Finite Group Databasebeta

← C107×#24124 #41050088

Subgroups — C107×#24124 #41050088

Order 27392.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C107C211yesmaximal, characteristic, complemented
2C2×#478×C107C211yesmaximal, characteristic, complemented
3C2×C4×D8×C107C211yesmaximal, characteristic, complemented
4C107×#2535C211yesmaximal, characteristic, complemented
5C107×#2034C211yesmaximal, characteristic, complemented
6C107×#2033C211yesmaximal, characteristic, complemented
7C107×#1999C211yesmaximal, characteristic, complemented
8C107×#1999C211yesmaximal, characteristic, complemented
9C107×#1991C211yesmaximal, characteristic, complemented
10C107×#1954C211yesmaximal, characteristic, complemented
11C107×#1875C211yesmaximal, characteristic, complemented
12C107×#1874C211yesmaximal, characteristic, complemented
13C107×#1854C211yesmaximal, characteristic, complemented
14C107×#1852C211yesmaximal, characteristic, complemented
15C107×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C107C2211yescharacteristic
17#553×C107—24no—
18#553×C107—24no—
19C2×#126×C107—21no—
20C2×#125×C107C2211yescharacteristic
21C2×#123×C107—21no—
22C2×#121×C107—21no—
23C2×#121×C107C2211yescharacteristic
24C2×#121×C107C2211yescharacteristic
25C2×#121×C107C2211yescharacteristic
26C2×#121×C107C2211yescharacteristic
27C2×C4×D4×C107—21no—
28C2×C4×D4×C107C2211yescharacteristic
29C2×C4×D4×C107C2211yescharacteristic
30C2×C4×D4×C107C2211yescharacteristic
31C2×#117×C107C2211yescharacteristic
32C22×C4⋊C4×C107C2211yescharacteristic
33#478×C107—24no—
34C4×D8×C107—24no—
35C2×#107×C107C2211yescharacteristic
36C2×#107×C107C2211yescharacteristic
37C2×#106×C107C2211yescharacteristic
38C2×C4⋊C8×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×C22⋊C8×C107C2211yescharacteristic
46C2×C22⋊C8×C107C2211yescharacteristic
47C2×C22⋊C8×C107C2211yescharacteristic
48C2×C22⋊C8×C107C2211yescharacteristic
49C2×C4×C8×C107C2211yescharacteristic
50#397×C107—21no—
51#392×C107—21no—
52#386×C107—21no—
53#386×C107—21no—
54#382×C107C2211yescharacteristic
55#380×C107C2211yescharacteristic
56#380×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#340×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic
62#340×C107C2211yescharacteristic
63C22×D4×C107—21no—
64C22×D4×C107—21no—
65C22×D4×C107—21no—
66C22×D4×C107—21no—
67C22×D4×C107D411yescharacteristic
68C22×D4×C107C2311yescharacteristic
69C22×D4×C107C2311yescharacteristic
70C23×C4×C107—21no—
71C23×C4×C107—21no—
72C23×C4×C107—21no—
73C23×C4×C107C2311yescharacteristic
74C23×C4×C107C2311yescharacteristic
75C2×D8×C107—22no—
76C2×D8×C107—22no—
77C2×D8×C107—22no—
78C22×C8×C107C2311yescharacteristic
79C22×C8×C107C2311yescharacteristic
80C22×C8×C107C2311yescharacteristic
81C22×C8×C107C2311yescharacteristic
82#126×C107—28no—
83#125×C107—22no—
84#125×C107D414yescomplemented
85#123×C107—28no—
86#121×C107—28no—
87#121×C107—22no—
88#121×C107—22no—
89#121×C107—22no—
90#121×C107—22no—
91#121×C107—22no—
92#121×C107—22no—
93#121×C107—41no—
94#121×C107—41no—
95C4×D4×C107—28no—
96C4×D4×C107—22no—
97C4×D4×C107—22no—
98C4×D4×C107—22no—
99C4×D4×C107—22no—
100C4×D4×C107—22no—
101C4×D4×C107D414yescomplemented
102#117×C107—22no—
103#117×C107—22no—
104C2×C4⋊C4×C107—21no—
105C2×C4⋊C4×C107—21no—
106C2×C4⋊C4×C107—21no—
107C2×C4⋊C4×C107—22no—
108C2×C4⋊C4×C107—22no—
109C2×C4⋊C4×C107D411yescharacteristic
110C2×C4⋊C4×C107C2311yescharacteristic
111C2×C4⋊C4×C107C2311yescharacteristic
112C2×C4⋊C4×C107C2311yescharacteristic
113C2×C4⋊C4×C107C2311yescharacteristic
114C2×C4⋊C4×C107C2311yescharacteristic
115C2×C4⋊C4×C107C2311yescharacteristic
116C2×C22⋊C4×C107—21no—
117C2×C22⋊C4×C107—21no—
118C2×C22⋊C4×C107—21no—
119C2×C22⋊C4×C107—21no—
120C2×C22⋊C4×C107—21no—
121C2×C22⋊C4×C107—21no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107D411yescharacteristic
126C2×C22⋊C4×C107D411yescharacteristic
127C2×C42×C107—21no—
128C2×C42×C107C2311yescharacteristic
129#107×C107—22no—
130#107×C107—22no—
131#106×C107—22no—
132C4⋊C8×C107—22no—
133#102×C107—22no—
134#102×C107—22no—
135#102×C107—22no—
136#102×C107—22no—
137#102×C107—41no—
138#102×C107—41no—
139C22⋊C8×C107—22no—
140C22⋊C8×C107—22no—
141C22⋊C8×C107—41no—
142C22⋊C8×C107—41no—
143C4×C8×C107—22no—
144#95×C107—21no—
145#95×C107—21no—
146#95×C107—21no—
147#95×C107—21no—
148C24×C107—21no—
149C24×C107—21no—
150C24×C107C2×D411yescharacteristic
151C24×C107C2×D411yescharacteristic
152C2×D4×C107—24no—
153C2×D4×C107—22no—
154C2×D4×C107—24no—
155C2×D4×C107—22no—
156C2×D4×C107—21no—
157C2×D4×C107—21no—
158C2×D4×C107—21no—
159C2×D4×C107—21no—
160C2×D4×C107—21no—
161C2×D4×C107—21no—
162C2×D4×C107—21no—
163C2×D4×C107—21no—
164C2×D4×C107—21no—
165C2×D4×C107—21no—
166C2×D4×C107—41no—
167C2×D4×C107—42no—
168C2×D4×C107—42no—
169C2×D4×C107—42no—
170C2×D4×C107—42no—
171C2×D4×C107—42no—
172C2×D4×C107—42no—
173C2×D4×C107—81no—
174C2×D4×C107—81no—
175C2×D4×C107—81no—
176C2×D4×C107—81no—
177C2×D4×C107C2×D412yes—
178C2×D4×C107#4112yes—
179C22×C4×C107—21no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—24no—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—21no—
186C22×C4×C107—21no—
187C22×C4×C107—21no—
188C22×C4×C107—21no—
189C22×C4×C107—21no—
190C22×C4×C107—21no—
191C22×C4×C107—21no—
192C22×C4×C107—21no—
193C22×C4×C107—21no—
194C22×C4×C107—21no—
195C22×C4×C107—24no—
196C22×C4×C107—21no—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—42no—
200C22×C4×C107—81no—
201C22×C4×C107—81no—
202C22×C4×C107—81no—
203C22×C4×C107—81no—
204C22×C4×C107—81no—
205C22×C4×C107—81no—
206C22×C4×C107C2×D411yescharacteristic
207C22×C4×C107C2×D411yescharacteristic
208C22×C4×C107C2×D411yescharacteristic
209C22×C4×C107C2×D411yescharacteristic
210C22×C4×C107C2411yescharacteristic
211D8×C107—28no—
212C2×C8×C107—21no—
213C2×C8×C107—21no—
214C2×C8×C107—21no—
215C2×C8×C107—21no—
216C2×C8×C107—21no—
217C2×C8×C107—21no—
218C2×C8×C107—21no—
219C2×C8×C107—21no—
220C2×C8×C107—21no—
221C2×C8×C107—21no—
222C2×C8×C107—21no—
223C2×C8×C107#4112yes—
224C4⋊C4×C107—24no—
225C4⋊C4×C107—24no—
226C4⋊C4×C107—24no—
227C4⋊C4×C107—22no—
228C4⋊C4×C107—21no—
229C4⋊C4×C107—21no—
230C4⋊C4×C107—21no—
231C4⋊C4×C107—21no—
232C4⋊C4×C107—21no—
233C4⋊C4×C107—21no—
234C4⋊C4×C107—21no—
235C4⋊C4×C107—21no—
236C4⋊C4×C107—21no—
237C4⋊C4×C107C2×D412yes—
238C4⋊C4×C107C2×D412yes—
239C4⋊C4×C107C2×D412yes—
240C22⋊C4×C107—24no—
241C22⋊C4×C107—24no—
242C22⋊C4×C107—24no—
243C22⋊C4×C107—24no—
244C22⋊C4×C107—22no—
245C22⋊C4×C107—22no—
246C22⋊C4×C107—42no—
247C22⋊C4×C107—42no—
248C22⋊C4×C107—42no—
249C22⋊C4×C107—81no—
250C22⋊C4×C107—81no—
251C42×C107—24no—
252C42×C107C2×D412yes—
253C42×C107C2×D412yes—
254C23×C107—21no—
255C23×C107—21no—
256C23×C107—21no—
257C23×C107—21no—
258C23×C107—21no—
259C23×C107—21no—
260C23×C107—21no—
261C23×C107—22no—
262C23×C107—22no—
263C23×C107—21no—
264C23×C107—21no—
265C23×C107—21no—
266C23×C107—21no—
267C23×C107—21no—
268C23×C107—21no—
269C23×C107—41no—
270C23×C107—41no—
271C23×C107—41no—
272C23×C107—41no—
273C23×C107—41no—
274C23×C107—41no—
275C23×C107—41no—
276C23×C107—41no—
277C23×C107—41no—
278C23×C107—41no—
279C23×C107—41no—
280C23×C107—41no—
281C23×C107#13512yes—
282C23×C107C22×D411yescharacteristic
283D4×C107—22no—
284D4×C107—22no—
285D4×C107—22no—
286D4×C107—22no—
287D4×C107—44no—
288D4×C107—48no—
289D4×C107—41no—
290D4×C107—41no—
291D4×C107—41no—
292D4×C107—41no—
293D4×C107—84no—
294D4×C107—84no—
295D4×C107—84no—
296C2×C4×C107—21no—
297C2×C4×C107—21no—
298C2×C4×C107—21no—
299C2×C4×C107—21no—
300C2×C4×C107—21no—
301C2×C4×C107—22no—
302C2×C4×C107—22no—
303C2×C4×C107—21no—
304C2×C4×C107—22no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—41no—
310C2×C4×C107—41no—
311C2×C4×C107—41no—
312C2×C4×C107—41no—
313C2×C4×C107—41no—
314C2×C4×C107—41no—
315C2×C4×C107—41no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—41no—
321C2×C4×C107—41no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107—41no—
329C2×C4×C107—41no—
330C2×C4×C107—41no—
331C2×C4×C107—41no—
332C2×C4×C107—84no—
333C2×C4×C107—84no—
334C2×C4×C107—84no—
335C2×C4×C107#12012yes—
336C2×C4×C107#12012yes—
337C2×C4×C107C22×D411yescharacteristic
338C2×C4×C107C22×D411yescharacteristic
339C2×C4×C107C2×#4111yescharacteristic
340C2×C4×C107C2×#4111yescharacteristic
341C2×C4×C107H(5,𝔽2)11yescharacteristic
342C2×C4×C1072−1+411yescharacteristic
343C8×C107—22no—
344C8×C107—41no—
345C8×C107—41no—
346C8×C107—41no—
347C22×C107—22no—
348C22×C107—22no—
349C22×C107—22no—
350C22×C107—41no—
351C22×C107—41no—
352C22×C107—41no—
353C22×C107—41no—
354C22×C107—41no—
355C22×C107—41no—
356C22×C107—41no—
357C22×C107—42no—
358C22×C107—42no—
359C22×C107—41no—
360C22×C107—42no—
361C22×C107—42no—
362C22×C107—41no—
363C22×C107—42no—
364C22×C107—41no—
365C22×C107—41no—
366C22×C107—42no—
367C22×C107—81no—
368C22×C107—81no—
369C22×C107—81no—
370C22×C107—81no—
371C22×C107—81no—
372C22×C107—81no—
373C22×C107—81no—
374C22×C107—81no—
375C22×C107C2×#12011yescharacteristic
376C22×C107#54611yescharacteristic
377C22×C107#54711yescharacteristic
378C22×C107C2×#13511yescharacteristic
379C22×C107#57511yescharacteristic
380C22×C107#57611yescharacteristic
381C22×C107#57611yescharacteristic
382C4×C107—22no—
383C4×C107—22no—
384C4×C107—41no—
385C4×C107—41no—
386C4×C107—42no—
387C4×C107—42no—
388C4×C107—42no—
389C4×C107—81no—
390C4×C107—81no—
391C4×C107—81no—
392C4×C107#52511yescharacteristic
393C4×C107#53711yescharacteristic
394C4×C107#54811yescharacteristic
395C4×C107#55011yescharacteristic
396#24124C10711yesmaximal, characteristic, direct product factor, Sylow
397C2×C107—42no—
398C2×C107—81no—
399C2×C107—82no—
400C2×C107—82no—
401C2×C107#240711yescharacteristic
402C2×C107#300211yescharacteristic
403C2×C107#300811yescharacteristic
404C2×C107#329711yescharacteristic
405C2×C107#332211yescharacteristic
406C2×C107#333911yescharacteristic
407C2×C107#335511yescharacteristic
408C2×#553C2×C10711yescharacteristic, complemented
409C2×#478C2×C10711yescharacteristic, complemented
410C2×C4×D8C2×C10711yescharacteristic, complemented
411#2535C2×C10711yescharacteristic, complemented
412#2034C2×C10711yescharacteristic, complemented
413#2033C2×C10711yescharacteristic, complemented
414#1999C2×C10711yescharacteristic, complemented
415#1999C2×C10711yescharacteristic, complemented
416#1991C2×C10711yescharacteristic, complemented
417#1954C2×C10711yescharacteristic, complemented
418#1875C2×C10711yescharacteristic, complemented
419#1874C2×C10711yescharacteristic, complemented
420#1854C2×C10711yescharacteristic, complemented
421#1852C2×C10711yescharacteristic, complemented
422#1804C2×C10711yescharacteristic, complemented
423C107#2412411yescharacteristic, direct product factor, Sylow
424C22×D8C22×C10711yescharacteristic
425#553—24no—
426#553—24no—
427C2×#126—21no—
428C2×#125C22×C10711yescharacteristic
429C2×#123—21no—
430C2×#121—21no—
431C2×#121C22×C10711yescharacteristic
432C2×#121C22×C10711yescharacteristic
433C2×#121C22×C10711yescharacteristic
434C2×#121C22×C10711yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C10711yescharacteristic
437C2×C4×D4C22×C10711yescharacteristic
438C2×C4×D4C22×C10711yescharacteristic
439C2×#117C22×C10711yescharacteristic
440C22×C4⋊C4C22×C10711yescharacteristic
441#478—24no—
442C4×D8—24no—
443C2×#107C22×C10711yescharacteristic
444C2×#107C22×C10711yescharacteristic
445C2×#106C22×C10711yescharacteristic
446C2×C4⋊C8C22×C10711yescharacteristic
447C2×#102C22×C10711yescharacteristic
448C2×#102C22×C10711yescharacteristic
449C2×#102C22×C10711yescharacteristic
450C2×#102C22×C10711yescharacteristic
451C2×#102C22×C10711yescharacteristic
452C2×#102C22×C10711yescharacteristic
453C2×C22⋊C8C22×C10711yescharacteristic
454C2×C22⋊C8C22×C10711yescharacteristic
455C2×C22⋊C8C22×C10711yescharacteristic
456C2×C22⋊C8C22×C10711yescharacteristic
457C2×C4×C8C22×C10711yescharacteristic
458#397—21no—
459#392—21no—
460#386—21no—
461#386—21no—
462#382C22×C10711yescharacteristic
463#380C22×C10711yescharacteristic
464#380C22×C10711yescharacteristic
465#340C22×C10711yescharacteristic
466#340C22×C10711yescharacteristic
467#340C22×C10711yescharacteristic
468#340C22×C10711yescharacteristic
469#340C22×C10711yescharacteristic
470#340C22×C10711yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C10711yescharacteristic
476C22×D4C23×C10711yescharacteristic
477C22×D4C23×C10711yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C10711yescharacteristic
482C23×C4C23×C10711yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C10711yescharacteristic
487C22×C8C23×C10711yescharacteristic
488C22×C8C23×C10711yescharacteristic
489C22×C8C23×C10711yescharacteristic
490#126—28no—
491#125—22no—
492#125D4×C10714yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C10714yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4D4×C10711yescharacteristic
518C2×C4⋊C4C23×C10711yescharacteristic
519C2×C4⋊C4C23×C10711yescharacteristic
520C2×C4⋊C4C23×C10711yescharacteristic
521C2×C4⋊C4C23×C10711yescharacteristic
522C2×C4⋊C4C23×C10711yescharacteristic
523C2×C4⋊C4C23×C10711yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4D4×C10711yescharacteristic
534C2×C22⋊C4D4×C10711yescharacteristic
535C2×C42—21no—
536C2×C42C23×C10711yescharacteristic
537#107—22no—
538#107—22no—
539#106—22no—
540C4⋊C8—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C10711yescharacteristic
559C24C2×D4×C10711yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C2×D4×C10712yes—
586C2×D4#41×C10712yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C10711yescharacteristic
615C22×C4C2×D4×C10711yescharacteristic
616C22×C4C2×D4×C10711yescharacteristic
617C22×C4C2×D4×C10711yescharacteristic
618C22×C4C24×C10711yescharacteristic
619D8—28no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8#41×C10712yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4C2×D4×C10712yes—
646C4⋊C4C2×D4×C10712yes—
647C4⋊C4C2×D4×C10712yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C10712yes—
661C42C2×D4×C10712yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#135×C10712yes—
690C23C22×D4×C10711yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#120×C10712yes—
744C2×C4#120×C10712yes—
745C2×C4C22×D4×C10711yescharacteristic
746C2×C4C22×D4×C10711yescharacteristic
747C2×C4C2×#41×C10711yescharacteristic
748C2×C4C2×#41×C10711yescharacteristic
749C2×C4H(5,𝔽2)×C10711yescharacteristic
750C2×C42−1+4×C10711yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C10711yescharacteristic
784C22#546×C10711yescharacteristic
785C22#547×C10711yescharacteristic
786C22C2×#135×C10711yescharacteristic
787C22#575×C10711yescharacteristic
788C22#576×C10711yescharacteristic
789C22#576×C10711yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4#525×C10711yescharacteristic
801C4#537×C10711yescharacteristic
802C4#548×C10711yescharacteristic
803C4#550×C10711yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2C107×#240711yescharacteristic
809C2C107×#300211yescharacteristic
810C2C107×#300811yescharacteristic
811C2C107×#329711yescharacteristic
812C2C107×#332211yescharacteristic
813C2C107×#333911yescharacteristic
814C2C107×#335511yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#553×C107C2semidirect
2. C2×#478×C107C2semidirect
3. C2×C4×D8×C107C2semidirect
4. C107×#2535C2semidirect
5. C107×#2034C2semidirect
6. C107×#2033C2semidirect
7. C107×#1999C2semidirect
8. C107×#1999C2semidirect
9. C107×#1991C2semidirect
10. C107×#1954C2semidirect
11. C107×#1875C2semidirect
12. C107×#1874C2semidirect
13. C107×#1854C2semidirect
14. C107×#1852C2semidirect
15. C107×#1804C2semidirect
84. #125×C107D4semidirect
101. C4×D4×C107D4semidirect
396. #24124C107direct (N × H)
408. C2×#553C2×C107semidirect
409. C2×#478C2×C107semidirect
410. C2×C4×D8C2×C107semidirect
411. #2535C2×C107semidirect
412. #2034C2×C107semidirect
413. #2033C2×C107semidirect
414. #1999C2×C107semidirect
415. #1999C2×C107semidirect
416. #1991C2×C107semidirect
417. #1954C2×C107semidirect
418. #1875C2×C107semidirect
419. #1874C2×C107semidirect
420. #1854C2×C107semidirect
421. #1852C2×C107semidirect
422. #1804C2×C107semidirect
423. C107#24124direct (N × H)
492. #125D4×C107semidirect
509. C4×D4D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1072
C2×#478×C1072
C2×C4×D8×C1072
C107×#25352
C107×#20342
C107×#20332
C107×#19992
C107×#19912
C107×#19542
C107×#18752
C107×#18742
C107×#18542
C107×#18522
C107×#18042
#24124107