Finite Group Databasebeta

← C107×#24436 #41050400

Subgroups — C107×#24436 #41050400

Order 27392.

1582 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C107C211yesmaximal, characteristic
2C2×#465×C107C211yesmaximal, characteristic, complemented
3C2×#452×C107C211yesmaximal, characteristic, complemented
4C2×#450×C107C211yesmaximal, characteristic, complemented
5C2×#416×C107C211yesmaximal, characteristic, complemented
6C107×#2415C211yesmaximal, characteristic, complemented
7C107×#2042C211yesmaximal, characteristic, complemented
8C107×#2035C211yesmaximal, characteristic, complemented
9C107×#2015C211yesmaximal, characteristic, complemented
10C107×#2001C211yesmaximal, characteristic, complemented
11C107×#1877C211yesmaximal, characteristic, complemented
12C107×#1875C211yesmaximal, characteristic, complemented
13C107×#1869C211yesmaximal, characteristic, complemented
14C107×#1864C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C23×D4×C107C2211yescharacteristic
18C22×Q16×C107C2211yescharacteristic, complemented
19C22×SD16×C107C2211yescharacteristic
20C22×SD16×C107C2211yescharacteristic
21C23×C8×C107C2211yescharacteristic, complemented
22#546×C107—24no—
23#546×C107—24no—
24C2×#124×C107C2211yescharacteristic
25C2×#123×C107—21no—
26C2×C22⋊Q8×C107C2211yescharacteristic
27C2×C22⋊Q8×C107C2211yescharacteristic
28C2×C22⋊Q8×C107C2211yescharacteristic, complemented
29C2×#121×C107—21no—
30C2×#121×C107C2211yescharacteristic
31C2×#120×C107—21no—
32C2×C4×D4×C107C2211yescharacteristic
33C2×C4×D4×C107C2211yescharacteristic
34C2×#117×C107C2211yescharacteristic, complemented
35C22×C22⋊C4×C107—21no—
36#465×C107—24no—
37#452×C107—24no—
38#450×C107—24no—
39C2×#106×C107C2211yescharacteristic, complemented
40#416×C107—24no—
41C2×#103×C107C2211yescharacteristic, complemented
42C2×#103×C107C2211yescharacteristic, complemented
43C2×#103×C107C2211yescharacteristic, complemented
44C2×#103×C107C2211yescharacteristic, complemented
45C2×#102×C107C2211yescharacteristic
46C2×#102×C107C2211yescharacteristic
47C2×#102×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49C2×#102×C107C2211yescharacteristic
50C2×#102×C107C2211yescharacteristic
51C2×C22⋊C8×C107C2211yescharacteristic
52C2×C22⋊C8×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic, complemented
54#397×C107—21no—
55#394×C107—21no—
56#391×C107C2211yescharacteristic, complemented
57#389×C107—21no—
58#389×C107C2211yescharacteristic, complemented
59#388×C107—21no—
60#380×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic, complemented
62#340×C107C2211yescharacteristic, complemented
63#336×C107C2211yescharacteristic, complemented
64#336×C107C2211yescharacteristic, complemented
65C25×C107—21no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—41no—
70C2×#41×C107—41no—
71C2×#41×C107D414yes—
72C22×Q8×C107C2311yescharacteristic
73C22×Q8×C107C2311yescharacteristic
74C22×D4×C107—21no—
75C22×D4×C107—21no—
76C22×D4×C107—22no—
77C22×D4×C107—22no—
78C22×D4×C107—22no—
79C22×D4×C107—22no—
80C22×D4×C107—21no—
81C22×D4×C107—41no—
82C22×D4×C107—41no—
83C22×D4×C107D411yescharacteristic
84C22×D4×C107C2311yescharacteristic
85C22×D4×C107C2311yescharacteristic
86C23×C4×C107—21no—
87C23×C4×C107—21no—
88C23×C4×C107C2311yescharacteristic
89C23×C4×C107C2311yescharacteristic
90C2×Q16×C107—22no—
91C2×Q16×C107—41no—
92C2×Q16×C107—41no—
93C2×SD16×C107—22no—
94C2×SD16×C107—22no—
95C2×SD16×C107—22no—
96C2×SD16×C107—22no—
97C2×SD16×C107—22no—
98C2×SD16×C107—41no—
99C22×C8×C107—22no—
100C22×C8×C107—22no—
101C22×C8×C107—41no—
102C22×C8×C107C2311yescharacteristic
103C22×C8×C107C2311yescharacteristic
104C22×C8×C107C2311yescharacteristic
105C22×C8×C107C2311yescharacteristic
106#124×C107—22no—
107#124×C107—22no—
108#123×C107—28no—
109C22⋊Q8×C107—22no—
110C22⋊Q8×C107—22no—
111C22⋊Q8×C107—22no—
112C22⋊Q8×C107—22no—
113C22⋊Q8×C107—22no—
114C22⋊Q8×C107—41no—
115#121×C107—28no—
116#121×C107—22no—
117#121×C107D414yes—
118#120×C107—28no—
119C4×D4×C107—22no—
120C4×D4×C107—22no—
121C4×D4×C107—22no—
122C4×D4×C107—22no—
123#117×C107—22no—
124#117×C107—41no—
125C2×C4⋊C4×C107—21no—
126C2×C4⋊C4×C107—21no—
127C2×C4⋊C4×C107—21no—
128C2×C4⋊C4×C107—21no—
129C2×C4⋊C4×C107D411yescharacteristic
130C2×C4⋊C4×C107C2311yescharacteristic
131C2×C4⋊C4×C107C2311yescharacteristic
132C2×C4⋊C4×C107C2311yescharacteristic
133C2×C4⋊C4×C107C2311yescharacteristic
134C2×C22⋊C4×C107—28no—
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×C107—21no—
143C2×C22⋊C4×C107—21no—
144C2×C22⋊C4×C107D411yescharacteristic
145C2×C22⋊C4×C107D411yescharacteristic
146C2×C42×C107—21no—
147C2×C42×C107C2311yescharacteristic
148#106×C107—22no—
149#103×C107—22no—
150#103×C107—22no—
151#103×C107—22no—
152#103×C107—22no—
153#102×C107—22no—
154#102×C107—22no—
155#102×C107—22no—
156#102×C107—22no—
157#102×C107—41no—
158#102×C107D414yescomplemented
159C22⋊C8×C107—22no—
160C22⋊C8×C107—22no—
161C22⋊C8×C107—41no—
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—42no—
170C24×C107—42no—
171C24×C107—42no—
172C24×C107—42no—
173C24×C107—81no—
174C24×C107—81no—
175C24×C107C2×D411yescharacteristic
176C24×C107C2×D411yescharacteristic
177#41×C107—28no—
178#41×C107—44no—
179#41×C107—44no—
180#41×C107—44no—
181C2×Q8×C107—21no—
182C2×Q8×C107—21no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107—21no—
188C2×Q8×C107—21no—
189C2×Q8×C107—21no—
190C2×Q8×C107—21no—
191C2×Q8×C107—21no—
192C2×Q8×C107C2×D412yes—
193C2×D4×C107—24no—
194C2×D4×C107—22no—
195C2×D4×C107—24no—
196C2×D4×C107—22no—
197C2×D4×C107—24no—
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—81no—
216C2×D4×C107—81no—
217C2×D4×C107C2×D412yes—
218C2×D4×C107C2×D412yes—
219C2×D4×C107C2×D412yes—
220C2×D4×C107#4112yes—
221C22×C4×C107—21no—
222C22×C4×C107—21no—
223C22×C4×C107—21no—
224C22×C4×C107—21no—
225C22×C4×C107—21no—
226C22×C4×C107—21no—
227C22×C4×C107—21no—
228C22×C4×C107—24no—
229C22×C4×C107—24no—
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—42no—
240C22×C4×C107—42no—
241C22×C4×C107—81no—
242C22×C4×C107—81no—
243C22×C4×C107C2×D411yescharacteristic
244C22×C4×C107C2×D411yescharacteristic
245C22×C4×C107C2×D411yescharacteristic
246C22×C4×C107C2×D411yescharacteristic
247C22×C4×C107C2×D412yes—
248C22×C4×C107C2×D412yes—
249C22×C4×C107C2411yescharacteristic
250Q16×C107—44no—
251SD16×C107—44no—
252SD16×C107—44no—
253C2×C8×C107—21no—
254C2×C8×C107—21no—
255C2×C8×C107—21no—
256C2×C8×C107—21no—
257C2×C8×C107—21no—
258C2×C8×C107—21no—
259C2×C8×C107—21no—
260C2×C8×C107—21no—
261C2×C8×C107—21no—
262C2×C8×C107—21no—
263C2×C8×C107—21no—
264C2×C8×C107—44no—
265C2×C8×C107C2×D412yes—
266C4⋊C4×C107—24no—
267C4⋊C4×C107—22no—
268C4⋊C4×C107—21no—
269C4⋊C4×C107—21no—
270C4⋊C4×C107—21no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—42no—
275C4⋊C4×C107—42no—
276C4⋊C4×C107—42no—
277C4⋊C4×C107C2×D412yes—
278C4⋊C4×C107C2×D412yes—
279C22⋊C4×C107—24no—
280C22⋊C4×C107—24no—
281C22⋊C4×C107—24no—
282C22⋊C4×C107—24no—
283C22⋊C4×C107—22no—
284C22⋊C4×C107—22no—
285C22⋊C4×C107—24no—
286C22⋊C4×C107—42no—
287C22⋊C4×C107—42no—
288C22⋊C4×C107—42no—
289C22⋊C4×C107—42no—
290C42×C107—21no—
291C42×C107—21no—
292C42×C107—42no—
293C23×C107—21no—
294C23×C107—22no—
295C23×C107—21no—
296C23×C107—21no—
297C23×C107—22no—
298C23×C107—21no—
299C23×C107—21no—
300C23×C107—22no—
301C23×C107—21no—
302C23×C107—21no—
303C23×C107—21no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—21no—
307C23×C107—21no—
308C23×C107—22no—
309C23×C107—48no—
310C23×C107—48no—
311C23×C107—41no—
312C23×C107—41no—
313C23×C107—41no—
314C23×C107—41no—
315C23×C107—41no—
316C23×C107—41no—
317C23×C107—41no—
318C23×C107—41no—
319C23×C107—41no—
320C23×C107—41no—
321C23×C107—84no—
322C23×C107—84no—
323C23×C107—84no—
324C23×C107—84no—
325C23×C107—84no—
326C23×C107#12012yes—
327C23×C107#13512yes—
328C23×C107C22×D411yescharacteristic
329Q8×C107—22no—
330Q8×C107—22no—
331Q8×C107—41no—
332Q8×C107—41no—
333Q8×C107—41no—
334Q8×C107—41no—
335Q8×C107—41no—
336Q8×C107—41no—
337D4×C107—22no—
338D4×C107—22no—
339D4×C107—22no—
340D4×C107—22no—
341D4×C107—22no—
342D4×C107—44no—
343D4×C107—48no—
344D4×C107—48no—
345D4×C107—41no—
346D4×C107—41no—
347D4×C107—84no—
348D4×C107#12114yes—
349C2×C4×C107—21no—
350C2×C4×C107—21no—
351C2×C4×C107—22no—
352C2×C4×C107—22no—
353C2×C4×C107—22no—
354C2×C4×C107—22no—
355C2×C4×C107—21no—
356C2×C4×C107—21no—
357C2×C4×C107—22no—
358C2×C4×C107—22no—
359C2×C4×C107—21no—
360C2×C4×C107—22no—
361C2×C4×C107—21no—
362C2×C4×C107—21no—
363C2×C4×C107—21no—
364C2×C4×C107—21no—
365C2×C4×C107—21no—
366C2×C4×C107—21no—
367C2×C4×C107—48no—
368C2×C4×C107—41no—
369C2×C4×C107—41no—
370C2×C4×C107—41no—
371C2×C4×C107—41no—
372C2×C4×C107—41no—
373C2×C4×C107—41no—
374C2×C4×C107—41no—
375C2×C4×C107—41no—
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—84no—
388C2×C4×C107#12012yes—
389C2×C4×C107C22×D411yescharacteristic
390C2×C4×C107C22×D411yescharacteristic
391C2×C4×C107C22×D411yescharacteristic
392C2×C4×C107C2×#4111yescharacteristic
393C2×C4×C107H(5,𝔽2)11yescharacteristic
394C2×C4×C107H(5,𝔽2)11yescharacteristic
395C8×C107—22no—
396C8×C107—41no—
397C8×C107—41no—
398C8×C107—41no—
399C22×C107—22no—
400C22×C107—24no—
401C22×C107—22no—
402C22×C107—22no—
403C22×C107—22no—
404C22×C107—22no—
405C22×C107—22no—
406C22×C107—41no—
407C22×C107—42no—
408C22×C107—42no—
409C22×C107—41no—
410C22×C107—41no—
411C22×C107—41no—
412C22×C107—42no—
413C22×C107—41no—
414C22×C107—42no—
415C22×C107—41no—
416C22×C107—42no—
417C22×C107—41no—
418C22×C107—41no—
419C22×C107—42no—
420C22×C107—42no—
421C22×C107—42no—
422C22×C107—42no—
423C22×C107—816no—
424C22×C107—81no—
425C22×C107—81no—
426C22×C107—81no—
427C22×C107—81no—
428C22×C107C2×#12011yescharacteristic
429C22×C107D4211yescharacteristic
430C22×C107#54611yescharacteristic
431C22×C107C2×#13511yescharacteristic
432C22×C107#57511yescharacteristic
433C22×C107#57711yescharacteristic
434C22×C107#57711yescharacteristic
435C4×C107—22no—
436C4×C107—41no—
437C4×C107—42no—
438C4×C107—41no—
439C4×C107—41no—
440C4×C107—42no—
441C4×C107—42no—
442C4×C107—81no—
443C4×C107—81no—
444C4×C107—81no—
445C4×C107C2×#12111yescharacteristic
446C4×C107#53411yescharacteristic
447C4×C107D4211yescharacteristic
448C4×C107#54611yescharacteristic
449#24436C10711yesmaximal, characteristic, direct product factor, Sylow
450C2×C107—42no—
451C2×C107—42no—
452C2×C107—44no—
453C2×C107—82no—
454C2×C107#241011yescharacteristic
455C2×C107#300211yescharacteristic
456C2×C107#300911yescharacteristic
457C2×C107#326711yescharacteristic
458C2×C107#328211yescharacteristic
459C2×C107#329611yescharacteristic
460C2×C107#331111yescharacteristic
461C2×#546C2×C10711yescharacteristic
462C2×#465C2×C10711yescharacteristic, complemented
463C2×#452C2×C10711yescharacteristic, complemented
464C2×#450C2×C10711yescharacteristic, complemented
465C2×#416C2×C10711yescharacteristic, complemented
466#2415C2×C10711yescharacteristic, complemented
467#2042C2×C10711yescharacteristic, complemented
468#2035C2×C10711yescharacteristic, complemented
469#2015C2×C10711yescharacteristic, complemented
470#2001C2×C10711yescharacteristic, complemented
471#1877C2×C10711yescharacteristic, complemented
472#1875C2×C10711yescharacteristic, complemented
473#1869C2×C10711yescharacteristic, complemented
474#1864C2×C10711yescharacteristic, complemented
475#1786C2×C10711yescharacteristic, complemented
476C107#2443611yescharacteristic, direct product factor, Sylow
477C22×#41C22×C10711yescharacteristic
478C23×D4C22×C10711yescharacteristic
479C22×Q16C22×C10711yescharacteristic, complemented
480C22×SD16C22×C10711yescharacteristic
481C22×SD16C22×C10711yescharacteristic
482C23×C8C22×C10711yescharacteristic, complemented
483#546—24no—
484#546—24no—
485C2×#124C22×C10711yescharacteristic
486C2×#123—21no—
487C2×C22⋊Q8C22×C10711yescharacteristic
488C2×C22⋊Q8C22×C10711yescharacteristic
489C2×C22⋊Q8C22×C10711yescharacteristic, complemented
490C2×#121—21no—
491C2×#121C22×C10711yescharacteristic
492C2×#120—21no—
493C2×C4×D4C22×C10711yescharacteristic
494C2×C4×D4C22×C10711yescharacteristic
495C2×#117C22×C10711yescharacteristic, complemented
496C22×C22⋊C4—21no—
497#465—24no—
498#452—24no—
499#450—24no—
500C2×#106C22×C10711yescharacteristic, complemented
501#416—24no—
502C2×#103C22×C10711yescharacteristic, complemented
503C2×#103C22×C10711yescharacteristic, complemented
504C2×#103C22×C10711yescharacteristic, complemented
505C2×#103C22×C10711yescharacteristic, complemented
506C2×#102C22×C10711yescharacteristic
507C2×#102C22×C10711yescharacteristic
508C2×#102C22×C10711yescharacteristic
509C2×#102C22×C10711yescharacteristic
510C2×#102C22×C10711yescharacteristic
511C2×#102C22×C10711yescharacteristic
512C2×C22⋊C8C22×C10711yescharacteristic
513C2×C22⋊C8C22×C10711yescharacteristic
514C2×C22⋊C8C22×C10711yescharacteristic, complemented
515#397—21no—
516#394—21no—
517#391C22×C10711yescharacteristic, complemented
518#389—21no—
519#389C22×C10711yescharacteristic, complemented
520#388—21no—
521#380C22×C10711yescharacteristic
522#340C22×C10711yescharacteristic, complemented
523#340C22×C10711yescharacteristic, complemented
524#336C22×C10711yescharacteristic, complemented
525#336C22×C10711yescharacteristic, complemented
526C25—21no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41D4×C10714yes—
533C22×Q8C23×C10711yescharacteristic
534C22×Q8C23×C10711yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—21no—
542C22×D4—41no—
543C22×D4—41no—
544C22×D4D4×C10711yescharacteristic
545C22×D4C23×C10711yescharacteristic
546C22×D4C23×C10711yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C23×C10711yescharacteristic
550C23×C4C23×C10711yescharacteristic
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—41no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8—41no—
563C22×C8C23×C10711yescharacteristic
564C22×C8C23×C10711yescharacteristic
565C22×C8C23×C10711yescharacteristic
566C22×C8C23×C10711yescharacteristic
567#124—22no—
568#124—22no—
569#123—28no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—41no—
576#121—28no—
577#121—22no—
578#121D4×C10714yes—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—41no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4D4×C10711yescharacteristic
591C2×C4⋊C4C23×C10711yescharacteristic
592C2×C4⋊C4C23×C10711yescharacteristic
593C2×C4⋊C4C23×C10711yescharacteristic
594C2×C4⋊C4C23×C10711yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C10711yescharacteristic
606C2×C22⋊C4D4×C10711yescharacteristic
607C2×C42—21no—
608C2×C42C23×C10711yescharacteristic
609#106—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—41no—
619#102D4×C10714yescomplemented
620C22⋊C8—22no—
621C22⋊C8—22no—
622C22⋊C8—41no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—81no—
635C24—81no—
636C24C2×D4×C10711yescharacteristic
637C24C2×D4×C10711yescharacteristic
638#41—28no—
639#41—44no—
640#41—44no—
641#41—44no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8C2×D4×C10712yes—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
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—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—44no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4C2×D4×C10712yes—
679C2×D4C2×D4×C10712yes—
680C2×D4C2×D4×C10712yes—
681C2×D4#41×C10712yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—81no—
703C22×C4—81no—
704C22×C4C2×D4×C10711yescharacteristic
705C22×C4C2×D4×C10711yescharacteristic
706C22×C4C2×D4×C10711yescharacteristic
707C22×C4C2×D4×C10711yescharacteristic
708C22×C4C2×D4×C10712yes—
709C22×C4C2×D4×C10712yes—
710C22×C4C24×C10711yescharacteristic
711Q16—44no—
712SD16—44no—
713SD16—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—44no—
726C2×C8C2×D4×C10712yes—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4C2×D4×C10712yes—
739C4⋊C4C2×D4×C10712yes—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C42—21no—
752C42—21no—
753C42—42no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—48no—
771C23—48no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—84no—
787C23#120×C10712yes—
788C23#135×C10712yes—
789C23C22×D4×C10711yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—44no—
804D4—48no—
805D4—48no—
806D4—41no—
807D4—41no—
808D4—84no—
809D4#121×C10714yes—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—48no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—84no—
849C2×C4#120×C10712yes—
850C2×C4C22×D4×C10711yescharacteristic
851C2×C4C22×D4×C10711yescharacteristic
852C2×C4C22×D4×C10711yescharacteristic
853C2×C4C2×#41×C10711yescharacteristic
854C2×C4H(5,𝔽2)×C10711yescharacteristic
855C2×C4H(5,𝔽2)×C10711yescharacteristic
856C8—22no—
857C8—41no—
858C8—41no—
859C8—41no—
860C22—22no—
861C22—24no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—816no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22C2×#120×C10711yescharacteristic
890C22D42×C10711yescharacteristic
891C22#546×C10711yescharacteristic
892C22C2×#135×C10711yescharacteristic
893C22#575×C10711yescharacteristic
894C22#577×C10711yescharacteristic
895C22#577×C10711yescharacteristic
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—42no—
902C4—42no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4C2×#121×C10711yescharacteristic
907C4#534×C10711yescharacteristic
908C4D42×C10711yescharacteristic
909C4#546×C10711yescharacteristic
910C2—42no—
911C2—42no—
912C2—44no—
913C2—82no—
914C2C107×#241011yescharacteristic
915C2C107×#300211yescharacteristic
916C2C107×#300911yescharacteristic
917C2C107×#326711yescharacteristic
918C2C107×#328211yescharacteristic
919C2C107×#329611yescharacteristic
920C2C107×#331111yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#546×C107C2
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
2. C2×#465×C107C2semidirect
3. C2×#452×C107C2semidirect
4. C2×#450×C107C2semidirect
5. C2×#416×C107C2semidirect
6. C107×#2415C2semidirect
7. C107×#2042C2semidirect
8. C107×#2035C2semidirect
9. C107×#2015C2semidirect
10. C107×#2001C2semidirect
11. C107×#1877C2semidirect
12. C107×#1875C2semidirect
13. C107×#1869C2semidirect
14. C107×#1864C2semidirect
15. C107×#1786C2semidirect
18. C22×Q16×C107C22semidirect
21. C23×C8×C107C22semidirect
28. C2×C22⋊Q8×C107C22semidirect
34. C2×#117×C107C22semidirect
39. C2×#106×C107C22semidirect
41. C2×#103×C107C22semidirect
42. C2×#103×C107C22semidirect
43. C2×#103×C107C22semidirect
44. C2×#103×C107C22semidirect
53. C2×C22⋊C8×C107C22semidirect
56. #391×C107C22semidirect
58. #389×C107C22semidirect
61. #340×C107C22semidirect
62. #340×C107C22semidirect
63. #336×C107C22semidirect
64. #336×C107C22semidirect
158. #102×C107D4semidirect
449. #24436C107direct (N × H)
462. C2×#465C2×C107semidirect
463. C2×#452C2×C107semidirect
464. C2×#450C2×C107semidirect
465. C2×#416C2×C107semidirect
466. #2415C2×C107semidirect
467. #2042C2×C107semidirect
468. #2035C2×C107semidirect
469. #2015C2×C107semidirect
470. #2001C2×C107semidirect
471. #1877C2×C107semidirect
472. #1875C2×C107semidirect
473. #1869C2×C107semidirect
474. #1864C2×C107semidirect
475. #1786C2×C107semidirect
476. C107#24436direct (N × H)
479. C22×Q16C22×C107semidirect
482. C23×C8C22×C107semidirect
489. C2×C22⋊Q8C22×C107semidirect
495. C2×#117C22×C107semidirect
500. C2×#106C22×C107semidirect
502. C2×#103C22×C107semidirect
503. C2×#103C22×C107semidirect
504. C2×#103C22×C107semidirect
505. C2×#103C22×C107semidirect
514. C2×C22⋊C8C22×C107semidirect
517. #391C22×C107semidirect
519. #389C22×C107semidirect
522. #340C22×C107semidirect
523. #340C22×C107semidirect
524. #336C22×C107semidirect
525. #336C22×C107semidirect
619. #102D4×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×#465×C1072
C2×#452×C1072
C2×#450×C1072
C2×#416×C1072
C107×#24152
C107×#20422
C107×#20352
C107×#20152
C107×#20012
C107×#18772
C107×#18752
C107×#18692
C107×#18642
C107×#17862
#24436107