Finite Group Databasebeta

← C107×#24393 #41050357

Subgroups — C107×#24393 #41050357

Order 27392.

1450 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C107C211yesmaximal, characteristic
2C2×#468×C107C211yesmaximal, characteristic, complemented
3C2×#467×C107C211yesmaximal, characteristic, complemented
4C2×#452×C107C211yesmaximal, characteristic, complemented
5C2×#408×C107C211yesmaximal, characteristic, complemented
6C107×#2616C211yesmaximal, characteristic, complemented
7C107×#2036C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#2001C211yesmaximal, characteristic, complemented
10C107×#2000C211yesmaximal, characteristic, complemented
11C107×#1894C211yesmaximal, characteristic, complemented
12C107×#1893C211yesmaximal, characteristic, complemented
13C107×#1872C211yesmaximal, characteristic, complemented
14C107×#1852C211yesmaximal, characteristic, complemented
15C107×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic
18C22×Q16×C107C2211yescharacteristic
19C22×SD16×C107C2211yescharacteristic
20C22×M16×C107C2211yescharacteristic
21C23×C8×C107C2211yescharacteristic
22#537×C107—24no—
23#537×C107—24no—
24C2×C22⋊Q8×C107—21no—
25C2×C22⋊Q8×C107C2211yescharacteristic
26C2×C22⋊Q8×C107C2211yescharacteristic
27C2×C22⋊Q8×C107C2211yescharacteristic
28C2×C22⋊Q8×C107C2211yescharacteristic
29C2×C22⋊Q8×C107C2211yescharacteristic
30C2×#121×C107—21no—
31C2×#121×C107—21no—
32C2×#121×C107—21no—
33C2×#121×C107C2211yescharacteristic
34C2×#121×C107C2211yescharacteristic
35C22×C4⋊C4×C107C2211yescharacteristic
36#468×C107—24no—
37#467×C107—24no—
38#452×C107—24no—
39C2×#107×C107C2211yescharacteristic
40C2×#107×C107C2211yescharacteristic
41C2×#103×C107C2211yescharacteristic
42C2×#103×C107C2211yescharacteristic
43C2×#103×C107C2211yescharacteristic
44C2×#103×C107C2211yescharacteristic
45C2×#103×C107C2211yescharacteristic
46C2×#102×C107C2211yescharacteristic
47C2×#102×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49#408×C107—24no—
50C2×C22⋊C8×C107C2211yescharacteristic
51C2×C22⋊C8×C107C2211yescharacteristic
52C2×C22⋊C8×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic
54#395×C107—21no—
55#394×C107—21no—
56#394×C107—21no—
57#394×C107—21no—
58#380×C107C2211yescharacteristic
59#380×C107C2211yescharacteristic
60#380×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic
62#340×C107C2211yescharacteristic
63#340×C107C2211yescharacteristic
64#340×C107C2211yescharacteristic
65C2×#41×C107—22no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—22no—
70C2×#41×C107—22no—
71C2×#41×C107—22no—
72C2×#41×C107—22no—
73C2×#41×C107—41no—
74C2×#41×C107—41no—
75C2×#41×C107—41no—
76C2×#41×C107—41no—
77C22×Q8×C107D411yescharacteristic
78C22×Q8×C107C2311yescharacteristic
79C22×Q8×C107C2311yescharacteristic
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107—21no—
83C22×D4×C107D411yescharacteristic
84C22×D4×C107D411yescharacteristic
85C22×D4×C107D411yescharacteristic
86C22×D4×C107C2311yescharacteristic
87C23×C4×C107—21no—
88C23×C4×C107—21no—
89C23×C4×C107C2311yescharacteristic
90C23×C4×C107C2311yescharacteristic
91C23×C4×C107C2311yescharacteristic
92C2×Q16×C107—22no—
93C2×Q16×C107—22no—
94C2×Q16×C107—41no—
95C2×SD16×C107—22no—
96C2×SD16×C107—22no—
97C2×SD16×C107—41no—
98C2×M16×C107—22no—
99C2×M16×C107—22no—
100C2×M16×C107—41no—
101C22×C8×C107—22no—
102C22×C8×C107—22no—
103C22×C8×C107—41no—
104C22×C8×C107C2311yescharacteristic
105C22×C8×C107C2311yescharacteristic
106C22×C8×C107C2311yescharacteristic
107C22×C8×C107C2311yescharacteristic
108C22⋊Q8×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—22no—
115C22⋊Q8×C107—22no—
116C22⋊Q8×C107—41no—
117C22⋊Q8×C107—41no—
118C22⋊Q8×C107D414yes—
119#121×C107—28no—
120#121×C107—28no—
121#121×C107—28no—
122#121×C107—22no—
123#121×C107—22no—
124#121×C107—22no—
125#121×C107D414yes—
126C2×C4⋊C4×C107—21no—
127C2×C4⋊C4×C107—21no—
128C2×C4⋊C4×C107—21no—
129C2×C4⋊C4×C107—22no—
130C2×C4⋊C4×C107—22no—
131C2×C4⋊C4×C107—21no—
132C2×C4⋊C4×C107—21no—
133C2×C4⋊C4×C107—21no—
134C2×C4⋊C4×C107C2311yescharacteristic
135C2×C4⋊C4×C107C2311yescharacteristic
136C2×C4⋊C4×C107C2311yescharacteristic
137C2×C4⋊C4×C107C2311yescharacteristic
138C2×C4⋊C4×C107C2311yescharacteristic
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×C107—21no—
146C2×C22⋊C4×C107—21no—
147C2×C22⋊C4×C107—21no—
148C2×C22⋊C4×C107—21no—
149#107×C107—22no—
150#107×C107—22no—
151#103×C107—22no—
152#103×C107—22no—
153#103×C107—22no—
154#103×C107—22no—
155#103×C107—41no—
156#102×C107—22no—
157#102×C107—22no—
158#102×C107—41no—
159C22⋊C8×C107—22no—
160C22⋊C8×C107—22no—
161C22⋊C8×C107—22no—
162C22⋊C8×C107D414yescomplemented
163#95×C107—21no—
164#95×C107—21no—
165#95×C107—21no—
166C24×C107—21no—
167C24×C107C2×D411yescharacteristic
168C24×C107C2×D411yescharacteristic
169C24×C107C2×D411yescharacteristic
170#41×C107—44no—
171#41×C107—44no—
172#41×C107—44no—
173#41×C107—44no—
174#41×C107—44no—
175#41×C107—44no—
176#41×C107—44no—
177#41×C107—44no—
178C2×Q8×C107—22no—
179C2×Q8×C107—22no—
180C2×Q8×C107—21no—
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—41no—
192C2×Q8×C107C2×D412yes—
193C2×D4×C107—24no—
194C2×D4×C107—22no—
195C2×D4×C107—22no—
196C2×D4×C107—22no—
197C2×D4×C107—22no—
198C2×D4×C107—24no—
199C2×D4×C107—24no—
200C2×D4×C107—22no—
201C2×D4×C107—22no—
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—41no—
209C2×D4×C107—41no—
210C2×D4×C107—42no—
211C2×D4×C107—42no—
212C2×D4×C107—81no—
213C2×D4×C107—81no—
214C2×D4×C107—81no—
215C2×D4×C107—81no—
216C2×D4×C107C2×D412yes—
217C22×C4×C107—21no—
218C22×C4×C107—21no—
219C22×C4×C107—21no—
220C22×C4×C107—21no—
221C22×C4×C107—21no—
222C22×C4×C107—21no—
223C22×C4×C107—21no—
224C22×C4×C107—21no—
225C22×C4×C107—24no—
226C22×C4×C107—21no—
227C22×C4×C107—21no—
228C22×C4×C107—21no—
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—42no—
241C22×C4×C107—42no—
242C22×C4×C107—81no—
243C22×C4×C107—81no—
244C22×C4×C107C2×D411yescharacteristic
245C22×C4×C107C2×D411yescharacteristic
246C22×C4×C107C2×D412yes—
247C22×C4×C107C2×D412yes—
248C22×C4×C107C2×D411yescharacteristic
249C22×C4×C107C2×D412yes—
250C22×C4×C107#4112yes—
251C22×C4×C107C2411yescharacteristic
252Q16×C107—44no—
253SD16×C107—44no—
254M16×C107—44no—
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—21no—
265C2×C8×C107—44no—
266C2×C8×C107C2×D412yes—
267C2×C8×C107C2×D412yes—
268C4⋊C4×C107—24no—
269C4⋊C4×C107—24no—
270C4⋊C4×C107—24no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—21no—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—21no—
279C4⋊C4×C107—42no—
280C4⋊C4×C107—42no—
281C4⋊C4×C107—42no—
282C4⋊C4×C107C2×D412yes—
283C4⋊C4×C107C2×D412yes—
284C22⋊C4×C107—24no—
285C22⋊C4×C107—24no—
286C22⋊C4×C107—24no—
287C22⋊C4×C107—24no—
288C22⋊C4×C107—42no—
289C22⋊C4×C107—42no—
290C22⋊C4×C107—42no—
291C22⋊C4×C107—81no—
292C22⋊C4×C107—81no—
293C22⋊C4×C107—81no—
294C23×C107—21no—
295C23×C107—21no—
296C23×C107—21no—
297C23×C107—21no—
298C23×C107—21no—
299C23×C107—21no—
300C23×C107—21no—
301C23×C107—21no—
302C23×C107—21no—
303C23×C107—21no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—21no—
307C23×C107—22no—
308C23×C107—21no—
309C23×C107—21no—
310C23×C107—21no—
311C23×C107—21no—
312C23×C107—21no—
313C23×C107—21no—
314C23×C107—41no—
315C23×C107—41no—
316C23×C107—41no—
317C23×C107—41no—
318C23×C107—41no—
319C23×C107—41no—
320C23×C107#12012yes—
321C23×C107#12112yes—
322C23×C107C22×D411yescharacteristic
323Q8×C107—22no—
324Q8×C107—22no—
325Q8×C107—44no—
326Q8×C107—41no—
327Q8×C107—41no—
328Q8×C107—41no—
329Q8×C107—41no—
330Q8×C107—41no—
331Q8×C107—41no—
332D4×C107—22no—
333D4×C107—22no—
334D4×C107—44no—
335D4×C107—44no—
336D4×C107—44no—
337D4×C107—48no—
338D4×C107—41no—
339D4×C107—41no—
340D4×C107—84no—
341D4×C107—84no—
342C2×C4×C107—21no—
343C2×C4×C107—21no—
344C2×C4×C107—21no—
345C2×C4×C107—21no—
346C2×C4×C107—22no—
347C2×C4×C107—22no—
348C2×C4×C107—22no—
349C2×C4×C107—22no—
350C2×C4×C107—22no—
351C2×C4×C107—22no—
352C2×C4×C107—22no—
353C2×C4×C107—22no—
354C2×C4×C107—22no—
355C2×C4×C107—22no—
356C2×C4×C107—22no—
357C2×C4×C107—21no—
358C2×C4×C107—21no—
359C2×C4×C107—21no—
360C2×C4×C107—48no—
361C2×C4×C107—41no—
362C2×C4×C107—41no—
363C2×C4×C107—41no—
364C2×C4×C107—41no—
365C2×C4×C107—41no—
366C2×C4×C107—41no—
367C2×C4×C107—41no—
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—84no—
384C2×C4×C107#12012yes—
385C2×C4×C107#12112yes—
386C2×C4×C107C22×D411yescharacteristic
387C2×C4×C107C22×D411yescharacteristic
388C2×C4×C107C22×D411yescharacteristic
389C2×C4×C107C2×#4111yescharacteristic
390C2×C4×C107H(5,𝔽2)11yescharacteristic
391C2×C4×C107H(5,𝔽2)11yescharacteristic
392C8×C107—22no—
393C8×C107—22no—
394C8×C107—41no—
395C8×C107—41no—
396C22×C107—22no—
397C22×C107—22no—
398C22×C107—22no—
399C22×C107—22no—
400C22×C107—22no—
401C22×C107—22no—
402C22×C107—41no—
403C22×C107—41no—
404C22×C107—41no—
405C22×C107—41no—
406C22×C107—41no—
407C22×C107—41no—
408C22×C107—41no—
409C22×C107—41no—
410C22×C107—42no—
411C22×C107—41no—
412C22×C107—41no—
413C22×C107—41no—
414C22×C107—41no—
415C22×C107—42no—
416C22×C107—41no—
417C22×C107—42no—
418C22×C107—41no—
419C22×C107—41no—
420C22×C107—81no—
421C22×C107—81no—
422C22×C107—81no—
423C22×C107—81no—
424C22×C107C2×#12011yescharacteristic
425C22×C107C2×#12111yescharacteristic
426C22×C107#53411yescharacteristic
427C22×C107#57611yescharacteristic
428C22×C107#57711yescharacteristic
429C22×C107#57811yescharacteristic
430C22×C107#57811yescharacteristic
431C4×C107—22no—
432C4×C107—22no—
433C4×C107—41no—
434C4×C107—42no—
435C4×C107—42no—
436C4×C107—42no—
437C4×C107—81no—
438C4×C107—81no—
439C4×C107—81no—
440C4×C107—81no—
441C4×C107D4211yescharacteristic
442C4×C107D4211yescharacteristic
443C4×C107#54611yescharacteristic
444C4×C107#54611yescharacteristic
445#24393C10711yesmaximal, characteristic, direct product factor, Sylow
446C2×C107—42no—
447C2×C107—42no—
448C2×C107—81no—
449C2×C107—82no—
450C2×C107#241011yescharacteristic
451C2×C107#301111yescharacteristic
452C2×C107#301211yescharacteristic
453C2×C107#306111yescharacteristic
454C2×C107#306311yescharacteristic
455C2×C107#320111yescharacteristic
456C2×C107#320311yescharacteristic
457C2×#537C2×C10711yescharacteristic
458C2×#468C2×C10711yescharacteristic, complemented
459C2×#467C2×C10711yescharacteristic, complemented
460C2×#452C2×C10711yescharacteristic, complemented
461C2×#408C2×C10711yescharacteristic, complemented
462#2616C2×C10711yescharacteristic, complemented
463#2036C2×C10711yescharacteristic, complemented
464#2033C2×C10711yescharacteristic, complemented
465#2001C2×C10711yescharacteristic, complemented
466#2000C2×C10711yescharacteristic, complemented
467#1894C2×C10711yescharacteristic, complemented
468#1893C2×C10711yescharacteristic, complemented
469#1872C2×C10711yescharacteristic, complemented
470#1852C2×C10711yescharacteristic, complemented
471#1788C2×C10711yescharacteristic, complemented
472C107#2439311yescharacteristic, direct product factor, Sylow
473C22×#41C22×C10711yescharacteristic
474C22×#41C22×C10711yescharacteristic
475C22×Q16C22×C10711yescharacteristic
476C22×SD16C22×C10711yescharacteristic
477C22×M16C22×C10711yescharacteristic
478C23×C8C22×C10711yescharacteristic
479#537—24no—
480#537—24no—
481C2×C22⋊Q8—21no—
482C2×C22⋊Q8C22×C10711yescharacteristic
483C2×C22⋊Q8C22×C10711yescharacteristic
484C2×C22⋊Q8C22×C10711yescharacteristic
485C2×C22⋊Q8C22×C10711yescharacteristic
486C2×C22⋊Q8C22×C10711yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121—21no—
490C2×#121C22×C10711yescharacteristic
491C2×#121C22×C10711yescharacteristic
492C22×C4⋊C4C22×C10711yescharacteristic
493#468—24no—
494#467—24no—
495#452—24no—
496C2×#107C22×C10711yescharacteristic
497C2×#107C22×C10711yescharacteristic
498C2×#103C22×C10711yescharacteristic
499C2×#103C22×C10711yescharacteristic
500C2×#103C22×C10711yescharacteristic
501C2×#103C22×C10711yescharacteristic
502C2×#103C22×C10711yescharacteristic
503C2×#102C22×C10711yescharacteristic
504C2×#102C22×C10711yescharacteristic
505C2×#102C22×C10711yescharacteristic
506#408—24no—
507C2×C22⋊C8C22×C10711yescharacteristic
508C2×C22⋊C8C22×C10711yescharacteristic
509C2×C22⋊C8C22×C10711yescharacteristic
510C2×C22⋊C8C22×C10711yescharacteristic
511#395—21no—
512#394—21no—
513#394—21no—
514#394—21no—
515#380C22×C10711yescharacteristic
516#380C22×C10711yescharacteristic
517#380C22×C10711yescharacteristic
518#340C22×C10711yescharacteristic
519#340C22×C10711yescharacteristic
520#340C22×C10711yescharacteristic
521#340C22×C10711yescharacteristic
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8D4×C10711yescharacteristic
535C22×Q8C23×C10711yescharacteristic
536C22×Q8C23×C10711yescharacteristic
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4D4×C10711yescharacteristic
541C22×D4D4×C10711yescharacteristic
542C22×D4D4×C10711yescharacteristic
543C22×D4C23×C10711yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C10711yescharacteristic
547C23×C4C23×C10711yescharacteristic
548C23×C4C23×C10711yescharacteristic
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8C23×C10711yescharacteristic
562C22×C8C23×C10711yescharacteristic
563C22×C8C23×C10711yescharacteristic
564C22×C8C23×C10711yescharacteristic
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8D4×C10714yes—
576#121—28no—
577#121—28no—
578#121—28no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121D4×C10714yes—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4C23×C10711yescharacteristic
592C2×C4⋊C4C23×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⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606#107—22no—
607#107—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8D4×C10714yescomplemented
620#95—21no—
621#95—21no—
622#95—21no—
623C24—21no—
624C24C2×D4×C10711yescharacteristic
625C24C2×D4×C10711yescharacteristic
626C24C2×D4×C10711yescharacteristic
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—41no—
649C2×Q8C2×D4×C10712yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—81no—
670C2×D4—81no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4C2×D4×C10712yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C2×D4×C10711yescharacteristic
702C22×C4C2×D4×C10711yescharacteristic
703C22×C4C2×D4×C10712yes—
704C22×C4C2×D4×C10712yes—
705C22×C4C2×D4×C10711yescharacteristic
706C22×C4C2×D4×C10712yes—
707C22×C4#41×C10712yes—
708C22×C4C24×C10711yescharacteristic
709Q16—44no—
710SD16—44no—
711M16—44no—
712C2×C8—21no—
713C2×C8—21no—
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—44no—
723C2×C8C2×D4×C10712yes—
724C2×C8C2×D4×C10712yes—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4C2×D4×C10712yes—
740C4⋊C4C2×D4×C10712yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C22⋊C4—81no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C10712yes—
778C23#121×C10712yes—
779C23C22×D4×C10711yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—44no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—44no—
792D4—44no—
793D4—44no—
794D4—48no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—48no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
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—84no—
841C2×C4#120×C10712yes—
842C2×C4#121×C10712yes—
843C2×C4C22×D4×C10711yescharacteristic
844C2×C4C22×D4×C10711yescharacteristic
845C2×C4C22×D4×C10711yescharacteristic
846C2×C4C2×#41×C10711yescharacteristic
847C2×C4H(5,𝔽2)×C10711yescharacteristic
848C2×C4H(5,𝔽2)×C10711yescharacteristic
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C10711yescharacteristic
882C22C2×#121×C10711yescharacteristic
883C22#534×C10711yescharacteristic
884C22#576×C10711yescharacteristic
885C22#577×C10711yescharacteristic
886C22#578×C10711yescharacteristic
887C22#578×C10711yescharacteristic
888C4—22no—
889C4—22no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4D42×C10711yescharacteristic
899C4D42×C10711yescharacteristic
900C4#546×C10711yescharacteristic
901C4#546×C10711yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—82no—
906C2C107×#241011yescharacteristic
907C2C107×#301111yescharacteristic
908C2C107×#301211yescharacteristic
909C2C107×#306111yescharacteristic
910C2C107×#306311yescharacteristic
911C2C107×#320111yescharacteristic
912C2C107×#320311yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#537×C107C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C22×#41×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#468×C107C2semidirect
3. C2×#467×C107C2semidirect
4. C2×#452×C107C2semidirect
5. C2×#408×C107C2semidirect
6. C107×#2616C2semidirect
7. C107×#2036C2semidirect
8. C107×#2033C2semidirect
9. C107×#2001C2semidirect
10. C107×#2000C2semidirect
11. C107×#1894C2semidirect
12. C107×#1893C2semidirect
13. C107×#1872C2semidirect
14. C107×#1852C2semidirect
15. C107×#1788C2semidirect
162. C22⋊C8×C107D4semidirect
445. #24393C107direct (N × H)
458. C2×#468C2×C107semidirect
459. C2×#467C2×C107semidirect
460. C2×#452C2×C107semidirect
461. C2×#408C2×C107semidirect
462. #2616C2×C107semidirect
463. #2036C2×C107semidirect
464. #2033C2×C107semidirect
465. #2001C2×C107semidirect
466. #2000C2×C107semidirect
467. #1894C2×C107semidirect
468. #1893C2×C107semidirect
469. #1872C2×C107semidirect
470. #1852C2×C107semidirect
471. #1788C2×C107semidirect
472. C107#24393direct (N × H)
619. C22⋊C8D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1072
C2×#468×C1072
C2×#467×C1072
C2×#452×C1072
C2×#408×C1072
C107×#26162
C107×#20362
C107×#20332
C107×#20012
C107×#20002
C107×#18942
C107×#18932
C107×#18722
C107×#18522
C107×#17882
#24393107