Finite Group Databasebeta

← C107×#19010 #41044974

Subgroups — C107×#19010 #41044974

Order 27392.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3529C211yesmaximal, characteristic, complemented
2C107×#3219C211yesmaximal, characteristic, complemented
3C107×#3214C211yesmaximal, characteristic, complemented
4C107×#3180C211yesmaximal, 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×#1532C211yesmaximal, characteristic, complemented
15C107×#1530C211yesmaximal, characteristic, complemented
16#563×C107—21no—
17#563×C107C2211yescharacteristic
18#562×C107—21no—
19#562×C107—21no—
20#562×C107C2211yescharacteristic
21#562×C107C2211yescharacteristic
22H(3,𝔽4)×C107C2211yescharacteristic
23#560×C107—21no—
24#560×C107—21no—
25#560×C107—21no—
26#532×C107—21no—
27#532×C107C2211yescharacteristic
28#532×C107C2211yescharacteristic, complemented
29#529×C107—21no—
30#529×C107—21no—
31#529×C107C2211yescharacteristic
32#529×C107C2211yescharacteristic
33#525×C107—21no—
34#525×C107—21no—
35#525×C107—21no—
36#501×C107C2211yescharacteristic, complemented
37#497×C107C2211yescharacteristic
38#496×C107C2211yescharacteristic
39#496×C107C2211yescharacteristic
40#496×C107C2211yescharacteristic
41#496×C107C2211yescharacteristic, complemented
42#491×C107C2211yescharacteristic, complemented
43#490×C107C2211yescharacteristic, complemented
44#490×C107C2211yescharacteristic, complemented
45#489×C107C2211yescharacteristic
46#489×C107C2211yescharacteristic
47#489×C107C2211yescharacteristic, complemented
48#466×C107—21no—
49#465×C107—21no—
50#464×C107—21no—
51#463×C107—21no—
52#461×C107—21no—
53#459×C107—21no—
54#452×C107—21no—
55#449×C107—21no—
56#449×C107—21no—
57#449×C107—21no—
58#442×C107—21no—
59#440×C107—21no—
60#432×C107C2211yescharacteristic, complemented
61#432×C107C2211yescharacteristic, complemented
62C2×#97×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
70#329×C107C2211yescharacteristic
71#329×C107C2211yescharacteristic
72#329×C107C2211yescharacteristic
73#329×C107C2211yescharacteristic, complemented
74#329×C107C2211yescharacteristic, complemented
75C2×#41×C107—21no—
76C2×#41×C107—21no—
77C2×#41×C107D411yescharacteristic
78C2×#41×C107D411yescharacteristic
79C23×C4×C107—21no—
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—
90C22×C8×C107—21no—
91C4⋊Q8×C107—21no—
92C4⋊Q8×C107D411yescharacteristic
93C4⋊Q8×C107C2311yescharacteristic
94#127×C107—21no—
95#127×C107D411yescharacteristic
96#127×C107C2311yescharacteristic
97#126×C107—21no—
98#126×C107—21no—
99#126×C107—21no—
100#126×C107—21no—
101#126×C107—21no—
102#126×C107—21no—
103#125×C107—21no—
104#125×C107—21no—
105#125×C107C2311yescharacteristic
106#125×C107C2311yescharacteristic
107#124×C107—21no—
108#124×C107—21no—
109#124×C107—21no—
110#124×C107—21no—
111#124×C107—21no—
112#124×C107C2311yescharacteristic
113#124×C107C2311yescharacteristic
114#124×C107C2311yescharacteristic
115#124×C107C2311yescharacteristic
116#123×C107—21no—
117#123×C107—21no—
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—
128C22⋊Q8×C107—21no—
129C22⋊Q8×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×C107D411yescharacteristic
137C22⋊Q8×C107D411yescharacteristic
138#121×C107—21no—
139#121×C107—21no—
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×C107—21no—
151#121×C107—21no—
152#121×C107—21no—
153#121×C107—21no—
154#121×C107D411yescharacteristic
155#121×C107D411yescharacteristic
156#120×C107—21no—
157#120×C107—21no—
158#120×C107—21no—
159#120×C107—21no—
160#120×C107—21no—
161#120×C107—21no—
162C4×Q8×C107D411yescharacteristic
163C4×Q8×C107D411yescharacteristic
164C4×D4×C107—21no—
165C4×D4×C107—21no—
166C4×D4×C107—21no—
167C4×D4×C107—21no—
168C4×D4×C107—21no—
169C4×D4×C107—21no—
170C4×D4×C107—21no—
171C4×D4×C107—21no—
172C4×D4×C107—21no—
173C4×D4×C107—21no—
174C4×D4×C107D411yescharacteristic
175C4×D4×C107D411yescharacteristic
176#117×C107—21no—
177#117×C107—21no—
178#117×C107—21no—
179C2×C42×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×C107—21no—
200#97×C107C2311yescharacteristic
201#97×C107C2311yescharacteristic
202#97×C107C2311yescharacteristic
203#97×C107C2311yescharacteristic
204#97×C107C2311yescharacteristic
205#97×C107C2311yescharacteristic
206C24×C107—21no—
207#41×C107—81no—
208#41×C107—81no—
209#41×C107—82no—
210#41×C107—81no—
211#41×C107—81no—
212C2×Q8×C107—21no—
213C2×Q8×C107—21no—
214C2×Q8×C107C2×D411yescharacteristic
215C2×Q8×C107C2×D411yescharacteristic
216C2×Q8×C107C2×D411yescharacteristic
217C2×Q8×C107C2×D411yescharacteristic
218C2×D4×C107—21no—
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—21no—
233C2×D4×C107—21no—
234C2×D4×C107—41no—
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—21no—
248C22×C4×C107—41no—
249C22×C4×C107—82no—
250C22×C4×C107C2×D411yescharacteristic
251C22×C4×C107C2×D411yescharacteristic
252C22×C4×C107C2×D411yescharacteristic
253Q16×C107—81no—
254SD16×C107—42no—
255SD16×C107—81no—
256SD16×C107—81no—
257SD16×C107—81no—
258SD16×C107—81no—
259D8×C107—42no—
260D8×C107—81no—
261D8×C107—81no—
262D8×C107—81no—
263C2×C8×C107—21no—
264C2×C8×C107—21no—
265C2×C8×C107—21no—
266C2×C8×C107—21no—
267C2×C8×C107—21no—
268C2×C8×C107—21no—
269C2×C8×C107—42no—
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×C107—21no—
285C4⋊C4×C107—21no—
286C4⋊C4×C107—21no—
287C4⋊C4×C107—21no—
288C4⋊C4×C107C2×D411yescharacteristic
289C4⋊C4×C107C2×D411yescharacteristic
290C4⋊C4×C107C2×D411yescharacteristic
291C4⋊C4×C107C2×D411yescharacteristic
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—41no—
331C23×C107—81no—
332C23×C107—81no—
333C23×C107—81no—
334C23×C107#12011yescharacteristic
335Q8×C107—41no—
336Q8×C107—41no—
337Q8×C107—41no—
338Q8×C107—41no—
339Q8×C107—41no—
340Q8×C107—41no—
341Q8×C107—81no—
342D4×C107—41no—
343D4×C107—41no—
344D4×C107—41no—
345D4×C107—41no—
346D4×C107—41no—
347D4×C107—41no—
348D4×C107—41no—
349D4×C107—41no—
350D4×C107—41no—
351D4×C107—41no—
352D4×C107—81no—
353D4×C107—81no—
354D4×C107—81no—
355D4×C107—81no—
356D4×C107—81no—
357D4×C107—81no—
358D4×C107—81no—
359D4×C107—81no—
360D4×C107—81no—
361D4×C107—81no—
362D4×C107—81no—
363D4×C107—81no—
364D4×C107—81no—
365D4×C107—82no—
366C2×C4×C107—21no—
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—41no—
375C2×C4×C107—41no—
376C2×C4×C107—41no—
377C2×C4×C107—42no—
378C2×C4×C107—42no—
379C2×C4×C107—42no—
380C2×C4×C107—42no—
381C2×C4×C107—41no—
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—84no—
416C22×C107—81no—
417C22×C107—81no—
418C22×C107—81no—
419C22×C107C2×#12011yescharacteristic
420C4×C107—21no—
421C4×C107—21no—
422C4×C107—21no—
423C4×C107—21no—
424C4×C107—21no—
425C4×C107—21no—
426C4×C107—41no—
427C4×C107—41no—
428C4×C107—41no—
429C4×C107—41no—
430C4×C107—41no—
431C4×C107—41no—
432C4×C107—41no—
433C4×C107—41no—
434C4×C107—81no—
435#19010C10711yesmaximal, characteristic, direct product factor, Sylow
436C2×C107—41no—
437C2×C107—81no—
438C2×C107—81no—
439C2×C107—81no—
440C2×C107—81no—
441C2×C107—161no—
442C2×C107#301811yescharacteristic
443C2×C107#301911yescharacteristic
444C2×C107#302111yescharacteristic
445#3529C2×C10711yescharacteristic, complemented
446#3219C2×C10711yescharacteristic, complemented
447#3214C2×C10711yescharacteristic, complemented
448#3180C2×C10711yescharacteristic, complemented
449#1664C2×C10711yescharacteristic, complemented
450#1662C2×C10711yescharacteristic, complemented
451#1661C2×C10711yescharacteristic, complemented
452#1659C2×C10711yescharacteristic, complemented
453#1657C2×C10711yescharacteristic, complemented
454#1656C2×C10711yescharacteristic, complemented
455#1656C2×C10711yescharacteristic, complemented
456#1655C2×C10711yescharacteristic, complemented
457#1535C2×C10711yescharacteristic, complemented
458#1532C2×C10711yescharacteristic, complemented
459#1530C2×C10711yescharacteristic, complemented
460C107#1901011yescharacteristic, direct product factor, Sylow
461#563—21no—
462#563C22×C10711yescharacteristic
463#562—21no—
464#562—21no—
465#562C22×C10711yescharacteristic
466#562C22×C10711yescharacteristic
467H(3,𝔽4)C22×C10711yescharacteristic
468#560—21no—
469#560—21no—
470#560—21no—
471#532—21no—
472#532C22×C10711yescharacteristic
473#532C22×C10711yescharacteristic, complemented
474#529—21no—
475#529—21no—
476#529C22×C10711yescharacteristic
477#529C22×C10711yescharacteristic
478#525—21no—
479#525—21no—
480#525—21no—
481#501C22×C10711yescharacteristic, complemented
482#497C22×C10711yescharacteristic
483#496C22×C10711yescharacteristic
484#496C22×C10711yescharacteristic
485#496C22×C10711yescharacteristic
486#496C22×C10711yescharacteristic, complemented
487#491C22×C10711yescharacteristic, complemented
488#490C22×C10711yescharacteristic, complemented
489#490C22×C10711yescharacteristic, complemented
490#489C22×C10711yescharacteristic
491#489C22×C10711yescharacteristic
492#489C22×C10711yescharacteristic, complemented
493#466—21no—
494#465—21no—
495#464—21no—
496#463—21no—
497#461—21no—
498#459—21no—
499#452—21no—
500#449—21no—
501#449—21no—
502#449—21no—
503#442—21no—
504#440—21no—
505#432C22×C10711yescharacteristic, complemented
506#432C22×C10711yescharacteristic, complemented
507C2×#97C22×C10711yescharacteristic, complemented
508#330C22×C10711yescharacteristic, complemented
509#330C22×C10711yescharacteristic, complemented
510#330C22×C10711yescharacteristic, complemented
511#330C22×C10711yescharacteristic, complemented
512#329C22×C10711yescharacteristic
513#329C22×C10711yescharacteristic
514#329C22×C10711yescharacteristic
515#329C22×C10711yescharacteristic
516#329C22×C10711yescharacteristic
517#329C22×C10711yescharacteristic
518#329C22×C10711yescharacteristic, complemented
519#329C22×C10711yescharacteristic, complemented
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C10711yescharacteristic
523C2×#41D4×C10711yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C10711yescharacteristic
538C4⋊Q8C23×C10711yescharacteristic
539#127—21no—
540#127D4×C10711yescharacteristic
541#127C23×C10711yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C10711yescharacteristic
551#125C23×C10711yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C10711yescharacteristic
558#124C23×C10711yescharacteristic
559#124C23×C10711yescharacteristic
560#124C23×C10711yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
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—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C10711yescharacteristic
582C22⋊Q8D4×C10711yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
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#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C10711yescharacteristic
600#121D4×C10711yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C10711yescharacteristic
608C4×Q8D4×C10711yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C10711yescharacteristic
620C4×D4D4×C10711yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C10711yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C10711yescharacteristic
646#97C23×C10711yescharacteristic
647#97C23×C10711yescharacteristic
648#97C23×C10711yescharacteristic
649#97C23×C10711yescharacteristic
650#97C23×C10711yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C10711yescharacteristic
660C2×Q8C2×D4×C10711yescharacteristic
661C2×Q8C2×D4×C10711yescharacteristic
662C2×Q8C2×D4×C10711yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
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—21no—
679C2×D4—41no—
680C2×D4C2×D4×C10711yescharacteristic
681C2×D4C2×D4×C10711yescharacteristic
682C2×D4C2×D4×C10711yescharacteristic
683C2×D4C2×D4×C10711yescharacteristic
684C22×C4—21no—
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×C4—82no—
695C22×C4C2×D4×C10711yescharacteristic
696C22×C4C2×D4×C10711yescharacteristic
697C22×C4C2×D4×C10711yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
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⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C10711yescharacteristic
734C4⋊C4C2×D4×C10711yescharacteristic
735C4⋊C4C2×D4×C10711yescharacteristic
736C4⋊C4C2×D4×C10711yescharacteristic
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—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C10711yescharacteristic
768C42C2×D4×C10711yescharacteristic
769C42C2×D4×C10711yescharacteristic
770C42C24×C10711yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C10711yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C10711yescharacteristic
834C2×C4#120×C10711yescharacteristic
835C2×C4#120×C10711yescharacteristic
836C2×C4C22×D4×C10711yescharacteristic
837C2×C4C22×D4×C10711yescharacteristic
838C2×C4C22×D4×C10711yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C10711yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2C107×#301811yescharacteristic
887C2C107×#301911yescharacteristic
888C2C107×#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×#3529C2semidirect
2. C107×#3219C2semidirect
3. C107×#3214C2semidirect
4. C107×#3180C2semidirect
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×#1532C2semidirect
15. C107×#1530C2semidirect
28. #532×C107C22semidirect
36. #501×C107C22semidirect
41. #496×C107C22semidirect
42. #491×C107C22semidirect
43. #490×C107C22semidirect
44. #490×C107C22semidirect
47. #489×C107C22semidirect
60. #432×C107C22semidirect
61. #432×C107C22semidirect
62. C2×#97×C107C22semidirect
63. #330×C107C22semidirect
64. #330×C107C22semidirect
65. #330×C107C22semidirect
66. #330×C107C22semidirect
73. #329×C107C22semidirect
74. #329×C107C22semidirect
435. #19010C107direct (N × H)
445. #3529C2×C107semidirect
446. #3219C2×C107semidirect
447. #3214C2×C107semidirect
448. #3180C2×C107semidirect
449. #1664C2×C107semidirect
450. #1662C2×C107semidirect
451. #1661C2×C107semidirect
452. #1659C2×C107semidirect
453. #1657C2×C107semidirect
454. #1656C2×C107semidirect
455. #1656C2×C107semidirect
456. #1655C2×C107semidirect
457. #1535C2×C107semidirect
458. #1532C2×C107semidirect
459. #1530C2×C107semidirect
460. C107#19010direct (N × H)
473. #532C22×C107semidirect
481. #501C22×C107semidirect
486. #496C22×C107semidirect
487. #491C22×C107semidirect
488. #490C22×C107semidirect
489. #490C22×C107semidirect
492. #489C22×C107semidirect
505. #432C22×C107semidirect
506. #432C22×C107semidirect
507. C2×#97C22×C107semidirect
508. #330C22×C107semidirect
509. #330C22×C107semidirect
510. #330C22×C107semidirect
511. #330C22×C107semidirect
518. #329C22×C107semidirect
519. #329C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35292
C107×#32192
C107×#32142
C107×#31802
C107×#16642
C107×#16622
C107×#16612
C107×#16592
C107×#16572
C107×#16562
C107×#16552
C107×#15352
C107×#15322
C107×#15302
#19010107