Finite Group Databasebeta

← C107×#24220 #41050184

Subgroups — C107×#24220 #41050184

Order 27392.

1556 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C107C211yesmaximal, characteristic
2C2×#464×C107C211yesmaximal, characteristic, complemented
3C2×#460×C107C211yesmaximal, characteristic, complemented
4C2×#452×C107C211yesmaximal, characteristic, complemented
5C2×#450×C107C211yesmaximal, characteristic, complemented
6C107×#2323C211yesmaximal, characteristic, complemented
7C107×#2042C211yesmaximal, characteristic, complemented
8C107×#2041C211yesmaximal, characteristic, complemented
9C107×#2015C211yesmaximal, characteristic, complemented
10C107×#2014C211yesmaximal, characteristic, complemented
11C107×#1983C211yesmaximal, characteristic, complemented
12C107×#1982C211yesmaximal, characteristic, complemented
13C107×#1798C211yesmaximal, characteristic, complemented
14C107×#1788C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C23×D4×C107C2211yescharacteristic
18C22×Q16×C107C2211yescharacteristic, complemented
19C22×SD16×C107C2211yescharacteristic
20C22×SD16×C107C2211yescharacteristic
21C22×SD16×C107C2211yescharacteristic, complemented
22#535×C107—24no—
23#535×C107—24no—
24C2×#127×C107C2211yescharacteristic
25C2×#127×C107C2211yescharacteristic
26C2×#124×C107C2211yescharacteristic
27C2×#124×C107C2211yescharacteristic
28C2×C22⋊Q8×C107C2211yescharacteristic
29C2×#121×C107—21no—
30C2×#121×C107—21no—
31C2×#120×C107—21no—
32C2×#120×C107—21no—
33C2×C4×Q8×C107C2211yescharacteristic, complemented
34C2×#117×C107C2211yescharacteristic
35#464×C107—24no—
36#460×C107—24no—
37#452×C107—24no—
38#450×C107—24no—
39C2×C4⋊C8×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×#102×C107C2211yescharacteristic, complemented
52C2×#102×C107C2211yescharacteristic, complemented
53C2×C22⋊C8×C107C2211yescharacteristic
54C2×C22⋊C8×C107C2211yescharacteristic
55#391×C107C2211yescharacteristic, complemented
56#389×C107—21no—
57#389×C107C2211yescharacteristic, complemented
58#388×C107—21no—
59#388×C107—21no—
60#387×C107—21no—
61#380×C107C2211yescharacteristic
62C4×C4⋊C4×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—22no—
70C2×#41×C107—41no—
71C2×#41×C107—41no—
72C22×Q8×C107C2311yescharacteristic
73C22×Q8×C107C2311yescharacteristic
74C22×D4×C107—21no—
75C22×D4×C107—22no—
76C22×D4×C107—22no—
77C22×D4×C107—21no—
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107—22no—
83C22×D4×C107—22no—
84C22×D4×C107—41no—
85C22×D4×C107—41no—
86C22×D4×C107C2311yescharacteristic
87C22×D4×C107C2311yescharacteristic
88C22×D4×C107C2311yescharacteristic
89C23×C4×C107—21no—
90C23×C4×C107C2311yescharacteristic
91C2×Q16×C107—22no—
92C2×Q16×C107—22no—
93C2×Q16×C107—41no—
94C2×SD16×C107—22no—
95C2×SD16×C107—22no—
96C2×SD16×C107—22no—
97C2×SD16×C107—22no—
98C2×SD16×C107—22no—
99C2×SD16×C107—22no—
100C2×SD16×C107—41no—
101C2×SD16×C107—41no—
102C2×SD16×C107—41no—
103C22×C8×C107C2311yescharacteristic
104C22×C8×C107C2311yescharacteristic
105C22×C8×C107C2311yescharacteristic
106C22×C8×C107C2311yescharacteristic
107#127×C107—22no—
108#127×C107—22no—
109#127×C107—22no—
110#127×C107D414yes—
111#124×C107—22no—
112#124×C107—22no—
113#124×C107—22no—
114#124×C107D414yes—
115C22⋊Q8×C107—22no—
116C22⋊Q8×C107D414yescomplemented
117#121×C107—28no—
118#121×C107—28no—
119#120×C107—28no—
120#120×C107—28no—
121C4×Q8×C107—22no—
122C4×Q8×C107—22no—
123#117×C107—22no—
124#117×C107—22no—
125C2×C4⋊C4×C107—21no—
126C2×C4⋊C4×C107—21no—
127C2×C4⋊C4×C107—21no—
128C2×C4⋊C4×C107D411yescharacteristic
129C2×C4⋊C4×C107D411yescharacteristic
130C2×C4⋊C4×C107C2311yescharacteristic
131C2×C4⋊C4×C107C2311yescharacteristic
132C2×C4⋊C4×C107C2311yescharacteristic
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×C107D411yescharacteristic
140C2×C22⋊C4×C107D411yescharacteristic
141C2×C42×C107—21no—
142C2×C42×C107—21no—
143C2×C42×C107C2311yescharacteristic
144C2×C42×C107C2311yescharacteristic
145C4⋊C8×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—
157#102×C107—41no—
158#102×C107—41no—
159C22⋊C8×C107—22no—
160C22⋊C8×C107—22no—
161#95×C107—21no—
162#95×C107—21no—
163#95×C107—21no—
164#95×C107—21no—
165#95×C107—21no—
166C24×C107—24no—
167C24×C107—21no—
168C24×C107—21no—
169C24×C107—21no—
170C24×C107—42no—
171C24×C107—42no—
172C24×C107—81no—
173C24×C107—81no—
174C24×C107—81no—
175C24×C107—81no—
176C24×C107C2×D411yescharacteristic
177#41×C107—44no—
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×C107C2×D412yes—
192C2×Q8×C107C2×D412yes—
193C2×D4×C107—24no—
194C2×D4×C107—24no—
195C2×D4×C107—24no—
196C2×D4×C107—24no—
197C2×D4×C107—24no—
198C2×D4×C107—24no—
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—21no—
207C2×D4×C107—21no—
208C2×D4×C107—21no—
209C2×D4×C107—21no—
210C2×D4×C107—21no—
211C2×D4×C107—21no—
212C2×D4×C107—21no—
213C2×D4×C107—21no—
214C2×D4×C107—44no—
215C2×D4×C107—44no—
216C2×D4×C107—44no—
217C2×D4×C107—44no—
218C2×D4×C107—42no—
219C2×D4×C107—42no—
220C2×D4×C107—42no—
221C2×D4×C107—42no—
222C2×D4×C107—81no—
223C2×D4×C107—81no—
224C2×D4×C107—81no—
225C2×D4×C107—81no—
226C2×D4×C107—81no—
227C2×D4×C107—81no—
228C2×D4×C107—81no—
229C2×D4×C107—81no—
230C2×D4×C107C2×D412yes—
231C2×D4×C107C2×D412yes—
232C2×D4×C107C2×D412yes—
233C22×C4×C107—21no—
234C22×C4×C107—21no—
235C22×C4×C107—21no—
236C22×C4×C107—21no—
237C22×C4×C107—24no—
238C22×C4×C107—21no—
239C22×C4×C107—21no—
240C22×C4×C107—21no—
241C22×C4×C107—21no—
242C22×C4×C107—21no—
243C22×C4×C107—42no—
244C22×C4×C107—42no—
245C22×C4×C107C2×D411yescharacteristic
246C22×C4×C107C2×D411yescharacteristic
247C22×C4×C107C2×D411yescharacteristic
248C22×C4×C107C2×D411yescharacteristic
249C22×C4×C107C2×D411yescharacteristic
250C22×C4×C107C2×D412yes—
251C22×C4×C107#4112yes—
252C22×C4×C107C2411yescharacteristic
253Q16×C107—44no—
254SD16×C107—44no—
255SD16×C107—44no—
256SD16×C107—44no—
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—21no—
265C2×C8×C107—21no—
266C2×C8×C107—21no—
267C2×C8×C107—21no—
268C2×C8×C107—21no—
269C4⋊C4×C107—22no—
270C4⋊C4×C107—22no—
271C4⋊C4×C107—24no—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—21no—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—42no—
278C4⋊C4×C107—81no—
279C4⋊C4×C107C2×D412yes—
280C22⋊C4×C107—24no—
281C22⋊C4×C107—24no—
282C22⋊C4×C107—24no—
283C22⋊C4×C107—24no—
284C22⋊C4×C107—24no—
285C22⋊C4×C107—22no—
286C22⋊C4×C107—22no—
287C22⋊C4×C107—81no—
288C42×C107—21no—
289C42×C107—21no—
290C42×C107—42no—
291C42×C107—81no—
292C42×C107C2×D412yes—
293C42×C107C2×D412yes—
294C23×C107—21no—
295C23×C107—21no—
296C23×C107—21no—
297C23×C107—21no—
298C23×C107—21no—
299C23×C107—21no—
300C23×C107—22no—
301C23×C107—22no—
302C23×C107—22no—
303C23×C107—48no—
304C23×C107—41no—
305C23×C107—41no—
306C23×C107—41no—
307C23×C107—41no—
308C23×C107—41no—
309C23×C107—41no—
310C23×C107—41no—
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—41no—
322C23×C107—84no—
323C23×C107—84no—
324C23×C107—84no—
325C23×C107—84no—
326C23×C107—84no—
327C23×C107—84no—
328C23×C107#12112yes—
329C23×C107C22×D411yescharacteristic
330Q8×C107—22no—
331Q8×C107—22no—
332Q8×C107—22no—
333Q8×C107—22no—
334Q8×C107—41no—
335Q8×C107—41no—
336Q8×C107—41no—
337Q8×C107—41no—
338D4×C107—22no—
339D4×C107—22no—
340D4×C107—22no—
341D4×C107—22no—
342D4×C107—22no—
343D4×C107—22no—
344D4×C107—48no—
345D4×C107—48no—
346D4×C107—41no—
347D4×C107—41no—
348D4×C107—41no—
349D4×C107—41no—
350D4×C107—41no—
351D4×C107—41no—
352D4×C107—84no—
353D4×C107—84no—
354D4×C107—84no—
355D4×C107—84no—
356C2×C4×C107—21no—
357C2×C4×C107—21no—
358C2×C4×C107—21no—
359C2×C4×C107—21no—
360C2×C4×C107—21no—
361C2×C4×C107—21no—
362C2×C4×C107—22no—
363C2×C4×C107—22no—
364C2×C4×C107—22no—
365C2×C4×C107—22no—
366C2×C4×C107—21no—
367C2×C4×C107—21no—
368C2×C4×C107—22no—
369C2×C4×C107—22no—
370C2×C4×C107—22no—
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#12012yes—
389C2×C4×C107#12012yes—
390C2×C4×C107#12112yes—
391C2×C4×C107C22×D411yescharacteristic
392C2×C4×C107C22×D411yescharacteristic
393C2×C4×C107C22×D411yescharacteristic
394C2×C4×C107C2×#4111yescharacteristic
395C2×C4×C107H(5,𝔽2)11yescharacteristic
396C2×C4×C107H(5,𝔽2)11yescharacteristic
397C8×C107—41no—
398C8×C107—41no—
399C8×C107—41no—
400C8×C107—41no—
401C22×C107—22no—
402C22×C107—22no—
403C22×C107—22no—
404C22×C107—41no—
405C22×C107—41no—
406C22×C107—41no—
407C22×C107—41no—
408C22×C107—42no—
409C22×C107—42no—
410C22×C107—42no—
411C22×C107—42no—
412C22×C107—42no—
413C22×C107—42no—
414C22×C107—42no—
415C22×C107—42no—
416C22×C107—42no—
417C22×C107—816no—
418C22×C107—81no—
419C22×C107—81no—
420C22×C107—81no—
421C22×C107—81no—
422C22×C107—81no—
423C22×C107—81no—
424C22×C107—81no—
425C22×C107—81no—
426C22×C107—81no—
427C22×C107—81no—
428C22×C107—81no—
429C22×C107—81no—
430C22×C107C2×#12011yescharacteristic
431C22×C107C2×#12111yescharacteristic
432C22×C107#53511yescharacteristic
433C22×C107#57611yescharacteristic
434C22×C107#57711yescharacteristic
435C22×C107#57711yescharacteristic
436C22×C107#57711yescharacteristic
437C4×C107—22no—
438C4×C107—22no—
439C4×C107—22no—
440C4×C107—42no—
441C4×C107—42no—
442C4×C107—41no—
443C4×C107—41no—
444C4×C107—42no—
445C4×C107—81no—
446C4×C107—81no—
447C4×C107D4211yescharacteristic
448C4×C107D4211yescharacteristic
449C4×C107#54611yescharacteristic
450C4×C107#54611yescharacteristic
451#24220C10711yesmaximal, characteristic, direct product factor, Sylow
452C2×C107—42no—
453C2×C107—82no—
454C2×C107—82no—
455C2×C107—82no—
456C2×C107#240811yescharacteristic
457C2×C107#300911yescharacteristic
458C2×C107#301211yescharacteristic
459C2×C107#304311yescharacteristic
460C2×C107#304511yescharacteristic
461C2×C107#322211yescharacteristic
462C2×C107#322411yescharacteristic
463C2×#535C2×C10711yescharacteristic
464C2×#464C2×C10711yescharacteristic, complemented
465C2×#460C2×C10711yescharacteristic, complemented
466C2×#452C2×C10711yescharacteristic, complemented
467C2×#450C2×C10711yescharacteristic, complemented
468#2323C2×C10711yescharacteristic, complemented
469#2042C2×C10711yescharacteristic, complemented
470#2041C2×C10711yescharacteristic, complemented
471#2015C2×C10711yescharacteristic, complemented
472#2014C2×C10711yescharacteristic, complemented
473#1983C2×C10711yescharacteristic, complemented
474#1982C2×C10711yescharacteristic, complemented
475#1798C2×C10711yescharacteristic, complemented
476#1788C2×C10711yescharacteristic, complemented
477#1786C2×C10711yescharacteristic, complemented
478C107#2422011yescharacteristic, direct product factor, Sylow
479C22×#41C22×C10711yescharacteristic
480C23×D4C22×C10711yescharacteristic
481C22×Q16C22×C10711yescharacteristic, complemented
482C22×SD16C22×C10711yescharacteristic
483C22×SD16C22×C10711yescharacteristic
484C22×SD16C22×C10711yescharacteristic, complemented
485#535—24no—
486#535—24no—
487C2×#127C22×C10711yescharacteristic
488C2×#127C22×C10711yescharacteristic
489C2×#124C22×C10711yescharacteristic
490C2×#124C22×C10711yescharacteristic
491C2×C22⋊Q8C22×C10711yescharacteristic
492C2×#121—21no—
493C2×#121—21no—
494C2×#120—21no—
495C2×#120—21no—
496C2×C4×Q8C22×C10711yescharacteristic, complemented
497C2×#117C22×C10711yescharacteristic
498#464—24no—
499#460—24no—
500#452—24no—
501#450—24no—
502C2×C4⋊C8C22×C10711yescharacteristic, complemented
503C2×C4⋊C8C22×C10711yescharacteristic, complemented
504C2×#103C22×C10711yescharacteristic, complemented
505C2×#103C22×C10711yescharacteristic, complemented
506C2×#103C22×C10711yescharacteristic, complemented
507C2×#102C22×C10711yescharacteristic
508C2×#102C22×C10711yescharacteristic
509C2×#102C22×C10711yescharacteristic
510C2×#102C22×C10711yescharacteristic
511C2×#102C22×C10711yescharacteristic
512C2×#102C22×C10711yescharacteristic
513C2×#102C22×C10711yescharacteristic, complemented
514C2×#102C22×C10711yescharacteristic, complemented
515C2×#102C22×C10711yescharacteristic, complemented
516C2×C22⋊C8C22×C10711yescharacteristic
517C2×C22⋊C8C22×C10711yescharacteristic
518#391C22×C10711yescharacteristic, complemented
519#389—21no—
520#389C22×C10711yescharacteristic, complemented
521#388—21no—
522#388—21no—
523#387—21no—
524#380C22×C10711yescharacteristic
525C4×C4⋊C4C22×C10711yescharacteristic, complemented
526#336C22×C10711yescharacteristic, complemented
527#336C22×C10711yescharacteristic, complemented
528C25—21no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C22×Q8C23×C10711yescharacteristic
536C22×Q8C23×C10711yescharacteristic
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—41no—
548C22×D4—41no—
549C22×D4C23×C10711yescharacteristic
550C22×D4C23×C10711yescharacteristic
551C22×D4C23×C10711yescharacteristic
552C23×C4—21no—
553C23×C4C23×C10711yescharacteristic
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—41no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C22×C8C23×C10711yescharacteristic
567C22×C8C23×C10711yescharacteristic
568C22×C8C23×C10711yescharacteristic
569C22×C8C23×C10711yescharacteristic
570#127—22no—
571#127—22no—
572#127—22no—
573#127D4×C10714yes—
574#124—22no—
575#124—22no—
576#124—22no—
577#124D4×C10714yes—
578C22⋊Q8—22no—
579C22⋊Q8D4×C10714yescomplemented
580#121—28no—
581#121—28no—
582#120—28no—
583#120—28no—
584C4×Q8—22no—
585C4×Q8—22no—
586#117—22no—
587#117—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4D4×C10711yescharacteristic
592C2×C4⋊C4D4×C10711yescharacteristic
593C2×C4⋊C4C23×C10711yescharacteristic
594C2×C4⋊C4C23×C10711yescharacteristic
595C2×C4⋊C4C23×C10711yescharacteristic
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⋊C4D4×C10711yescharacteristic
603C2×C22⋊C4D4×C10711yescharacteristic
604C2×C42—21no—
605C2×C42—21no—
606C2×C42C23×C10711yescharacteristic
607C2×C42C23×C10711yescharacteristic
608C4⋊C8—22no—
609C4⋊C8—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102—41no—
620#102—41no—
621#102—41no—
622C22⋊C8—22no—
623C22⋊C8—22no—
624#95—21no—
625#95—21no—
626#95—21no—
627#95—21no—
628#95—21no—
629C24—24no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24—81no—
638C24—81no—
639C24C2×D4×C10711yescharacteristic
640#41—44no—
641#41—44no—
642#41—44no—
643#41—44no—
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×Q8—21no—
654C2×Q8C2×D4×C10712yes—
655C2×Q8C2×D4×C10712yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—81no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4—81no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4—81no—
693C2×D4C2×D4×C10712yes—
694C2×D4C2×D4×C10712yes—
695C2×D4C2×D4×C10712yes—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—24no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4C2×D4×C10711yescharacteristic
709C22×C4C2×D4×C10711yescharacteristic
710C22×C4C2×D4×C10711yescharacteristic
711C22×C4C2×D4×C10711yescharacteristic
712C22×C4C2×D4×C10711yescharacteristic
713C22×C4C2×D4×C10712yes—
714C22×C4#41×C10712yes—
715C22×C4C24×C10711yescharacteristic
716Q16—44no—
717SD16—44no—
718SD16—44no—
719SD16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—42no—
741C4⋊C4—81no—
742C4⋊C4C2×D4×C10712yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—81no—
751C42—21no—
752C42—21no—
753C42—42no—
754C42—81no—
755C42C2×D4×C10712yes—
756C42C2×D4×C10712yes—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—48no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#121×C10712yes—
792C23C22×D4×C10711yescharacteristic
793Q8—22no—
794Q8—22no—
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—84no—
816D4—84no—
817D4—84no—
818D4—84no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—48no—
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—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4#120×C10712yes—
852C2×C4#120×C10712yes—
853C2×C4#121×C10712yes—
854C2×C4C22×D4×C10711yescharacteristic
855C2×C4C22×D4×C10711yescharacteristic
856C2×C4C22×D4×C10711yescharacteristic
857C2×C4C2×#41×C10711yescharacteristic
858C2×C4H(5,𝔽2)×C10711yescharacteristic
859C2×C4H(5,𝔽2)×C10711yescharacteristic
860C8—41no—
861C8—41no—
862C8—41no—
863C8—41no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—816no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22C2×#120×C10711yescharacteristic
894C22C2×#121×C10711yescharacteristic
895C22#535×C10711yescharacteristic
896C22#576×C10711yescharacteristic
897C22#577×C10711yescharacteristic
898C22#577×C10711yescharacteristic
899C22#577×C10711yescharacteristic
900C4—22no—
901C4—22no—
902C4—22no—
903C4—42no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—81no—
909C4—81no—
910C4D42×C10711yescharacteristic
911C4D42×C10711yescharacteristic
912C4#546×C10711yescharacteristic
913C4#546×C10711yescharacteristic
914C2—42no—
915C2—82no—
916C2—82no—
917C2—82no—
918C2C107×#240811yescharacteristic
919C2C107×#300911yescharacteristic
920C2C107×#301211yescharacteristic
921C2C107×#304311yescharacteristic
922C2C107×#304511yescharacteristic
923C2C107×#322211yescharacteristic
924C2C107×#322411yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#535×C107C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×#117×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#464×C107C2semidirect
3. C2×#460×C107C2semidirect
4. C2×#452×C107C2semidirect
5. C2×#450×C107C2semidirect
6. C107×#2323C2semidirect
7. C107×#2042C2semidirect
8. C107×#2041C2semidirect
9. C107×#2015C2semidirect
10. C107×#2014C2semidirect
11. C107×#1983C2semidirect
12. C107×#1982C2semidirect
13. C107×#1798C2semidirect
14. C107×#1788C2semidirect
15. C107×#1786C2semidirect
18. C22×Q16×C107C22semidirect
21. C22×SD16×C107C22semidirect
33. C2×C4×Q8×C107C22semidirect
39. C2×C4⋊C8×C107C22semidirect
40. C2×C4⋊C8×C107C22semidirect
41. C2×#103×C107C22semidirect
42. C2×#103×C107C22semidirect
43. C2×#103×C107C22semidirect
50. C2×#102×C107C22semidirect
51. C2×#102×C107C22semidirect
52. C2×#102×C107C22semidirect
55. #391×C107C22semidirect
57. #389×C107C22semidirect
62. C4×C4⋊C4×C107C22semidirect
63. #336×C107C22semidirect
64. #336×C107C22semidirect
116. C22⋊Q8×C107D4semidirect
451. #24220C107direct (N × H)
464. C2×#464C2×C107semidirect
465. C2×#460C2×C107semidirect
466. C2×#452C2×C107semidirect
467. C2×#450C2×C107semidirect
468. #2323C2×C107semidirect
469. #2042C2×C107semidirect
470. #2041C2×C107semidirect
471. #2015C2×C107semidirect
472. #2014C2×C107semidirect
473. #1983C2×C107semidirect
474. #1982C2×C107semidirect
475. #1798C2×C107semidirect
476. #1788C2×C107semidirect
477. #1786C2×C107semidirect
478. C107#24220direct (N × H)
481. C22×Q16C22×C107semidirect
484. C22×SD16C22×C107semidirect
496. C2×C4×Q8C22×C107semidirect
502. C2×C4⋊C8C22×C107semidirect
503. C2×C4⋊C8C22×C107semidirect
504. C2×#103C22×C107semidirect
505. C2×#103C22×C107semidirect
506. C2×#103C22×C107semidirect
513. C2×#102C22×C107semidirect
514. C2×#102C22×C107semidirect
515. C2×#102C22×C107semidirect
518. #391C22×C107semidirect
520. #389C22×C107semidirect
525. C4×C4⋊C4C22×C107semidirect
526. #336C22×C107semidirect
527. #336C22×C107semidirect
579. C22⋊Q8D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1072
C2×#464×C1072
C2×#460×C1072
C2×#452×C1072
C2×#450×C1072
C107×#23232
C107×#20422
C107×#20412
C107×#20152
C107×#20142
C107×#19832
C107×#19822
C107×#17982
C107×#17882
C107×#17862
#24220107