Finite Group Databasebeta

← C107×#24245 #41050209

Subgroups — C107×#24245 #41050209

Order 27392.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C107C211yesmaximal, characteristic, complemented
2C2×#463×C107C211yesmaximal, characteristic, complemented
3C2×#449×C107C211yesmaximal, characteristic, complemented
4C2×#447×C107C211yesmaximal, characteristic, complemented
5C2×C4×D8×C107C211yesmaximal, characteristic, complemented
6C107×#2535C211yesmaximal, characteristic, complemented
7C107×#2036C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1958C211yesmaximal, characteristic, complemented
12C107×#1954C211yesmaximal, characteristic, complemented
13C107×#1804C211yesmaximal, characteristic, complemented
14C107×#1788C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C23×D4×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic, complemented
19C22×D8×C107C2211yescharacteristic
20C22×D8×C107C2211yescharacteristic
21#546×C107—24no—
22#546×C107—24no—
23C2×#124×C107C2211yescharacteristic
24C2×#123×C107—21no—
25C2×C22⋊Q8×C107C2211yescharacteristic
26C2×#121×C107—21no—
27C2×#121×C107C2211yescharacteristic
28C2×#121×C107C2211yescharacteristic
29C2×#121×C107C2211yescharacteristic, complemented
30C2×#120×C107—21no—
31C2×C4×D4×C107C2211yescharacteristic
32C2×C4×D4×C107C2211yescharacteristic
33C2×C4×D4×C107C2211yescharacteristic, complemented
34C22×C22⋊C4×C107—21no—
35#463×C107—24no—
36#449×C107—24no—
37#447×C107—24no—
38C4×D8×C107—24no—
39C2×#107×C107C2211yescharacteristic, complemented
40C2×C4⋊C8×C107C2211yescharacteristic, complemented
41C2×#103×C107C2211yescharacteristic, complemented
42C2×#103×C107C2211yescharacteristic, complemented
43C2×#103×C107C2211yescharacteristic, complemented
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic
46C2×#102×C107C2211yescharacteristic
47C2×#102×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49C2×#102×C107C2211yescharacteristic
50C2×#102×C107C2211yescharacteristic, complemented
51C2×C22⋊C8×C107C2211yescharacteristic
52C2×C22⋊C8×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic, complemented
54C2×C22⋊C8×C107C2211yescharacteristic, complemented
55C2×C4×C8×C107C2211yescharacteristic, complemented
56#397×C107—21no—
57#392×C107—21no—
58#386×C107—21no—
59#386×C107—21no—
60#382×C107C2211yescharacteristic, complemented
61#380×C107C2211yescharacteristic
62#380×C107C2211yescharacteristic, complemented
63#340×C107C2211yescharacteristic, complemented
64#340×C107C2211yescharacteristic, complemented
65C25×C107—21no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—22no—
70C2×#41×C107—41no—
71C2×#41×C107—41no—
72C22×Q8×C107C2311yescharacteristic
73C22×D4×C107—21no—
74C22×D4×C107—21no—
75C22×D4×C107—22no—
76C22×D4×C107—22no—
77C22×D4×C107—22no—
78C22×D4×C107—22no—
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107—41no—
83C22×D4×C107—41no—
84C22×D4×C107D411yescharacteristic
85C22×D4×C107C2311yescharacteristic
86C22×D4×C107C2311yescharacteristic
87C22×D4×C107C2311yescharacteristic
88C23×C4×C107—21no—
89C23×C4×C107—21no—
90C23×C4×C107—21no—
91C23×C4×C107C2311yescharacteristic
92C23×C4×C107C2311yescharacteristic
93C2×SD16×C107—22no—
94C2×SD16×C107—22no—
95C2×SD16×C107—41no—
96C2×D8×C107—22no—
97C2×D8×C107—22no—
98C2×D8×C107—22no—
99C2×D8×C107—22no—
100C2×D8×C107—41no—
101C2×D8×C107D414yescomplemented
102C22×C8×C107C2311yescharacteristic
103C22×C8×C107C2311yescharacteristic
104C22×C8×C107C2311yescharacteristic
105C22×C8×C107C2311yescharacteristic
106#124×C107—22no—
107#124×C107D414yescomplemented
108#123×C107—28no—
109C22⋊Q8×C107—22no—
110C22⋊Q8×C107—22no—
111#121×C107—28no—
112#121×C107—22no—
113#121×C107—22no—
114#121×C107—22no—
115#121×C107—22no—
116#121×C107—41no—
117#121×C107—41no—
118#120×C107—28no—
119C4×D4×C107—22no—
120C4×D4×C107—22no—
121C4×D4×C107—22no—
122C4×D4×C107—22no—
123C4×D4×C107—22no—
124C4×D4×C107D414yescomplemented
125C2×C4⋊C4×C107—21no—
126C2×C4⋊C4×C107D411yescharacteristic
127C2×C4⋊C4×C107C2311yescharacteristic
128C2×C4⋊C4×C107C2311yescharacteristic
129C2×C4⋊C4×C107C2311yescharacteristic
130C2×C4⋊C4×C107C2311yescharacteristic
131C2×C22⋊C4×C107—28no—
132C2×C22⋊C4×C107—21no—
133C2×C22⋊C4×C107—21no—
134C2×C22⋊C4×C107—21no—
135C2×C22⋊C4×C107—21no—
136C2×C22⋊C4×C107—21no—
137C2×C22⋊C4×C107—21no—
138C2×C22⋊C4×C107—21no—
139C2×C22⋊C4×C107—21no—
140C2×C22⋊C4×C107—21no—
141C2×C22⋊C4×C107—21no—
142C2×C22⋊C4×C107D411yescharacteristic
143C2×C22⋊C4×C107D411yescharacteristic
144C2×C42×C107C2311yescharacteristic
145#107×C107—22no—
146C4⋊C8×C107—22no—
147#103×C107—22no—
148#103×C107—22no—
149#103×C107—41no—
150#102×C107—22no—
151#102×C107—22no—
152#102×C107—22no—
153#102×C107—22no—
154#102×C107—22no—
155#102×C107—22no—
156#102×C107—41no—
157C22⋊C8×C107—22no—
158C22⋊C8×C107—22no—
159C22⋊C8×C107—41no—
160C22⋊C8×C107—41no—
161C4×C8×C107—22no—
162#95×C107—21no—
163#95×C107—21no—
164#95×C107—21no—
165#95×C107—21no—
166C24×C107—21no—
167C24×C107—24no—
168C24×C107—21no—
169C24×C107—21no—
170C24×C107—42no—
171C24×C107—42no—
172C24×C107—42no—
173C24×C107—42no—
174C24×C107—81no—
175C24×C107—81no—
176C24×C107C2×D411yescharacteristic
177C24×C107C2×D411yescharacteristic
178#41×C107—44no—
179#41×C107—44no—
180#41×C107—44no—
181#41×C107—44no—
182C2×Q8×C107—21no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107C2×D412yes—
188C2×D4×C107—24no—
189C2×D4×C107—24no—
190C2×D4×C107—22no—
191C2×D4×C107—24no—
192C2×D4×C107—22no—
193C2×D4×C107—21no—
194C2×D4×C107—21no—
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—41no—
207C2×D4×C107—42no—
208C2×D4×C107—42no—
209C2×D4×C107—44no—
210C2×D4×C107—44no—
211C2×D4×C107—44no—
212C2×D4×C107—42no—
213C2×D4×C107—42no—
214C2×D4×C107—44no—
215C2×D4×C107—42no—
216C2×D4×C107—42no—
217C2×D4×C107—42no—
218C2×D4×C107—42no—
219C2×D4×C107—81no—
220C2×D4×C107—81no—
221C2×D4×C107—81no—
222C2×D4×C107—81no—
223C2×D4×C107C2×D412yes—
224C2×D4×C107C2×D412yes—
225C2×D4×C107C2×D412yes—
226C2×D4×C107C2×D412yes—
227C2×D4×C107#4112yes—
228C22×C4×C107—24no—
229C22×C4×C107—21no—
230C22×C4×C107—21no—
231C22×C4×C107—21no—
232C22×C4×C107—21no—
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—21no—
241C22×C4×C107—21no—
242C22×C4×C107—21no—
243C22×C4×C107—24no—
244C22×C4×C107—21no—
245C22×C4×C107—21no—
246C22×C4×C107—21no—
247C22×C4×C107—42no—
248C22×C4×C107—42no—
249C22×C4×C107—42no—
250C22×C4×C107—81no—
251C22×C4×C107—81no—
252C22×C4×C107—81no—
253C22×C4×C107—81no—
254C22×C4×C107C2×D411yescharacteristic
255C22×C4×C107C2×D411yescharacteristic
256C22×C4×C107C2×D411yescharacteristic
257C22×C4×C107C2×D411yescharacteristic
258C22×C4×C107C2411yescharacteristic
259SD16×C107—44no—
260D8×C107—28no—
261D8×C107—44no—
262C2×C8×C107—21no—
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—21no—
270C2×C8×C107—21no—
271C2×C8×C107—21no—
272C2×C8×C107—21no—
273C2×C8×C107C2×D412yes—
274C4⋊C4×C107—24no—
275C4⋊C4×C107—22no—
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×C107C2×D412yes—
284C22⋊C4×C107—24no—
285C22⋊C4×C107—24no—
286C22⋊C4×C107—22no—
287C22⋊C4×C107—24no—
288C22⋊C4×C107—24no—
289C22⋊C4×C107—24no—
290C22⋊C4×C107—22no—
291C22⋊C4×C107—42no—
292C22⋊C4×C107—42no—
293C22⋊C4×C107—42no—
294C22⋊C4×C107—81no—
295C22⋊C4×C107—81no—
296C42×C107C2×D412yes—
297C42×C107C2×D412yes—
298C23×C107—21no—
299C23×C107—22no—
300C23×C107—21no—
301C23×C107—22no—
302C23×C107—21no—
303C23×C107—22no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—21no—
307C23×C107—22no—
308C23×C107—21no—
309C23×C107—22no—
310C23×C107—21no—
311C23×C107—21no—
312C23×C107—21no—
313C23×C107—21no—
314C23×C107—21no—
315C23×C107—21no—
316C23×C107—48no—
317C23×C107—48no—
318C23×C107—41no—
319C23×C107—41no—
320C23×C107—41no—
321C23×C107—41no—
322C23×C107—41no—
323C23×C107—41no—
324C23×C107—41no—
325C23×C107—41no—
326C23×C107—41no—
327C23×C107—41no—
328C23×C107—41no—
329C23×C107—41no—
330C23×C107—41no—
331C23×C107—41no—
332C23×C107—41no—
333C23×C107—41no—
334C23×C107—84no—
335C23×C107—84no—
336C23×C107—84no—
337C23×C107—84no—
338C23×C107—84no—
339C23×C107#13512yes—
340C23×C107C22×D411yescharacteristic
341Q8×C107—22no—
342Q8×C107—22no—
343Q8×C107—41no—
344Q8×C107—41no—
345D4×C107—22no—
346D4×C107—22no—
347D4×C107—22no—
348D4×C107—22no—
349D4×C107—22no—
350D4×C107—22no—
351D4×C107—22no—
352D4×C107—44no—
353D4×C107—48no—
354D4×C107—48no—
355D4×C107—41no—
356D4×C107—41no—
357D4×C107—41no—
358D4×C107—41no—
359D4×C107—84no—
360D4×C107—84no—
361D4×C107—84no—
362D4×C107#12114yes—
363C2×C4×C107—21no—
364C2×C4×C107—21no—
365C2×C4×C107—21no—
366C2×C4×C107—21no—
367C2×C4×C107—22no—
368C2×C4×C107—21no—
369C2×C4×C107—22no—
370C2×C4×C107—21no—
371C2×C4×C107—21no—
372C2×C4×C107—21no—
373C2×C4×C107—21no—
374C2×C4×C107—21no—
375C2×C4×C107—48no—
376C2×C4×C107—41no—
377C2×C4×C107—41no—
378C2×C4×C107—41no—
379C2×C4×C107—41no—
380C2×C4×C107—41no—
381C2×C4×C107—41no—
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—41no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—41no—
392C2×C4×C107—41no—
393C2×C4×C107—41no—
394C2×C4×C107—41no—
395C2×C4×C107—41no—
396C2×C4×C107—41no—
397C2×C4×C107—84no—
398C2×C4×C107—84no—
399C2×C4×C107#12012yes—
400C2×C4×C107#12012yes—
401C2×C4×C107C22×D411yescharacteristic
402C2×C4×C107C22×D411yescharacteristic
403C2×C4×C107C22×D411yescharacteristic
404C2×C4×C107C2×#4111yescharacteristic
405C2×C4×C107H(5,𝔽2)11yescharacteristic
406C2×C4×C107H(5,𝔽2)11yescharacteristic
407C8×C107—22no—
408C8×C107—41no—
409C8×C107—41no—
410C8×C107—41no—
411C22×C107—24no—
412C22×C107—22no—
413C22×C107—22no—
414C22×C107—22no—
415C22×C107—41no—
416C22×C107—42no—
417C22×C107—42no—
418C22×C107—41no—
419C22×C107—41no—
420C22×C107—42no—
421C22×C107—42no—
422C22×C107—42no—
423C22×C107—41no—
424C22×C107—42no—
425C22×C107—41no—
426C22×C107—42no—
427C22×C107—42no—
428C22×C107—41no—
429C22×C107—42no—
430C22×C107—41no—
431C22×C107—42no—
432C22×C107—41no—
433C22×C107—42no—
434C22×C107—42no—
435C22×C107—41no—
436C22×C107—41no—
437C22×C107—41no—
438C22×C107—816no—
439C22×C107—81no—
440C22×C107—81no—
441C22×C107—81no—
442C22×C107—81no—
443C22×C107—81no—
444C22×C107—81no—
445C22×C107—81no—
446C22×C107—81no—
447C22×C107C2×#12011yescharacteristic
448C22×C107D4211yescharacteristic
449C22×C107#54611yescharacteristic
450C22×C107C2×#13511yescharacteristic
451C22×C107#57511yescharacteristic
452C22×C107#57611yescharacteristic
453C22×C107#57611yescharacteristic
454C4×C107—22no—
455C4×C107—22no—
456C4×C107—41no—
457C4×C107—41no—
458C4×C107—42no—
459C4×C107—42no—
460C4×C107—81no—
461C4×C107—81no—
462C4×C107—81no—
463C4×C107C2×#12111yescharacteristic
464C4×C107#53511yescharacteristic
465C4×C107D4211yescharacteristic
466C4×C107#54611yescharacteristic
467#24245C10711yesmaximal, characteristic, direct product factor, Sylow
468C2×C107—42no—
469C2×C107—44no—
470C2×C107—81no—
471C2×C107—82no—
472C2×C107—82no—
473C2×C107#240811yescharacteristic
474C2×C107#300211yescharacteristic
475C2×C107#300811yescharacteristic
476C2×C107#327311yescharacteristic
477C2×C107#328011yescharacteristic
478C2×C107#329711yescharacteristic
479C2×C107#332211yescharacteristic
480C2×#546C2×C10711yescharacteristic, complemented
481C2×#463C2×C10711yescharacteristic, complemented
482C2×#449C2×C10711yescharacteristic, complemented
483C2×#447C2×C10711yescharacteristic, complemented
484C2×C4×D8C2×C10711yescharacteristic, complemented
485#2535C2×C10711yescharacteristic, complemented
486#2036C2×C10711yescharacteristic, complemented
487#2033C2×C10711yescharacteristic, complemented
488#2000C2×C10711yescharacteristic, complemented
489#1999C2×C10711yescharacteristic, complemented
490#1958C2×C10711yescharacteristic, complemented
491#1954C2×C10711yescharacteristic, complemented
492#1804C2×C10711yescharacteristic, complemented
493#1788C2×C10711yescharacteristic, complemented
494#1786C2×C10711yescharacteristic, complemented
495C107#2424511yescharacteristic, direct product factor, Sylow
496C22×#41C22×C10711yescharacteristic
497C23×D4C22×C10711yescharacteristic
498C22×SD16C22×C10711yescharacteristic, complemented
499C22×D8C22×C10711yescharacteristic
500C22×D8C22×C10711yescharacteristic
501#546—24no—
502#546—24no—
503C2×#124C22×C10711yescharacteristic
504C2×#123—21no—
505C2×C22⋊Q8C22×C10711yescharacteristic
506C2×#121—21no—
507C2×#121C22×C10711yescharacteristic
508C2×#121C22×C10711yescharacteristic
509C2×#121C22×C10711yescharacteristic, complemented
510C2×#120—21no—
511C2×C4×D4C22×C10711yescharacteristic
512C2×C4×D4C22×C10711yescharacteristic
513C2×C4×D4C22×C10711yescharacteristic, complemented
514C22×C22⋊C4—21no—
515#463—24no—
516#449—24no—
517#447—24no—
518C4×D8—24no—
519C2×#107C22×C10711yescharacteristic, complemented
520C2×C4⋊C8C22×C10711yescharacteristic, complemented
521C2×#103C22×C10711yescharacteristic, complemented
522C2×#103C22×C10711yescharacteristic, complemented
523C2×#103C22×C10711yescharacteristic, complemented
524C2×#102C22×C10711yescharacteristic
525C2×#102C22×C10711yescharacteristic
526C2×#102C22×C10711yescharacteristic
527C2×#102C22×C10711yescharacteristic
528C2×#102C22×C10711yescharacteristic
529C2×#102C22×C10711yescharacteristic
530C2×#102C22×C10711yescharacteristic, complemented
531C2×C22⋊C8C22×C10711yescharacteristic
532C2×C22⋊C8C22×C10711yescharacteristic
533C2×C22⋊C8C22×C10711yescharacteristic, complemented
534C2×C22⋊C8C22×C10711yescharacteristic, complemented
535C2×C4×C8C22×C10711yescharacteristic, complemented
536#397—21no—
537#392—21no—
538#386—21no—
539#386—21no—
540#382C22×C10711yescharacteristic, complemented
541#380C22×C10711yescharacteristic
542#380C22×C10711yescharacteristic, complemented
543#340C22×C10711yescharacteristic, complemented
544#340C22×C10711yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C10711yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C10711yescharacteristic
565C22×D4C23×C10711yescharacteristic
566C22×D4C23×C10711yescharacteristic
567C22×D4C23×C10711yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C10711yescharacteristic
572C23×C4C23×C10711yescharacteristic
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—41no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8D4×C10714yescomplemented
582C22×C8C23×C10711yescharacteristic
583C22×C8C23×C10711yescharacteristic
584C22×C8C23×C10711yescharacteristic
585C22×C8C23×C10711yescharacteristic
586#124—22no—
587#124D4×C10714yescomplemented
588#123—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591#121—28no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121—41no—
598#120—28no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4D4×C10714yescomplemented
605C2×C4⋊C4—21no—
606C2×C4⋊C4D4×C10711yescharacteristic
607C2×C4⋊C4C23×C10711yescharacteristic
608C2×C4⋊C4C23×C10711yescharacteristic
609C2×C4⋊C4C23×C10711yescharacteristic
610C2×C4⋊C4C23×C10711yescharacteristic
611C2×C22⋊C4—28no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4D4×C10711yescharacteristic
623C2×C22⋊C4D4×C10711yescharacteristic
624C2×C42C23×C10711yescharacteristic
625#107—22no—
626C4⋊C8—22no—
627#103—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636#102—41no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8—41no—
640C22⋊C8—41no—
641C4×C8—22no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C10711yescharacteristic
657C24C2×D4×C10711yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C10712yes—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C10712yes—
704C2×D4C2×D4×C10712yes—
705C2×D4C2×D4×C10712yes—
706C2×D4C2×D4×C10712yes—
707C2×D4#41×C10712yes—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4—81no—
734C22×C4C2×D4×C10711yescharacteristic
735C22×C4C2×D4×C10711yescharacteristic
736C22×C4C2×D4×C10711yescharacteristic
737C22×C4C2×D4×C10711yescharacteristic
738C22×C4C24×C10711yescharacteristic
739SD16—44no—
740D8—28no—
741D8—44no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8C2×D4×C10712yes—
754C4⋊C4—24no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4C2×D4×C10712yes—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—22no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42C2×D4×C10712yes—
777C42C2×D4×C10712yes—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#135×C10712yes—
820C23C22×D4×C10711yescharacteristic
821Q8—22no—
822Q8—22no—
823Q8—41no—
824Q8—41no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—44no—
833D4—48no—
834D4—48no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#121×C10714yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4#120×C10712yes—
880C2×C4#120×C10712yes—
881C2×C4C22×D4×C10711yescharacteristic
882C2×C4C22×D4×C10711yescharacteristic
883C2×C4C22×D4×C10711yescharacteristic
884C2×C4C2×#41×C10711yescharacteristic
885C2×C4H(5,𝔽2)×C10711yescharacteristic
886C2×C4H(5,𝔽2)×C10711yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—41no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—42no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C10711yescharacteristic
928C22D42×C10711yescharacteristic
929C22#546×C10711yescharacteristic
930C22C2×#135×C10711yescharacteristic
931C22#575×C10711yescharacteristic
932C22#576×C10711yescharacteristic
933C22#576×C10711yescharacteristic
934C4—22no—
935C4—22no—
936C4—41no—
937C4—41no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×#121×C10711yescharacteristic
944C4#535×C10711yescharacteristic
945C4D42×C10711yescharacteristic
946C4#546×C10711yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—82no—
952C2C107×#240811yescharacteristic
953C2C107×#300211yescharacteristic
954C2C107×#300811yescharacteristic
955C2C107×#327311yescharacteristic
956C2C107×#328011yescharacteristic
957C2C107×#329711yescharacteristic
958C2C107×#332211yescharacteristic
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×#546×C107C2semidirect
2. C2×#463×C107C2semidirect
3. C2×#449×C107C2semidirect
4. C2×#447×C107C2semidirect
5. C2×C4×D8×C107C2semidirect
6. C107×#2535C2semidirect
7. C107×#2036C2semidirect
8. C107×#2033C2semidirect
9. C107×#2000C2semidirect
10. C107×#1999C2semidirect
11. C107×#1958C2semidirect
12. C107×#1954C2semidirect
13. C107×#1804C2semidirect
14. C107×#1788C2semidirect
15. C107×#1786C2semidirect
18. C22×SD16×C107C22semidirect
29. C2×#121×C107C22semidirect
33. C2×C4×D4×C107C22semidirect
39. C2×#107×C107C22semidirect
40. C2×C4⋊C8×C107C22semidirect
41. C2×#103×C107C22semidirect
42. C2×#103×C107C22semidirect
43. C2×#103×C107C22semidirect
50. C2×#102×C107C22semidirect
53. C2×C22⋊C8×C107C22semidirect
54. C2×C22⋊C8×C107C22semidirect
55. C2×C4×C8×C107C22semidirect
60. #382×C107C22semidirect
62. #380×C107C22semidirect
63. #340×C107C22semidirect
64. #340×C107C22semidirect
101. C2×D8×C107D4semidirect
107. #124×C107D4semidirect
124. C4×D4×C107D4semidirect
467. #24245C107direct (N × H)
480. C2×#546C2×C107semidirect
481. C2×#463C2×C107semidirect
482. C2×#449C2×C107semidirect
483. C2×#447C2×C107semidirect
484. C2×C4×D8C2×C107semidirect
485. #2535C2×C107semidirect
486. #2036C2×C107semidirect
487. #2033C2×C107semidirect
488. #2000C2×C107semidirect
489. #1999C2×C107semidirect
490. #1958C2×C107semidirect
491. #1954C2×C107semidirect
492. #1804C2×C107semidirect
493. #1788C2×C107semidirect
494. #1786C2×C107semidirect
495. C107#24245direct (N × H)
498. C22×SD16C22×C107semidirect
509. C2×#121C22×C107semidirect
513. C2×C4×D4C22×C107semidirect
519. C2×#107C22×C107semidirect
520. C2×C4⋊C8C22×C107semidirect
521. C2×#103C22×C107semidirect
522. C2×#103C22×C107semidirect
523. C2×#103C22×C107semidirect
530. C2×#102C22×C107semidirect
533. C2×C22⋊C8C22×C107semidirect
534. C2×C22⋊C8C22×C107semidirect
535. C2×C4×C8C22×C107semidirect
540. #382C22×C107semidirect
542. #380C22×C107semidirect
543. #340C22×C107semidirect
544. #340C22×C107semidirect
581. C2×D8D4×C107semidirect
587. #124D4×C107semidirect
604. C4×D4D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1072
C2×#463×C1072
C2×#449×C1072
C2×#447×C1072
C2×C4×D8×C1072
C107×#25352
C107×#20362
C107×#20332
C107×#20002
C107×#19992
C107×#19582
C107×#19542
C107×#18042
C107×#17882
C107×#17862
#24245107