Finite Group Databasebeta

← C107×#24432 #41050396

Subgroups — C107×#24432 #41050396

Order 27392.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C107C211yesmaximal, characteristic
2C2×#465×C107C211yesmaximal, characteristic, complemented
3C2×#450×C107C211yesmaximal, characteristic, complemented
4C2×#450×C107C211yesmaximal, characteristic, complemented
5C22×#102×C107C211yesmaximal, characteristic, complemented
6C107×#2417C211yesmaximal, characteristic, complemented
7C107×#2041C211yesmaximal, characteristic, complemented
8C107×#2034C211yesmaximal, characteristic, complemented
9C107×#2014C211yesmaximal, characteristic, complemented
10C107×#2000C211yesmaximal, characteristic, complemented
11C107×#1877C211yesmaximal, characteristic, complemented
12C107×#1874C211yesmaximal, characteristic, complemented
13C107×#1869C211yesmaximal, characteristic, complemented
14C107×#1864C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C107—21no—
17C23×D4×C107C2211yescharacteristic
18C23×D4×C107C2211yescharacteristic
19C22×SD16×C107C2211yescharacteristic
20C22×SD16×C107C2211yescharacteristic, complemented
21C22×SD16×C107C2211yescharacteristic, complemented
22C23×C8×C107C2211yescharacteristic, complemented
23D42×C107—24no—
24D42×C107—24no—
25C2×#127×C107C2211yescharacteristic
26C2×C22⋊Q8×C107C2211yescharacteristic, complemented
27C2×C22⋊Q8×C107C2211yescharacteristic, complemented
28C2×#121×C107—21no—
29C2×#121×C107C2211yescharacteristic
30C2×#121×C107C2211yescharacteristic
31C2×#120×C107—21no—
32C2×#120×C107—21no—
33C2×C4×D4×C107C2211yescharacteristic
34C2×C4×D4×C107C2211yescharacteristic
35C22×C4⋊C4×C107C2211yescharacteristic, complemented
36#465×C107—24no—
37#450×C107—24no—
38#450×C107—24no—
39C2×#106×C107C2211yescharacteristic, complemented
40C2×#103×C107C2211yescharacteristic, complemented
41C2×#102×C107—24no—
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic, complemented
46C2×#102×C107C2211yescharacteristic, complemented
47C2×#102×C107C2211yescharacteristic, complemented
48C2×#102×C107C2211yescharacteristic, complemented
49C2×#102×C107C2211yescharacteristic, complemented
50C2×#102×C107C2211yescharacteristic, complemented
51C2×C22⋊C8×C107C2211yescharacteristic, complemented
52C2×C22⋊C8×C107C2211yescharacteristic, complemented
53C2×C22⋊C8×C107C2211yescharacteristic, complemented
54#398×C107—21no—
55#396×C107—21no—
56#391×C107C2211yescharacteristic, complemented
57#389×C107C2211yescharacteristic, complemented
58#386×C107—21no—
59#380×C107—21no—
60#380×C107C2211yescharacteristic, complemented
61#340×C107C2211yescharacteristic, complemented
62#340×C107C2211yescharacteristic, complemented
63#336×C107C2211yescharacteristic, complemented
64#336×C107C2211yescharacteristic, complemented
65C25×C107—21no—
66C25×C107—21no—
67C22×Q8×C107C2311yescharacteristic
68C22×D4×C107—22no—
69C22×D4×C107—22no—
70C22×D4×C107—28no—
71C22×D4×C107—21no—
72C22×D4×C107—21no—
73C22×D4×C107—22no—
74C22×D4×C107—22no—
75C22×D4×C107—22no—
76C22×D4×C107—22no—
77C22×D4×C107—21no—
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107—22no—
81C22×D4×C107—21no—
82C22×D4×C107—41no—
83C22×D4×C107—41no—
84C22×D4×C107—41no—
85C22×D4×C107—41no—
86C22×D4×C107—44no—
87C22×D4×C107—44no—
88C22×D4×C107D411yescharacteristic
89C22×D4×C107D414yes—
90C22×D4×C107C2311yescharacteristic
91C22×D4×C107C2311yescharacteristic
92C22×D4×C107C2311yescharacteristic
93C23×C4×C107—21no—
94C23×C4×C107—21no—
95C23×C4×C107C2311yescharacteristic
96C23×C4×C107C2311yescharacteristic
97C2×SD16×C107—22no—
98C2×SD16×C107—22no—
99C2×SD16×C107—22no—
100C2×SD16×C107—22no—
101C2×SD16×C107—22no—
102C2×SD16×C107—22no—
103C2×SD16×C107—41no—
104C2×SD16×C107—41no—
105C2×SD16×C107—41no—
106C22×C8×C107—22no—
107C22×C8×C107—22no—
108C22×C8×C107—41no—
109C22×C8×C107C2311yescharacteristic
110C22×C8×C107C2311yescharacteristic
111C22×C8×C107C2311yescharacteristic
112C22×C8×C107C2311yescharacteristic
113#127×C107—22no—
114#127×C107—22no—
115C22⋊Q8×C107—22no—
116C22⋊Q8×C107—22no—
117C22⋊Q8×C107—22no—
118C22⋊Q8×C107—41no—
119#121×C107—28no—
120#121×C107—22no—
121#121×C107—22no—
122#121×C107—22no—
123#121×C107D414yes—
124#120×C107—28no—
125#120×C107—28no—
126C4×D4×C107—22no—
127C4×D4×C107—22no—
128C4×D4×C107—22no—
129C4×D4×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×C107—21no—
135C2×C4⋊C4×C107—41no—
136C2×C4⋊C4×C107D411yescharacteristic
137C2×C4⋊C4×C107C2311yescharacteristic
138C2×C4⋊C4×C107C2311yescharacteristic
139C2×C4⋊C4×C107C2311yescharacteristic
140C2×C4⋊C4×C107C2311yescharacteristic
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×C107D411yescharacteristic
148C2×C22⋊C4×C107D411yescharacteristic
149C2×C42×C107C2311yescharacteristic
150#106×C107—22no—
151#103×C107—22no—
152#102×C107—22no—
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—
160#102×C107D414yescomplemented
161C22⋊C8×C107—22no—
162C22⋊C8×C107—22no—
163C22⋊C8×C107—41no—
164#95×C107—21no—
165#95×C107—21no—
166#95×C107—21no—
167#95×C107—21no—
168C24×C107—21no—
169C24×C107—24no—
170C24×C107—21no—
171C24×C107—21no—
172C24×C107—24no—
173C24×C107—42no—
174C24×C107—42no—
175C24×C107—42no—
176C24×C107—42no—
177C24×C107—42no—
178C24×C107—42no—
179C24×C107—42no—
180C24×C107—42no—
181C24×C107—81no—
182C24×C107—81no—
183C24×C107—81no—
184C24×C107—81no—
185C24×C107C2×D411yescharacteristic
186C24×C107C2×D411yescharacteristic
187C2×Q8×C107—21no—
188C2×Q8×C107—21no—
189C2×Q8×C107—21no—
190C2×Q8×C107—21no—
191C2×Q8×C107—21no—
192C2×Q8×C107—21no—
193C2×D4×C107—22no—
194C2×D4×C107—22no—
195C2×D4×C107—28no—
196C2×D4×C107—24no—
197C2×D4×C107—24no—
198C2×D4×C107—24no—
199C2×D4×C107—24no—
200C2×D4×C107—24no—
201C2×D4×C107—24no—
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—21no—
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—42no—
223C2×D4×C107—44no—
224C2×D4×C107—44no—
225C2×D4×C107—432no—
226C2×D4×C107—44no—
227C2×D4×C107—42no—
228C2×D4×C107—42no—
229C2×D4×C107—42no—
230C2×D4×C107—42no—
231C2×D4×C107—44no—
232C2×D4×C107—42no—
233C2×D4×C107—81no—
234C2×D4×C107—81no—
235C2×D4×C107SD1614yescomplemented
236C2×D4×C107C2×D412yes—
237C2×D4×C107C2×D412yes—
238C2×D4×C107C2×D412yes—
239C2×D4×C107C2×D412yes—
240C2×D4×C107#4112yes—
241C22×C4×C107—21no—
242C22×C4×C107—21no—
243C22×C4×C107—21no—
244C22×C4×C107—21no—
245C22×C4×C107—24no—
246C22×C4×C107—21no—
247C22×C4×C107—21no—
248C22×C4×C107—21no—
249C22×C4×C107—21no—
250C22×C4×C107—21no—
251C22×C4×C107—21no—
252C22×C4×C107—21no—
253C22×C4×C107—21no—
254C22×C4×C107—21no—
255C22×C4×C107—21no—
256C22×C4×C107—21no—
257C22×C4×C107—42no—
258C22×C4×C107—42no—
259C22×C4×C107—42no—
260C22×C4×C107—42no—
261C22×C4×C107—81no—
262C22×C4×C107C2×D411yescharacteristic
263C22×C4×C107C2×D411yescharacteristic
264C22×C4×C107C2×D411yescharacteristic
265C22×C4×C107C2×D412yes—
266C22×C4×C107C2×D412yes—
267C22×C4×C107C2×D411yescharacteristic
268C22×C4×C107C2411yescharacteristic
269SD16×C107—44no—
270SD16×C107—44no—
271SD16×C107—44no—
272C2×C8×C107—21no—
273C2×C8×C107—21no—
274C2×C8×C107—21no—
275C2×C8×C107—21no—
276C2×C8×C107—21no—
277C2×C8×C107—21no—
278C2×C8×C107—21no—
279C2×C8×C107—21no—
280C2×C8×C107—21no—
281C2×C8×C107—21no—
282C2×C8×C107—21no—
283C2×C8×C107—44no—
284C2×C8×C107C2×D412yescomplemented
285C4⋊C4×C107—22no—
286C4⋊C4×C107—21no—
287C4⋊C4×C107—21no—
288C4⋊C4×C107—21no—
289C4⋊C4×C107—21no—
290C4⋊C4×C107—21no—
291C4⋊C4×C107—21no—
292C4⋊C4×C107—42no—
293C4⋊C4×C107—42no—
294C4⋊C4×C107—42no—
295C4⋊C4×C107—81no—
296C4⋊C4×C107C2×D412yes—
297C4⋊C4×C107C2×D412yescomplemented
298C22⋊C4×C107—24no—
299C22⋊C4×C107—24no—
300C22⋊C4×C107—22no—
301C22⋊C4×C107—24no—
302C22⋊C4×C107—22no—
303C22⋊C4×C107—42no—
304C22⋊C4×C107—42no—
305C22⋊C4×C107—81no—
306C42×C107—21no—
307C42×C107—21no—
308C23×C107—21no—
309C23×C107—21no—
310C23×C107—21no—
311C23×C107—21no—
312C23×C107—21no—
313C23×C107—22no—
314C23×C107—21no—
315C23×C107—22no—
316C23×C107—21no—
317C23×C107—22no—
318C23×C107—21no—
319C23×C107—21no—
320C23×C107—21no—
321C23×C107—22no—
322C23×C107—22no—
323C23×C107—48no—
324C23×C107—48no—
325C23×C107—48no—
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—41no—
338C23×C107—41no—
339C23×C107—41no—
340C23×C107—41no—
341C23×C107—41no—
342C23×C107—48no—
343C23×C107—84no—
344C23×C107—84no—
345C23×C107—84no—
346C23×C107—84no—
347C23×C107—84no—
348C23×C107—84no—
349C23×C107—84no—
350C23×C107—84no—
351C23×C107—84no—
352C23×C107—84no—
353C23×C107#12012yes—
354C23×C107C2×SD1612yes—
355C23×C107C2×SD1612yes—
356C23×C107AGL(1,ℤ/8)12yes—
357C23×C107C22×D411yescharacteristic
358Q8×C107—41no—
359Q8×C107—41no—
360Q8×C107—41no—
361Q8×C107—41no—
362D4×C107—28no—
363D4×C107—22no—
364D4×C107—22no—
365D4×C107—22no—
366D4×C107—22no—
367D4×C107—22no—
368D4×C107—22no—
369D4×C107—22no—
370D4×C107—48no—
371D4×C107—48no—
372D4×C107—48no—
373D4×C107—48no—
374D4×C107—48no—
375D4×C107—41no—
376D4×C107—41no—
377D4×C107—41no—
378D4×C107—41no—
379D4×C107—84no—
380D4×C107#12114yes—
381C2×C4×C107—21no—
382C2×C4×C107—21no—
383C2×C4×C107—21no—
384C2×C4×C107—21no—
385C2×C4×C107—22no—
386C2×C4×C107—22no—
387C2×C4×C107—22no—
388C2×C4×C107—22no—
389C2×C4×C107—21no—
390C2×C4×C107—21no—
391C2×C4×C107—22no—
392C2×C4×C107—22no—
393C2×C4×C107—21no—
394C2×C4×C107—21no—
395C2×C4×C107—21no—
396C2×C4×C107—21no—
397C2×C4×C107—48no—
398C2×C4×C107—41no—
399C2×C4×C107—41no—
400C2×C4×C107—41no—
401C2×C4×C107—41no—
402C2×C4×C107—41no—
403C2×C4×C107—41no—
404C2×C4×C107—41no—
405C2×C4×C107—41no—
406C2×C4×C107—41no—
407C2×C4×C107—41no—
408C2×C4×C107—41no—
409C2×C4×C107—41no—
410C2×C4×C107—41no—
411C2×C4×C107—41no—
412C2×C4×C107—41no—
413C2×C4×C107—41no—
414C2×C4×C107—41no—
415C2×C4×C107—84no—
416C2×C4×C107#12012yes—
417C2×C4×C107C2×SD1612yes—
418C2×C4×C107C22×D411yescharacteristic
419C2×C4×C107C22×D411yescharacteristic
420C2×C4×C107C22×D411yescharacteristic
421C2×C4×C107C2×#4111yescharacteristic
422C2×C4×C107H(5,𝔽2)11yescharacteristic
423C2×C4×C107H(5,𝔽2)11yescharacteristic
424C8×C107—22no—
425C8×C107—41no—
426C8×C107—41no—
427C8×C107—41no—
428C22×C107—22no—
429C22×C107—22no—
430C22×C107—22no—
431C22×C107—22no—
432C22×C107—22no—
433C22×C107—22no—
434C22×C107—24no—
435C22×C107—22no—
436C22×C107—22no—
437C22×C107—22no—
438C22×C107—41no—
439C22×C107—42no—
440C22×C107—41no—
441C22×C107—42no—
442C22×C107—41no—
443C22×C107—42no—
444C22×C107—42no—
445C22×C107—42no—
446C22×C107—41no—
447C22×C107—42no—
448C22×C107—42no—
449C22×C107—42no—
450C22×C107—42no—
451C22×C107—42no—
452C22×C107—42no—
453C22×C107—42no—
454C22×C107—816no—
455C22×C107—816no—
456C22×C107—81no—
457C22×C107—81no—
458C22×C107—81no—
459C22×C107—81no—
460C22×C107—81no—
461C22×C107—81no—
462C22×C107—81no—
463C22×C107—81no—
464C22×C107#45014yescomplemented
465C22×C107C2×#12011yescharacteristic
466C22×C107D4211yescharacteristic
467C22×C107#54611yescharacteristic
468C22×C107C22×SD1611yescharacteristic
469C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C107#57611yescharacteristic
471C22×C107#57711yescharacteristic
472C4×C107—22no—
473C4×C107—22no—
474C4×C107—41no—
475C4×C107—42no—
476C4×C107—42no—
477C4×C107—41no—
478C4×C107—81no—
479C4×C107—81no—
480C4×C107—81no—
481C4×C107C2×#12111yescharacteristic
482C4×C107#53411yescharacteristic
483C4×C107D4211yescharacteristic
484C4×C107#54611yescharacteristic
485#24432C10711yesmaximal, characteristic, direct product factor, Sylow
486C2×C107—24no—
487C2×C107—42no—
488C2×C107—44no—
489C2×C107—82no—
490C2×C107—82no—
491C2×C107#241011yescharacteristic
492C2×C107C2×#45011yescharacteristic
493C2×C107#301211yescharacteristic
494C2×C107#326411yescharacteristic
495C2×C107D4×SD1611yescharacteristic
496C2×C107#329511yescharacteristic
497C2×C107#331011yescharacteristic
498C2×D42C2×C10711yescharacteristic
499C2×#465C2×C10711yescharacteristic, complemented
500C2×#450C2×C10711yescharacteristic, complemented
501C2×#450C2×C10711yescharacteristic, complemented
502C22×#102C2×C10711yescharacteristic, complemented
503#2417C2×C10711yescharacteristic, complemented
504#2041C2×C10711yescharacteristic, complemented
505#2034C2×C10711yescharacteristic, complemented
506#2014C2×C10711yescharacteristic, complemented
507#2000C2×C10711yescharacteristic, complemented
508#1877C2×C10711yescharacteristic, complemented
509#1874C2×C10711yescharacteristic, complemented
510#1869C2×C10711yescharacteristic, complemented
511#1864C2×C10711yescharacteristic, complemented
512#1786C2×C10711yescharacteristic, complemented
513C107#2443211yescharacteristic, direct product factor, Sylow
514C23×D4—21no—
515C23×D4C22×C10711yescharacteristic
516C23×D4C22×C10711yescharacteristic
517C22×SD16C22×C10711yescharacteristic
518C22×SD16C22×C10711yescharacteristic, complemented
519C22×SD16C22×C10711yescharacteristic, complemented
520C23×C8C22×C10711yescharacteristic, complemented
521D42—24no—
522D42—24no—
523C2×#127C22×C10711yescharacteristic
524C2×C22⋊Q8C22×C10711yescharacteristic, complemented
525C2×C22⋊Q8C22×C10711yescharacteristic, complemented
526C2×#121—21no—
527C2×#121C22×C10711yescharacteristic
528C2×#121C22×C10711yescharacteristic
529C2×#120—21no—
530C2×#120—21no—
531C2×C4×D4C22×C10711yescharacteristic
532C2×C4×D4C22×C10711yescharacteristic
533C22×C4⋊C4C22×C10711yescharacteristic, complemented
534#465—24no—
535#450—24no—
536#450—24no—
537C2×#106C22×C10711yescharacteristic, complemented
538C2×#103C22×C10711yescharacteristic, complemented
539C2×#102—24no—
540C2×#102C22×C10711yescharacteristic
541C2×#102C22×C10711yescharacteristic
542C2×#102C22×C10711yescharacteristic
543C2×#102C22×C10711yescharacteristic, complemented
544C2×#102C22×C10711yescharacteristic, complemented
545C2×#102C22×C10711yescharacteristic, complemented
546C2×#102C22×C10711yescharacteristic, complemented
547C2×#102C22×C10711yescharacteristic, complemented
548C2×#102C22×C10711yescharacteristic, complemented
549C2×C22⋊C8C22×C10711yescharacteristic, complemented
550C2×C22⋊C8C22×C10711yescharacteristic, complemented
551C2×C22⋊C8C22×C10711yescharacteristic, complemented
552#398—21no—
553#396—21no—
554#391C22×C10711yescharacteristic, complemented
555#389C22×C10711yescharacteristic, complemented
556#386—21no—
557#380—21no—
558#380C22×C10711yescharacteristic, complemented
559#340C22×C10711yescharacteristic, complemented
560#340C22×C10711yescharacteristic, complemented
561#336C22×C10711yescharacteristic, complemented
562#336C22×C10711yescharacteristic, complemented
563C25—21no—
564C25—21no—
565C22×Q8C23×C10711yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C10711yescharacteristic
587C22×D4D4×C10714yes—
588C22×D4C23×C10711yescharacteristic
589C22×D4C23×C10711yescharacteristic
590C22×D4C23×C10711yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C10711yescharacteristic
594C23×C4C23×C10711yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C10711yescharacteristic
608C22×C8C23×C10711yescharacteristic
609C22×C8C23×C10711yescharacteristic
610C22×C8C23×C10711yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C10714yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C10711yescharacteristic
635C2×C4⋊C4C23×C10711yescharacteristic
636C2×C4⋊C4C23×C10711yescharacteristic
637C2×C4⋊C4C23×C10711yescharacteristic
638C2×C4⋊C4C23×C10711yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C10711yescharacteristic
646C2×C22⋊C4D4×C10711yescharacteristic
647C2×C42C23×C10711yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C10714yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C10711yescharacteristic
684C24C2×D4×C10711yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C10714yescomplemented
734C2×D4C2×D4×C10712yes—
735C2×D4C2×D4×C10712yes—
736C2×D4C2×D4×C10712yes—
737C2×D4C2×D4×C10712yes—
738C2×D4#41×C10712yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C10711yescharacteristic
761C22×C4C2×D4×C10711yescharacteristic
762C22×C4C2×D4×C10711yescharacteristic
763C22×C4C2×D4×C10712yes—
764C22×C4C2×D4×C10712yes—
765C22×C4C2×D4×C10711yescharacteristic
766C22×C4C24×C10711yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C10712yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C10712yes—
795C4⋊C4C2×D4×C10712yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—48no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C10712yes—
852C23C2×SD16×C10712yes—
853C23C2×SD16×C10712yes—
854C23AGL(1,ℤ/8)×C10712yes—
855C23C22×D4×C10711yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C10714yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C10712yes—
915C2×C4C2×SD16×C10712yes—
916C2×C4C22×D4×C10711yescharacteristic
917C2×C4C22×D4×C10711yescharacteristic
918C2×C4C22×D4×C10711yescharacteristic
919C2×C4C2×#41×C10711yescharacteristic
920C2×C4H(5,𝔽2)×C10711yescharacteristic
921C2×C4H(5,𝔽2)×C10711yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—24no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—42no—
940C22—41no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22#450×C10714yescomplemented
963C22C2×#120×C10711yescharacteristic
964C22D42×C10711yescharacteristic
965C22#546×C10711yescharacteristic
966C22C22×SD16×C10711yescharacteristic
967C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
968C22#576×C10711yescharacteristic
969C22#577×C10711yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C10711yescharacteristic
980C4#534×C10711yescharacteristic
981C4D42×C10711yescharacteristic
982C4#546×C10711yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C107×#241011yescharacteristic
989C2C2×#450×C10711yescharacteristic
990C2C107×#301211yescharacteristic
991C2C107×#326411yescharacteristic
992C2D4×SD16×C10711yescharacteristic
993C2C107×#329511yescharacteristic
994C2C107×#331011yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×D42×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×#450×C107C2semidirect
4. C2×#450×C107C2semidirect
5. C22×#102×C107C2semidirect
6. C107×#2417C2semidirect
7. C107×#2041C2semidirect
8. C107×#2034C2semidirect
9. C107×#2014C2semidirect
10. C107×#2000C2semidirect
11. C107×#1877C2semidirect
12. C107×#1874C2semidirect
13. C107×#1869C2semidirect
14. C107×#1864C2semidirect
15. C107×#1786C2semidirect
20. C22×SD16×C107C22semidirect
21. C22×SD16×C107C22semidirect
22. C23×C8×C107C22semidirect
26. C2×C22⋊Q8×C107C22semidirect
27. C2×C22⋊Q8×C107C22semidirect
35. C22×C4⋊C4×C107C22semidirect
39. C2×#106×C107C22semidirect
40. C2×#103×C107C22semidirect
45. C2×#102×C107C22semidirect
46. C2×#102×C107C22semidirect
47. C2×#102×C107C22semidirect
48. C2×#102×C107C22semidirect
49. C2×#102×C107C22semidirect
50. C2×#102×C107C22semidirect
51. C2×C22⋊C8×C107C22semidirect
52. C2×C22⋊C8×C107C22semidirect
53. C2×C22⋊C8×C107C22semidirect
56. #391×C107C22semidirect
57. #389×C107C22semidirect
60. #380×C107C22semidirect
61. #340×C107C22semidirect
62. #340×C107C22semidirect
63. #336×C107C22semidirect
64. #336×C107C22semidirect
160. #102×C107D4semidirect
235. C2×D4×C107SD16semidirect
284. C2×C8×C107C2×D4semidirect
297. C4⋊C4×C107C2×D4semidirect
464. C22×C107#450semidirect
485. #24432C107direct (N × H)
499. C2×#465C2×C107semidirect
500. C2×#450C2×C107semidirect
501. C2×#450C2×C107semidirect
502. C22×#102C2×C107semidirect
503. #2417C2×C107semidirect
504. #2041C2×C107semidirect
505. #2034C2×C107semidirect
506. #2014C2×C107semidirect
507. #2000C2×C107semidirect
508. #1877C2×C107semidirect
509. #1874C2×C107semidirect
510. #1869C2×C107semidirect
511. #1864C2×C107semidirect
512. #1786C2×C107semidirect
513. C107#24432direct (N × H)
518. C22×SD16C22×C107semidirect
519. C22×SD16C22×C107semidirect
520. C23×C8C22×C107semidirect
524. C2×C22⋊Q8C22×C107semidirect
525. C2×C22⋊Q8C22×C107semidirect
533. C22×C4⋊C4C22×C107semidirect
537. C2×#106C22×C107semidirect
538. C2×#103C22×C107semidirect
543. C2×#102C22×C107semidirect
544. C2×#102C22×C107semidirect
545. C2×#102C22×C107semidirect
546. C2×#102C22×C107semidirect
547. C2×#102C22×C107semidirect
548. C2×#102C22×C107semidirect
549. C2×C22⋊C8C22×C107semidirect
550. C2×C22⋊C8C22×C107semidirect
551. C2×C22⋊C8C22×C107semidirect
554. #391C22×C107semidirect
555. #389C22×C107semidirect
558. #380C22×C107semidirect
559. #340C22×C107semidirect
560. #340C22×C107semidirect
561. #336C22×C107semidirect
562. #336C22×C107semidirect
658. #102D4×C107semidirect
733. C2×D4SD16×C107semidirect
782. C2×C8C2×D4×C107semidirect
795. C4⋊C4C2×D4×C107semidirect
962. C22#450×C107semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1072
C2×#465×C1072
C2×#450×C1072
C22×#102×C1072
C107×#24172
C107×#20412
C107×#20342
C107×#20142
C107×#20002
C107×#18772
C107×#18742
C107×#18692
C107×#18642
C107×#17862
#24432107