Finite Group Databasebeta

← C107×#32709 #41058673

Subgroups — C107×#32709 #41058673

Order 27392.

1062 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2848C211yesmaximal, characteristic, complemented
2C107×#2847C211yesmaximal, characteristic
3C107×#2077C211yesmaximal, characteristic, complemented
4C107×#2076C211yesmaximal, characteristic, complemented
5C107×#2075C211yesmaximal, characteristic, complemented
6C107×#2036C211yesmaximal, characteristic, complemented
7C107×#2036C211yesmaximal, characteristic, complemented
8C107×#2035C211yesmaximal, characteristic, complemented
9C107×#2034C211yesmaximal, characteristic, complemented
10C107×#2033C211yesmaximal, characteristic, complemented
11C107×#2033C211yesmaximal, characteristic, complemented
12C107×#2000C211yesmaximal, characteristic, complemented
13C107×#2000C211yesmaximal, characteristic, complemented
14C107×#2000C211yesmaximal, characteristic, complemented
15C107×#1779C211yesmaximal, characteristic, complemented
16C24×C4×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic, complemented
18C2×C22⋊Q8×C107C2211yescharacteristic
19C2×C22⋊Q8×C107C2211yescharacteristic
20C2×C22⋊Q8×C107C2211yescharacteristic
21C2×#121×C107C2211yescharacteristic
22C2×#121×C107C2211yescharacteristic
23C2×#121×C107C2211yescharacteristic
24C2×#120×C107—21no—
25C2×#107×C107C2211yescharacteristic, complemented
26C2×#107×C107C2211yescharacteristic, complemented
27C2×#106×C107C2211yescharacteristic, complemented
28C2×#103×C107C2211yescharacteristic, complemented
29C2×#103×C107C2211yescharacteristic, complemented
30C2×#103×C107C2211yescharacteristic, complemented
31C2×#102×C107C2211yescharacteristic, complemented
32C2×#102×C107C2211yescharacteristic, complemented
33C2×#102×C107C2211yescharacteristic, complemented
34C2×C22⋊C8×C107C2211yescharacteristic
35C2×C22⋊C8×C107C2211yescharacteristic
36C2×C22⋊C8×C107C2211yescharacteristic
37C2×C22⋊C8×C107C2211yescharacteristic
38C2×C22⋊C8×C107C2211yescharacteristic
39C2×C22⋊C8×C107C2211yescharacteristic
40#386×C107—21no—
41#386×C107—21no—
42#386×C107—21no—
43#385×C107—21no—
44#385×C107—21no—
45#385×C107—21no—
46#380×C107C2211yescharacteristic
47#380×C107C2211yescharacteristic
48#380×C107C2211yescharacteristic
49#380×C107C2211yescharacteristic
50#380×C107C2211yescharacteristic
51#380×C107C2211yescharacteristic
52#379×C107—21no—
53#340×C107C2211yescharacteristic, complemented
54#340×C107C2211yescharacteristic, complemented
55#340×C107C2211yescharacteristic, complemented
56#340×C107C2211yescharacteristic, complemented
57#340×C107C2211yescharacteristic, complemented
58#340×C107C2211yescharacteristic, complemented
59C25×C107D411yescharacteristic
60C22×Q8×C107C2311yescharacteristic
61C22×D4×C107—21no—
62C22×D4×C107—21no—
63C22×D4×C107—21no—
64C22×D4×C107C2311yescharacteristic
65C23×C4×C107—41no—
66C23×C4×C107—41no—
67C23×C4×C107—41no—
68C23×C4×C107—41no—
69C23×C4×C107—41no—
70C23×C4×C107—41no—
71C23×C4×C107D411yescharacteristic
72C23×C4×C107D411yescharacteristic
73C23×C4×C107D411yescharacteristic
74C23×C4×C107C2311yescharacteristic
75C23×C4×C107C2311yescharacteristic
76C23×C4×C107C2311yescharacteristic
77C2×SD16×C107—41no—
78C2×SD16×C107—41no—
79C2×SD16×C107—41no—
80C22×C8×C107C2311yescharacteristic
81C22×C8×C107C2311yescharacteristic
82C22×C8×C107C2311yescharacteristic
83C22×C8×C107C2311yescharacteristic
84C22⋊Q8×C107—41no—
85C22⋊Q8×C107—41no—
86C22⋊Q8×C107—41no—
87C22⋊Q8×C107—41no—
88C22⋊Q8×C107—41no—
89C22⋊Q8×C107—41no—
90#121×C107—41no—
91#121×C107—41no—
92#121×C107—41no—
93#121×C107—41no—
94#121×C107—41no—
95#121×C107—41no—
96#120×C107—44no—
97C2×C4⋊C4×C107—21no—
98C2×C4⋊C4×C107—21no—
99C2×C4⋊C4×C107—21no—
100C2×C4⋊C4×C107C2311yescharacteristic
101C2×C4⋊C4×C107C2311yescharacteristic
102C2×C4⋊C4×C107C2311yescharacteristic
103C2×C4⋊C4×C107C2311yescharacteristic
104C2×C4⋊C4×C107C2311yescharacteristic
105C2×C4⋊C4×C107C2311yescharacteristic
106C2×C22⋊C4×C107—21no—
107C2×C22⋊C4×C107—21no—
108C2×C22⋊C4×C107—21no—
109C2×C22⋊C4×C107—21no—
110C2×C22⋊C4×C107—21no—
111C2×C22⋊C4×C107—21no—
112C2×C22⋊C4×C107—21no—
113C2×C22⋊C4×C107—21no—
114C2×C22⋊C4×C107—21no—
115C2×C22⋊C4×C107—21no—
116C2×C22⋊C4×C107—21no—
117C2×C22⋊C4×C107—21no—
118#107×C107—41no—
119#107×C107—41no—
120#106×C107—41no—
121#103×C107—41no—
122#103×C107—41no—
123#103×C107—41no—
124#102×C107—41no—
125#102×C107—41no—
126#102×C107—41no—
127C22⋊C8×C107—41no—
128C22⋊C8×C107—41no—
129C22⋊C8×C107—41no—
130C22⋊C8×C107—41no—
131C22⋊C8×C107—41no—
132C22⋊C8×C107—41no—
133#95×C107—21no—
134#95×C107—21no—
135#95×C107—21no—
136#95×C107—21no—
137#95×C107—21no—
138#95×C107—21no—
139C24×C107—22no—
140C24×C107—22no—
141C24×C107—22no—
142C24×C107—21no—
143C24×C107—41no—
144C24×C107—41no—
145C24×C107—41no—
146C24×C107—41no—
147C24×C107C2×D411yescharacteristic
148C24×C107C2×D411yescharacteristic
149C24×C107C2×D411yescharacteristic
150C2×Q8×C107—21no—
151C2×Q8×C107—21no—
152C2×Q8×C107—21no—
153C2×Q8×C107—21no—
154C2×Q8×C107—21no—
155C2×Q8×C107—21no—
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—42no—
163C2×D4×C107—42no—
164C2×D4×C107—42no—
165C2×D4×C107—42no—
166C2×D4×C107—42no—
167C2×D4×C107—42no—
168C2×D4×C107—42no—
169C2×D4×C107—42no—
170C2×D4×C107—42no—
171C22×C4×C107—21no—
172C22×C4×C107—21no—
173C22×C4×C107—21no—
174C22×C4×C107—21no—
175C22×C4×C107—21no—
176C22×C4×C107—21no—
177C22×C4×C107—21no—
178C22×C4×C107—21no—
179C22×C4×C107—21no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—21no—
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—21no—
196C22×C4×C107—41no—
197C22×C4×C107—41no—
198C22×C4×C107—41no—
199C22×C4×C107—41no—
200C22×C4×C107—41no—
201C22×C4×C107—41no—
202C22×C4×C107—41no—
203C22×C4×C107—41no—
204C22×C4×C107—41no—
205C22×C4×C107—44no—
206C22×C4×C107—44no—
207C22×C4×C107—44no—
208C22×C4×C107—44no—
209C22×C4×C107C2×D411yescharacteristic
210C22×C4×C107C2×D411yescharacteristic
211C22×C4×C107C2×D411yescharacteristic
212C22×C4×C107C2411yescharacteristic
213SD16×C107—44no—
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—21no—
225C2×C8×C107—21no—
226C4⋊C4×C107—21no—
227C4⋊C4×C107—21no—
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×C107—21no—
238C4⋊C4×C107—42no—
239C4⋊C4×C107—42no—
240C4⋊C4×C107—42no—
241C22⋊C4×C107—42no—
242C22⋊C4×C107—42no—
243C22⋊C4×C107—42no—
244C22⋊C4×C107—42no—
245C22⋊C4×C107—42no—
246C22⋊C4×C107—42no—
247C22⋊C4×C107—42no—
248C22⋊C4×C107—42no—
249C22⋊C4×C107—42no—
250C22⋊C4×C107—42no—
251C22⋊C4×C107—42no—
252C22⋊C4×C107—42no—
253C23×C107—21no—
254C23×C107—21no—
255C23×C107—21no—
256C23×C107—21no—
257C23×C107—21no—
258C23×C107—21no—
259C23×C107—21no—
260C23×C107—21no—
261C23×C107—21no—
262C23×C107—21no—
263C23×C107—21no—
264C23×C107—21no—
265C23×C107—21no—
266C23×C107—21no—
267C23×C107—21no—
268C23×C107—21no—
269C23×C107—21no—
270C23×C107—21no—
271C23×C107—44no—
272C23×C107—44no—
273C23×C107—44no—
274C23×C107—44no—
275C23×C107—44no—
276C23×C107—44no—
277C23×C107—44no—
278C23×C107—41no—
279C23×C107—41no—
280C23×C107—41no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—41no—
285C23×C107#13512yes—
286C23×C107AGL(1,ℤ/8)12yes—
287C23×C107#13712yes—
288C23×C107C22×D411yescharacteristic
289Q8×C107—41no—
290Q8×C107—41no—
291Q8×C107—41no—
292Q8×C107—41no—
293D4×C107—41no—
294D4×C107—41no—
295D4×C107—41no—
296D4×C107—41no—
297D4×C107—84no—
298D4×C107—84no—
299D4×C107—84no—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—44no—
310C2×C4×C107—44no—
311C2×C4×C107—44no—
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—41no—
336C2×C4×C107—41no—
337C2×C4×C107—41no—
338C2×C4×C107—41no—
339C2×C4×C107—41no—
340C2×C4×C107—41no—
341C2×C4×C107—41no—
342C2×C4×C107—41no—
343C2×C4×C107—41no—
344C2×C4×C107—41no—
345C2×C4×C107H(5,𝔽2)11yescharacteristic
346C2×C4×C107H(5,𝔽2)11yescharacteristic
347C2×C4×C107H(5,𝔽2)11yescharacteristic
348C2×C4×C107H(5,𝔽2)11yescharacteristic
349C2×C4×C107H(5,𝔽2)11yescharacteristic
350C2×C4×C107H(5,𝔽2)11yescharacteristic
351C8×C107—41no—
352C8×C107—41no—
353C8×C107—41no—
354C8×C107—41no—
355C22×C107—22no—
356C22×C107—22no—
357C22×C107—22no—
358C22×C107—22no—
359C22×C107—22no—
360C22×C107—22no—
361C22×C107—22no—
362C22×C107—22no—
363C22×C107—22no—
364C22×C107—416no—
365C22×C107—41no—
366C22×C107—41no—
367C22×C107—41no—
368C22×C107—41no—
369C22×C107—41no—
370C22×C107—41no—
371C22×C107—41no—
372C22×C107—41no—
373C22×C107—41no—
374C22×C107—41no—
375C22×C107—41no—
376C22×C107—41no—
377C22×C107—81no—
378C22×C107—81no—
379C22×C107—81no—
380C22×C107—81no—
381C22×C107—81no—
382C22×C107—81no—
383C22×C107—81no—
384C22×C107#53411yescharacteristic
385C22×C107#53411yescharacteristic
386C22×C107#53411yescharacteristic
387C22×C107C2×#13511yescharacteristic
388C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C107C2×#13711yescharacteristic
390C22×C107#57511yescharacteristic
391C4×C107—41no—
392C4×C107—41no—
393C4×C107—41no—
394C4×C107—81no—
395C4×C107—81no—
396C4×C107—81no—
397C4×C107—81no—
398C4×C107—81no—
399C4×C107—81no—
400C4×C107—81no—
401C4×C107#56011yescharacteristic
402C4×C107#56011yescharacteristic
403C4×C107#56011yescharacteristic
404C4×C107H(3,𝔽4)11yescharacteristic
405#32709C10711yesmaximal, characteristic, direct product factor, Sylow
406C2×C107—42no—
407C2×C107—42no—
408C2×C107—42no—
409C2×C107—161no—
410C2×C107#281211yescharacteristic
411C2×C107#318811yescharacteristic
412C2×C107#319011yescharacteristic
413C2×C107#319111yescharacteristic
414C2×C107#319311yescharacteristic
415C2×C107#319411yescharacteristic
416C2×C107#319611yescharacteristic
417#2848C2×C10711yescharacteristic, complemented
418#2847C2×C10711yescharacteristic
419#2077C2×C10711yescharacteristic, complemented
420#2076C2×C10711yescharacteristic, complemented
421#2075C2×C10711yescharacteristic, complemented
422#2036C2×C10711yescharacteristic, complemented
423#2036C2×C10711yescharacteristic, complemented
424#2035C2×C10711yescharacteristic, complemented
425#2034C2×C10711yescharacteristic, complemented
426#2033C2×C10711yescharacteristic, complemented
427#2033C2×C10711yescharacteristic, complemented
428#2000C2×C10711yescharacteristic, complemented
429#2000C2×C10711yescharacteristic, complemented
430#2000C2×C10711yescharacteristic, complemented
431#1779C2×C10711yescharacteristic, complemented
432C107#3270911yescharacteristic, direct product factor, Sylow
433C24×C4C22×C10711yescharacteristic
434C22×SD16C22×C10711yescharacteristic, complemented
435C2×C22⋊Q8C22×C10711yescharacteristic
436C2×C22⋊Q8C22×C10711yescharacteristic
437C2×C22⋊Q8C22×C10711yescharacteristic
438C2×#121C22×C10711yescharacteristic
439C2×#121C22×C10711yescharacteristic
440C2×#121C22×C10711yescharacteristic
441C2×#120—21no—
442C2×#107C22×C10711yescharacteristic, complemented
443C2×#107C22×C10711yescharacteristic, complemented
444C2×#106C22×C10711yescharacteristic, complemented
445C2×#103C22×C10711yescharacteristic, complemented
446C2×#103C22×C10711yescharacteristic, complemented
447C2×#103C22×C10711yescharacteristic, complemented
448C2×#102C22×C10711yescharacteristic, complemented
449C2×#102C22×C10711yescharacteristic, complemented
450C2×#102C22×C10711yescharacteristic, complemented
451C2×C22⋊C8C22×C10711yescharacteristic
452C2×C22⋊C8C22×C10711yescharacteristic
453C2×C22⋊C8C22×C10711yescharacteristic
454C2×C22⋊C8C22×C10711yescharacteristic
455C2×C22⋊C8C22×C10711yescharacteristic
456C2×C22⋊C8C22×C10711yescharacteristic
457#386—21no—
458#386—21no—
459#386—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#380C22×C10711yescharacteristic
464#380C22×C10711yescharacteristic
465#380C22×C10711yescharacteristic
466#380C22×C10711yescharacteristic
467#380C22×C10711yescharacteristic
468#380C22×C10711yescharacteristic
469#379—21no—
470#340C22×C10711yescharacteristic, complemented
471#340C22×C10711yescharacteristic, complemented
472#340C22×C10711yescharacteristic, complemented
473#340C22×C10711yescharacteristic, complemented
474#340C22×C10711yescharacteristic, complemented
475#340C22×C10711yescharacteristic, complemented
476C25D4×C10711yescharacteristic
477C22×Q8C23×C10711yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4C23×C10711yescharacteristic
482C23×C4—41no—
483C23×C4—41no—
484C23×C4—41no—
485C23×C4—41no—
486C23×C4—41no—
487C23×C4—41no—
488C23×C4D4×C10711yescharacteristic
489C23×C4D4×C10711yescharacteristic
490C23×C4D4×C10711yescharacteristic
491C23×C4C23×C10711yescharacteristic
492C23×C4C23×C10711yescharacteristic
493C23×C4C23×C10711yescharacteristic
494C2×SD16—41no—
495C2×SD16—41no—
496C2×SD16—41no—
497C22×C8C23×C10711yescharacteristic
498C22×C8C23×C10711yescharacteristic
499C22×C8C23×C10711yescharacteristic
500C22×C8C23×C10711yescharacteristic
501C22⋊Q8—41no—
502C22⋊Q8—41no—
503C22⋊Q8—41no—
504C22⋊Q8—41no—
505C22⋊Q8—41no—
506C22⋊Q8—41no—
507#121—41no—
508#121—41no—
509#121—41no—
510#121—41no—
511#121—41no—
512#121—41no—
513#120—44no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4C23×C10711yescharacteristic
518C2×C4⋊C4C23×C10711yescharacteristic
519C2×C4⋊C4C23×C10711yescharacteristic
520C2×C4⋊C4C23×C10711yescharacteristic
521C2×C4⋊C4C23×C10711yescharacteristic
522C2×C4⋊C4C23×C10711yescharacteristic
523C2×C22⋊C4—21no—
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⋊C4—21no—
534C2×C22⋊C4—21no—
535#107—41no—
536#107—41no—
537#106—41no—
538#103—41no—
539#103—41no—
540#103—41no—
541#102—41no—
542#102—41no—
543#102—41no—
544C22⋊C8—41no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547C22⋊C8—41no—
548C22⋊C8—41no—
549C22⋊C8—41no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—21no—
560C24—41no—
561C24—41no—
562C24—41no—
563C24—41no—
564C24C2×D4×C10711yescharacteristic
565C24C2×D4×C10711yescharacteristic
566C24C2×D4×C10711yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
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—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4C2×D4×C10711yescharacteristic
627C22×C4C2×D4×C10711yescharacteristic
628C22×C4C2×D4×C10711yescharacteristic
629C22×C4C24×C10711yescharacteristic
630SD16—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23#135×C10712yes—
703C23AGL(1,ℤ/8)×C10712yes—
704C23#137×C10712yes—
705C23C22×D4×C10711yescharacteristic
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
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—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4H(5,𝔽2)×C10711yescharacteristic
763C2×C4H(5,𝔽2)×C10711yescharacteristic
764C2×C4H(5,𝔽2)×C10711yescharacteristic
765C2×C4H(5,𝔽2)×C10711yescharacteristic
766C2×C4H(5,𝔽2)×C10711yescharacteristic
767C2×C4H(5,𝔽2)×C10711yescharacteristic
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—416no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22#534×C10711yescharacteristic
802C22#534×C10711yescharacteristic
803C22#534×C10711yescharacteristic
804C22C2×#135×C10711yescharacteristic
805C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
806C22C2×#137×C10711yescharacteristic
807C22#575×C10711yescharacteristic
808C4—41no—
809C4—41no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4#560×C10711yescharacteristic
819C4#560×C10711yescharacteristic
820C4#560×C10711yescharacteristic
821C4H(3,𝔽4)×C10711yescharacteristic
822C2—42no—
823C2—42no—
824C2—42no—
825C2—161no—
826C2C107×#281211yescharacteristic
827C2C107×#318811yescharacteristic
828C2C107×#319011yescharacteristic
829C2C107×#319111yescharacteristic
830C2C107×#319311yescharacteristic
831C2C107×#319411yescharacteristic
832C2C107×#319611yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C24×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2848C2semidirect
3. C107×#2077C2semidirect
4. C107×#2076C2semidirect
5. C107×#2075C2semidirect
6. C107×#2036C2semidirect
7. C107×#2036C2semidirect
8. C107×#2035C2semidirect
9. C107×#2034C2semidirect
10. C107×#2033C2semidirect
11. C107×#2033C2semidirect
12. C107×#2000C2semidirect
13. C107×#2000C2semidirect
14. C107×#2000C2semidirect
15. C107×#1779C2semidirect
17. C22×SD16×C107C22semidirect
25. C2×#107×C107C22semidirect
26. C2×#107×C107C22semidirect
27. C2×#106×C107C22semidirect
28. C2×#103×C107C22semidirect
29. C2×#103×C107C22semidirect
30. C2×#103×C107C22semidirect
31. C2×#102×C107C22semidirect
32. C2×#102×C107C22semidirect
33. C2×#102×C107C22semidirect
53. #340×C107C22semidirect
54. #340×C107C22semidirect
55. #340×C107C22semidirect
56. #340×C107C22semidirect
57. #340×C107C22semidirect
58. #340×C107C22semidirect
405. #32709C107direct (N × H)
417. #2848C2×C107semidirect
419. #2077C2×C107semidirect
420. #2076C2×C107semidirect
421. #2075C2×C107semidirect
422. #2036C2×C107semidirect
423. #2036C2×C107semidirect
424. #2035C2×C107semidirect
425. #2034C2×C107semidirect
426. #2033C2×C107semidirect
427. #2033C2×C107semidirect
428. #2000C2×C107semidirect
429. #2000C2×C107semidirect
430. #2000C2×C107semidirect
431. #1779C2×C107semidirect
432. C107#32709direct (N × H)
434. C22×SD16C22×C107semidirect
442. C2×#107C22×C107semidirect
443. C2×#107C22×C107semidirect
444. C2×#106C22×C107semidirect
445. C2×#103C22×C107semidirect
446. C2×#103C22×C107semidirect
447. C2×#103C22×C107semidirect
448. C2×#102C22×C107semidirect
449. C2×#102C22×C107semidirect
450. C2×#102C22×C107semidirect
470. #340C22×C107semidirect
471. #340C22×C107semidirect
472. #340C22×C107semidirect
473. #340C22×C107semidirect
474. #340C22×C107semidirect
475. #340C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#28482
C107×#28472
C107×#20772
C107×#20762
C107×#20752
C107×#20362
C107×#20352
C107×#20342
C107×#20332
C107×#20002
C107×#17792
#32709107