Finite Group Databasebeta

← C101×#18415 #38800566

Subgroups — C101×#18415 #38800566

Order 25856.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3534C211yesmaximal, characteristic
2C101×#3196C211yesmaximal, characteristic, complemented
3C101×#3187C211yesmaximal, characteristic, complemented
4C101×#2663C211yesmaximal, characteristic, complemented
5C101×#1618C211yesmaximal, characteristic, complemented
6C101×#1616C211yesmaximal, characteristic, complemented
7C101×#1615C211yesmaximal, characteristic, complemented
8C101×#1613C211yesmaximal, characteristic, complemented
9C101×#1606C211yesmaximal, characteristic, complemented
10C101×#1604C211yesmaximal, characteristic, complemented
11C101×#1603C211yesmaximal, characteristic, complemented
12C101×#1601C211yesmaximal, characteristic, complemented
13C101×#1507C211yesmaximal, characteristic, complemented
14C101×#1501C211yesmaximal, characteristic, complemented
15C101×#1468C211yesmaximal, characteristic, complemented
16#562×C101—21no—
17#560×C101—21no—
18#553×C101—21no—
19#551×C101—21no—
20#546×C101—21no—
21#546×C101—21no—
22#546×C101—21no—
23D42×C101—21no—
24#540×C101—21no—
25#539×C101—21no—
26#539×C101C2211yescharacteristic
27#538×C101—21no—
28#538×C101C2211yescharacteristic
29#537×C101C2211yescharacteristic
30#534×C101—21no—
31#534×C101C2211yescharacteristic
32#525×C101C2211yescharacteristic
33C2×#123×C101C2211yescharacteristic
34C2×C22⋊Q8×C101C2211yescharacteristic, complemented
35C2×#121×C101C2211yescharacteristic
36#485×C101—21no—
37#484×C101C2211yescharacteristic, complemented
38#483×C101—21no—
39#481×C101C2211yescharacteristic
40#481×C101C2211yescharacteristic, complemented
41#481×C101C2211yescharacteristic, complemented
42#470×C101—21no—
43#468×C101—21no—
44#465×C101—21no—
45#465×C101—21no—
46#452×C101—21no—
47#451×C101C2211yescharacteristic, complemented
48#450×C101—21no—
49#448×C101C2211yescharacteristic
50#448×C101C2211yescharacteristic, complemented
51#448×C101C2211yescharacteristic, complemented
52#407×C101C2211yescharacteristic, complemented
53C2×C22⋊C8×C101C2211yescharacteristic, complemented
54#400×C101C2211yescharacteristic, complemented
55#399×C101C2211yescharacteristic, complemented
56#397×C101—21no—
57#395×C101C2211yescharacteristic, complemented
58#394×C101—21no—
59#393×C101C2211yescharacteristic, complemented
60#389×C101—21no—
61#388×C101—21no—
62C4×C22⋊C4×C101C2211yescharacteristic, complemented
63#328×C101C2211yescharacteristic, complemented
64#328×C101C2211yescharacteristic, complemented
65#327×C101C2211yescharacteristic
66#327×C101C2211yescharacteristic
67#327×C101C2211yescharacteristic, complemented
68#327×C101C2211yescharacteristic, complemented
69#327×C101C2211yescharacteristic, complemented
70#327×C101C2211yescharacteristic, complemented
71#324×C101C2211yescharacteristic, complemented
72#324×C101C2211yescharacteristic, complemented
73#323×C101C2211yescharacteristic, complemented
74#323×C101C2211yescharacteristic, complemented
75C2×#41×C101—21no—
76C2×#41×C101D411yescharacteristic
77C22×Q8×C101C2311yescharacteristic
78C22×D4×C101—21no—
79C22×D4×C101—21no—
80C22×D4×C101—21no—
81C22×D4×C101D411yescharacteristic
82C22×D4×C101D411yescharacteristic
83C23×C4×C101C2311yescharacteristic
84C2×Q16×C101—21no—
85C2×SD16×C101—21no—
86C2×SD16×C101—21no—
87C2×SD16×C101—21no—
88C2×M16×C101—21no—
89C22×C8×C101—21no—
90#127×C101—21no—
91#126×C101—21no—
92#126×C101—21no—
93#126×C101—21no—
94#126×C101—21no—
95#125×C101—21no—
96#125×C101—21no—
97#124×C101—21no—
98#124×C101—21no—
99#124×C101—21no—
100#123×C101—21no—
101#123×C101—21no—
102#123×C101—21no—
103#123×C101—21no—
104#123×C101—21no—
105#123×C101—21no—
106#123×C101—21no—
107#123×C101—21no—
108#123×C101—21no—
109#123×C101—21no—
110#123×C101—21no—
111#123×C101—21no—
112#123×C101—21no—
113#123×C101—21no—
114C22⋊Q8×C101—21no—
115C22⋊Q8×C101—21no—
116C22⋊Q8×C101—21no—
117C22⋊Q8×C101—21no—
118C22⋊Q8×C101—21no—
119C22⋊Q8×C101—21no—
120C22⋊Q8×C101—21no—
121C22⋊Q8×C101—21no—
122C22⋊Q8×C101—21no—
123C22⋊Q8×C101D411yescharacteristic
124C22⋊Q8×C101C2311yescharacteristic
125#121×C101—21no—
126#121×C101—21no—
127#121×C101—21no—
128#121×C101—21no—
129#121×C101—21no—
130#121×C101—21no—
131#121×C101—21no—
132#121×C101—21no—
133#121×C101—21no—
134#121×C101—21no—
135#121×C101—21no—
136#121×C101—21no—
137#121×C101—21no—
138#121×C101—21no—
139#121×C101—21no—
140#121×C101D411yescharacteristic
141#121×C101D411yescharacteristic
142#121×C101D411yescharacteristic
143#121×C101C2311yescharacteristic
144#121×C101C2311yescharacteristic
145#121×C101C2311yescharacteristic
146#120×C101—21no—
147#120×C101—21no—
148#120×C101—21no—
149#120×C101—21no—
150#120×C101—21no—
151#120×C101—21no—
152#120×C101—21no—
153#120×C101—21no—
154C4×D4×C101—21no—
155C4×D4×C101—21no—
156C4×D4×C101—21no—
157C4×D4×C101—21no—
158C4×D4×C101—21no—
159C4×D4×C101—21no—
160C4×D4×C101—21no—
161C4×D4×C101—21no—
162#117×C101—21no—
163#117×C101D411yescharacteristic
164C2×C4⋊C4×C101—21no—
165C2×C4⋊C4×C101—21no—
166C2×C4⋊C4×C101—21no—
167C2×C4⋊C4×C101D411yescharacteristic
168C2×C4⋊C4×C101D411yescharacteristic
169C2×C4⋊C4×C101C2311yescharacteristic
170C2×C4⋊C4×C101C2311yescharacteristic
171C2×C22⋊C4×C101—21no—
172C2×C22⋊C4×C101—21no—
173C2×C22⋊C4×C101—21no—
174C2×C22⋊C4×C101—21no—
175C2×C22⋊C4×C101—21no—
176C2×C22⋊C4×C101—21no—
177C2×C22⋊C4×C101—21no—
178C2×C22⋊C4×C101D411yescharacteristic
179C2×C22⋊C4×C101D411yescharacteristic
180C2×C22⋊C4×C101C2311yescharacteristic
181C2×C42×C101—21no—
182#107×C101—21no—
183#106×C101—21no—
184#106×C101—21no—
185#106×C101—21no—
186#103×C101—21no—
187#103×C101—21no—
188#103×C101—21no—
189#103×C101—21no—
190#103×C101—21no—
191#102×C101—21no—
192#102×C101—21no—
193#102×C101—21no—
194C22⋊C8×C101—21no—
195C22⋊C8×C101—21no—
196C22⋊C8×C101C2311yescharacteristic
197C22⋊C8×C101C2311yescharacteristic
198C22⋊C8×C101C2311yescharacteristic
199C22⋊C8×C101C2311yescharacteristic
200#95×C101—21no—
201#95×C101—21no—
202#95×C101—21no—
203#95×C101—21no—
204#95×C101C2311yescharacteristic
205#95×C101C2311yescharacteristic
206C24×C101—21no—
207C24×C101—21no—
208C24×C101C2×D411yescharacteristic
209C24×C101C2×D411yescharacteristic
210#41×C101—81no—
211#41×C101—81no—
212#41×C101—81no—
213C2×Q8×C101—21no—
214C2×Q8×C101—21no—
215C2×Q8×C101—21no—
216C2×Q8×C101—81no—
217C2×Q8×C101C2×D411yescharacteristic
218C2×D4×C101—21no—
219C2×D4×C101—21no—
220C2×D4×C101—21no—
221C2×D4×C101—21no—
222C2×D4×C101—21no—
223C2×D4×C101—21no—
224C2×D4×C101—21no—
225C2×D4×C101—21no—
226C2×D4×C101—21no—
227C2×D4×C101—21no—
228C2×D4×C101—21no—
229C2×D4×C101—21no—
230C2×D4×C101—21no—
231C2×D4×C101—21no—
232C2×D4×C101—21no—
233C2×D4×C101—21no—
234C2×D4×C101—21no—
235C2×D4×C101—81no—
236C2×D4×C101—81no—
237C2×D4×C101—81no—
238C2×D4×C101—81no—
239C2×D4×C101—81no—
240C2×D4×C101—81no—
241C2×D4×C101—82no—
242C2×D4×C101C2×D411yescharacteristic
243C2×D4×C101C2×D411yescharacteristic
244C2×D4×C101C2×D411yescharacteristic
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—81no—
257C22×C4×C101C2×D411yescharacteristic
258C22×C4×C101C2×D411yescharacteristic
259C22×C4×C101C2×D411yescharacteristic
260C22×C4×C101C2×D411yescharacteristic
261C22×C4×C101C2×D411yescharacteristic
262C22×C4×C101C2×D411yescharacteristic
263C22×C4×C101C2×D411yescharacteristic
264C22×C4×C101C2×D411yescharacteristic
265C22×C4×C101C2411yescharacteristic
266Q16×C101—81no—
267SD16×C101—81no—
268SD16×C101—81no—
269SD16×C101—81no—
270M16×C101—81no—
271C2×C8×C101—21no—
272C2×C8×C101—21no—
273C2×C8×C101—21no—
274C2×C8×C101—21no—
275C2×C8×C101—81no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101—21no—
278C4⋊C4×C101—21no—
279C4⋊C4×C101—21no—
280C4⋊C4×C101—21no—
281C4⋊C4×C101—21no—
282C4⋊C4×C101—21no—
283C4⋊C4×C101—21no—
284C4⋊C4×C101—21no—
285C4⋊C4×C101—21no—
286C4⋊C4×C101—21no—
287C4⋊C4×C101—21no—
288C4⋊C4×C101—21no—
289C4⋊C4×C101—21no—
290C4⋊C4×C101—21no—
291C4⋊C4×C101—42no—
292C4⋊C4×C101—41no—
293C4⋊C4×C101—41no—
294C4⋊C4×C101—81no—
295C4⋊C4×C101C2×D411yescharacteristic
296C4⋊C4×C101C2×D411yescharacteristic
297C4⋊C4×C101C2×D411yescharacteristic
298C4⋊C4×C101C2×D411yescharacteristic
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×C101—21no—
309C22⋊C4×C101—21no—
310C22⋊C4×C101—21no—
311C22⋊C4×C101—21no—
312C22⋊C4×C101—21no—
313C22⋊C4×C101—21no—
314C22⋊C4×C101—21no—
315C22⋊C4×C101—21no—
316C22⋊C4×C101—21no—
317C22⋊C4×C101—21no—
318C22⋊C4×C101—21no—
319C22⋊C4×C101—21no—
320C22⋊C4×C101—21no—
321C22⋊C4×C101—21no—
322C22⋊C4×C101—21no—
323C22⋊C4×C101—21no—
324C22⋊C4×C101—42no—
325C22⋊C4×C101—42no—
326C22⋊C4×C101—41no—
327C22⋊C4×C101—41no—
328C22⋊C4×C101—81no—
329C42×C101—21no—
330C42×C101—21no—
331C42×C101—21no—
332C42×C101—81no—
333C23×C101—21no—
334C23×C101—21no—
335C23×C101—21no—
336C23×C101—21no—
337C23×C101—21no—
338C23×C101—21no—
339C23×C101—21no—
340C23×C101—21no—
341C23×C101—41no—
342C23×C101—41no—
343C23×C101—42no—
344C23×C101—41no—
345C23×C101—41no—
346C23×C101—81no—
347C23×C101—81no—
348C23×C101—81no—
349C23×C101—81no—
350C23×C101—81no—
351C23×C101#12011yescharacteristic
352C23×C101#12011yescharacteristic
353C23×C101C22×D411yescharacteristic
354Q8×C101—41no—
355Q8×C101—41no—
356Q8×C101—41no—
357Q8×C101—41no—
358Q8×C101—41no—
359Q8×C101—81no—
360D4×C101—41no—
361D4×C101—41no—
362D4×C101—41no—
363D4×C101—42no—
364D4×C101—42no—
365D4×C101—41no—
366D4×C101—41no—
367D4×C101—41no—
368D4×C101—41no—
369D4×C101—41no—
370D4×C101—41no—
371D4×C101—81no—
372D4×C101—81no—
373D4×C101—81no—
374D4×C101—81no—
375D4×C101—81no—
376D4×C101—81no—
377D4×C101—81no—
378D4×C101—81no—
379D4×C101—81no—
380D4×C101—81no—
381D4×C101—81no—
382D4×C101—81no—
383C2×C4×C101—22no—
384C2×C4×C101—21no—
385C2×C4×C101—21no—
386C2×C4×C101—21no—
387C2×C4×C101—21no—
388C2×C4×C101—21no—
389C2×C4×C101—21no—
390C2×C4×C101—21no—
391C2×C4×C101—21no—
392C2×C4×C101—21no—
393C2×C4×C101—21no—
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—81no—
414C2×C4×C101—81no—
415C2×C4×C101—81no—
416C2×C4×C101—81no—
417C2×C4×C101—81no—
418C2×C4×C101—81no—
419C2×C4×C101—81no—
420C2×C4×C101#12011yescharacteristic
421C2×C4×C101#12011yescharacteristic
422C2×C4×C101C22×D411yescharacteristic
423C2×C4×C101C22×D411yescharacteristic
424C8×C101—41no—
425C8×C101—41no—
426C8×C101—41no—
427C8×C101—41no—
428C22×C101—21no—
429C22×C101—21no—
430C22×C101—21no—
431C22×C101—21no—
432C22×C101—21no—
433C22×C101—21no—
434C22×C101—21no—
435C22×C101—21no—
436C22×C101—41no—
437C22×C101—41no—
438C22×C101—41no—
439C22×C101—41no—
440C22×C101—41no—
441C22×C101—41no—
442C22×C101—41no—
443C22×C101—41no—
444C22×C101—41no—
445C22×C101—41no—
446C22×C101—41no—
447C22×C101—41no—
448C22×C101—81no—
449C22×C101—81no—
450C22×C101—81no—
451C22×C101—81no—
452C22×C101—162no—
453C22×C101—162no—
454C22×C101C2×#12011yescharacteristic
455C22×C101#57711yescharacteristic
456C22×C101#57711yescharacteristic
457C4×C101—21no—
458C4×C101—21no—
459C4×C101—21no—
460C4×C101—21no—
461C4×C101—42no—
462C4×C101—41no—
463C4×C101—41no—
464C4×C101—41no—
465C4×C101—41no—
466C4×C101—41no—
467C4×C101—41no—
468C4×C101—41no—
469C4×C101—41no—
470C4×C101—81no—
471C4×C101—81no—
472C4×C101—81no—
473#18415C10111yesmaximal, characteristic, direct product factor, Sylow
474C2×C101—21no—
475C2×C101—21no—
476C2×C101—41no—
477C2×C101—41no—
478C2×C101—81no—
479C2×C101—81no—
480C2×C101—81no—
481C2×C101—81no—
482C2×C101#300911yescharacteristic
483C2×C101#301811yescharacteristic
484C2×C101#302611yescharacteristic
485#3534C2×C10111yescharacteristic
486#3196C2×C10111yescharacteristic, complemented
487#3187C2×C10111yescharacteristic, complemented
488#2663C2×C10111yescharacteristic, complemented
489#1618C2×C10111yescharacteristic, complemented
490#1616C2×C10111yescharacteristic, complemented
491#1615C2×C10111yescharacteristic, complemented
492#1613C2×C10111yescharacteristic, complemented
493#1606C2×C10111yescharacteristic, complemented
494#1604C2×C10111yescharacteristic, complemented
495#1603C2×C10111yescharacteristic, complemented
496#1601C2×C10111yescharacteristic, complemented
497#1507C2×C10111yescharacteristic, complemented
498#1501C2×C10111yescharacteristic, complemented
499#1468C2×C10111yescharacteristic, complemented
500C101#1841511yescharacteristic, direct product factor, Sylow
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C10111yescharacteristic
512#538—21no—
513#538C22×C10111yescharacteristic
514#537C22×C10111yescharacteristic
515#534—21no—
516#534C22×C10111yescharacteristic
517#525C22×C10111yescharacteristic
518C2×#123C22×C10111yescharacteristic
519C2×C22⋊Q8C22×C10111yescharacteristic, complemented
520C2×#121C22×C10111yescharacteristic
521#485—21no—
522#484C22×C10111yescharacteristic, complemented
523#483—21no—
524#481C22×C10111yescharacteristic
525#481C22×C10111yescharacteristic, complemented
526#481C22×C10111yescharacteristic, complemented
527#470—21no—
528#468—21no—
529#465—21no—
530#465—21no—
531#452—21no—
532#451C22×C10111yescharacteristic, complemented
533#450—21no—
534#448C22×C10111yescharacteristic
535#448C22×C10111yescharacteristic, complemented
536#448C22×C10111yescharacteristic, complemented
537#407C22×C10111yescharacteristic, complemented
538C2×C22⋊C8C22×C10111yescharacteristic, complemented
539#400C22×C10111yescharacteristic, complemented
540#399C22×C10111yescharacteristic, complemented
541#397—21no—
542#395C22×C10111yescharacteristic, complemented
543#394—21no—
544#393C22×C10111yescharacteristic, complemented
545#389—21no—
546#388—21no—
547C4×C22⋊C4C22×C10111yescharacteristic, complemented
548#328C22×C10111yescharacteristic, complemented
549#328C22×C10111yescharacteristic, complemented
550#327C22×C10111yescharacteristic
551#327C22×C10111yescharacteristic
552#327C22×C10111yescharacteristic, complemented
553#327C22×C10111yescharacteristic, complemented
554#327C22×C10111yescharacteristic, complemented
555#327C22×C10111yescharacteristic, complemented
556#324C22×C10111yescharacteristic, complemented
557#324C22×C10111yescharacteristic, complemented
558#323C22×C10111yescharacteristic, complemented
559#323C22×C10111yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C10111yescharacteristic
562C22×Q8C23×C10111yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C10111yescharacteristic
567C22×D4D4×C10111yescharacteristic
568C23×C4C23×C10111yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C10111yescharacteristic
609C22⋊Q8C23×C10111yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C10111yescharacteristic
626#121D4×C10111yescharacteristic
627#121D4×C10111yescharacteristic
628#121C23×C10111yescharacteristic
629#121C23×C10111yescharacteristic
630#121C23×C10111yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C10111yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C10111yescharacteristic
653C2×C4⋊C4D4×C10111yescharacteristic
654C2×C4⋊C4C23×C10111yescharacteristic
655C2×C4⋊C4C23×C10111yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C10111yescharacteristic
664C2×C22⋊C4D4×C10111yescharacteristic
665C2×C22⋊C4C23×C10111yescharacteristic
666C2×C42—21no—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C10111yescharacteristic
682C22⋊C8C23×C10111yescharacteristic
683C22⋊C8C23×C10111yescharacteristic
684C22⋊C8C23×C10111yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C10111yescharacteristic
690#95C23×C10111yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C10111yescharacteristic
694C24C2×D4×C10111yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C10111yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C10111yescharacteristic
728C2×D4C2×D4×C10111yescharacteristic
729C2×D4C2×D4×C10111yescharacteristic
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—81no—
742C22×C4C2×D4×C10111yescharacteristic
743C22×C4C2×D4×C10111yescharacteristic
744C22×C4C2×D4×C10111yescharacteristic
745C22×C4C2×D4×C10111yescharacteristic
746C22×C4C2×D4×C10111yescharacteristic
747C22×C4C2×D4×C10111yescharacteristic
748C22×C4C2×D4×C10111yescharacteristic
749C22×C4C2×D4×C10111yescharacteristic
750C22×C4C24×C10111yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C10111yescharacteristic
781C4⋊C4C2×D4×C10111yescharacteristic
782C4⋊C4C2×D4×C10111yescharacteristic
783C4⋊C4C2×D4×C10111yescharacteristic
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
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—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C10111yescharacteristic
837C23#120×C10111yescharacteristic
838C23C22×D4×C10111yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C10111yescharacteristic
906C2×C4#120×C10111yescharacteristic
907C2×C4C22×D4×C10111yescharacteristic
908C2×C4C22×D4×C10111yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C10111yescharacteristic
940C22#577×C10111yescharacteristic
941C22#577×C10111yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C101×#300911yescharacteristic
967C2C101×#301811yescharacteristic
968C2C101×#302611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#3196C2semidirect
3. C101×#3187C2semidirect
4. C101×#2663C2semidirect
5. C101×#1618C2semidirect
6. C101×#1616C2semidirect
7. C101×#1615C2semidirect
8. C101×#1613C2semidirect
9. C101×#1606C2semidirect
10. C101×#1604C2semidirect
11. C101×#1603C2semidirect
12. C101×#1601C2semidirect
13. C101×#1507C2semidirect
14. C101×#1501C2semidirect
15. C101×#1468C2semidirect
34. C2×C22⋊Q8×C101C22semidirect
37. #484×C101C22semidirect
40. #481×C101C22semidirect
41. #481×C101C22semidirect
47. #451×C101C22semidirect
50. #448×C101C22semidirect
51. #448×C101C22semidirect
52. #407×C101C22semidirect
53. C2×C22⋊C8×C101C22semidirect
54. #400×C101C22semidirect
55. #399×C101C22semidirect
57. #395×C101C22semidirect
59. #393×C101C22semidirect
62. C4×C22⋊C4×C101C22semidirect
63. #328×C101C22semidirect
64. #328×C101C22semidirect
67. #327×C101C22semidirect
68. #327×C101C22semidirect
69. #327×C101C22semidirect
70. #327×C101C22semidirect
71. #324×C101C22semidirect
72. #324×C101C22semidirect
73. #323×C101C22semidirect
74. #323×C101C22semidirect
473. #18415C101direct (N × H)
486. #3196C2×C101semidirect
487. #3187C2×C101semidirect
488. #2663C2×C101semidirect
489. #1618C2×C101semidirect
490. #1616C2×C101semidirect
491. #1615C2×C101semidirect
492. #1613C2×C101semidirect
493. #1606C2×C101semidirect
494. #1604C2×C101semidirect
495. #1603C2×C101semidirect
496. #1601C2×C101semidirect
497. #1507C2×C101semidirect
498. #1501C2×C101semidirect
499. #1468C2×C101semidirect
500. C101#18415direct (N × H)
519. C2×C22⋊Q8C22×C101semidirect
522. #484C22×C101semidirect
525. #481C22×C101semidirect
526. #481C22×C101semidirect
532. #451C22×C101semidirect
535. #448C22×C101semidirect
536. #448C22×C101semidirect
537. #407C22×C101semidirect
538. C2×C22⋊C8C22×C101semidirect
539. #400C22×C101semidirect
540. #399C22×C101semidirect
542. #395C22×C101semidirect
544. #393C22×C101semidirect
547. C4×C22⋊C4C22×C101semidirect
548. #328C22×C101semidirect
549. #328C22×C101semidirect
552. #327C22×C101semidirect
553. #327C22×C101semidirect
554. #327C22×C101semidirect
555. #327C22×C101semidirect
556. #324C22×C101semidirect
557. #324C22×C101semidirect
558. #323C22×C101semidirect
559. #323C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35342
C101×#31962
C101×#31872
C101×#26632
C101×#16182
C101×#16162
C101×#16152
C101×#16132
C101×#16062
C101×#16042
C101×#16032
C101×#16012
C101×#15072
C101×#15012
C101×#14682
#18415101