊C4×C101—22no—
237C22⋊C4×C101—22no—
238C22⋊C4×C101—24no—
239C22⋊C4×C101—22no—
240C22⋊C4×C101—22no—
241C22⋊C4×C101—22no—
242C22⋊C4×C101—22no—
243C22⋊C4×C101—21no—
244C22⋊C4×C101—22no—
245C22⋊C4×C101—21no—
246C22⋊C4×C101—22no—
247C22⋊C4×C101—21no—
248C22⋊C4×C101—22no—
249C22⋊C4×C101—21no—
250C22⋊C4×C101—21no—
251C22⋊C4×C101—22no—
252C22⋊C4×C101—22no—
253C22⋊C4×C101—22no—
254C22⋊C4×C101—21no—
255C22⋊C4×C101—22no—
256C22⋊C4×C101—22no—
257C22⋊C4×C101—21no—
258C22⋊C4×C101—44no—
259C22⋊C4×C101—41no—
260C22⋊C4×C101—41no—
261C22⋊C4×C101—41no—
262C22⋊C4×C101—41no—
263C22⋊C4×C101—81no—
264C22⋊C4×C101—82no—
265C22⋊C4×C101—81no—
266C22⋊C4×C101—82no—
267C22⋊C4×C101—81no—
268C22⋊C4×C101—82no—
269C22⋊C4×C101#4112yescomplemented
270C42×C101—22no—
271C42×C101—22no—
272C42×C101—21no—
273C42×C101—21no—
274C42×C101—81no—
275C23×C101—21no—
276C23×C101—22no—
277C23×C101—22no—
278C23×C101—21no—
279C23×C101—22no—
280C23×C101—22no—
281C23×C101—21no—
282C23×C101—22no—
283C23×C101—22no—
284C23×C101—41no—
285C23×C101—41no—
286C23×C101—41no—
287C23×C101—41no—
288C23×C101—42no—
289C23×C101—41no—
290C23×C101—42no—
291C23×C101—41no—
292C23×C101—41no—
293C23×C101—42no—
294C23×C101—41no—
295C23×C101—42no—
296C23×C101—42no—
297C23×C101—42no—
298C23×C101—41no—
299C23×C101—41no—
300C23×C101—41no—
301C23×C101—41no—
302C23×C101—82no—
303C23×C101—82no—
304C23×C101—82no—
305C23×C101—82no—
306C23×C101C22×D411yescharacteristic
307C23×C101C22×D411yescharacteristic
308C23×C101C22×D411yescharacteristic
309C23×C101C2×#4111yescharacteristic
310C23×C101C2×#4111yescharacteristic
311C23×C101H(5,𝔽2)11yescharacteristic
312C23×C1012−1+411yescharacteristic
313Q8×C101—42no—
314Q8×C101—81no—
315D4×C101—42no—
316D4×C101—42no—
317D4×C101—42no—
318D4×C101—41no—
319D4×C101—41no—
320D4×C101—41no—
321D4×C101—42no—
322D4×C101—42no—
323D4×C101—41no—
324D4×C101—81no—
325D4×C101—82no—
326D4×C101—84no—
327D4×C101—82no—
328D4×C101—88no—
329C2×C4×C101—21no—
330C2×C4×C101—22no—
331C2×C4×C101—21no—
332C2×C4×C101—21no—
333C2×C4×C101—22no—
334C2×C4×C101—22no—
335C2×C4×C101—21no—
336C2×C4×C101—22no—
337C2×C4×C101—21no—
338C2×C4×C101—22no—
339C2×C4×C101—22no—
340C2×C4×C101—41no—
341C2×C4×C101—41no—
342C2×C4×C101—41no—
343C2×C4×C101—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—42no—
347C2×C4×C101—41no—
348C2×C4×C101—41no—
349C2×C4×C101—41no—
350C2×C4×C101—42no—
351C2×C4×C101—41no—
352C2×C4×C101—42no—
353C2×C4×C101—41no—
354C2×C4×C101—41no—
355C2×C4×C101—42no—
356C2×C4×C101—42no—
357C2×C4×C101—41no—
358C2×C4×C101—42no—
359C2×C4×C101—42no—
360C2×C4×C101—42no—
361C2×C4×C101—41no—
362C2×C4×C101—42no—
363C2×C4×C101—41no—
364C2×C4×C101—41no—
365C2×C4×C101—42no—
366C2×C4×C101—42no—
367C2×C4×C101—81no—
368C2×C4×C101—82no—
369C2×C4×C101—82no—
370C2×C4×C101#12011yescharacteristic
371C2×C4×C101#12011yescharacteristic
372C2×C4×C101#12011yescharacteristic
373C2×C4×C101#12011yescharacteristic
374C22×C101—21no—
375C22×C101—21no—
376C22×C101—21no—
377C22×C101—21no—
378C22×C101—21no—
379C22×C101—21no—
380C22×C101—41no—
381C22×C101—41no—
382C22×C101—41no—
383C22×C101—41no—
384C22×C101—42no—
385C22×C101—42no—
386C22×C101—44no—
387C22×C101—42no—
388C22×C101—44no—
389C22×C101—41no—
390C22×C101—42no—
391C22×C101—42no—
392C22×C101—41no—
393C22×C101—42no—
394C22×C101—42no—
395C22×C101—41no—
396C22×C101—82no—
397C22×C101—81no—
398C22×C101—82no—
399C22×C101—82no—
400C22×C101—81no—
401C22×C101—81no—
402C22×C101—82no—
403C22×C101—81no—
404C22×C101—81no—
405C22×C101C2×#12011yescharacteristic
406C22×C101#52511yescharacteristic
407C22×C101#53711yescharacteristic
408C22×C101#54611yescharacteristic
409C22×C101#54711yescharacteristic
410C22×C101#54811yescharacteristic
411C22×C101#55011yescharacteristic
412C4×C101—21no—
413C4×C101—21no—
414C4×C101—21no—
415C4×C101—21no—
416C4×C101—42no—
417C4×C101—41no—
418C4×C101—42no—
419C4×C101—41no—
420C4×C101—42no—
421C4×C101—41no—
422C4×C101—42no—
423C4×C101—82no—
424C4×C101—81no—
425C4×C101—82no—
426C4×C101—81no—
427#24142C10111yesmaximal, characteristic, direct product factor, Sylow
428C2×C101—21no—
429C2×C101—21no—
430C2×C101—21no—
431C2×C101—21no—
432C2×C101—21no—
433C2×C101—21no—
434C2×C101—82no—
435C2×C101—81no—
436C2×C101—82no—
437C2×C101#240711yescharacteristic
438C2×C101#302611yescharacteristic
439C2×C101#302711yescharacteristic
440#3505C2×C10111yescharacteristic, complemented
441#2626C2×C10111yescharacteristic, complemented
442#2617C2×C10111yescharacteristic, complemented
443#2321C2×C10111yescharacteristic, complemented
444#2044C2×C10112yescomplemented
445#2021C2×C10112yescomplemented
446#1996C2×C10111yescharacteristic, complemented
447#1964C2×C10111yescharacteristic, complemented
448#1889C2×C10112yescomplemented
449#1867C2×C10112yescomplemented
450#1799C2×C10111yescharacteristic, complemented
451C101#2414211yescharacteristic, direct product factor, Sylow
452#553—22no—
453#553—21no—
454#552—21no—
455#551—22no—
456#548—21no—
457#546—21no—
458#539—21no—
459#538—21no—
460#534C22×C10112yes—
461#529—21no—
462#525—21no—
463C2×C22⋊Q8C22×C10111yescharacteristic
464C2×#121C22×C10111yescharacteristic
465C2×#120C22×C10111yescharacteristic
466C2×#120C22×C10112yes—
467#518C22×C10112yes—
468C2×C4×D4C22×C10111yescharacteristic
469C22×C22⋊C4C22×C10111yescharacteristic
470C2×#99C22×C10112yes—
471C2×#99C22×C10112yes—
472C2×#99C22×C10112yes—
473#399—21no—
474#397—21no—
475#396—22no—
476#394—22no—
477#393—21no—
478#392—21no—
479#390—21no—
480#388—21no—
481#388—21no—
482#386—21no—
483#386C22×C10111yescharacteristic
484#386C22×C10112yes—
485#385C22×C10111yescharacteristic
486#385C22×C10112yes—
487#380C22×C10111yescharacteristic
488#380C22×C10111yescharacteristic
489#379C22×C10111yescharacteristic
490#379C22×C10112yes—
491C4×C22⋊C4C22×C10111yescharacteristic
492#342C22×C10112yes—
493#342C22×C10112yes—
494#342C22×C10112yes—
495C25C23×C10111yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C10111yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C10111yescharacteristic, complemented
501C22×D4C23×C10111yescharacteristic
502C22×D4C23×C10112yes—
503C23×C4D4×C10111yescharacteristic, complemented
504C23×C4C23×C10111yescharacteristic
505C23×C4C23×C10111yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C10111yescharacteristic, complemented
557C2×C4⋊C4D4×C10111yescharacteristic, complemented
558C2×C4⋊C4D4×C10112yescomplemented
559C2×C4⋊C4D4×C10111yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C10111yescharacteristic, complemented
576C2×C22⋊C4D4×C10112yescomplemented
577C2×C22⋊C4C23×C10112yes—
578C2×C22⋊C4C23×C10111yescharacteristic
579C2×C22⋊C4C23×C10112yes—
580C2×C22⋊C4C23×C10111yescharacteristic
581C2×C22⋊C4C23×C10112yes—
582C2×C22⋊C4C23×C10111yescharacteristic
583C2×C42—21no—
584C2×C42D4×C10111yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C10112yes—
604C24C2×D4×C10111yescharacteristic
605C24#41×C10112yescomplemented
606C24C24×C10111yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C10111yescharacteristic
649C22×C4C2×D4×C10112yes—
650C22×C4C2×D4×C10111yescharacteristic
651C22×C4C2×D4×C10112yes—
652C22×C4C2×D4×C10111yescharacteristic
653C22×C4C2×D4×C10112yes—
654C22×C4C2×D4×C10111yescharacteristic
655C22×C4C2×D4×C10111yescharacteristic
656C22×C4C2×D4×C10111yescharacteristic
657C22×C4C2×D4×C10111yescharacteristic
658C22×C4C2×D4×C10111yescharacteristic
659C22×C4C2×D4×C10111yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C10112yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C10111yescharacteristic
747C23C22×D4×C10111yescharacteristic
748C23C22×D4×C10111yescharacteristic
749C23C2×#41×C10111yescharacteristic
750C23C2×#41×C10111yescharacteristic
751C23H(5,𝔽2)×C10111yescharacteristic
752C232−1+4×C10111yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C10111yescharacteristic
811C2×C4#120×C10111yescharacteristic
812C2×C4#120×C10111yescharacteristic
813C2×C4#120×C10111yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C10111yescharacteristic
846C22#525×C10111yescharacteristic
847C22#537×C10111yescharacteristic
848C22#546×C10111yescharacteristic
849C22#547×C10111yescharacteristic
850C22#548×C10111yescharacteristic
851C22#550×C10111yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C101×#240711yescharacteristic
877C2C101×#302611yescharacteristic
878C2C101×#302711yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC24C24×C101
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3505C2semidirect
2. C101×#2626C2semidirect
3. C101×#2617C2semidirect
4. C101×#2321C2semidirect
5. C101×#2044C2semidirect
6. C101×#2021C2semidirect
7. C101×#1996C2semidirect
8. C101×#1964C2semidirect
9. C101×#1889C2semidirect
10. C101×#1867C2semidirect
11. C101×#1799C2semidirect
57. C22×Q8×C101D4semidirect
60. C22×D4×C101D4semidirect
63. C23×C4×C101D4semidirect
116. C2×C4⋊C4×C101D4semidirect
117. C2×C4⋊C4×C101D4semidirect
118. C2×C4⋊C4×C101D4semidirect
119. C2×C4⋊C4×C101D4semidirect
135. C2×C22⋊C4×C101D4semidirect
136. C2×C22⋊C4×C101D4semidirect
144. C2×C42×C101D4semidirect
165. C24×C101#41semidirect
269. C22⋊C4×C101#41semidirect
427. #24142C101direct (N × H)
440. #3505C2×C101semidirect
441. #2626C2×C101semidirect
442. #2617C2×C101semidirect
443. #2321C2×C101semidirect
444. #2044C2×C101semidirect
445. #2021C2×C101semidirect
446. #1996C2×C101semidirect
447. #1964C2×C101semidirect
448. #1889C2×C101semidirect
449. #1867C2×C101semidirect
450. #1799C2×C101semidirect
451. C101#24142direct (N × H)
497. C22×Q8D4×C101semidirect
500. C22×D4D4×C101semidirect
503. C23×C4D4×C101semidirect
556. C2×C4⋊C4D4×C101semidirect
557. C2×C4⋊C4D4×C101semidirect
558. C2×C4⋊C4D4×C101semidirect
559. C2×C4⋊C4D4×C101semidirect
575. C2×C22⋊C4D4×C101semidirect
576. C2×C22⋊C4D4×C101semidirect
584. C2×C42D4×C101semidirect
605. C24#41×C101semidirect
709. C22⋊C4#41×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35052
C101×#26262
C101×#26172
C101×#23212
C101×#20442
C101×#20212
C101×#19962
C101×#19642
C101×#18892
C101×#18672
C101×#17992
#24142101