Finite Group Databasebeta

← C103×#18974 #39924249

Subgroups — C103×#18974 #39924249

Order 26368.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3546C211yesmaximal, characteristic
2C103×#3254C211yesmaximal, characteristic, complemented
3C103×#3248C211yesmaximal, characteristic, complemented
4C103×#3228C211yesmaximal, characteristic, complemented
5C103×#1654C211yesmaximal, characteristic, complemented
6C103×#1652C211yesmaximal, characteristic, complemented
7C103×#1650C211yesmaximal, characteristic, complemented
8C103×#1647C211yesmaximal, characteristic, complemented
9C103×#1642C211yesmaximal, characteristic, complemented
10C103×#1641C211yesmaximal, characteristic, complemented
11C103×#1639C211yesmaximal, characteristic, complemented
12C103×#1639C211yesmaximal, characteristic, complemented
13C103×#1547C211yesmaximal, characteristic, complemented
14C103×#1495C211yesmaximal, characteristic, complemented
15C103×#1480C211yesmaximal, 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#500×C103C2211yescharacteristic, complemented
35#498×C103C2211yescharacteristic, complemented
36#486×C103C2211yescharacteristic
37#486×C103C2211yescharacteristic
38#482×C103—22no—
39#479×C103—21no—
40#478×C103—22no—
41#477×C103—21no—
42#475×C103C2211yescharacteristic, complemented
43#474×C103C2211yescharacteristic
44#474×C103C2211yescharacteristic
45#474×C103C2211yescharacteristic, complemented
46#468×C103—21no—
47#468×C103—21no—
48#467×C103—21no—
49#465×C103—21no—
50#464×C103—21no—
51#462×C103C2211yescharacteristic, complemented
52#461×C103C2211yescharacteristic
53#461×C103C2211yescharacteristic
54#461×C103C2211yescharacteristic, complemented
55#460×C103—21no—
56#431×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—21no—
79C2×SD16×C103—21no—
80C2×SD16×C103—21no—
81C2×M16×C103—21no—
82C22×C8×C103—21no—
83C4⋊Q8×C103D411yescharacteristic
84C4⋊Q8×C103C2311yescharacteristic
85C4⋊Q8×C103C2311yescharacteristic
86C4⋊Q8×C103C2311yescharacteristic
87#127×C103—22no—
88#127×C103—21no—
89#127×C103D411yescharacteristic
90#127×C103C2311yescharacteristic
91#126×C103—22no—
92#126×C103—22no—
93#126×C103—21no—
94#125×C103—21no—
95#125×C103D411yescharacteristic
96#124×C103—22no—
97#124×C103—21no—
98#124×C103—21no—
99#124×C103—21no—
100#124×C103D411yescharacteristic
101#123×C103—22no—
102#123×C103—22no—
103#123×C103—21no—
104#123×C103—22no—
105C22⋊Q8×C103—22no—
106C22⋊Q8×C103—21no—
107C22⋊Q8×C103—21no—
108C22⋊Q8×C103—21no—
109C22⋊Q8×C103—21no—
110C22⋊Q8×C103D411yescharacteristic
111#121×C103—22no—
112#121×C103—22no—
113#121×C103—22no—
114#121×C103—22no—
115#121×C103—22no—
116#121×C103—21no—
117#121×C103—22no—
118#121×C103—21no—
119#121×C103—21no—
120#121×C103—21no—
121#121×C103—21no—
122#121×C103—21no—
123#121×C103D411yescharacteristic
124#121×C103D411yescharacteristic
125#121×C103D411yescharacteristic
126#121×C103D412yes—
127#120×C103—22no—
128#120×C103—22no—
129#120×C103—22no—
130#120×C103—22no—
131C4×Q8×C103—21no—
132C4×Q8×C103—21no—
133C4×Q8×C103—21no—
134C4×Q8×C103C2311yescharacteristic
135C4×D4×C103—22no—
136C4×D4×C103—21no—
137C4×D4×C103—21no—
138C4×D4×C103—21no—
139C4×D4×C103—21no—
140C4×D4×C103D412yes—
141C4×D4×C103C2311yescharacteristic
142C4×D4×C103C2311yescharacteristic
143C4×D4×C103C2311yescharacteristic
144#117×C103—21no—
145#117×C103—21no—
146#117×C103—21no—
147C2×C4⋊C4×C103—21no—
148C2×C22⋊C4×C103—22no—
149C2×C42×C103C2311yescharacteristic
150#107×C103—21no—
151#107×C103—21no—
152#107×C103—21no—
153#107×C103—22no—
154#106×C103—21no—
155#106×C103—22no—
156C4⋊C8×C103—21no—
157C4⋊C8×C103—21no—
158C4⋊C8×C103—21no—
159C4⋊C8×C103C2311yescharacteristic
160C4⋊C8×C103C2311yescharacteristic
161C4⋊C8×C103C2311yescharacteristic
162C4⋊C8×C103C2311yescharacteristic
163#103×C103—21no—
164#103×C103—21no—
165#103×C103—21no—
166#103×C103—21no—
167#103×C103—21no—
168#102×C103—21no—
169#102×C103—21no—
170#102×C103—21no—
171#102×C103—22no—
172#102×C103—22no—
173C22⋊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—81no—
222SD16×C103—81no—
223SD16×C103—81no—
224M16×C103—81no—
225C2×C8×C103—21no—
226C2×C8×C103—21no—
227C2×C8×C103—21no—
228C2×C8×C103—21no—
229C2×C8×C103—21no—
230C2×C8×C103—21no—
231C2×C8×C103—81no—
232C4⋊C4×C103—22no—
233C4⋊C4×C103—22no—
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—21no—
244C4⋊C4×C103—41no—
245C4⋊C4×C103—41no—
246C4⋊C4×C103C2×D411yescharacteristic
247C4⋊C4×C103C2×D411yescharacteristic
248C4⋊C4×C103C2×D411yescharacteristic
249C4⋊C4×C103C2×D411yescharacteristic
250C4⋊C4×C103C2×D412yes—
251C22⋊C4×C103—22no—
252C22⋊C4×C103—22no—
253C22⋊C4×C103—22no—
254C22⋊C4×C103—22no—
255C22⋊C4×C103—22no—
256C22⋊C4×C103—21no—
257C22⋊C4×C103—21no—
258C22⋊C4×C103—21no—
259C22⋊C4×C103—21no—
260C22⋊C4×C103—21no—
261C22⋊C4×C103—21no—
262C22⋊C4×C103—22no—
263C22⋊C4×C103—22no—
264C22⋊C4×C103—21no—
265C22⋊C4×C103—21no—
266C22⋊C4×C103—21no—
267C22⋊C4×C103—41no—
268C42×C103—22no—
269C42×C103—21no—
270C42×C103—41no—
271C42×C103C2×D411yescharacteristic
272C42×C103C2×D411yescharacteristic
273C42×C103C2×D411yescharacteristic
274C42×C103C2411yescharacteristic
275C23×C103—21no—
276C23×C103—21no—
277C23×C103—22no—
278C23×C103—21no—
279C23×C103—82no—
280C23×C103—82no—
281C23×C103—82no—
282C23×C103#12011yescharacteristic
283Q8×C103—21no—
284Q8×C103—21no—
285Q8×C103—41no—
286Q8×C103—41no—
287Q8×C103—41no—
288Q8×C103—41no—
289Q8×C103—41no—
290Q8×C103—41no—
291Q8×C103—81no—
292D4×C103—21no—
293D4×C103—21no—
294D4×C103—21no—
295D4×C103—21no—
296D4×C103—21no—
297D4×C103—21no—
298D4×C103—42no—
299D4×C103—41no—
300D4×C103—41no—
301D4×C103—41no—
302D4×C103—41no—
303D4×C103—81no—
304D4×C103—81no—
305D4×C103—81no—
306D4×C103—81no—
307D4×C103—81no—
308D4×C103—82no—
309D4×C103—82no—
310D4×C103—82no—
311D4×C103—82no—
312D4×C103—82no—
313D4×C103—82no—
314C2×C4×C103—21no—
315C2×C4×C103—21no—
316C2×C4×C103—21no—
317C2×C4×C103—21no—
318C2×C4×C103—21no—
319C2×C4×C103—21no—
320C2×C4×C103—21no—
321C2×C4×C103—22no—
322C2×C4×C103—21no—
323C2×C4×C103—21no—
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—41no—
332C2×C4×C103—41no—
333C2×C4×C103—82no—
334C2×C4×C103—82no—
335C2×C4×C103—82no—
336C2×C4×C103#12011yescharacteristic
337C2×C4×C103#12011yescharacteristic
338C2×C4×C103#12011yescharacteristic
339C2×C4×C103C22×D411yescharacteristic
340C2×C4×C103C22×D411yescharacteristic
341C2×C4×C103C22×D411yescharacteristic
342C8×C103—41no—
343C8×C103—41no—
344C8×C103—41no—
345C8×C103—41no—
346C8×C103—41no—
347C8×C103—41no—
348C22×C103—21no—
349C22×C103—21no—
350C22×C103—21no—
351C22×C103—41no—
352C22×C103—41no—
353C22×C103—41no—
354C22×C103—41no—
355C22×C103—42no—
356C22×C103—42no—
357C22×C103—41no—
358C22×C103—41no—
359C22×C103—42no—
360C22×C103—41no—
361C22×C103—41no—
362C22×C103—41no—
363C22×C103—164no—
364C22×C103C2×#12011yescharacteristic
365C4×C103—21no—
366C4×C103—21no—
367C4×C103—21no—
368C4×C103—21no—
369C4×C103—41no—
370C4×C103—41no—
371C4×C103—41no—
372C4×C103—41no—
373C4×C103—42no—
374C4×C103—41no—
375C4×C103—81no—
376C4×C103—81no—
377C4×C103#57611yescharacteristic
378C4×C103#57611yescharacteristic
379C4×C103#57711yescharacteristic
380C4×C103#57711yescharacteristic
381#18974C10311yesmaximal, characteristic, direct product factor, Sylow
382C2×C103—41no—
383C2×C103—81no—
384C2×C103—82no—
385C2×C103—81no—
386C2×C103—81no—
387C2×C103#301211yescharacteristic
388C2×C103#301211yescharacteristic
389C2×C103#302211yescharacteristic
390#3546C2×C10311yescharacteristic
391#3254C2×C10311yescharacteristic, complemented
392#3248C2×C10311yescharacteristic, complemented
393#3228C2×C10311yescharacteristic, complemented
394#1654C2×C10311yescharacteristic, complemented
395#1652C2×C10311yescharacteristic, complemented
396#1650C2×C10311yescharacteristic, complemented
397#1647C2×C10311yescharacteristic, complemented
398#1642C2×C10311yescharacteristic, complemented
399#1641C2×C10311yescharacteristic, complemented
400#1639C2×C10311yescharacteristic, complemented
401#1639C2×C10311yescharacteristic, complemented
402#1547C2×C10311yescharacteristic, complemented
403#1495C2×C10311yescharacteristic, complemented
404#1480C2×C10311yescharacteristic, complemented
405C103#1897411yescharacteristic, direct product factor, Sylow
406#560—22no—
407#556C22×C10311yescharacteristic
408#553—21no—
409#550—21no—
410#550C22×C10311yescharacteristic
411#547C22×C10311yescharacteristic
412#546—21no—
413#546—21no—
414D42C22×C10311yescharacteristic
415#542—21no—
416#538—22no—
417#537—21no—
418#535—21no—
419#535—21no—
420#533C22×C10311yescharacteristic, complemented
421#532C22×C10311yescharacteristic
422#532C22×C10311yescharacteristic
423#529C22×C10311yescharacteristic
424#500C22×C10311yescharacteristic, complemented
425#498C22×C10311yescharacteristic, complemented
426#486C22×C10311yescharacteristic
427#486C22×C10311yescharacteristic
428#482—22no—
429#479—21no—
430#478—22no—
431#477—21no—
432#475C22×C10311yescharacteristic, complemented
433#474C22×C10311yescharacteristic
434#474C22×C10311yescharacteristic
435#474C22×C10311yescharacteristic, complemented
436#468—21no—
437#468—21no—
438#467—21no—
439#465—21no—
440#464—21no—
441#462C22×C10311yescharacteristic, complemented
442#461C22×C10311yescharacteristic
443#461C22×C10311yescharacteristic
444#461C22×C10311yescharacteristic, complemented
445#460—21no—
446#431C22×C10311yescharacteristic, complemented
447#423C22×C10311yescharacteristic, complemented
448C2×C4⋊C8C22×C10311yescharacteristic, complemented
449#332C22×C10311yescharacteristic, complemented
450#332C22×C10311yescharacteristic, complemented
451#331C22×C10311yescharacteristic
452#331C22×C10311yescharacteristic
453Q8⋊C8C22×C10311yescharacteristic, complemented
454Q8⋊C8C22×C10311yescharacteristic, complemented
455D4⋊C8C22×C10311yescharacteristic
456D4⋊C8C22×C10311yescharacteristic
457D4⋊C8C22×C10311yescharacteristic
458D4⋊C8C22×C10311yescharacteristic
459D4⋊C8C22×C10311yescharacteristic, complemented
460D4⋊C8C22×C10311yescharacteristic, complemented
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C10311yescharacteristic
474C4⋊Q8C23×C10311yescharacteristic
475C4⋊Q8C23×C10311yescharacteristic
476C4⋊Q8C23×C10311yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C10311yescharacteristic
480#127C23×C10311yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C10311yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C10311yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C10311yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C10311yescharacteristic
514#121D4×C10311yescharacteristic
515#121D4×C10311yescharacteristic
516#121D4×C10312yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C10311yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C10312yes—
531C4×D4C23×C10311yescharacteristic
532C4×D4C23×C10311yescharacteristic
533C4×D4C23×C10311yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C10311yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C10311yescharacteristic
550C4⋊C8C23×C10311yescharacteristic
551C4⋊C8C23×C10311yescharacteristic
552C4⋊C8C23×C10311yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C10311yescharacteristic
565C4×C8C23×C10311yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C10311yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C10311yescharacteristic
598C2×D4C2×D4×C10311yescharacteristic
599C2×D4C2×D4×C10311yescharacteristic
600C2×D4C2×D4×C10312yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C10311yescharacteristic
608C22×C4C2×D4×C10311yescharacteristic
609C22×C4C2×D4×C10311yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C10311yescharacteristic
637C4⋊C4C2×D4×C10311yescharacteristic
638C4⋊C4C2×D4×C10311yescharacteristic
639C4⋊C4C2×D4×C10311yescharacteristic
640C4⋊C4C2×D4×C10312yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C10311yescharacteristic
662C42C2×D4×C10311yescharacteristic
663C42C2×D4×C10311yescharacteristic
664C42C24×C10311yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C10311yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—82no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C10311yescharacteristic
727C2×C4#120×C10311yescharacteristic
728C2×C4#120×C10311yescharacteristic
729C2×C4C22×D4×C10311yescharacteristic
730C2×C4C22×D4×C10311yescharacteristic
731C2×C4C22×D4×C10311yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C10311yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4#576×C10311yescharacteristic
768C4#576×C10311yescharacteristic
769C4#577×C10311yescharacteristic
770C4#577×C10311yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2C103×#301211yescharacteristic
777C2C103×#301211yescharacteristic
778C2C103×#302211yescharacteristic
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×#3254C2semidirect
3. C103×#3248C2semidirect
4. C103×#3228C2semidirect
5. C103×#1654C2semidirect
6. C103×#1652C2semidirect
7. C103×#1650C2semidirect
8. C103×#1647C2semidirect
9. C103×#1642C2semidirect
10. C103×#1641C2semidirect
11. C103×#1639C2semidirect
12. C103×#1639C2semidirect
13. C103×#1547C2semidirect
14. C103×#1495C2semidirect
15. C103×#1480C2semidirect
30. #533×C103C22semidirect
34. #500×C103C22semidirect
35. #498×C103C22semidirect
42. #475×C103C22semidirect
45. #474×C103C22semidirect
51. #462×C103C22semidirect
54. #461×C103C22semidirect
56. #431×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
381. #18974C103direct (N × H)
391. #3254C2×C103semidirect
392. #3248C2×C103semidirect
393. #3228C2×C103semidirect
394. #1654C2×C103semidirect
395. #1652C2×C103semidirect
396. #1650C2×C103semidirect
397. #1647C2×C103semidirect
398. #1642C2×C103semidirect
399. #1641C2×C103semidirect
400. #1639C2×C103semidirect
401. #1639C2×C103semidirect
402. #1547C2×C103semidirect
403. #1495C2×C103semidirect
404. #1480C2×C103semidirect
405. C103#18974direct (N × H)
420. #533C22×C103semidirect
424. #500C22×C103semidirect
425. #498C22×C103semidirect
432. #475C22×C103semidirect
435. #474C22×C103semidirect
441. #462C22×C103semidirect
444. #461C22×C103semidirect
446. #431C22×C103semidirect
447. #423C22×C103semidirect
448. C2×C4⋊C8C22×C103semidirect
449. #332C22×C103semidirect
450. #332C22×C103semidirect
453. Q8⋊C8C22×C103semidirect
454. Q8⋊C8C22×C103semidirect
459. D4⋊C8C22×C103semidirect
460. 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×#32542
C103×#32482
C103×#32282
C103×#16542
C103×#16522
C103×#16502
C103×#16472
C103×#16422
C103×#16412
C103×#16392
C103×#15472
C103×#14952
C103×#14802
#18974103