Finite Group Databasebeta

← C107×#24136 #41050100

Subgroups — C107×#24136 #41050100

Order 27392.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 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×#442×C107C211yesmaximal, characteristic, complemented
4C107×#2537C211yesmaximal, characteristic, complemented
5C107×#2034C211yesmaximal, characteristic, complemented
6C107×#2033C211yesmaximal, characteristic, complemented
7C107×#1999C211yesmaximal, characteristic, complemented
8C107×#1999C211yesmaximal, characteristic, complemented
9C107×#1992C211yesmaximal, characteristic, complemented
10C107×#1955C211yesmaximal, characteristic, complemented
11C107×#1875C211yesmaximal, characteristic, complemented
12C107×#1874C211yesmaximal, characteristic, complemented
13C107×#1854C211yesmaximal, characteristic, complemented
14C107×#1853C211yesmaximal, characteristic, complemented
15C107×#1802C211yesmaximal, 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×C107—21no—
24C2×#121×C107C2211yescharacteristic
25C2×#121×C107C2211yescharacteristic
26C2×#121×C107C2211yescharacteristic
27C2×#121×C107C2211yescharacteristic
28C2×C4×D4×C107—21no—
29C2×C4×D4×C107C2211yescharacteristic
30C2×C4×D4×C107C2211yescharacteristic
31C2×C4×D4×C107C2211yescharacteristic
32C2×#117×C107C2211yescharacteristic
33C22×C4⋊C4×C107C2211yescharacteristic
34#478×C107—24no—
35#442×C107—24no—
36C2×#107×C107C2211yescharacteristic
37C2×#106×C107C2211yescharacteristic
38C2×#106×C107C2211yescharacteristic
39C2×C4⋊C8×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic
46C2×C22⋊C8×C107C2211yescharacteristic
47C2×C22⋊C8×C107C2211yescharacteristic
48C2×C22⋊C8×C107C2211yescharacteristic
49C2×C22⋊C8×C107C2211yescharacteristic
50C2×#97×C107C2211yescharacteristic
51#394×C107—21no—
52#394×C107—21no—
53#384×C107C2211yescharacteristic
54#380×C107—21no—
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—
95#121×C107—44no—
96C4×D4×C107—28no—
97C4×D4×C107—22no—
98C4×D4×C107—22no—
99C4×D4×C107—22no—
100C4×D4×C107—22no—
101C4×D4×C107—22no—
102C4×D4×C107D414yescomplemented
103#117×C107—22no—
104#117×C107—22no—
105C2×C4⋊C4×C107—21no—
106C2×C4⋊C4×C107—21no—
107C2×C4⋊C4×C107—21no—
108C2×C4⋊C4×C107—22no—
109C2×C4⋊C4×C107—22no—
110C2×C4⋊C4×C107—21no—
111C2×C4⋊C4×C107—21no—
112C2×C4⋊C4×C107D411yescharacteristic
113C2×C4⋊C4×C107C2311yescharacteristic
114C2×C4⋊C4×C107C2311yescharacteristic
115C2×C4⋊C4×C107C2311yescharacteristic
116C2×C4⋊C4×C107C2311yescharacteristic
117C2×C4⋊C4×C107C2311yescharacteristic
118C2×C4⋊C4×C107C2311yescharacteristic
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×C107—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—21no—
128C2×C22⋊C4×C107D411yescharacteristic
129C2×C22⋊C4×C107D411yescharacteristic
130C2×C42×C107—21no—
131C2×C42×C107C2311yescharacteristic
132#107×C107—22no—
133#106×C107—22no—
134#106×C107—22no—
135C4⋊C8×C107—22no—
136#102×C107—22no—
137#102×C107—22no—
138#102×C107—22no—
139#102×C107—22no—
140#102×C107—41no—
141#102×C107—41no—
142C22⋊C8×C107—22no—
143C22⋊C8×C107—22no—
144C22⋊C8×C107—41no—
145C22⋊C8×C107—41no—
146#97×C107—22no—
147#95×C107—21no—
148#95×C107—21no—
149C24×C107—21no—
150C24×C107—21no—
151C24×C107C2×D411yescharacteristic
152C24×C107C2×D411yescharacteristic
153C2×D4×C107—24no—
154C2×D4×C107—22no—
155C2×D4×C107—24no—
156C2×D4×C107—22no—
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—21no—
167C2×D4×C107—41no—
168C2×D4×C107—42no—
169C2×D4×C107—42no—
170C2×D4×C107—42no—
171C2×D4×C107—42no—
172C2×D4×C107—42no—
173C2×D4×C107—42no—
174C2×D4×C107—81no—
175C2×D4×C107—81no—
176C2×D4×C107—81no—
177C2×D4×C107—81no—
178C2×D4×C107C2×D412yes—
179C2×D4×C107#4112yes—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—21no—
183C22×C4×C107—24no—
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—21no—
196C22×C4×C107—24no—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—42no—
201C22×C4×C107—42no—
202C22×C4×C107—42no—
203C22×C4×C107—81no—
204C22×C4×C107—81no—
205C22×C4×C107—81no—
206C22×C4×C107—81no—
207C22×C4×C107C2×D411yescharacteristic
208C22×C4×C107C2×D411yescharacteristic
209C22×C4×C107C2×D411yescharacteristic
210C22×C4×C107C2×D411yescharacteristic
211C22×C4×C107C2411yescharacteristic
212D8×C107—28no—
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—21no—
224C2×C8×C107#4112yes—
225C4⋊C4×C107—24no—
226C4⋊C4×C107—24no—
227C4⋊C4×C107—24no—
228C4⋊C4×C107—22no—
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×C107—21no—
238C4⋊C4×C107—42no—
239C4⋊C4×C107—81no—
240C4⋊C4×C107C2×D412yes—
241C4⋊C4×C107C2×D412yes—
242C4⋊C4×C107C2×D412yes—
243C22⋊C4×C107—24no—
244C22⋊C4×C107—24no—
245C22⋊C4×C107—24no—
246C22⋊C4×C107—24no—
247C22⋊C4×C107—22no—
248C22⋊C4×C107—22no—
249C22⋊C4×C107—42no—
250C22⋊C4×C107—42no—
251C22⋊C4×C107—42no—
252C22⋊C4×C107—42no—
253C22⋊C4×C107—42no—
254C42×C107—24no—
255C42×C107C2×D412yes—
256C42×C107C2×D412yes—
257C23×C107—21no—
258C23×C107—21no—
259C23×C107—21no—
260C23×C107—21no—
261C23×C107—21no—
262C23×C107—21no—
263C23×C107—21no—
264C23×C107—22no—
265C23×C107—22no—
266C23×C107—21no—
267C23×C107—21no—
268C23×C107—21no—
269C23×C107—21no—
270C23×C107—21no—
271C23×C107—21no—
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—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107AGL(1,ℤ/8)12yes—
285C23×C107C22×D411yescharacteristic
286D4×C107—22no—
287D4×C107—22no—
288D4×C107—22no—
289D4×C107—22no—
290D4×C107—44no—
291D4×C107—48no—
292D4×C107—41no—
293D4×C107—41no—
294D4×C107—41no—
295D4×C107—41no—
296D4×C107—84no—
297D4×C107—84no—
298D4×C107—84no—
299C2×C4×C107—21no—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—22no—
305C2×C4×C107—22no—
306C2×C4×C107—21no—
307C2×C4×C107—22no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
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—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
335C2×C4×C107—84no—
336C2×C4×C107—84no—
337C2×C4×C107—84no—
338C2×C4×C107#12012yes—
339C2×C4×C107#12012yes—
340C2×C4×C107C22×D411yescharacteristic
341C2×C4×C107C22×D411yescharacteristic
342C2×C4×C107C2×#4111yescharacteristic
343C2×C4×C107C2×#4111yescharacteristic
344C2×C4×C107H(5,𝔽2)11yescharacteristic
345C2×C4×C1072−1+411yescharacteristic
346C8×C107—22no—
347C8×C107—41no—
348C8×C107—41no—
349C8×C107—41no—
350C22×C107—22no—
351C22×C107—22no—
352C22×C107—22no—
353C22×C107—41no—
354C22×C107—41no—
355C22×C107—41no—
356C22×C107—41no—
357C22×C107—41no—
358C22×C107—41no—
359C22×C107—41no—
360C22×C107—42no—
361C22×C107—42no—
362C22×C107—41no—
363C22×C107—42no—
364C22×C107—42no—
365C22×C107—41no—
366C22×C107—41no—
367C22×C107—42no—
368C22×C107—41no—
369C22×C107—42no—
370C22×C107—81no—
371C22×C107—81no—
372C22×C107—81no—
373C22×C107—81no—
374C22×C107—81no—
375C22×C107—81no—
376C22×C107—81no—
377C22×C107—81no—
378C22×C107C2×#12011yescharacteristic
379C22×C107#54611yescharacteristic
380C22×C107#54711yescharacteristic
381C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C107#57511yescharacteristic
383C22×C107#57611yescharacteristic
384C22×C107#57711yescharacteristic
385C4×C107—22no—
386C4×C107—22no—
387C4×C107—41no—
388C4×C107—41no—
389C4×C107—42no—
390C4×C107—42no—
391C4×C107—42no—
392C4×C107—81no—
393C4×C107—81no—
394C4×C107—81no—
395C4×C107#52511yescharacteristic
396C4×C107#53711yescharacteristic
397C4×C107#54811yescharacteristic
398C4×C107#55011yescharacteristic
399#24136C10711yesmaximal, characteristic, direct product factor, Sylow
400C2×C107—42no—
401C2×C107—81no—
402C2×C107—82no—
403C2×C107—82no—
404C2×C107#240711yescharacteristic
405C2×C107#300611yescharacteristic
406C2×C107#301211yescharacteristic
407C2×C107#330711yescharacteristic
408C2×C107#331811yescharacteristic
409C2×C107#334511yescharacteristic
410C2×C107#334711yescharacteristic
411C2×#553C2×C10711yescharacteristic, complemented
412C2×#478C2×C10711yescharacteristic, complemented
413C2×#442C2×C10711yescharacteristic, complemented
414#2537C2×C10711yescharacteristic, complemented
415#2034C2×C10711yescharacteristic, complemented
416#2033C2×C10711yescharacteristic, complemented
417#1999C2×C10711yescharacteristic, complemented
418#1999C2×C10711yescharacteristic, complemented
419#1992C2×C10711yescharacteristic, complemented
420#1955C2×C10711yescharacteristic, complemented
421#1875C2×C10711yescharacteristic, complemented
422#1874C2×C10711yescharacteristic, complemented
423#1854C2×C10711yescharacteristic, complemented
424#1853C2×C10711yescharacteristic, complemented
425#1802C2×C10711yescharacteristic, complemented
426C107#2413611yescharacteristic, direct product factor, Sylow
427C22×D8C22×C10711yescharacteristic
428#553—24no—
429#553—24no—
430C2×#126—21no—
431C2×#125C22×C10711yescharacteristic
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C10711yescharacteristic
436C2×#121C22×C10711yescharacteristic
437C2×#121C22×C10711yescharacteristic
438C2×#121C22×C10711yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C10711yescharacteristic
441C2×C4×D4C22×C10711yescharacteristic
442C2×C4×D4C22×C10711yescharacteristic
443C2×#117C22×C10711yescharacteristic
444C22×C4⋊C4C22×C10711yescharacteristic
445#478—24no—
446#442—24no—
447C2×#107C22×C10711yescharacteristic
448C2×#106C22×C10711yescharacteristic
449C2×#106C22×C10711yescharacteristic
450C2×C4⋊C8C22×C10711yescharacteristic
451C2×#102C22×C10711yescharacteristic
452C2×#102C22×C10711yescharacteristic
453C2×#102C22×C10711yescharacteristic
454C2×#102C22×C10711yescharacteristic
455C2×#102C22×C10711yescharacteristic
456C2×#102C22×C10711yescharacteristic
457C2×C22⋊C8C22×C10711yescharacteristic
458C2×C22⋊C8C22×C10711yescharacteristic
459C2×C22⋊C8C22×C10711yescharacteristic
460C2×C22⋊C8C22×C10711yescharacteristic
461C2×#97C22×C10711yescharacteristic
462#394—21no—
463#394—21no—
464#384C22×C10711yescharacteristic
465#380—21no—
466#380C22×C10711yescharacteristic
467#380C22×C10711yescharacteristic
468#340C22×C10711yescharacteristic
469#340C22×C10711yescharacteristic
470#340C22×C10711yescharacteristic
471#340C22×C10711yescharacteristic
472#340C22×C10711yescharacteristic
473#340C22×C10711yescharacteristic
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C10711yescharacteristic
479C22×D4C23×C10711yescharacteristic
480C22×D4C23×C10711yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C10711yescharacteristic
485C23×C4C23×C10711yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C22×C8C23×C10711yescharacteristic
490C22×C8C23×C10711yescharacteristic
491C22×C8C23×C10711yescharacteristic
492C22×C8C23×C10711yescharacteristic
493#126—28no—
494#125—22no—
495#125D4×C10714yescomplemented
496#123—28no—
497#121—28no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—41no—
505#121—41no—
506#121—44no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C10714yescomplemented
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C10711yescharacteristic
524C2×C4⋊C4C23×C10711yescharacteristic
525C2×C4⋊C4C23×C10711yescharacteristic
526C2×C4⋊C4C23×C10711yescharacteristic
527C2×C4⋊C4C23×C10711yescharacteristic
528C2×C4⋊C4C23×C10711yescharacteristic
529C2×C4⋊C4C23×C10711yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4D4×C10711yescharacteristic
540C2×C22⋊C4D4×C10711yescharacteristic
541C2×C42—21no—
542C2×C42C23×C10711yescharacteristic
543#107—22no—
544#106—22no—
545#106—22no—
546C4⋊C8—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557#97—22no—
558#95—21no—
559#95—21no—
560C24—21no—
561C24—21no—
562C24C2×D4×C10711yescharacteristic
563C24C2×D4×C10711yescharacteristic
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4C2×D4×C10712yes—
590C2×D4#41×C10712yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
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—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C2×D4×C10711yescharacteristic
619C22×C4C2×D4×C10711yescharacteristic
620C22×C4C2×D4×C10711yescharacteristic
621C22×C4C2×D4×C10711yescharacteristic
622C22×C4C24×C10711yescharacteristic
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8#41×C10712yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—81no—
651C4⋊C4C2×D4×C10712yes—
652C4⋊C4C2×D4×C10712yes—
653C4⋊C4C2×D4×C10712yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—24no—
666C42C2×D4×C10712yes—
667C42C2×D4×C10712yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23AGL(1,ℤ/8)×C10712yes—
696C23C22×D4×C10711yescharacteristic
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
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—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4#120×C10712yes—
750C2×C4#120×C10712yes—
751C2×C4C22×D4×C10711yescharacteristic
752C2×C4C22×D4×C10711yescharacteristic
753C2×C4C2×#41×C10711yescharacteristic
754C2×C4C2×#41×C10711yescharacteristic
755C2×C4H(5,𝔽2)×C10711yescharacteristic
756C2×C42−1+4×C10711yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—41no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×#120×C10711yescharacteristic
790C22#546×C10711yescharacteristic
791C22#547×C10711yescharacteristic
792C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
793C22#575×C10711yescharacteristic
794C22#576×C10711yescharacteristic
795C22#577×C10711yescharacteristic
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4#525×C10711yescharacteristic
807C4#537×C10711yescharacteristic
808C4#548×C10711yescharacteristic
809C4#550×C10711yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2C107×#240711yescharacteristic
815C2C107×#300611yescharacteristic
816C2C107×#301211yescharacteristic
817C2C107×#330711yescharacteristic
818C2C107×#331811yescharacteristic
819C2C107×#334511yescharacteristic
820C2C107×#334711yescharacteristic
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×#442×C107C2semidirect
4. C107×#2537C2semidirect
5. C107×#2034C2semidirect
6. C107×#2033C2semidirect
7. C107×#1999C2semidirect
8. C107×#1999C2semidirect
9. C107×#1992C2semidirect
10. C107×#1955C2semidirect
11. C107×#1875C2semidirect
12. C107×#1874C2semidirect
13. C107×#1854C2semidirect
14. C107×#1853C2semidirect
15. C107×#1802C2semidirect
84. #125×C107D4semidirect
102. C4×D4×C107D4semidirect
399. #24136C107direct (N × H)
411. C2×#553C2×C107semidirect
412. C2×#478C2×C107semidirect
413. C2×#442C2×C107semidirect
414. #2537C2×C107semidirect
415. #2034C2×C107semidirect
416. #2033C2×C107semidirect
417. #1999C2×C107semidirect
418. #1999C2×C107semidirect
419. #1992C2×C107semidirect
420. #1955C2×C107semidirect
421. #1875C2×C107semidirect
422. #1874C2×C107semidirect
423. #1854C2×C107semidirect
424. #1853C2×C107semidirect
425. #1802C2×C107semidirect
426. C107#24136direct (N × H)
495. #125D4×C107semidirect
513. 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×#442×C1072
C107×#25372
C107×#20342
C107×#20332
C107×#19992
C107×#19922
C107×#19552
C107×#18752
C107×#18742
C107×#18542
C107×#18532
C107×#18022
#24136107