Finite Group Databasebeta

← C107×#18224 #41044188

Subgroups — C107×#18224 #41044188

Order 27392.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3534C211yesmaximal, characteristic, complemented
2C107×#3003C211yesmaximal, characteristic, complemented
3C2×#447×C107C211yesmaximal, characteristic, complemented
4C107×#2613C211yesmaximal, characteristic, complemented
5C107×#1600C212yesmaximal, complemented
6C107×#1598C212yesmaximal, complemented
7C107×#1597C212yesmaximal, complemented
8C107×#1595C212yesmaximal, complemented
9C107×#1516C211yesmaximal, characteristic, complemented
10C107×#1510C211yesmaximal, characteristic, complemented
11C107×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C107C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C107—21no—
14C22×D8×C107—21no—
15#562×C107—21no—
16#560×C107—21no—
17#553×C107—21no—
18#551×C107—21no—
19#546×C107—21no—
20#546×C107—21no—
21#546×C107—21no—
22D42×C107—21no—
23#540×C107—21no—
24#539×C107—21no—
25#539×C107C2211yescharacteristic, complemented
26#538×C107—21no—
27#538×C107C2211yescharacteristic, complemented
28#537×C107C2211yescharacteristic, complemented
29#534×C107—21no—
30#534×C107C2211yescharacteristic, complemented
31#525×C107C2211yescharacteristic
32C2×#123×C107C2211yescharacteristic
33C2×#121×C107C2211yescharacteristic
34C2×#120×C107—21no—
35#450×C107—21no—
36#450×C107C2212yescomplemented
37#447×C107—21no—
38#447×C107—21no—
39#447×C107—21no—
40#447×C107C2212yes—
41#447×C107C2212yescomplemented
42#447×C107C2212yescomplemented
43#418×C107—21no—
44C2×#102×C107—21no—
45#407×C107C2211yescharacteristic, complemented
46C2×C22⋊C8×C107C2211yescharacteristic, complemented
47#394×C107—21no—
48#394×C107C2212yescomplemented
49#392×C107—21no—
50#392×C107C2212yescomplemented
51#381×C107C2211yescharacteristic, complemented
52#379×C107—21no—
53#328×C107C2212yescomplemented
54#327×C107C2212yescomplemented
55#327×C107C2212yescomplemented
56#327×C107C2212yescomplemented
57#324×C107C2212yescomplemented
58#323×C107C2212yescomplemented
59C25×C107—21no—
60C2×#41×C107—21no—
61C2×#41×C107D411yescharacteristic, complemented
62C22×D4×C107—21no—
63C22×D4×C107—21no—
64C22×D4×C107—21no—
65C22×D4×C107—22no—
66C22×D4×C107—21no—
67C22×D4×C107—21no—
68C22×D4×C107—21no—
69C22×D4×C107—21no—
70C22×D4×C107—21no—
71C22×D4×C107—44no—
72C22×D4×C107D411yescharacteristic
73C22×D4×C107D411yescharacteristic, complemented
74C22×D4×C107C2312yes—
75C23×C4×C107C2311yescharacteristic
76AGL(1,ℤ/8)×C107—44no—
77C2×SD16×C107—22no—
78C2×D8×C107—22no—
79C2×D8×C107—22no—
80C2×D8×C107—22no—
81C2×D8×C107—44no—
82C2×M16×C107—21no—
83C22×C8×C107—21no—
84#127×C107—21no—
85#126×C107—21no—
86#126×C107—21no—
87#126×C107—21no—
88#126×C107—21no—
89#125×C107—21no—
90#125×C107—21no—
91#124×C107—21no—
92#124×C107—21no—
93#124×C107—21no—
94#123×C107—21no—
95#123×C107—21no—
96#123×C107—21no—
97#123×C107—21no—
98#123×C107—21no—
99#123×C107—21no—
100#123×C107—21no—
101#123×C107—21no—
102#123×C107—21no—
103#123×C107—21no—
104#123×C107—21no—
105#123×C107—21no—
106#123×C107—21no—
107#123×C107—21no—
108C22⋊Q8×C107—21no—
109C22⋊Q8×C107—21no—
110C22⋊Q8×C107—21no—
111C22⋊Q8×C107—21no—
112C22⋊Q8×C107—21no—
113C22⋊Q8×C107D411yescharacteristic, complemented
114C22⋊Q8×C107C2311yescharacteristic
115#121×C107—21no—
116#121×C107—21no—
117#121×C107—21no—
118#121×C107—21no—
119#121×C107—21no—
120#121×C107—21no—
121#121×C107—21no—
122#121×C107—21no—
123#121×C107—21no—
124#121×C107—21no—
125#121×C107—21no—
126#121×C107—21no—
127#121×C107—21no—
128#121×C107—21no—
129#121×C107—21no—
130#121×C107D411yescharacteristic, complemented
131#121×C107D411yescharacteristic, complemented
132#121×C107D411yescharacteristic, complemented
133#121×C107C2311yescharacteristic
134#121×C107C2311yescharacteristic
135#121×C107C2311yescharacteristic
136#120×C107—21no—
137#120×C107—21no—
138#120×C107—21no—
139#120×C107—21no—
140#120×C107—21no—
141#120×C107—21no—
142#120×C107—21no—
143#120×C107—21no—
144#120×C107—44no—
145C4×D4×C107—21no—
146C4×D4×C107—21no—
147C4×D4×C107—21no—
148C4×D4×C107—21no—
149C4×D4×C107—21no—
150C4×D4×C107—21no—
151C4×D4×C107—21no—
152C4×D4×C107—21no—
153#117×C107—21no—
154#117×C107D411yescharacteristic, complemented
155C2×C4⋊C4×C107D411yescharacteristic
156C2×C4⋊C4×C107D411yescharacteristic, complemented
157C2×C4⋊C4×C107C2311yescharacteristic
158C2×C22⋊C4×C107—21no—
159C2×C22⋊C4×C107—21no—
160C2×C22⋊C4×C107—21no—
161C2×C22⋊C4×C107—21no—
162C2×C22⋊C4×C107—22no—
163C2×C22⋊C4×C107—22no—
164C2×C22⋊C4×C107—22no—
165C2×C22⋊C4×C107D411yescharacteristic
166C2×C22⋊C4×C107D411yescharacteristic
167C2×C22⋊C4×C107C2311yescharacteristic
168#102×C107—22no—
169#102×C107—22no—
170#102×C107—22no—
171#102×C107—22no—
172C22⋊C8×C107—21no—
173C22⋊C8×C107—21no—
174C22⋊C8×C107C2312yes—
175C22⋊C8×C107C2312yes—
176#95×C107—21no—
177#95×C107C2312yes—
178C24×C107—24no—
179C24×C107—21no—
180C24×C107—22no—
181C24×C107—21no—
182C24×C107—42no—
183C24×C107—41no—
184C24×C107—41no—
185C24×C107—82no—
186C24×C107—82no—
187C24×C107C2×D411yescharacteristic
188C24×C107C2×D411yescharacteristic
189#41×C107—42no—
190#41×C107—82no—
191C2×Q8×C107—21no—
192C2×Q8×C107C2×D411yescharacteristic
193C2×D4×C107—24no—
194C2×D4×C107—24no—
195C2×D4×C107—21no—
196C2×D4×C107—21no—
197C2×D4×C107—21no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—21no—
203C2×D4×C107—21no—
204C2×D4×C107—21no—
205C2×D4×C107—21no—
206C2×D4×C107—21no—
207C2×D4×C107—21no—
208C2×D4×C107—21no—
209C2×D4×C107—21no—
210C2×D4×C107—21no—
211C2×D4×C107—21no—
212C2×D4×C107—22no—
213C2×D4×C107—22no—
214C2×D4×C107—42no—
215C2×D4×C107—42no—
216C2×D4×C107—42no—
217C2×D4×C107—44no—
218C2×D4×C107—44no—
219C2×D4×C107—44no—
220C2×D4×C107—44no—
221C2×D4×C107—42no—
222C2×D4×C107—44no—
223C2×D4×C107—41no—
224C2×D4×C107—41no—
225C2×D4×C107—82no—
226C2×D4×C107—82no—
227C2×D4×C107—82no—
228C2×D4×C107—82no—
229C2×D4×C107—82no—
230C2×D4×C107C2×D411yescharacteristic
231C2×D4×C107C2×D411yescharacteristic
232C2×D4×C107C2×D411yescharacteristic
233C22×C4×C107—21no—
234C22×C4×C107—21no—
235C22×C4×C107—21no—
236C22×C4×C107—21no—
237C22×C4×C107—21no—
238C22×C4×C107—21no—
239C22×C4×C107—21no—
240C22×C4×C107—22no—
241C22×C4×C107—42no—
242C22×C4×C107C2×D411yescharacteristic
243C22×C4×C107C2×D411yescharacteristic
244C22×C4×C107C2×D411yescharacteristic
245C22×C4×C107C2×D411yescharacteristic
246C22×C4×C107C2×D411yescharacteristic
247C22×C4×C107C2×D411yescharacteristic
248C22×C4×C107C2×D411yescharacteristic
249C22×C4×C107C2×D411yescharacteristic
250C22×C4×C107C2411yescharacteristic
251SD16×C107—44no—
252D8×C107—44no—
253D8×C107—44no—
254D8×C107—44no—
255M16×C107—42no—
256C2×C8×C107—22no—
257C2×C8×C107—22no—
258C2×C8×C107—42no—
259C4⋊C4×C107—21no—
260C4⋊C4×C107—21no—
261C4⋊C4×C107—21no—
262C4⋊C4×C107—21no—
263C4⋊C4×C107—21no—
264C4⋊C4×C107—21no—
265C4⋊C4×C107—21no—
266C4⋊C4×C107—21no—
267C4⋊C4×C107—21no—
268C4⋊C4×C107—21no—
269C4⋊C4×C107—21no—
270C4⋊C4×C107—21no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107C2×D411yescharacteristic
273C4⋊C4×C107C2×D411yescharacteristic
274C4⋊C4×C107C2×D411yescharacteristic
275C4⋊C4×C107C2×D411yescharacteristic
276C22⋊C4×C107—21no—
277C22⋊C4×C107—21no—
278C22⋊C4×C107—21no—
279C22⋊C4×C107—21no—
280C22⋊C4×C107—21no—
281C22⋊C4×C107—21no—
282C22⋊C4×C107—21no—
283C22⋊C4×C107—21no—
284C22⋊C4×C107—21no—
285C22⋊C4×C107—21no—
286C22⋊C4×C107—21no—
287C22⋊C4×C107—21no—
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—44no—
302C22⋊C4×C107—42no—
303C22⋊C4×C107—82no—
304C22⋊C4×C107—82no—
305C42×C107—21no—
306C42×C107—21no—
307C42×C107—21no—
308C23×C107—22no—
309C23×C107—22no—
310C23×C107—24no—
311C23×C107—21no—
312C23×C107—21no—
313C23×C107—21no—
314C23×C107—21no—
315C23×C107—22no—
316C23×C107—41no—
317C23×C107—42no—
318C23×C107—42no—
319C23×C107—44no—
320C23×C107—42no—
321C23×C107—41no—
322C23×C107—41no—
323C23×C107—42no—
324C23×C107—42no—
325C23×C107—42no—
326C23×C107—44no—
327C23×C107—42no—
328C23×C107—81no—
329C23×C107—81no—
330C23×C107—82no—
331C23×C107—82no—
332C23×C107—82no—
333C23×C107—82no—
334C23×C107—88no—
335C23×C107—81no—
336C23×C107—81no—
337C23×C107—81no—
338C23×C107—88no—
339C23×C107#12011yescharacteristic
340C23×C107#12011yescharacteristic
341C23×C107C22×D411yescharacteristic
342Q8×C107—41no—
343Q8×C107—81no—
344D4×C107—24no—
345D4×C107—24no—
346D4×C107—41no—
347D4×C107—41no—
348D4×C107—41no—
349D4×C107—42no—
350D4×C107—42no—
351D4×C107—44no—
352D4×C107—44no—
353D4×C107—42no—
354D4×C107—42no—
355D4×C107—42no—
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—81no—
367D4×C107—81no—
368D4×C107—81no—
369D4×C107—81no—
370D4×C107—88no—
371C2×C4×C107—22no—
372C2×C4×C107—22no—
373C2×C4×C107—21no—
374C2×C4×C107—21no—
375C2×C4×C107—21no—
376C2×C4×C107—21no—
377C2×C4×C107—21no—
378C2×C4×C107—21no—
379C2×C4×C107—21no—
380C2×C4×C107—21no—
381C2×C4×C107—22no—
382C2×C4×C107—41no—
383C2×C4×C107—41no—
384C2×C4×C107—41no—
385C2×C4×C107—41no—
386C2×C4×C107—41no—
387C2×C4×C107—41no—
388C2×C4×C107—42no—
389C2×C4×C107—42no—
390C2×C4×C107—42no—
391C2×C4×C107—81no—
392C2×C4×C107—81no—
393C2×C4×C107—81no—
394C2×C4×C107—81no—
395C2×C4×C107—81no—
396C2×C4×C107—81no—
397C2×C4×C107—81no—
398C2×C4×C107#12011yescharacteristic
399C2×C4×C107#12011yescharacteristic
400C2×C4×C107C22×D411yescharacteristic
401C2×C4×C107C22×D411yescharacteristic
402C8×C107—42no—
403C8×C107—42no—
404C22×C107—21no—
405C22×C107—21no—
406C22×C107—21no—
407C22×C107—21no—
408C22×C107—21no—
409C22×C107—21no—
410C22×C107—21no—
411C22×C107—44no—
412C22×C107—44no—
413C22×C107—44no—
414C22×C107—41no—
415C22×C107—41no—
416C22×C107—41no—
417C22×C107—41no—
418C22×C107—41no—
419C22×C107—41no—
420C22×C107—41no—
421C22×C107—41no—
422C22×C107—41no—
423C22×C107—41no—
424C22×C107—44no—
425C22×C107—41no—
426C22×C107—41no—
427C22×C107—82no—
428C22×C107—82no—
429C22×C107—82no—
430C22×C107—88no—
431C22×C107—88no—
432C22×C107—82no—
433C22×C107—82no—
434C22×C107—162no—
435C22×C107—162no—
436C22×C107B(4,𝔽2)12yes—
437C22×C107C2×#12011yescharacteristic
438C22×C107#57612yes—
439C4×C107—21no—
440C4×C107—21no—
441C4×C107—21no—
442C4×C107—21no—
443C4×C107—41no—
444C4×C107—41no—
445C4×C107—41no—
446C4×C107—41no—
447C4×C107—41no—
448C4×C107—41no—
449C4×C107—41no—
450C4×C107—41no—
451C4×C107—82no—
452#18224C10711yesmaximal, characteristic, direct product factor, Sylow
453C2×C107—22no—
454C2×C107—22no—
455C2×C107—41no—
456C2×C107—84no—
457C2×C107—81no—
458C2×C107—81no—
459C2×C107—81no—
460C2×C107—81no—
461C2×C107#300811yescharacteristic
462C2×C107#302111yescharacteristic
463C2×C107C2×B(4,𝔽2)11yescharacteristic
464#3534C2×C10711yescharacteristic, complemented
465#3003C2×C10711yescharacteristic, complemented
466C2×#447C2×C10711yescharacteristic, complemented
467#2613C2×C10711yescharacteristic, complemented
468#1600C2×C10712yescomplemented
469#1598C2×C10712yescomplemented
470#1597C2×C10712yescomplemented
471#1595C2×C10712yescomplemented
472#1516C2×C10711yescharacteristic, complemented
473#1510C2×C10711yescharacteristic, complemented
474#1468C2×C10711yescharacteristic, complemented
475C107#1822411yescharacteristic, direct product factor, Sylow
476C23×D4C22×C10711yescharacteristic, complemented
477C2×AGL(1,ℤ/8)—21no—
478C22×D8—21no—
479#562—21no—
480#560—21no—
481#553—21no—
482#551—21no—
483#546—21no—
484#546—21no—
485#546—21no—
486D42—21no—
487#540—21no—
488#539—21no—
489#539C22×C10711yescharacteristic, complemented
490#538—21no—
491#538C22×C10711yescharacteristic, complemented
492#537C22×C10711yescharacteristic, complemented
493#534—21no—
494#534C22×C10711yescharacteristic, complemented
495#525C22×C10711yescharacteristic
496C2×#123C22×C10711yescharacteristic
497C2×#121C22×C10711yescharacteristic
498C2×#120—21no—
499#450—21no—
500#450C22×C10712yescomplemented
501#447—21no—
502#447—21no—
503#447—21no—
504#447C22×C10712yes—
505#447C22×C10712yescomplemented
506#447C22×C10712yescomplemented
507#418—21no—
508C2×#102—21no—
509#407C22×C10711yescharacteristic, complemented
510C2×C22⋊C8C22×C10711yescharacteristic, complemented
511#394—21no—
512#394C22×C10712yescomplemented
513#392—21no—
514#392C22×C10712yescomplemented
515#381C22×C10711yescharacteristic, complemented
516#379—21no—
517#328C22×C10712yescomplemented
518#327C22×C10712yescomplemented
519#327C22×C10712yescomplemented
520#327C22×C10712yescomplemented
521#324C22×C10712yescomplemented
522#323C22×C10712yescomplemented
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C10711yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C10711yescharacteristic
537C22×D4D4×C10711yescharacteristic, complemented
538C22×D4C23×C10712yes—
539C23×C4C23×C10711yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
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—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C10711yescharacteristic, complemented
578C22⋊Q8C23×C10711yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
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#121D4×C10711yescharacteristic, complemented
595#121D4×C10711yescharacteristic, complemented
596#121D4×C10711yescharacteristic, complemented
597#121C23×C10711yescharacteristic
598#121C23×C10711yescharacteristic
599#121C23×C10711yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C10711yescharacteristic, complemented
619C2×C4⋊C4D4×C10711yescharacteristic
620C2×C4⋊C4D4×C10711yescharacteristic, complemented
621C2×C4⋊C4C23×C10711yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C10711yescharacteristic
630C2×C22⋊C4D4×C10711yescharacteristic
631C2×C22⋊C4C23×C10711yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C10712yes—
639C22⋊C8C23×C10712yes—
640#95—21no—
641#95C23×C10712yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C10711yescharacteristic
652C24C2×D4×C10711yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C10711yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
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—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C10711yescharacteristic
695C2×D4C2×D4×C10711yescharacteristic
696C2×D4C2×D4×C10711yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C10711yescharacteristic
707C22×C4C2×D4×C10711yescharacteristic
708C22×C4C2×D4×C10711yescharacteristic
709C22×C4C2×D4×C10711yescharacteristic
710C22×C4C2×D4×C10711yescharacteristic
711C22×C4C2×D4×C10711yescharacteristic
712C22×C4C2×D4×C10711yescharacteristic
713C22×C4C2×D4×C10711yescharacteristic
714C22×C4C24×C10711yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
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⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C10711yescharacteristic
737C4⋊C4C2×D4×C10711yescharacteristic
738C4⋊C4C2×D4×C10711yescharacteristic
739C4⋊C4C2×D4×C10711yescharacteristic
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—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—44no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C10711yescharacteristic
804C23#120×C10711yescharacteristic
805C23C22×D4×C10711yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C10711yescharacteristic
863C2×C4#120×C10711yescharacteristic
864C2×C4C22×D4×C10711yescharacteristic
865C2×C4C22×D4×C10711yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22B(4,𝔽2)×C10712yes—
901C22C2×#120×C10711yescharacteristic
902C22#576×C10712yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C107×#300811yescharacteristic
925C2C107×#302111yescharacteristic
926C2C2×B(4,𝔽2)×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3534C2semidirect
2. C107×#3003C2semidirect
3. C2×#447×C107C2semidirect
4. C107×#2613C2semidirect
5. C107×#1600C2semidirect
6. C107×#1598C2semidirect
7. C107×#1597C2semidirect
8. C107×#1595C2semidirect
9. C107×#1516C2semidirect
10. C107×#1510C2semidirect
11. C107×#1468C2semidirect
12. C23×D4×C107C22semidirect
25. #539×C107C22semidirect
27. #538×C107C22semidirect
28. #537×C107C22semidirect
30. #534×C107C22semidirect
36. #450×C107C22semidirect
41. #447×C107C22semidirect
42. #447×C107C22semidirect
45. #407×C107C22semidirect
46. C2×C22⋊C8×C107C22semidirect
48. #394×C107C22semidirect
50. #392×C107C22semidirect
51. #381×C107C22semidirect
53. #328×C107C22semidirect
54. #327×C107C22semidirect
55. #327×C107C22semidirect
56. #327×C107C22semidirect
57. #324×C107C22semidirect
58. #323×C107C22semidirect
61. C2×#41×C107D4semidirect
73. C22×D4×C107D4semidirect
113. C22⋊Q8×C107D4semidirect
130. #121×C107D4semidirect
131. #121×C107D4semidirect
132. #121×C107D4semidirect
154. #117×C107D4semidirect
156. C2×C4⋊C4×C107D4semidirect
452. #18224C107direct (N × H)
464. #3534C2×C107semidirect
465. #3003C2×C107semidirect
466. C2×#447C2×C107semidirect
467. #2613C2×C107semidirect
468. #1600C2×C107semidirect
469. #1598C2×C107semidirect
470. #1597C2×C107semidirect
471. #1595C2×C107semidirect
472. #1516C2×C107semidirect
473. #1510C2×C107semidirect
474. #1468C2×C107semidirect
475. C107#18224direct (N × H)
476. C23×D4C22×C107semidirect
489. #539C22×C107semidirect
491. #538C22×C107semidirect
492. #537C22×C107semidirect
494. #534C22×C107semidirect
500. #450C22×C107semidirect
505. #447C22×C107semidirect
506. #447C22×C107semidirect
509. #407C22×C107semidirect
510. C2×C22⋊C8C22×C107semidirect
512. #394C22×C107semidirect
514. #392C22×C107semidirect
515. #381C22×C107semidirect
517. #328C22×C107semidirect
518. #327C22×C107semidirect
519. #327C22×C107semidirect
520. #327C22×C107semidirect
521. #324C22×C107semidirect
522. #323C22×C107semidirect
525. C2×#41D4×C107semidirect
537. C22×D4D4×C107semidirect
577. C22⋊Q8D4×C107semidirect
594. #121D4×C107semidirect
595. #121D4×C107semidirect
596. #121D4×C107semidirect
618. #117D4×C107semidirect
620. C2×C4⋊C4D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35342
C107×#30032
C2×#447×C1072
C107×#26132
C107×#16002
C107×#15982
C107×#15972
C107×#15952
C107×#15162
C107×#15102
C107×#14682
#18224107