Finite Group Databasebeta

← C107×#19068 #41045032

Subgroups — C107×#19068 #41045032

Order 27392.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3545C211yesmaximal, characteristic, complemented
2C107×#3219C211yesmaximal, characteristic, complemented
3C107×#3213C211yesmaximal, characteristic, complemented
4C107×#3171C211yesmaximal, characteristic, complemented
5C107×#1664C211yesmaximal, characteristic, complemented
6C107×#1662C211yesmaximal, characteristic, complemented
7C107×#1661C211yesmaximal, characteristic, complemented
8C107×#1659C211yesmaximal, characteristic, complemented
9C107×#1657C211yesmaximal, characteristic, complemented
10C107×#1656C211yesmaximal, characteristic, complemented
11C107×#1656C211yesmaximal, characteristic, complemented
12C107×#1655C211yesmaximal, characteristic, complemented
13C107×#1535C211yesmaximal, characteristic, complemented
14C107×#1529C211yesmaximal, characteristic, complemented
15C107×#1527C211yesmaximal, characteristic, complemented
16#563×C107C2211yescharacteristic
17#562×C107C2211yescharacteristic
18#562×C107C2211yescharacteristic
19H(3,𝔽4)×C107C2211yescharacteristic
20#555×C107—21no—
21#551×C107—21no—
22#551×C107—21no—
23#551×C107—21no—
24#546×C107—21no—
25#546×C107—21no—
26#542×C107—21no—
27#542×C107—21no—
28#538×C107—21no—
29#538×C107—21no—
30#536×C107—21no—
31#534×C107—21no—
32#532×C107C2211yescharacteristic, complemented
33#529×C107C2211yescharacteristic
34#529×C107C2211yescharacteristic
35C2×#124×C107C2211yescharacteristic
36#501×C107C2211yescharacteristic, complemented
37#497×C107C2211yescharacteristic, complemented
38#496×C107C2211yescharacteristic
39#496×C107C2211yescharacteristic, complemented
40#496×C107C2211yescharacteristic, complemented
41#496×C107C2211yescharacteristic, complemented
42#491×C107C2211yescharacteristic, complemented
43#490×C107C2211yescharacteristic, complemented
44#490×C107C2211yescharacteristic, complemented
45#489×C107C2211yescharacteristic
46#489×C107C2211yescharacteristic, complemented
47#489×C107C2211yescharacteristic, complemented
48#469×C107—21no—
49#468×C107—21no—
50#464×C107—21no—
51#463×C107—21no—
52#463×C107—21no—
53#463×C107—21no—
54#452×C107—21no—
55#449×C107—21no—
56#448×C107—21no—
57#447×C107—21no—
58C4×SD16×C107—21no—
59C4×D8×C107—21no—
60#432×C107C2211yescharacteristic, complemented
61#432×C107C2211yescharacteristic, complemented
62C4×M16×C107C2211yescharacteristic, complemented
63#330×C107C2211yescharacteristic, complemented
64#330×C107C2211yescharacteristic, complemented
65#330×C107C2211yescharacteristic, complemented
66#330×C107C2211yescharacteristic, complemented
67#329×C107C2211yescharacteristic
68#329×C107C2211yescharacteristic
69#329×C107C2211yescharacteristic, complemented
70#329×C107C2211yescharacteristic, complemented
71#329×C107C2211yescharacteristic, complemented
72#329×C107C2211yescharacteristic, complemented
73#329×C107C2211yescharacteristic, complemented
74#329×C107C2211yescharacteristic, complemented
75C2×#41×C107—21no—
76C2×#41×C107—21no—
77C22×Q8×C107D411yescharacteristic
78C22×D4×C107—21no—
79C22×D4×C107D411yescharacteristic
80C2×Q16×C107—21no—
81C2×SD16×C107—21no—
82C2×SD16×C107—21no—
83C2×SD16×C107—21no—
84C2×SD16×C107—21no—
85C2×SD16×C107—21no—
86C2×D8×C107—21no—
87C2×D8×C107—21no—
88C2×D8×C107—21no—
89C2×D8×C107—21no—
90C2×M16×C107—21no—
91C4⋊Q8×C107—21no—
92C4⋊Q8×C107—21no—
93C4⋊Q8×C107C2311yescharacteristic
94#127×C107C2311yescharacteristic
95#126×C107—21no—
96#126×C107—21no—
97#126×C107—21no—
98#126×C107—21no—
99#126×C107—21no—
100#126×C107—21no—
101#125×C107C2311yescharacteristic
102#125×C107C2311yescharacteristic
103#124×C107—21no—
104#124×C107—21no—
105#124×C107—21no—
106#124×C107—21no—
107#124×C107—21no—
108#124×C107—21no—
109#124×C107—21no—
110#124×C107—21no—
111#124×C107—21no—
112#124×C107D411yescharacteristic
113#124×C107D411yescharacteristic
114#124×C107C2311yescharacteristic
115#124×C107C2311yescharacteristic
116#124×C107C2311yescharacteristic
117#124×C107C2311yescharacteristic
118#123×C107—21no—
119#123×C107—21no—
120#123×C107—21no—
121#123×C107—21no—
122#123×C107—21no—
123#123×C107—21no—
124#123×C107—21no—
125#123×C107—21no—
126#123×C107—21no—
127#123×C107—21no—
128#123×C107—21no—
129#123×C107—21no—
130C22⋊Q8×C107—21no—
131C22⋊Q8×C107—21no—
132C22⋊Q8×C107—21no—
133C22⋊Q8×C107—21no—
134C22⋊Q8×C107—21no—
135C22⋊Q8×C107—21no—
136C22⋊Q8×C107—21no—
137C22⋊Q8×C107—21no—
138C22⋊Q8×C107D411yescharacteristic
139C22⋊Q8×C107D411yescharacteristic
140#121×C107—21no—
141#121×C107—21no—
142#121×C107—21no—
143#121×C107—21no—
144#121×C107—21no—
145#121×C107—21no—
146#121×C107—21no—
147#121×C107—21no—
148#121×C107—21no—
149#121×C107—21no—
150#121×C107D411yescharacteristic
151#121×C107D411yescharacteristic
152#120×C107—21no—
153#120×C107—21no—
154#120×C107—21no—
155#120×C107—21no—
156#120×C107—21no—
157#120×C107—21no—
158C4×Q8×C107D411yescharacteristic
159C4×Q8×C107D411yescharacteristic
160C4×D4×C107—21no—
161C4×D4×C107—21no—
162C4×D4×C107—21no—
163C4×D4×C107—21no—
164C4×D4×C107—21no—
165C4×D4×C107—21no—
166C4×D4×C107—21no—
167C4×D4×C107—21no—
168C4×D4×C107D411yescharacteristic
169C4×D4×C107D411yescharacteristic
170#117×C107—21no—
171#117×C107—21no—
172#117×C107—21no—
173#117×C107—21no—
174#117×C107—21no—
175C2×C22⋊C4×C107—21no—
176C2×C22⋊C4×C107—21no—
177C2×C22⋊C4×C107—21no—
178C2×C22⋊C4×C107—21no—
179C2×C22⋊C4×C107—21no—
180C2×C42×C107C2311yescharacteristic
181#107×C107—21no—
182#106×C107—21no—
183C4⋊C8×C107—21no—
184C4⋊C8×C107—21no—
185#103×C107—21no—
186#103×C107—21no—
187#103×C107—21no—
188#103×C107—21no—
189#103×C107—21no—
190#102×C107—21no—
191#102×C107—21no—
192#102×C107—21no—
193#102×C107—21no—
194#102×C107—21no—
195#102×C107—21no—
196#102×C107—21no—
197C22⋊C8×C107—21no—
198C22⋊C8×C107—21no—
199#97×C107C2311yescharacteristic
200#97×C107C2311yescharacteristic
201#97×C107C2311yescharacteristic
202#97×C107C2311yescharacteristic
203#97×C107C2311yescharacteristic
204#97×C107C2311yescharacteristic
205C4×C8×C107—21no—
206C24×C107—21no—
207C24×C107—21no—
208#41×C107—82no—
209#41×C107—81no—
210#41×C107—81no—
211C2×Q8×C107—21no—
212C2×Q8×C107—21no—
213C2×Q8×C107—21no—
214C2×Q8×C107—81no—
215C2×Q8×C107C2×D411yescharacteristic
216C2×Q8×C107C2×D411yescharacteristic
217C2×Q8×C107C2×D411yescharacteristic
218C2×Q8×C107C2×D411yescharacteristic
219C2×D4×C107—21no—
220C2×D4×C107—21no—
221C2×D4×C107—21no—
222C2×D4×C107—21no—
223C2×D4×C107—21no—
224C2×D4×C107—21no—
225C2×D4×C107—21no—
226C2×D4×C107—21no—
227C2×D4×C107—21no—
228C2×D4×C107—21no—
229C2×D4×C107—21no—
230C2×D4×C107—21no—
231C2×D4×C107—21no—
232C2×D4×C107—41no—
233C2×D4×C107—81no—
234C2×D4×C107—82no—
235C2×D4×C107C2×D411yescharacteristic
236C2×D4×C107C2×D411yescharacteristic
237C2×D4×C107C2×D411yescharacteristic
238C2×D4×C107C2×D411yescharacteristic
239C22×C4×C107—21no—
240C22×C4×C107—21no—
241C22×C4×C107—21no—
242C22×C4×C107—21no—
243C22×C4×C107—21no—
244C22×C4×C107—21no—
245C22×C4×C107—21no—
246C22×C4×C107—21no—
247C22×C4×C107—41no—
248C22×C4×C107C2×D411yescharacteristic
249C22×C4×C107C2×D411yescharacteristic
250C22×C4×C107C2×D411yescharacteristic
251Q16×C107—81no—
252SD16×C107—42no—
253SD16×C107—81no—
254SD16×C107—81no—
255SD16×C107—81no—
256SD16×C107—81no—
257D8×C107—42no—
258D8×C107—81no—
259D8×C107—81no—
260D8×C107—81no—
261M16×C107—42no—
262C2×C8×C107—21no—
263C2×C8×C107—21no—
264C2×C8×C107—21no—
265C2×C8×C107—21no—
266C2×C8×C107—21no—
267C2×C8×C107—21no—
268C4⋊C4×C107—21no—
269C4⋊C4×C107—21no—
270C4⋊C4×C107—21no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—21no—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—21no—
279C4⋊C4×C107—21no—
280C4⋊C4×C107—21no—
281C4⋊C4×C107—21no—
282C4⋊C4×C107—21no—
283C4⋊C4×C107—21no—
284C4⋊C4×C107C2×D411yescharacteristic
285C4⋊C4×C107C2×D411yescharacteristic
286C4⋊C4×C107C2×D411yescharacteristic
287C4⋊C4×C107C2×D411yescharacteristic
288C22⋊C4×C107—21no—
289C22⋊C4×C107—21no—
290C22⋊C4×C107—21no—
291C22⋊C4×C107—21no—
292C22⋊C4×C107—21no—
293C22⋊C4×C107—21no—
294C22⋊C4×C107—21no—
295C22⋊C4×C107—21no—
296C22⋊C4×C107—21no—
297C22⋊C4×C107—21no—
298C22⋊C4×C107—21no—
299C22⋊C4×C107—21no—
300C22⋊C4×C107—21no—
301C22⋊C4×C107—21no—
302C22⋊C4×C107—21no—
303C22⋊C4×C107—21no—
304C22⋊C4×C107—21no—
305C22⋊C4×C107—21no—
306C22⋊C4×C107—21no—
307C22⋊C4×C107—21no—
308C22⋊C4×C107—21no—
309C22⋊C4×C107—21no—
310C22⋊C4×C107—21no—
311C22⋊C4×C107—21no—
312C22⋊C4×C107—21no—
313C22⋊C4×C107—21no—
314C22⋊C4×C107—21no—
315C22⋊C4×C107—21no—
316C22⋊C4×C107—41no—
317C22⋊C4×C107—41no—
318C42×C107—21no—
319C42×C107—21no—
320C42×C107—21no—
321C42×C107—21no—
322C42×C107C2×D411yescharacteristic
323C42×C107C2×D411yescharacteristic
324C42×C107C2×D411yescharacteristic
325C42×C107C2411yescharacteristic
326C23×C107—21no—
327C23×C107—21no—
328C23×C107—21no—
329C23×C107—21no—
330C23×C107—42no—
331C23×C107—41no—
332C23×C107—81no—
333C23×C107—81no—
334C23×C107—81no—
335C23×C107—81no—
336C23×C107—81no—
337C23×C107#12011yescharacteristic
338Q8×C107—41no—
339Q8×C107—41no—
340Q8×C107—41no—
341Q8×C107—41no—
342Q8×C107—41no—
343Q8×C107—41no—
344Q8×C107—81no—
345Q8×C107—81no—
346D4×C107—41no—
347D4×C107—41no—
348D4×C107—41no—
349D4×C107—41no—
350D4×C107—41no—
351D4×C107—41no—
352D4×C107—41no—
353D4×C107—41no—
354D4×C107—41no—
355D4×C107—41no—
356D4×C107—42no—
357D4×C107—42no—
358D4×C107—81no—
359D4×C107—81no—
360D4×C107—81no—
361D4×C107—81no—
362D4×C107—81no—
363D4×C107—81no—
364D4×C107—81no—
365D4×C107—81no—
366D4×C107—82no—
367C2×C4×C107—21no—
368C2×C4×C107—21no—
369C2×C4×C107—21no—
370C2×C4×C107—21no—
371C2×C4×C107—21no—
372C2×C4×C107—21no—
373C2×C4×C107—21no—
374C2×C4×C107—21no—
375C2×C4×C107—41no—
376C2×C4×C107—41no—
377C2×C4×C107—41no—
378C2×C4×C107—42no—
379C2×C4×C107—41no—
380C2×C4×C107—81no—
381C2×C4×C107—81no—
382C2×C4×C107—82no—
383C2×C4×C107—81no—
384C2×C4×C107—81no—
385C2×C4×C107—81no—
386C2×C4×C107—81no—
387C2×C4×C107—81no—
388C2×C4×C107#12011yescharacteristic
389C2×C4×C107#12011yescharacteristic
390C2×C4×C107#12011yescharacteristic
391C2×C4×C107C22×D411yescharacteristic
392C2×C4×C107C22×D411yescharacteristic
393C2×C4×C107C22×D411yescharacteristic
394C8×C107—22no—
395C8×C107—41no—
396C8×C107—41no—
397C8×C107—41no—
398C8×C107—41no—
399C8×C107—41no—
400C22×C107—21no—
401C22×C107—21no—
402C22×C107—21no—
403C22×C107—41no—
404C22×C107—41no—
405C22×C107—41no—
406C22×C107—41no—
407C22×C107—41no—
408C22×C107—41no—
409C22×C107—41no—
410C22×C107—41no—
411C22×C107—41no—
412C22×C107—41no—
413C22×C107—41no—
414C22×C107—41no—
415C22×C107—81no—
416C22×C107—81no—
417C22×C107—81no—
418C22×C107—162no—
419C22×C107—162no—
420C22×C107C2×#12011yescharacteristic
421C4×C107—21no—
422C4×C107—21no—
423C4×C107—21no—
424C4×C107—21no—
425C4×C107—21no—
426C4×C107—21no—
427C4×C107—41no—
428C4×C107—41no—
429C4×C107—41no—
430C4×C107—41no—
431C4×C107—41no—
432C4×C107—41no—
433C4×C107—41no—
434C4×C107—41no—
435C4×C107—81no—
436#19068C10711yesmaximal, characteristic, direct product factor, Sylow
437C2×C107—41no—
438C2×C107—81no—
439C2×C107—81no—
440C2×C107—81no—
441C2×C107—81no—
442C2×C107—161no—
443C2×C107#301811yescharacteristic
444C2×C107#301911yescharacteristic
445C2×C107#302111yescharacteristic
446#3545C2×C10711yescharacteristic, complemented
447#3219C2×C10711yescharacteristic, complemented
448#3213C2×C10711yescharacteristic, complemented
449#3171C2×C10711yescharacteristic, complemented
450#1664C2×C10711yescharacteristic, complemented
451#1662C2×C10711yescharacteristic, complemented
452#1661C2×C10711yescharacteristic, complemented
453#1659C2×C10711yescharacteristic, complemented
454#1657C2×C10711yescharacteristic, complemented
455#1656C2×C10711yescharacteristic, complemented
456#1656C2×C10711yescharacteristic, complemented
457#1655C2×C10711yescharacteristic, complemented
458#1535C2×C10711yescharacteristic, complemented
459#1529C2×C10711yescharacteristic, complemented
460#1527C2×C10711yescharacteristic, complemented
461C107#1906811yescharacteristic, direct product factor, Sylow
462#563C22×C10711yescharacteristic
463#562C22×C10711yescharacteristic
464#562C22×C10711yescharacteristic
465H(3,𝔽4)C22×C10711yescharacteristic
466#555—21no—
467#551—21no—
468#551—21no—
469#551—21no—
470#546—21no—
471#546—21no—
472#542—21no—
473#542—21no—
474#538—21no—
475#538—21no—
476#536—21no—
477#534—21no—
478#532C22×C10711yescharacteristic, complemented
479#529C22×C10711yescharacteristic
480#529C22×C10711yescharacteristic
481C2×#124C22×C10711yescharacteristic
482#501C22×C10711yescharacteristic, complemented
483#497C22×C10711yescharacteristic, complemented
484#496C22×C10711yescharacteristic
485#496C22×C10711yescharacteristic, complemented
486#496C22×C10711yescharacteristic, complemented
487#496C22×C10711yescharacteristic, complemented
488#491C22×C10711yescharacteristic, complemented
489#490C22×C10711yescharacteristic, complemented
490#490C22×C10711yescharacteristic, complemented
491#489C22×C10711yescharacteristic
492#489C22×C10711yescharacteristic, complemented
493#489C22×C10711yescharacteristic, complemented
494#469—21no—
495#468—21no—
496#464—21no—
497#463—21no—
498#463—21no—
499#463—21no—
500#452—21no—
501#449—21no—
502#448—21no—
503#447—21no—
504C4×SD16—21no—
505C4×D8—21no—
506#432C22×C10711yescharacteristic, complemented
507#432C22×C10711yescharacteristic, complemented
508C4×M16C22×C10711yescharacteristic, complemented
509#330C22×C10711yescharacteristic, complemented
510#330C22×C10711yescharacteristic, complemented
511#330C22×C10711yescharacteristic, complemented
512#330C22×C10711yescharacteristic, complemented
513#329C22×C10711yescharacteristic
514#329C22×C10711yescharacteristic
515#329C22×C10711yescharacteristic, complemented
516#329C22×C10711yescharacteristic, complemented
517#329C22×C10711yescharacteristic, complemented
518#329C22×C10711yescharacteristic, complemented
519#329C22×C10711yescharacteristic, complemented
520#329C22×C10711yescharacteristic, complemented
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C10711yescharacteristic
524C22×D4—21no—
525C22×D4D4×C10711yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C10711yescharacteristic
540#127C23×C10711yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C10711yescharacteristic
548#125C23×C10711yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C10711yescharacteristic
559#124D4×C10711yescharacteristic
560#124C23×C10711yescharacteristic
561#124C23×C10711yescharacteristic
562#124C23×C10711yescharacteristic
563#124C23×C10711yescharacteristic
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C10711yescharacteristic
585C22⋊Q8D4×C10711yescharacteristic
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121D4×C10711yescharacteristic
597#121D4×C10711yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C10711yescharacteristic
605C4×Q8D4×C10711yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C10711yescharacteristic
615C4×D4D4×C10711yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C10711yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C10711yescharacteristic
646#97C23×C10711yescharacteristic
647#97C23×C10711yescharacteristic
648#97C23×C10711yescharacteristic
649#97C23×C10711yescharacteristic
650#97C23×C10711yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C10711yescharacteristic
662C2×Q8C2×D4×C10711yescharacteristic
663C2×Q8C2×D4×C10711yescharacteristic
664C2×Q8C2×D4×C10711yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C10711yescharacteristic
682C2×D4C2×D4×C10711yescharacteristic
683C2×D4C2×D4×C10711yescharacteristic
684C2×D4C2×D4×C10711yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4C2×D4×C10711yescharacteristic
695C22×C4C2×D4×C10711yescharacteristic
696C22×C4C2×D4×C10711yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C2×D4×C10711yescharacteristic
731C4⋊C4C2×D4×C10711yescharacteristic
732C4⋊C4C2×D4×C10711yescharacteristic
733C4⋊C4C2×D4×C10711yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C10711yescharacteristic
769C42C2×D4×C10711yescharacteristic
770C42C2×D4×C10711yescharacteristic
771C42C24×C10711yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C10711yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C10711yescharacteristic
835C2×C4#120×C10711yescharacteristic
836C2×C4#120×C10711yescharacteristic
837C2×C4C22×D4×C10711yescharacteristic
838C2×C4C22×D4×C10711yescharacteristic
839C2×C4C22×D4×C10711yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C10711yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C107×#301811yescharacteristic
889C2C107×#301911yescharacteristic
890C2C107×#302111yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC42C24×C107
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3545C2semidirect
2. C107×#3219C2semidirect
3. C107×#3213C2semidirect
4. C107×#3171C2semidirect
5. C107×#1664C2semidirect
6. C107×#1662C2semidirect
7. C107×#1661C2semidirect
8. C107×#1659C2semidirect
9. C107×#1657C2semidirect
10. C107×#1656C2semidirect
11. C107×#1656C2semidirect
12. C107×#1655C2semidirect
13. C107×#1535C2semidirect
14. C107×#1529C2semidirect
15. C107×#1527C2semidirect
32. #532×C107C22semidirect
36. #501×C107C22semidirect
37. #497×C107C22semidirect
39. #496×C107C22semidirect
40. #496×C107C22semidirect
41. #496×C107C22semidirect
42. #491×C107C22semidirect
43. #490×C107C22semidirect
44. #490×C107C22semidirect
46. #489×C107C22semidirect
47. #489×C107C22semidirect
60. #432×C107C22semidirect
61. #432×C107C22semidirect
62. C4×M16×C107C22semidirect
63. #330×C107C22semidirect
64. #330×C107C22semidirect
65. #330×C107C22semidirect
66. #330×C107C22semidirect
69. #329×C107C22semidirect
70. #329×C107C22semidirect
71. #329×C107C22semidirect
72. #329×C107C22semidirect
73. #329×C107C22semidirect
74. #329×C107C22semidirect
436. #19068C107direct (N × H)
446. #3545C2×C107semidirect
447. #3219C2×C107semidirect
448. #3213C2×C107semidirect
449. #3171C2×C107semidirect
450. #1664C2×C107semidirect
451. #1662C2×C107semidirect
452. #1661C2×C107semidirect
453. #1659C2×C107semidirect
454. #1657C2×C107semidirect
455. #1656C2×C107semidirect
456. #1656C2×C107semidirect
457. #1655C2×C107semidirect
458. #1535C2×C107semidirect
459. #1529C2×C107semidirect
460. #1527C2×C107semidirect
461. C107#19068direct (N × H)
478. #532C22×C107semidirect
482. #501C22×C107semidirect
483. #497C22×C107semidirect
485. #496C22×C107semidirect
486. #496C22×C107semidirect
487. #496C22×C107semidirect
488. #491C22×C107semidirect
489. #490C22×C107semidirect
490. #490C22×C107semidirect
492. #489C22×C107semidirect
493. #489C22×C107semidirect
506. #432C22×C107semidirect
507. #432C22×C107semidirect
508. C4×M16C22×C107semidirect
509. #330C22×C107semidirect
510. #330C22×C107semidirect
511. #330C22×C107semidirect
512. #330C22×C107semidirect
515. #329C22×C107semidirect
516. #329C22×C107semidirect
517. #329C22×C107semidirect
518. #329C22×C107semidirect
519. #329C22×C107semidirect
520. #329C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35452
C107×#32192
C107×#32132
C107×#31712
C107×#16642
C107×#16622
C107×#16612
C107×#16592
C107×#16572
C107×#16562
C107×#16552
C107×#15352
C107×#15292
C107×#15272
#19068107