Finite Group Databasebeta

← C103×#18705 #39923980

Subgroups — C103×#18705 #39923980

Order 26368.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3546C211yesmaximal, characteristic
2C103×#3252C211yesmaximal, characteristic, complemented
3C103×#3235C211yesmaximal, characteristic, complemented
4C103×#3167C211yesmaximal, characteristic, complemented
5C103×#1654C211yesmaximal, characteristic, complemented
6C103×#1652C211yesmaximal, characteristic, complemented
7C103×#1641C211yesmaximal, characteristic, complemented
8C103×#1639C211yesmaximal, characteristic, complemented
9C103×#1638C211yesmaximal, characteristic, complemented
10C103×#1635C211yesmaximal, characteristic, complemented
11C103×#1631C211yesmaximal, characteristic, complemented
12C103×#1629C211yesmaximal, characteristic, complemented
13C103×#1557C211yesmaximal, characteristic, complemented
14C103×#1494C211yesmaximal, characteristic, complemented
15C103×#1492C211yesmaximal, characteristic, complemented
16#560×C103—22no—
17#556×C103C2211yescharacteristic
18#553×C103—21no—
19#550×C103—21no—
20#550×C103C2211yescharacteristic
21#547×C103C2211yescharacteristic
22#546×C103—21no—
23#546×C103—21no—
24D42×C103C2211yescharacteristic
25#542×C103—21no—
26#538×C103—22no—
27#537×C103—21no—
28#535×C103—21no—
29#535×C103—21no—
30#533×C103C2211yescharacteristic, complemented
31#532×C103C2211yescharacteristic
32#532×C103C2211yescharacteristic
33#529×C103C2211yescharacteristic
34#501×C103—21no—
35#498×C103C2211yescharacteristic, complemented
36#492×C103C2211yescharacteristic
37#490×C103—21no—
38#487×C103C2211yescharacteristic, complemented
39#486×C103C2211yescharacteristic
40#482×C103—21no—
41#482×C103—21no—
42#479×C103—21no—
43#477×C103C2211yescharacteristic, complemented
44#476×C103C2211yescharacteristic
45#476×C103C2211yescharacteristic
46#476×C103C2211yescharacteristic, complemented
47#474×C103C2211yescharacteristic
48#474×C103C2211yescharacteristic, complemented
49#470×C103—21no—
50#468×C103—21no—
51#465×C103—22no—
52#464×C103—21no—
53#462×C103C2211yescharacteristic, complemented
54#461×C103C2211yescharacteristic
55C4×SD16×C103—22no—
56#432×C103C2211yescharacteristic, complemented
57#423×C103C2211yescharacteristic, complemented
58C2×C4×C8×C103C2211yescharacteristic, complemented
59#332×C103C2211yescharacteristic, complemented
60#332×C103C2211yescharacteristic, complemented
61#331×C103C2211yescharacteristic
62#331×C103C2211yescharacteristic
63Q8⋊C8×C103C2211yescharacteristic, complemented
64Q8⋊C8×C103C2211yescharacteristic, complemented
65D4⋊C8×C103C2211yescharacteristic
66D4⋊C8×C103C2211yescharacteristic
67D4⋊C8×C103C2211yescharacteristic
68D4⋊C8×C103C2211yescharacteristic
69D4⋊C8×C103C2211yescharacteristic, complemented
70D4⋊C8×C103C2211yescharacteristic, complemented
71C2×#41×C103—21no—
72C2×#41×C103—21no—
73C2×#41×C103—21no—
74C2×#41×C103—21no—
75C22×D4×C103—21no—
76C22×D4×C103—21no—
77C2×Q16×C103—21no—
78C2×SD16×C103—22no—
79C2×SD16×C103—21no—
80C2×M16×C103—21no—
81C22×C8×C103—21no—
82C4⋊Q8×C103D411yescharacteristic
83C4⋊Q8×C103C2311yescharacteristic
84C4⋊Q8×C103C2311yescharacteristic
85C4⋊Q8×C103C2311yescharacteristic
86#127×C103—22no—
87#127×C103—21no—
88#127×C103D411yescharacteristic
89#127×C103C2311yescharacteristic
90#126×C103—22no—
91#126×C103—22no—
92#126×C103—21no—
93#125×C103—21no—
94#125×C103D411yescharacteristic
95#124×C103—22no—
96#124×C103—21no—
97#124×C103—21no—
98#124×C103—21no—
99#124×C103D411yescharacteristic
100#123×C103—22no—
101#123×C103—22no—
102#123×C103—21no—
103#123×C103—22no—
104C22⋊Q8×C103—22no—
105C22⋊Q8×C103—21no—
106C22⋊Q8×C103—21no—
107C22⋊Q8×C103—21no—
108C22⋊Q8×C103—21no—
109C22⋊Q8×C103D411yescharacteristic
110#121×C103—22no—
111#121×C103—22no—
112#121×C103—22no—
113#121×C103—22no—
114#121×C103—22no—
115#121×C103—21no—
116#121×C103—22no—
117#121×C103—21no—
118#121×C103—21no—
119#121×C103—21no—
120#121×C103—21no—
121#121×C103—21no—
122#121×C103D412yes—
123#121×C103D411yescharacteristic
124#121×C103D411yescharacteristic
125#121×C103D411yescharacteristic
126#120×C103—22no—
127#120×C103—22no—
128#120×C103—22no—
129#120×C103—22no—
130C4×Q8×C103—21no—
131C4×Q8×C103—21no—
132C4×Q8×C103—21no—
133C4×Q8×C103C2311yescharacteristic
134C4×D4×C103—22no—
135C4×D4×C103—21no—
136C4×D4×C103—21no—
137C4×D4×C103—21no—
138C4×D4×C103—21no—
139C4×D4×C103D412yes—
140C4×D4×C103C2311yescharacteristic
141C4×D4×C103C2311yescharacteristic
142C4×D4×C103C2311yescharacteristic
143#117×C103—21no—
144#117×C103—21no—
145#117×C103—21no—
146C2×C4⋊C4×C103—21no—
147C2×C22⋊C4×C103—22no—
148C2×C42×C103C2311yescharacteristic
149#107×C103—21no—
150#107×C103—21no—
151#107×C103—21no—
152#106×C103—22no—
153#106×C103—21no—
154#106×C103—21no—
155#106×C103—21no—
156C4⋊C8×C103—21no—
157C4⋊C8×C103C2311yescharacteristic
158C4⋊C8×C103C2311yescharacteristic
159C4⋊C8×C103C2311yescharacteristic
160C4⋊C8×C103C2311yescharacteristic
161#103×C103—21no—
162#103×C103—22no—
163#103×C103—21no—
164#103×C103—21no—
165#102×C103—22no—
166#102×C103—21no—
167#102×C103—21no—
168#102×C103—21no—
169#102×C103—21no—
170#102×C103—21no—
171C22⋊C8×C103—21no—
172#97×C103—21no—
173C4×C8×C103—21no—
174C4×C8×C103C2311yescharacteristic
175C4×C8×C103C2311yescharacteristic
176C24×C103—22no—
177#41×C103—81no—
178#41×C103—81no—
179#41×C103—81no—
180#41×C103—81no—
181#41×C103—81no—
182#41×C103—81no—
183#41×C103—81no—
184#41×C103—81no—
185C2×Q8×C103—21no—
186C2×Q8×C103—21no—
187C2×Q8×C103—21no—
188C2×Q8×C103—21no—
189C2×Q8×C103C2×D411yescharacteristic
190C2×D4×C103—22no—
191C2×D4×C103—22no—
192C2×D4×C103—22no—
193C2×D4×C103—22no—
194C2×D4×C103—22no—
195C2×D4×C103—21no—
196C2×D4×C103—21no—
197C2×D4×C103—22no—
198C2×D4×C103—21no—
199C2×D4×C103—21no—
200C2×D4×C103—21no—
201C2×D4×C103—21no—
202C2×D4×C103—21no—
203C2×D4×C103—81no—
204C2×D4×C103—81no—
205C2×D4×C103—81no—
206C2×D4×C103—81no—
207C2×D4×C103C2×D411yescharacteristic
208C2×D4×C103C2×D411yescharacteristic
209C2×D4×C103C2×D411yescharacteristic
210C2×D4×C103C2×D412yes—
211C22×C4×C103—22no—
212C22×C4×C103—22no—
213C22×C4×C103—21no—
214C22×C4×C103—21no—
215C22×C4×C103—21no—
216C22×C4×C103—22no—
217C22×C4×C103C2×D411yescharacteristic
218C22×C4×C103C2×D411yescharacteristic
219C22×C4×C103C2×D411yescharacteristic
220Q16×C103—81no—
221SD16×C103—44no—
222SD16×C103—81no—
223M16×C103—81no—
224C2×C8×C103—21no—
225C2×C8×C103—21no—
226C2×C8×C103—21no—
227C2×C8×C103—21no—
228C2×C8×C103—21no—
229C2×C8×C103—21no—
230C2×C8×C103—42no—
231C4⋊C4×C103—22no—
232C4⋊C4×C103—22no—
233C4⋊C4×C103—21no—
234C4⋊C4×C103—21no—
235C4⋊C4×C103—21no—
236C4⋊C4×C103—21no—
237C4⋊C4×C103—21no—
238C4⋊C4×C103—21no—
239C4⋊C4×C103—21no—
240C4⋊C4×C103—21no—
241C4⋊C4×C103—21no—
242C4⋊C4×C103—21no—
243C4⋊C4×C103—41no—
244C4⋊C4×C103—41no—
245C4⋊C4×C103C2×D411yescharacteristic
246C4⋊C4×C103C2×D412yes—
247C4⋊C4×C103C2×D411yescharacteristic
248C4⋊C4×C103C2×D411yescharacteristic
249C4⋊C4×C103C2×D411yescharacteristic
250C22⋊C4×C103—22no—
251C22⋊C4×C103—22no—
252C22⋊C4×C103—22no—
253C22⋊C4×C103—22no—
254C22⋊C4×C103—22no—
255C22⋊C4×C103—21no—
256C22⋊C4×C103—21no—
257C22⋊C4×C103—21no—
258C22⋊C4×C103—21no—
259C22⋊C4×C103—21no—
260C22⋊C4×C103—21no—
261C22⋊C4×C103—22no—
262C22⋊C4×C103—22no—
263C22⋊C4×C103—21no—
264C22⋊C4×C103—21no—
265C22⋊C4×C103—21no—
266C22⋊C4×C103—41no—
267C42×C103—22no—
268C42×C103—21no—
269C42×C103—41no—
270C42×C103C2×D411yescharacteristic
271C42×C103C2×D411yescharacteristic
272C42×C103C2×D411yescharacteristic
273C42×C103C2411yescharacteristic
274C23×C103—21no—
275C23×C103—21no—
276C23×C103—22no—
277C23×C103—21no—
278C23×C103—82no—
279C23×C103—82no—
280C23×C103—82no—
281C23×C103#12011yescharacteristic
282Q8×C103—21no—
283Q8×C103—21no—
284Q8×C103—42no—
285Q8×C103—41no—
286Q8×C103—41no—
287Q8×C103—41no—
288Q8×C103—41no—
289Q8×C103—81no—
290D4×C103—21no—
291D4×C103—21no—
292D4×C103—21no—
293D4×C103—21no—
294D4×C103—21no—
295D4×C103—21no—
296D4×C103—42no—
297D4×C103—41no—
298D4×C103—41no—
299D4×C103—41no—
300D4×C103—41no—
301D4×C103—81no—
302D4×C103—81no—
303D4×C103—81no—
304D4×C103—82no—
305D4×C103—81no—
306D4×C103—81no—
307D4×C103—82no—
308D4×C103—82no—
309D4×C103—82no—
310D4×C103—82no—
311D4×C103—82no—
312C2×C4×C103—21no—
313C2×C4×C103—21no—
314C2×C4×C103—21no—
315C2×C4×C103—21no—
316C2×C4×C103—21no—
317C2×C4×C103—21no—
318C2×C4×C103—21no—
319C2×C4×C103—22no—
320C2×C4×C103—21no—
321C2×C4×C103—21no—
322C2×C4×C103—41no—
323C2×C4×C103—41no—
324C2×C4×C103—41no—
325C2×C4×C103—41no—
326C2×C4×C103—41no—
327C2×C4×C103—41no—
328C2×C4×C103—41no—
329C2×C4×C103—41no—
330C2×C4×C103—41no—
331C2×C4×C103—82no—
332C2×C4×C103—82no—
333C2×C4×C103—82no—
334C2×C4×C103#12011yescharacteristic
335C2×C4×C103#12011yescharacteristic
336C2×C4×C103#12011yescharacteristic
337C2×C4×C103C22×D411yescharacteristic
338C2×C4×C103C22×D411yescharacteristic
339C2×C4×C103C22×D411yescharacteristic
340C8×C103—22no—
341C8×C103—41no—
342C8×C103—41no—
343C8×C103—41no—
344C8×C103—41no—
345C8×C103—41no—
346C22×C103—21no—
347C22×C103—21no—
348C22×C103—21no—
349C22×C103—41no—
350C22×C103—41no—
351C22×C103—42no—
352C22×C103—41no—
353C22×C103—41no—
354C22×C103—41no—
355C22×C103—42no—
356C22×C103—41no—
357C22×C103—42no—
358C22×C103—41no—
359C22×C103—41no—
360C22×C103—41no—
361C22×C103—164no—
362C22×C103C2×#12011yescharacteristic
363C4×C103—21no—
364C4×C103—21no—
365C4×C103—21no—
366C4×C103—21no—
367C4×C103—41no—
368C4×C103—42no—
369C4×C103—41no—
370C4×C103—41no—
371C4×C103—41no—
372C4×C103—41no—
373C4×C103—81no—
374C4×C103—81no—
375C4×C103#57611yescharacteristic
376C4×C103#57711yescharacteristic
377C4×C103#57711yescharacteristic
378C4×C103#57711yescharacteristic
379#18705C10311yesmaximal, characteristic, direct product factor, Sylow
380C2×C103—41no—
381C2×C103—81no—
382C2×C103—82no—
383C2×C103—81no—
384C2×C103—81no—
385C2×C103#300911yescharacteristic
386C2×C103#301211yescharacteristic
387C2×C103#301811yescharacteristic
388#3546C2×C10311yescharacteristic
389#3252C2×C10311yescharacteristic, complemented
390#3235C2×C10311yescharacteristic, complemented
391#3167C2×C10311yescharacteristic, complemented
392#1654C2×C10311yescharacteristic, complemented
393#1652C2×C10311yescharacteristic, complemented
394#1641C2×C10311yescharacteristic, complemented
395#1639C2×C10311yescharacteristic, complemented
396#1638C2×C10311yescharacteristic, complemented
397#1635C2×C10311yescharacteristic, complemented
398#1631C2×C10311yescharacteristic, complemented
399#1629C2×C10311yescharacteristic, complemented
400#1557C2×C10311yescharacteristic, complemented
401#1494C2×C10311yescharacteristic, complemented
402#1492C2×C10311yescharacteristic, complemented
403C103#1870511yescharacteristic, direct product factor, Sylow
404#560—22no—
405#556C22×C10311yescharacteristic
406#553—21no—
407#550—21no—
408#550C22×C10311yescharacteristic
409#547C22×C10311yescharacteristic
410#546—21no—
411#546—21no—
412D42C22×C10311yescharacteristic
413#542—21no—
414#538—22no—
415#537—21no—
416#535—21no—
417#535—21no—
418#533C22×C10311yescharacteristic, complemented
419#532C22×C10311yescharacteristic
420#532C22×C10311yescharacteristic
421#529C22×C10311yescharacteristic
422#501—21no—
423#498C22×C10311yescharacteristic, complemented
424#492C22×C10311yescharacteristic
425#490—21no—
426#487C22×C10311yescharacteristic, complemented
427#486C22×C10311yescharacteristic
428#482—21no—
429#482—21no—
430#479—21no—
431#477C22×C10311yescharacteristic, complemented
432#476C22×C10311yescharacteristic
433#476C22×C10311yescharacteristic
434#476C22×C10311yescharacteristic, complemented
435#474C22×C10311yescharacteristic
436#474C22×C10311yescharacteristic, complemented
437#470—21no—
438#468—21no—
439#465—22no—
440#464—21no—
441#462C22×C10311yescharacteristic, complemented
442#461C22×C10311yescharacteristic
443C4×SD16—22no—
444#432C22×C10311yescharacteristic, complemented
445#423C22×C10311yescharacteristic, complemented
446C2×C4×C8C22×C10311yescharacteristic, complemented
447#332C22×C10311yescharacteristic, complemented
448#332C22×C10311yescharacteristic, complemented
449#331C22×C10311yescharacteristic
450#331C22×C10311yescharacteristic
451Q8⋊C8C22×C10311yescharacteristic, complemented
452Q8⋊C8C22×C10311yescharacteristic, complemented
453D4⋊C8C22×C10311yescharacteristic
454D4⋊C8C22×C10311yescharacteristic
455D4⋊C8C22×C10311yescharacteristic
456D4⋊C8C22×C10311yescharacteristic
457D4⋊C8C22×C10311yescharacteristic, complemented
458D4⋊C8C22×C10311yescharacteristic, complemented
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×Q16—21no—
466C2×SD16—22no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C10311yescharacteristic
471C4⋊Q8C23×C10311yescharacteristic
472C4⋊Q8C23×C10311yescharacteristic
473C4⋊Q8C23×C10311yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C10311yescharacteristic
477#127C23×C10311yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C10311yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C10311yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C10311yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C10311yescharacteristic
511#121D4×C10311yescharacteristic
512#121D4×C10311yescharacteristic
513#121D4×C10312yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C10311yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C10312yes—
528C4×D4C23×C10311yescharacteristic
529C4×D4C23×C10311yescharacteristic
530C4×D4C23×C10311yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C10311yescharacteristic
537#107—21no—
538#107—21no—
539#107—21no—
540#106—22no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C10311yescharacteristic
546C4⋊C8C23×C10311yescharacteristic
547C4⋊C8C23×C10311yescharacteristic
548C4⋊C8C23×C10311yescharacteristic
549#103—21no—
550#103—22no—
551#103—21no—
552#103—21no—
553#102—22no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C10311yescharacteristic
563C4×C8C23×C10311yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C10311yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C10311yescharacteristic
596C2×D4C2×D4×C10311yescharacteristic
597C2×D4C2×D4×C10311yescharacteristic
598C2×D4C2×D4×C10312yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C10311yescharacteristic
606C22×C4C2×D4×C10311yescharacteristic
607C22×C4C2×D4×C10311yescharacteristic
608Q16—81no—
609SD16—44no—
610SD16—81no—
611M16—81no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C10311yescharacteristic
634C4⋊C4C2×D4×C10312yes—
635C4⋊C4C2×D4×C10311yescharacteristic
636C4⋊C4C2×D4×C10311yescharacteristic
637C4⋊C4C2×D4×C10311yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C10311yescharacteristic
659C42C2×D4×C10311yescharacteristic
660C42C2×D4×C10311yescharacteristic
661C42C24×C10311yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C10311yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—82no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C10311yescharacteristic
723C2×C4#120×C10311yescharacteristic
724C2×C4#120×C10311yescharacteristic
725C2×C4C22×D4×C10311yescharacteristic
726C2×C4C22×D4×C10311yescharacteristic
727C2×C4C22×D4×C10311yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C10311yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4#576×C10311yescharacteristic
764C4#577×C10311yescharacteristic
765C4#577×C10311yescharacteristic
766C4#577×C10311yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C103×#300911yescharacteristic
773C2C103×#301211yescharacteristic
774C2C103×#301811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3546C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3252C2semidirect
3. C103×#3235C2semidirect
4. C103×#3167C2semidirect
5. C103×#1654C2semidirect
6. C103×#1652C2semidirect
7. C103×#1641C2semidirect
8. C103×#1639C2semidirect
9. C103×#1638C2semidirect
10. C103×#1635C2semidirect
11. C103×#1631C2semidirect
12. C103×#1629C2semidirect
13. C103×#1557C2semidirect
14. C103×#1494C2semidirect
15. C103×#1492C2semidirect
30. #533×C103C22semidirect
35. #498×C103C22semidirect
38. #487×C103C22semidirect
43. #477×C103C22semidirect
46. #476×C103C22semidirect
48. #474×C103C22semidirect
53. #462×C103C22semidirect
56. #432×C103C22semidirect
57. #423×C103C22semidirect
58. C2×C4×C8×C103C22semidirect
59. #332×C103C22semidirect
60. #332×C103C22semidirect
63. Q8⋊C8×C103C22semidirect
64. Q8⋊C8×C103C22semidirect
69. D4⋊C8×C103C22semidirect
70. D4⋊C8×C103C22semidirect
379. #18705C103direct (N × H)
389. #3252C2×C103semidirect
390. #3235C2×C103semidirect
391. #3167C2×C103semidirect
392. #1654C2×C103semidirect
393. #1652C2×C103semidirect
394. #1641C2×C103semidirect
395. #1639C2×C103semidirect
396. #1638C2×C103semidirect
397. #1635C2×C103semidirect
398. #1631C2×C103semidirect
399. #1629C2×C103semidirect
400. #1557C2×C103semidirect
401. #1494C2×C103semidirect
402. #1492C2×C103semidirect
403. C103#18705direct (N × H)
418. #533C22×C103semidirect
423. #498C22×C103semidirect
426. #487C22×C103semidirect
431. #477C22×C103semidirect
434. #476C22×C103semidirect
436. #474C22×C103semidirect
441. #462C22×C103semidirect
444. #432C22×C103semidirect
445. #423C22×C103semidirect
446. C2×C4×C8C22×C103semidirect
447. #332C22×C103semidirect
448. #332C22×C103semidirect
451. Q8⋊C8C22×C103semidirect
452. Q8⋊C8C22×C103semidirect
457. D4⋊C8C22×C103semidirect
458. D4⋊C8C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35462
C103×#32522
C103×#32352
C103×#31672
C103×#16542
C103×#16522
C103×#16412
C103×#16392
C103×#16382
C103×#16352
C103×#16312
C103×#16292
C103×#15572
C103×#14942
C103×#14922
#18705103