Finite Group Databasebeta

← C107×#24257 #41050221

Subgroups — C107×#24257 #41050221

Order 27392.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 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×#442×C107C211yesmaximal, characteristic, complemented
6C107×#2537C211yesmaximal, characteristic, complemented
7C107×#2035C211yesmaximal, characteristic, complemented
8C107×#2034C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1959C211yesmaximal, characteristic, complemented
12C107×#1955C211yesmaximal, characteristic, complemented
13C107×#1802C211yesmaximal, 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×C107—21no—
28C2×#121×C107C2211yescharacteristic
29C2×#121×C107C2211yescharacteristic
30C2×#121×C107C2211yescharacteristic, complemented
31C2×#120×C107—21no—
32C2×C4×D4×C107C2211yescharacteristic
33C2×C4×D4×C107C2211yescharacteristic
34C2×C4×D4×C107C2211yescharacteristic, complemented
35C22×C22⋊C4×C107—21no—
36#463×C107—24no—
37#449×C107—24no—
38#447×C107—24no—
39#442×C107—24no—
40C2×#106×C107C2211yescharacteristic, complemented
41C2×C4⋊C8×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×#102×C107C2211yescharacteristic, complemented
52C2×C22⋊C8×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic
54C2×C22⋊C8×C107C2211yescharacteristic, complemented
55C2×C22⋊C8×C107C2211yescharacteristic, complemented
56C2×#97×C107C2211yescharacteristic, complemented
57#394×C107—21no—
58#394×C107—21no—
59#384×C107C2211yescharacteristic, complemented
60#380×C107—21no—
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#121×C107—44no—
119#120×C107—28no—
120C4×D4×C107—22no—
121C4×D4×C107—22no—
122C4×D4×C107—22no—
123C4×D4×C107—22no—
124C4×D4×C107—22no—
125C4×D4×C107D414yescomplemented
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×C107—21no—
145C2×C22⋊C4×C107D411yescharacteristic
146C2×C22⋊C4×C107D411yescharacteristic
147C2×C42×C107C2311yescharacteristic
148#106×C107—22no—
149C4⋊C8×C107—22no—
150#103×C107—22no—
151#103×C107—22no—
152#103×C107—41no—
153#102×C107—22no—
154#102×C107—22no—
155#102×C107—22no—
156#102×C107—22no—
157#102×C107—22no—
158#102×C107—22no—
159#102×C107—41no—
160C22⋊C8×C107—22no—
161C22⋊C8×C107—22no—
162C22⋊C8×C107—41no—
163C22⋊C8×C107—41no—
164#97×C107—22no—
165#95×C107—21no—
166#95×C107—21no—
167C24×C107—21no—
168C24×C107—24no—
169C24×C107—21no—
170C24×C107—21no—
171C24×C107—42no—
172C24×C107—42no—
173C24×C107—42no—
174C24×C107—42no—
175C24×C107—81no—
176C24×C107—81no—
177C24×C107C2×D411yescharacteristic
178C24×C107C2×D411yescharacteristic
179#41×C107—44no—
180#41×C107—44no—
181#41×C107—44no—
182#41×C107—44no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107—21no—
188C2×Q8×C107C2×D412yes—
189C2×D4×C107—24no—
190C2×D4×C107—24no—
191C2×D4×C107—22no—
192C2×D4×C107—24no—
193C2×D4×C107—22no—
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—21no—
207C2×D4×C107—41no—
208C2×D4×C107—42no—
209C2×D4×C107—42no—
210C2×D4×C107—44no—
211C2×D4×C107—44no—
212C2×D4×C107—44no—
213C2×D4×C107—42no—
214C2×D4×C107—42no—
215C2×D4×C107—44no—
216C2×D4×C107—42no—
217C2×D4×C107—42no—
218C2×D4×C107—42no—
219C2×D4×C107—42no—
220C2×D4×C107—81no—
221C2×D4×C107—81no—
222C2×D4×C107—81no—
223C2×D4×C107—81no—
224C2×D4×C107C2×D412yes—
225C2×D4×C107C2×D412yes—
226C2×D4×C107C2×D412yes—
227C2×D4×C107C2×D412yes—
228C2×D4×C107#4112yes—
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—21no—
240C22×C4×C107—21no—
241C22×C4×C107—21no—
242C22×C4×C107—21no—
243C22×C4×C107—21no—
244C22×C4×C107—24no—
245C22×C4×C107—21no—
246C22×C4×C107—21no—
247C22×C4×C107—21no—
248C22×C4×C107—42no—
249C22×C4×C107—42no—
250C22×C4×C107—42no—
251C22×C4×C107—42no—
252C22×C4×C107—42no—
253C22×C4×C107—81no—
254C22×C4×C107—81no—
255C22×C4×C107C2×D411yescharacteristic
256C22×C4×C107C2×D411yescharacteristic
257C22×C4×C107C2×D411yescharacteristic
258C22×C4×C107C2×D411yescharacteristic
259C22×C4×C107C2411yescharacteristic
260SD16×C107—44no—
261D8×C107—28no—
262D8×C107—44no—
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×C107—21no—
274C2×C8×C107C2×D412yes—
275C4⋊C4×C107—24no—
276C4⋊C4×C107—22no—
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×C107—21no—
284C4⋊C4×C107—42no—
285C4⋊C4×C107—81no—
286C4⋊C4×C107C2×D412yes—
287C22⋊C4×C107—24no—
288C22⋊C4×C107—24no—
289C22⋊C4×C107—22no—
290C22⋊C4×C107—24no—
291C22⋊C4×C107—24no—
292C22⋊C4×C107—24no—
293C22⋊C4×C107—22no—
294C22⋊C4×C107—42no—
295C22⋊C4×C107—42no—
296C22⋊C4×C107—42no—
297C22⋊C4×C107—42no—
298C22⋊C4×C107—42no—
299C42×C107C2×D412yes—
300C42×C107C2×D412yes—
301C23×C107—21no—
302C23×C107—22no—
303C23×C107—21no—
304C23×C107—22no—
305C23×C107—21no—
306C23×C107—22no—
307C23×C107—21no—
308C23×C107—21no—
309C23×C107—21no—
310C23×C107—22no—
311C23×C107—21no—
312C23×C107—22no—
313C23×C107—21no—
314C23×C107—21no—
315C23×C107—21no—
316C23×C107—21no—
317C23×C107—21no—
318C23×C107—21no—
319C23×C107—48no—
320C23×C107—48no—
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—41no—
335C23×C107—41no—
336C23×C107—41no—
337C23×C107—84no—
338C23×C107—84no—
339C23×C107—84no—
340C23×C107—84no—
341C23×C107—84no—
342C23×C107AGL(1,ℤ/8)12yes—
343C23×C107C22×D411yescharacteristic
344Q8×C107—22no—
345Q8×C107—22no—
346Q8×C107—41no—
347Q8×C107—41no—
348D4×C107—22no—
349D4×C107—22no—
350D4×C107—22no—
351D4×C107—22no—
352D4×C107—22no—
353D4×C107—22no—
354D4×C107—22no—
355D4×C107—44no—
356D4×C107—48no—
357D4×C107—48no—
358D4×C107—41no—
359D4×C107—41no—
360D4×C107—41no—
361D4×C107—41no—
362D4×C107—84no—
363D4×C107—84no—
364D4×C107—84no—
365D4×C107#12114yescomplemented
366C2×C4×C107—21no—
367C2×C4×C107—21no—
368C2×C4×C107—21no—
369C2×C4×C107—21no—
370C2×C4×C107—22no—
371C2×C4×C107—21no—
372C2×C4×C107—22no—
373C2×C4×C107—21no—
374C2×C4×C107—21no—
375C2×C4×C107—21no—
376C2×C4×C107—21no—
377C2×C4×C107—21no—
378C2×C4×C107—48no—
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—41no—
398C2×C4×C107—41no—
399C2×C4×C107—41no—
400C2×C4×C107—84no—
401C2×C4×C107—84no—
402C2×C4×C107#12012yes—
403C2×C4×C107#12012yes—
404C2×C4×C107C22×D411yescharacteristic
405C2×C4×C107C22×D411yescharacteristic
406C2×C4×C107C22×D411yescharacteristic
407C2×C4×C107C2×#4111yescharacteristic
408C2×C4×C107H(5,𝔽2)11yescharacteristic
409C2×C4×C107H(5,𝔽2)11yescharacteristic
410C8×C107—22no—
411C8×C107—41no—
412C8×C107—41no—
413C8×C107—41no—
414C22×C107—24no—
415C22×C107—22no—
416C22×C107—22no—
417C22×C107—22no—
418C22×C107—41no—
419C22×C107—42no—
420C22×C107—42no—
421C22×C107—41no—
422C22×C107—42no—
423C22×C107—42no—
424C22×C107—41no—
425C22×C107—42no—
426C22×C107—41no—
427C22×C107—42no—
428C22×C107—41no—
429C22×C107—42no—
430C22×C107—42no—
431C22×C107—41no—
432C22×C107—42no—
433C22×C107—41no—
434C22×C107—42no—
435C22×C107—41no—
436C22×C107—42no—
437C22×C107—41no—
438C22×C107—42no—
439C22×C107—41no—
440C22×C107—41no—
441C22×C107—816no—
442C22×C107—81no—
443C22×C107—81no—
444C22×C107—81no—
445C22×C107—81no—
446C22×C107—81no—
447C22×C107—81no—
448C22×C107—81no—
449C22×C107—81no—
450C22×C107C2×#12011yescharacteristic
451C22×C107D4211yescharacteristic
452C22×C107#54611yescharacteristic
453C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
454C22×C107#57511yescharacteristic
455C22×C107#57611yescharacteristic
456C22×C107#57711yescharacteristic
457C4×C107—22no—
458C4×C107—22no—
459C4×C107—41no—
460C4×C107—41no—
461C4×C107—42no—
462C4×C107—42no—
463C4×C107—81no—
464C4×C107—81no—
465C4×C107—81no—
466C4×C107C2×#12111yescharacteristic
467C4×C107#53511yescharacteristic
468C4×C107D4211yescharacteristic
469C4×C107#54611yescharacteristic
470#24257C10711yesmaximal, characteristic, direct product factor, Sylow
471C2×C107—42no—
472C2×C107—44no—
473C2×C107—81no—
474C2×C107—82no—
475C2×C107—82no—
476C2×C107#240811yescharacteristic
477C2×C107#300611yescharacteristic
478C2×C107#301211yescharacteristic
479C2×C107#326411yescharacteristic
480C2×C107#326711yescharacteristic
481C2×C107#330611yescharacteristic
482C2×C107#331911yescharacteristic
483C2×#546C2×C10711yescharacteristic, complemented
484C2×#463C2×C10711yescharacteristic, complemented
485C2×#449C2×C10711yescharacteristic, complemented
486C2×#447C2×C10711yescharacteristic, complemented
487C2×#442C2×C10711yescharacteristic, complemented
488#2537C2×C10711yescharacteristic, complemented
489#2035C2×C10711yescharacteristic, complemented
490#2034C2×C10711yescharacteristic, complemented
491#2000C2×C10711yescharacteristic, complemented
492#1999C2×C10711yescharacteristic, complemented
493#1959C2×C10711yescharacteristic, complemented
494#1955C2×C10711yescharacteristic, complemented
495#1802C2×C10711yescharacteristic, complemented
496#1788C2×C10711yescharacteristic, complemented
497#1786C2×C10711yescharacteristic, complemented
498C107#2425711yescharacteristic, direct product factor, Sylow
499C22×#41C22×C10711yescharacteristic
500C23×D4C22×C10711yescharacteristic
501C22×SD16C22×C10711yescharacteristic, complemented
502C22×D8C22×C10711yescharacteristic
503C22×D8C22×C10711yescharacteristic
504#546—24no—
505#546—24no—
506C2×#124C22×C10711yescharacteristic
507C2×#123—21no—
508C2×C22⋊Q8C22×C10711yescharacteristic
509C2×#121—21no—
510C2×#121—21no—
511C2×#121C22×C10711yescharacteristic
512C2×#121C22×C10711yescharacteristic
513C2×#121C22×C10711yescharacteristic, complemented
514C2×#120—21no—
515C2×C4×D4C22×C10711yescharacteristic
516C2×C4×D4C22×C10711yescharacteristic
517C2×C4×D4C22×C10711yescharacteristic, complemented
518C22×C22⋊C4—21no—
519#463—24no—
520#449—24no—
521#447—24no—
522#442—24no—
523C2×#106C22×C10711yescharacteristic, complemented
524C2×C4⋊C8C22×C10711yescharacteristic, complemented
525C2×#103C22×C10711yescharacteristic, complemented
526C2×#103C22×C10711yescharacteristic, complemented
527C2×#103C22×C10711yescharacteristic, complemented
528C2×#102C22×C10711yescharacteristic
529C2×#102C22×C10711yescharacteristic
530C2×#102C22×C10711yescharacteristic
531C2×#102C22×C10711yescharacteristic
532C2×#102C22×C10711yescharacteristic
533C2×#102C22×C10711yescharacteristic
534C2×#102C22×C10711yescharacteristic, complemented
535C2×C22⋊C8C22×C10711yescharacteristic
536C2×C22⋊C8C22×C10711yescharacteristic
537C2×C22⋊C8C22×C10711yescharacteristic, complemented
538C2×C22⋊C8C22×C10711yescharacteristic, complemented
539C2×#97C22×C10711yescharacteristic, complemented
540#394—21no—
541#394—21no—
542#384C22×C10711yescharacteristic, complemented
543#380—21no—
544#380C22×C10711yescharacteristic
545#380C22×C10711yescharacteristic, complemented
546#340C22×C10711yescharacteristic, complemented
547#340C22×C10711yescharacteristic, complemented
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C10711yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C10711yescharacteristic
568C22×D4C23×C10711yescharacteristic
569C22×D4C23×C10711yescharacteristic
570C22×D4C23×C10711yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C10711yescharacteristic
575C23×C4C23×C10711yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C10714yescomplemented
585C22×C8C23×C10711yescharacteristic
586C22×C8C23×C10711yescharacteristic
587C22×C8C23×C10711yescharacteristic
588C22×C8C23×C10711yescharacteristic
589#124—22no—
590#124D4×C10714yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C10714yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C10711yescharacteristic
613C2×C4⋊C4C23×C10711yescharacteristic
614C2×C4⋊C4C23×C10711yescharacteristic
615C2×C4⋊C4C23×C10711yescharacteristic
616C2×C4⋊C4C23×C10711yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C10711yescharacteristic
629C2×C22⋊C4D4×C10711yescharacteristic
630C2×C42C23×C10711yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C10711yescharacteristic
661C24C2×D4×C10711yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C10712yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
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—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C10712yes—
708C2×D4C2×D4×C10712yes—
709C2×D4C2×D4×C10712yes—
710C2×D4C2×D4×C10712yes—
711C2×D4#41×C10712yes—
712C22×C4—24no—
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—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C10711yescharacteristic
739C22×C4C2×D4×C10711yescharacteristic
740C22×C4C2×D4×C10711yescharacteristic
741C22×C4C2×D4×C10711yescharacteristic
742C22×C4C24×C10711yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C10712yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C10712yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C10712yes—
783C42C2×D4×C10712yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C10712yes—
826C23C22×D4×C10711yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C10714yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
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—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C10712yes—
886C2×C4#120×C10712yes—
887C2×C4C22×D4×C10711yescharacteristic
888C2×C4C22×D4×C10711yescharacteristic
889C2×C4C22×D4×C10711yescharacteristic
890C2×C4C2×#41×C10711yescharacteristic
891C2×C4H(5,𝔽2)×C10711yescharacteristic
892C2×C4H(5,𝔽2)×C10711yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—41no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C10711yescharacteristic
934C22D42×C10711yescharacteristic
935C22#546×C10711yescharacteristic
936C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
937C22#575×C10711yescharacteristic
938C22#576×C10711yescharacteristic
939C22#577×C10711yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C10711yescharacteristic
950C4#535×C10711yescharacteristic
951C4D42×C10711yescharacteristic
952C4#546×C10711yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2C107×#240811yescharacteristic
959C2C107×#300611yescharacteristic
960C2C107×#301211yescharacteristic
961C2C107×#326411yescharacteristic
962C2C107×#326711yescharacteristic
963C2C107×#330611yescharacteristic
964C2C107×#331911yescharacteristic
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×#442×C107C2semidirect
6. C107×#2537C2semidirect
7. C107×#2035C2semidirect
8. C107×#2034C2semidirect
9. C107×#2000C2semidirect
10. C107×#1999C2semidirect
11. C107×#1959C2semidirect
12. C107×#1955C2semidirect
13. C107×#1802C2semidirect
14. C107×#1788C2semidirect
15. C107×#1786C2semidirect
18. C22×SD16×C107C22semidirect
30. C2×#121×C107C22semidirect
34. C2×C4×D4×C107C22semidirect
40. C2×#106×C107C22semidirect
41. C2×C4⋊C8×C107C22semidirect
42. C2×#103×C107C22semidirect
43. C2×#103×C107C22semidirect
44. C2×#103×C107C22semidirect
51. C2×#102×C107C22semidirect
54. C2×C22⋊C8×C107C22semidirect
55. C2×C22⋊C8×C107C22semidirect
56. C2×#97×C107C22semidirect
59. #384×C107C22semidirect
62. #380×C107C22semidirect
63. #340×C107C22semidirect
64. #340×C107C22semidirect
101. C2×D8×C107D4semidirect
107. #124×C107D4semidirect
125. C4×D4×C107D4semidirect
365. D4×C107#121semidirect
470. #24257C107direct (N × H)
483. C2×#546C2×C107semidirect
484. C2×#463C2×C107semidirect
485. C2×#449C2×C107semidirect
486. C2×#447C2×C107semidirect
487. C2×#442C2×C107semidirect
488. #2537C2×C107semidirect
489. #2035C2×C107semidirect
490. #2034C2×C107semidirect
491. #2000C2×C107semidirect
492. #1999C2×C107semidirect
493. #1959C2×C107semidirect
494. #1955C2×C107semidirect
495. #1802C2×C107semidirect
496. #1788C2×C107semidirect
497. #1786C2×C107semidirect
498. C107#24257direct (N × H)
501. C22×SD16C22×C107semidirect
513. C2×#121C22×C107semidirect
517. C2×C4×D4C22×C107semidirect
523. C2×#106C22×C107semidirect
524. C2×C4⋊C8C22×C107semidirect
525. C2×#103C22×C107semidirect
526. C2×#103C22×C107semidirect
527. C2×#103C22×C107semidirect
534. C2×#102C22×C107semidirect
537. C2×C22⋊C8C22×C107semidirect
538. C2×C22⋊C8C22×C107semidirect
539. C2×#97C22×C107semidirect
542. #384C22×C107semidirect
545. #380C22×C107semidirect
546. #340C22×C107semidirect
547. #340C22×C107semidirect
584. C2×D8D4×C107semidirect
590. #124D4×C107semidirect
608. C4×D4D4×C107semidirect
848. D4#121×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×#442×C1072
C107×#25372
C107×#20352
C107×#20342
C107×#20002
C107×#19992
C107×#19592
C107×#19552
C107×#18022
C107×#17882
C107×#17862
#24257107