Finite Group Databasebeta

← C101×#18607 #38800758

Subgroups — C101×#18607 #38800758

Order 25856.

930 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3517C211yesmaximal, characteristic
2C101×#3252C211yesmaximal, characteristic, complemented
3C101×#3182C211yesmaximal, characteristic, complemented
4C101×#3076C211yesmaximal, characteristic, complemented
5C101×#1648C211yesmaximal, characteristic, complemented
6C101×#1647C211yesmaximal, characteristic, complemented
7C101×#1642C211yesmaximal, characteristic, complemented
8C101×#1641C211yesmaximal, characteristic, complemented
9C101×#1636C211yesmaximal, characteristic, complemented
10C101×#1635C211yesmaximal, characteristic, complemented
11C101×#1631C211yesmaximal, characteristic, complemented
12C101×#1631C211yesmaximal, characteristic, complemented
13C101×#1547C211yesmaximal, characteristic, complemented
14C101×#1489C211yesmaximal, characteristic, complemented
15C101×#1483C211yesmaximal, characteristic, complemented
16#557×C101C2211yescharacteristic
17#553×C101—22no—
18#553×C101—21no—
19#550×C101—21no—
20#550×C101—21no—
21#550×C101C2211yescharacteristic
22#550×C101C2211yescharacteristic
23#547×C101—21no—
24#547×C101C2211yescharacteristic
25#540×C101—22no—
26#540×C101—21no—
27#533×C101C2211yescharacteristic
28#532×C101—21no—
29#532×C101C2211yescharacteristic
30#529×C101—21no—
31#529×C101C2211yescharacteristic
32#520×C101—21no—
33C4×#41×C101C2211yescharacteristic
34#500×C101C2211yescharacteristic
35#492×C101C2211yescharacteristic
36#487×C101C2211yescharacteristic
37#486×C101C2211yescharacteristic
38#479×C101—21no—
39#479×C101—21no—
40#478×C101—21no—
41#477×C101C2211yescharacteristic
42#477×C101C2211yescharacteristic
43#476×C101C2211yescharacteristic
44#476×C101C2211yescharacteristic
45#475×C101C2211yescharacteristic
46#474×C101C2211yescharacteristic
47#470×C101—21no—
48#468×C101—22no—
49#468×C101—21no—
50#464×C101—21no—
51#462×C101C2211yescharacteristic
52#461×C101C2211yescharacteristic
53#440×C101—22no—
54#427×C101—21no—
55#423×C101C2211yescharacteristic
56C2×C4⋊C8×C101C2211yescharacteristic
57#416×C101—21no—
58C4×M16×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62#331×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65Q8⋊C8×C101C2211yescharacteristic
66Q8⋊C8×C101C2211yescharacteristic
67D4⋊C8×C101C2211yescharacteristic
68D4⋊C8×C101C2211yescharacteristic
69D4⋊C8×C101C2211yescharacteristic
70D4⋊C8×C101C2211yescharacteristic
71C2×#41×C101—21no—
72C2×#41×C101—21no—
73C2×#41×C101—21no—
74C2×#41×C101—21no—
75C2×#41×C101D411yescharacteristic
76C2×Q16×C101—21no—
77C2×SD16×C101—22no—
78C2×SD16×C101—21no—
79C2×M16×C101—21no—
80C2×M16×C101—21no—
81C22×C8×C101—21no—
82C4⋊Q8×C101—21no—
83C4⋊Q8×C101C2311yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86#127×C101—22no—
87#127×C101—21no—
88#127×C101—21no—
89#127×C101C2311yescharacteristic
90#126×C101—22no—
91#126×C101—21no—
92#125×C101—22no—
93#125×C101—21no—
94#125×C101—21no—
95#125×C101D411yescharacteristic
96#124×C101—21no—
97#124×C101D411yescharacteristic
98#123×C101—22no—
99#123×C101—22no—
100#123×C101—22no—
101#123×C101—21no—
102#123×C101—22no—
103C22⋊Q8×C101—21no—
104C22⋊Q8×C101—21no—
105C22⋊Q8×C101—21no—
106C22⋊Q8×C101D411yescharacteristic
107#121×C101—22no—
108#121×C101—22no—
109#121×C101—22no—
110#121×C101—22no—
111#121×C101—22no—
112#121×C101—21no—
113#121×C101—22no—
114#121×C101—22no—
115#121×C101—21no—
116#121×C101—21no—
117#121×C101—21no—
118#121×C101D411yescharacteristic
119#121×C101D412yes—
120C4×Q8×C101—21no—
121C4×Q8×C101—21no—
122C4×Q8×C101—21no—
123C4×Q8×C101—21no—
124C4×Q8×C101D411yescharacteristic
125C4×Q8×C101C2311yescharacteristic
126C4×Q8×C101C2311yescharacteristic
127C4×D4×C101—22no—
128C4×D4×C101—22no—
129C4×D4×C101—22no—
130C4×D4×C101—22no—
131C4×D4×C101—21no—
132C4×D4×C101—21no—
133C4×D4×C101—21no—
134C4×D4×C101—21no—
135C4×D4×C101—21no—
136C4×D4×C101—21no—
137C4×D4×C101D412yes—
138C4×D4×C101D411yescharacteristic
139C4×D4×C101C2311yescharacteristic
140C4×D4×C101C2311yescharacteristic
141#117×C101—22no—
142#117×C101—21no—
143#117×C101—21no—
144#117×C101—21no—
145#117×C101D411yescharacteristic
146C2×C4⋊C4×C101—22no—
147C2×C4⋊C4×C101—21no—
148C2×C42×C101—21no—
149C2×C42×C101C2311yescharacteristic
150#107×C101—21no—
151#107×C101—21no—
152#107×C101—22no—
153#107×C101—21no—
154#106×C101—21no—
155#106×C101—21no—
156#106×C101—21no—
157C4⋊C8×C101—21no—
158C4⋊C8×C101—21no—
159C4⋊C8×C101C2311yescharacteristic
160C4⋊C8×C101C2311yescharacteristic
161C4⋊C8×C101C2311yescharacteristic
162C4⋊C8×C101C2311yescharacteristic
163#103×C101—21no—
164#103×C101—21no—
165#103×C101—21no—
166#103×C101—22no—
167#103×C101—21no—
168#103×C101—21no—
169#102×C101—21no—
170#102×C101—21no—
171#102×C101—22no—
172#102×C101—21no—
173#97×C101—21no—
174C4×C8×C101C2311yescharacteristic
175C4×C8×C101C2311yescharacteristic
176#41×C101—22no—
177#41×C101—41no—
178#41×C101—42no—
179#41×C101—42no—
180#41×C101—81no—
181#41×C101—81no—
182#41×C101—81no—
183#41×C101—81no—
184#41×C101—81no—
185#41×C101—81no—
186C2×Q8×C101—21no—
187C2×Q8×C101—21no—
188C2×Q8×C101—21no—
189C2×Q8×C101C2×D411yescharacteristic
190C2×Q8×C101C2×D411yescharacteristic
191C2×D4×C101—22no—
192C2×D4×C101—21no—
193C2×D4×C101—22no—
194C2×D4×C101—22no—
195C2×D4×C101—22no—
196C2×D4×C101—22no—
197C2×D4×C101—21no—
198C2×D4×C101—22no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101C2×D411yescharacteristic
202C2×D4×C101C2×D411yescharacteristic
203C2×D4×C101C2×D412yes—
204C22×C4×C101—22no—
205C22×C4×C101—22no—
206C22×C4×C101—22no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—21no—
211C22×C4×C101—22no—
212C22×C4×C101C2×D411yescharacteristic
213C22×C4×C101C2×D411yescharacteristic
214C22×C4×C101C2×D411yescharacteristic
215Q16×C101—81no—
216SD16×C101—44no—
217SD16×C101—81no—
218M16×C101—42no—
219M16×C101—81no—
220C2×C8×C101—21no—
221C2×C8×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101—21no—
225C2×C8×C101—21no—
226C2×C8×C101—42no—
227C4⋊C4×C101—22no—
228C4⋊C4×C101—22no—
229C4⋊C4×C101—22no—
230C4⋊C4×C101—22no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—41no—
243C4⋊C4×C101—41no—
244C4⋊C4×C101C2×D411yescharacteristic
245C4⋊C4×C101C2×D412yes—
246C4⋊C4×C101C2×D411yescharacteristic
247C4⋊C4×C101C2×D411yescharacteristic
248C4⋊C4×C101C2×D411yescharacteristic
249C22⋊C4×C101—22no—
250C22⋊C4×C101—22no—
251C22⋊C4×C101—22no—
252C22⋊C4×C101—21no—
253C22⋊C4×C101—21no—
254C22⋊C4×C101—21no—
255C22⋊C4×C101—21no—
256C22⋊C4×C101—22no—
257C22⋊C4×C101—21no—
258C22⋊C4×C101—21no—
259C22⋊C4×C101—22no—
260C22⋊C4×C101—21no—
261C22⋊C4×C101—21no—
262C22⋊C4×C101—41no—
263C42×C101—22no—
264C42×C101—21no—
265C42×C101—21no—
266C42×C101—21no—
267C42×C101—21no—
268C42×C101—41no—
269C42×C101C2×D411yescharacteristic
270C42×C101C2×D411yescharacteristic
271C42×C101C2×D411yescharacteristic
272C42×C101C2411yescharacteristic
273C23×C101—21no—
274C23×C101—21no—
275C23×C101—22no—
276C23×C101#12011yescharacteristic
277Q8×C101—21no—
278Q8×C101—21no—
279Q8×C101—21no—
280Q8×C101—42no—
281Q8×C101—41no—
282Q8×C101—41no—
283Q8×C101—41no—
284Q8×C101—41no—
285Q8×C101#13712yes—
286D4×C101—21no—
287D4×C101—21no—
288D4×C101—21no—
289D4×C101—21no—
290D4×C101—42no—
291D4×C101—42no—
292D4×C101—44no—
293D4×C101—41no—
294D4×C101—41no—
295D4×C101—41no—
296D4×C101—41no—
297D4×C101—81no—
298D4×C101—82no—
299D4×C101—82no—
300D4×C101—82no—
301D4×C101—82no—
302D4×C101—82no—
303C2×C4×C101—21no—
304C2×C4×C101—21no—
305C2×C4×C101—21no—
306C2×C4×C101—21no—
307C2×C4×C101—21no—
308C2×C4×C101—21no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—22no—
313C2×C4×C101—21no—
314C2×C4×C101—41no—
315C2×C4×C101—42no—
316C2×C4×C101—44no—
317C2×C4×C101—41no—
318C2×C4×C101—41no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101—41no—
322C2×C4×C101—41no—
323C2×C4×C101—81no—
324C2×C4×C101—82no—
325C2×C4×C101—82no—
326C2×C4×C101—82no—
327C2×C4×C101#12011yescharacteristic
328C2×C4×C101#12011yescharacteristic
329C2×C4×C101#12011yescharacteristic
330C2×C4×C101C22×D411yescharacteristic
331C2×C4×C101C22×D411yescharacteristic
332C2×C4×C101C22×D411yescharacteristic
333C8×C101—22no—
334C8×C101—41no—
335C8×C101—41no—
336C8×C101—41no—
337C8×C101—41no—
338C8×C101—41no—
339C22×C101—21no—
340C22×C101—21no—
341C22×C101—21no—
342C22×C101—41no—
343C22×C101—42no—
344C22×C101—41no—
345C22×C101—41no—
346C22×C101—41no—
347C22×C101—42no—
348C22×C101—41no—
349C22×C101—42no—
350C22×C101—41no—
351C22×C101C2×#12011yescharacteristic
352C4×C101—21no—
353C4×C101—22no—
354C4×C101—21no—
355C4×C101—21no—
356C4×C101—21no—
357C4×C101—41no—
358C4×C101—41no—
359C4×C101—41no—
360C4×C101—42no—
361C4×C101—41no—
362C4×C101—41no—
363C4×C101—81no—
364C4×C101—81no—
365C4×C101C2×#13711yescharacteristic
366C4×C101#57511yescharacteristic
367C4×C101#57611yescharacteristic
368C4×C101#57711yescharacteristic
369#18607C10111yesmaximal, characteristic, direct product factor, Sylow
370C2×C101—41no—
371C2×C101—81no—
372C2×C101—81no—
373C2×C101—82no—
374C2×C101#300711yescharacteristic
375C2×C101#301211yescharacteristic
376C2×C101#301811yescharacteristic
377#3517C2×C10111yescharacteristic
378#3252C2×C10111yescharacteristic, complemented
379#3182C2×C10111yescharacteristic, complemented
380#3076C2×C10111yescharacteristic, complemented
381#1648C2×C10111yescharacteristic, complemented
382#1647C2×C10111yescharacteristic, complemented
383#1642C2×C10111yescharacteristic, complemented
384#1641C2×C10111yescharacteristic, complemented
385#1636C2×C10111yescharacteristic, complemented
386#1635C2×C10111yescharacteristic, complemented
387#1631C2×C10111yescharacteristic, complemented
388#1631C2×C10111yescharacteristic, complemented
389#1547C2×C10111yescharacteristic, complemented
390#1489C2×C10111yescharacteristic, complemented
391#1483C2×C10111yescharacteristic, complemented
392C101#1860711yescharacteristic, direct product factor, Sylow
393#557C22×C10111yescharacteristic
394#553—22no—
395#553—21no—
396#550—21no—
397#550—21no—
398#550C22×C10111yescharacteristic
399#550C22×C10111yescharacteristic
400#547—21no—
401#547C22×C10111yescharacteristic
402#540—22no—
403#540—21no—
404#533C22×C10111yescharacteristic
405#532—21no—
406#532C22×C10111yescharacteristic
407#529—21no—
408#529C22×C10111yescharacteristic
409#520—21no—
410C4×#41C22×C10111yescharacteristic
411#500C22×C10111yescharacteristic
412#492C22×C10111yescharacteristic
413#487C22×C10111yescharacteristic
414#486C22×C10111yescharacteristic
415#479—21no—
416#479—21no—
417#478—21no—
418#477C22×C10111yescharacteristic
419#477C22×C10111yescharacteristic
420#476C22×C10111yescharacteristic
421#476C22×C10111yescharacteristic
422#475C22×C10111yescharacteristic
423#474C22×C10111yescharacteristic
424#470—21no—
425#468—22no—
426#468—21no—
427#464—21no—
428#462C22×C10111yescharacteristic
429#461C22×C10111yescharacteristic
430#440—22no—
431#427—21no—
432#423C22×C10111yescharacteristic
433C2×C4⋊C8C22×C10111yescharacteristic
434#416—21no—
435C4×M16C22×C10111yescharacteristic
436#332C22×C10111yescharacteristic
437#332C22×C10111yescharacteristic
438#331C22×C10111yescharacteristic
439#331C22×C10111yescharacteristic
440Q8⋊C8C22×C10111yescharacteristic
441Q8⋊C8C22×C10111yescharacteristic
442Q8⋊C8C22×C10111yescharacteristic
443Q8⋊C8C22×C10111yescharacteristic
444D4⋊C8C22×C10111yescharacteristic
445D4⋊C8C22×C10111yescharacteristic
446D4⋊C8C22×C10111yescharacteristic
447D4⋊C8C22×C10111yescharacteristic
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41D4×C10111yescharacteristic
453C2×Q16—21no—
454C2×SD16—22no—
455C2×SD16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C22×C8—21no—
459C4⋊Q8—21no—
460C4⋊Q8C23×C10111yescharacteristic
461C4⋊Q8C23×C10111yescharacteristic
462C4⋊Q8C23×C10111yescharacteristic
463#127—22no—
464#127—21no—
465#127—21no—
466#127C23×C10111yescharacteristic
467#126—22no—
468#126—21no—
469#125—22no—
470#125—21no—
471#125—21no—
472#125D4×C10111yescharacteristic
473#124—21no—
474#124D4×C10111yescharacteristic
475#123—22no—
476#123—22no—
477#123—22no—
478#123—21no—
479#123—22no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8D4×C10111yescharacteristic
484#121—22no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—21no—
490#121—22no—
491#121—22no—
492#121—21no—
493#121—21no—
494#121—21no—
495#121D4×C10111yescharacteristic
496#121D4×C10112yes—
497C4×Q8—21no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8D4×C10111yescharacteristic
502C4×Q8C23×C10111yescharacteristic
503C4×Q8C23×C10111yescharacteristic
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4D4×C10111yescharacteristic
515C4×D4D4×C10112yes—
516C4×D4C23×C10111yescharacteristic
517C4×D4C23×C10111yescharacteristic
518#117—22no—
519#117—21no—
520#117—21no—
521#117—21no—
522#117D4×C10111yescharacteristic
523C2×C4⋊C4—22no—
524C2×C4⋊C4—21no—
525C2×C42—21no—
526C2×C42C23×C10111yescharacteristic
527#107—21no—
528#107—21no—
529#107—22no—
530#107—21no—
531#106—21no—
532#106—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8—21no—
536C4⋊C8C23×C10111yescharacteristic
537C4⋊C8C23×C10111yescharacteristic
538C4⋊C8C23×C10111yescharacteristic
539C4⋊C8C23×C10111yescharacteristic
540#103—21no—
541#103—21no—
542#103—21no—
543#103—22no—
544#103—21no—
545#103—21no—
546#102—21no—
547#102—21no—
548#102—22no—
549#102—21no—
550#97—21no—
551C4×C8C23×C10111yescharacteristic
552C4×C8C23×C10111yescharacteristic
553#41—22no—
554#41—41no—
555#41—42no—
556#41—42no—
557#41—81no—
558#41—81no—
559#41—81no—
560#41—81no—
561#41—81no—
562#41—81no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8C2×D4×C10111yescharacteristic
567C2×Q8C2×D4×C10111yescharacteristic
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4C2×D4×C10111yescharacteristic
579C2×D4C2×D4×C10111yescharacteristic
580C2×D4C2×D4×C10112yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4C2×D4×C10111yescharacteristic
590C22×C4C2×D4×C10111yescharacteristic
591C22×C4C2×D4×C10111yescharacteristic
592Q16—81no—
593SD16—44no—
594SD16—81no—
595M16—42no—
596M16—81no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—42no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4C2×D4×C10111yescharacteristic
622C4⋊C4C2×D4×C10112yes—
623C4⋊C4C2×D4×C10111yescharacteristic
624C4⋊C4C2×D4×C10111yescharacteristic
625C4⋊C4C2×D4×C10111yescharacteristic
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—41no—
640C42—22no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—41no—
646C42C2×D4×C10111yescharacteristic
647C42C2×D4×C10111yescharacteristic
648C42C2×D4×C10111yescharacteristic
649C42C24×C10111yescharacteristic
650C23—21no—
651C23—21no—
652C23—22no—
653C23#120×C10111yescharacteristic
654Q8—21no—
655Q8—21no—
656Q8—21no—
657Q8—42no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8#137×C10112yes—
663D4—21no—
664D4—21no—
665D4—21no—
666D4—21no—
667D4—42no—
668D4—42no—
669D4—44no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—82no—
675D4—81no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—82no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4#120×C10111yescharacteristic
705C2×C4#120×C10111yescharacteristic
706C2×C4#120×C10111yescharacteristic
707C2×C4C22×D4×C10111yescharacteristic
708C2×C4C22×D4×C10111yescharacteristic
709C2×C4C22×D4×C10111yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—41no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22C2×#120×C10111yescharacteristic
729C4—21no—
730C4—22no—
731C4—21no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4C2×#137×C10111yescharacteristic
743C4#575×C10111yescharacteristic
744C4#576×C10111yescharacteristic
745C4#577×C10111yescharacteristic
746C2—41no—
747C2—81no—
748C2—81no—
749C2—82no—
750C2C101×#300711yescharacteristic
751C2C101×#301211yescharacteristic
752C2C101×#301811yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3517C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#3252C2semidirect
3. C101×#3182C2semidirect
4. C101×#3076C2semidirect
5. C101×#1648C2semidirect
6. C101×#1647C2semidirect
7. C101×#1642C2semidirect
8. C101×#1641C2semidirect
9. C101×#1636C2semidirect
10. C101×#1635C2semidirect
11. C101×#1631C2semidirect
12. C101×#1631C2semidirect
13. C101×#1547C2semidirect
14. C101×#1489C2semidirect
15. C101×#1483C2semidirect
369. #18607C101direct (N × H)
378. #3252C2×C101semidirect
379. #3182C2×C101semidirect
380. #3076C2×C101semidirect
381. #1648C2×C101semidirect
382. #1647C2×C101semidirect
383. #1642C2×C101semidirect
384. #1641C2×C101semidirect
385. #1636C2×C101semidirect
386. #1635C2×C101semidirect
387. #1631C2×C101semidirect
388. #1631C2×C101semidirect
389. #1547C2×C101semidirect
390. #1489C2×C101semidirect
391. #1483C2×C101semidirect
392. C101#18607direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#35172
C101×#32522
C101×#31822
C101×#30762
C101×#16482
C101×#16472
C101×#16422
C101×#16412
C101×#16362
C101×#16352
C101×#16312
C101×#15472
C101×#14892
C101×#14832
#18607101