Finite Group Databasebeta

← C107×#25376 #41051340

Subgroups — C107×#25376 #41051340

Order 27392.

1162 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#496×C107C211yesmaximal, characteristic, complemented
2C2×#463×C107C211yesmaximal, characteristic, complemented
3C2×#459×C107C211yesmaximal, characteristic, complemented
4C2×#459×C107C211yesmaximal, characteristic, complemented
5C107×#2544C211yesmaximal, characteristic, complemented
6C107×#2366C211yesmaximal, characteristic, complemented
7C107×#2055C211yesmaximal, characteristic, complemented
8C107×#2054C211yesmaximal, characteristic, complemented
9C107×#2012C211yesmaximal, characteristic, complemented
10C107×#2011C211yesmaximal, characteristic, complemented
11C107×#1983C211yesmaximal, characteristic, complemented
12C107×#1940C211yesmaximal, characteristic, complemented
13C107×#1879C211yesmaximal, characteristic, complemented
14C107×#1877C211yesmaximal, characteristic, complemented
15C107×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×D8×C107C2211yescharacteristic
19C22×D8×C107C2211yescharacteristic
20C22×D8×C107C2211yescharacteristic
21C22×D8×C107C2211yescharacteristic
22C2×#127×C107C2211yescharacteristic
23C2×#127×C107C2211yescharacteristic
24C2×#124×C107C2211yescharacteristic
25C2×#124×C107C2211yescharacteristic
26C2×C4×D4×C107—21no—
27C2×C4×D4×C107C2211yescharacteristic
28C2×C4×D4×C107C2211yescharacteristic
29C2×C4×D4×C107C2211yescharacteristic
30#496×C107—24no—
31#463×C107—24no—
32#459×C107—24no—
33#459×C107—24no—
34C2×C4⋊C8×C107C2211yescharacteristic
35C2×C4⋊C8×C107C2211yescharacteristic
36C2×C4⋊C8×C107C2211yescharacteristic
37C2×#103×C107C2211yescharacteristic
38C2×#103×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×#97×C107C2211yescharacteristic
46#394×C107—21no—
47#394×C107—21no—
48#391×C107C2211yescharacteristic
49#390×C107—21no—
50#390×C107C2211yescharacteristic
51#390×C107C2211yescharacteristic
52#390×C107C2211yescharacteristic
53#386×C107—21no—
54#386×C107—21no—
55#386×C107—21no—
56#386×C107—21no—
57C4×C4⋊C4×C107C2211yescharacteristic
58C4×C4⋊C4×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#340×C107C2211yescharacteristic
61#336×C107C2211yescharacteristic
62#336×C107C2211yescharacteristic
63C22×Q8×C107C2311yescharacteristic
64C22×D4×C107—21no—
65C22×D4×C107—21no—
66C22×D4×C107—21no—
67C22×D4×C107—21no—
68C22×D4×C107C2311yescharacteristic
69C22×D4×C107C2311yescharacteristic
70C22×D4×C107C2311yescharacteristic
71C22×D4×C107C2311yescharacteristic
72C23×C4×C107—21no—
73C23×C4×C107—21no—
74C23×C4×C107—21no—
75C2×SD16×C107—22no—
76C2×SD16×C107—22no—
77C2×SD16×C107—22no—
78C2×SD16×C107—22no—
79C2×SD16×C107—41no—
80C2×SD16×C107—41no—
81C2×D8×C107—22no—
82C2×D8×C107—22no—
83C2×D8×C107—22no—
84C2×D8×C107—22no—
85C2×D8×C107—22no—
86C2×D8×C107—22no—
87C2×D8×C107—22no—
88C2×D8×C107—22no—
89C2×D8×C107—41no—
90C2×D8×C107—41no—
91C2×D8×C107—41no—
92C2×D8×C107—41no—
93C22×C8×C107C2311yescharacteristic
94C22×C8×C107C2311yescharacteristic
95C22×C8×C107C2311yescharacteristic
96C22×C8×C107C2311yescharacteristic
97#127×C107—22no—
98#127×C107—22no—
99#127×C107—41no—
100#127×C107D414yescomplemented
101#124×C107—22no—
102#124×C107—22no—
103#124×C107—22no—
104#124×C107—41no—
105C4×D4×C107—22no—
106C4×D4×C107—22no—
107C4×D4×C107—22no—
108C4×D4×C107—22no—
109C4×D4×C107—41no—
110C4×D4×C107—41no—
111C4×D4×C107—44no—
112C2×C4⋊C4×C107D411yescharacteristic
113C2×C4⋊C4×C107D411yescharacteristic
114C2×C4⋊C4×C107C2311yescharacteristic
115C2×C4⋊C4×C107C2311yescharacteristic
116C2×C4⋊C4×C107C2311yescharacteristic
117C2×C22⋊C4×C107—21no—
118C2×C22⋊C4×C107—21no—
119C2×C22⋊C4×C107—21no—
120C2×C22⋊C4×C107—21no—
121C2×C22⋊C4×C107—21no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—21no—
128C2×C22⋊C4×C107—21no—
129C2×C22⋊C4×C107—21no—
130C2×C42×C107—21no—
131C2×C42×C107C2311yescharacteristic
132C2×C42×C107C2311yescharacteristic
133C2×C42×C107C2311yescharacteristic
134C4⋊C8×C107—22no—
135C4⋊C8×C107—22no—
136C4⋊C8×C107—22no—
137#103×C107—22no—
138#103×C107—41no—
139#102×C107—22no—
140#102×C107—22no—
141#102×C107—22no—
142#102×C107—22no—
143#102×C107—41no—
144#102×C107D414yescomplemented
145#97×C107—22no—
146#95×C107—21no—
147#95×C107—21no—
148#95×C107—21no—
149#95×C107D411yescharacteristic
150#95×C107D411yescharacteristic
151C24×C107—21no—
152C24×C107—21no—
153C24×C107—21no—
154C24×C107—21no—
155C2×Q8×C107—21no—
156C2×Q8×C107—21no—
157C2×Q8×C107—21no—
158C2×Q8×C107—21no—
159C2×Q8×C107—21no—
160C2×Q8×C107—21no—
161C2×D4×C107—24no—
162C2×D4×C107—24no—
163C2×D4×C107—21no—
164C2×D4×C107—21no—
165C2×D4×C107—21no—
166C2×D4×C107—21no—
167C2×D4×C107—21no—
168C2×D4×C107—21no—
169C2×D4×C107—21no—
170C2×D4×C107—21no—
171C2×D4×C107—21no—
172C2×D4×C107—21no—
173C2×D4×C107—21no—
174C2×D4×C107—21no—
175C2×D4×C107—21no—
176C2×D4×C107—21no—
177C2×D4×C107—21no—
178C2×D4×C107—21no—
179C2×D4×C107—21no—
180C2×D4×C107—21no—
181C2×D4×C107—21no—
182C2×D4×C107—21no—
183C2×D4×C107—21no—
184C2×D4×C107—42no—
185C2×D4×C107—42no—
186C2×D4×C107—42no—
187C2×D4×C107—42no—
188C2×D4×C107—42no—
189C2×D4×C107—42no—
190C2×D4×C107—81no—
191C2×D4×C107—81no—
192C2×D4×C107—81no—
193C2×D4×C107—81no—
194C2×D4×C107C2×D412yes—
195C2×D4×C107C2×D412yes—
196C2×D4×C107C2×D412yes—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—42no—
202C22×C4×C107—42no—
203C22×C4×C107—42no—
204C22×C4×C107—42no—
205C22×C4×C107—42no—
206C22×C4×C107—81no—
207C22×C4×C107—81no—
208C22×C4×C107—81no—
209C22×C4×C107—81no—
210C22×C4×C107C2×D411yescharacteristic
211C22×C4×C107C2×D411yescharacteristic
212C22×C4×C107C2×D411yescharacteristic
213C22×C4×C107C2×D411yescharacteristic
214C22×C4×C107C2×D411yescharacteristic
215C22×C4×C107C2×D411yescharacteristic
216C22×C4×C107C2411yescharacteristic
217SD16×C107—44no—
218SD16×C107—44no—
219D8×C107—44no—
220D8×C107—44no—
221D8×C107—44no—
222D8×C107—44no—
223C2×C8×C107—21no—
224C2×C8×C107—21no—
225C2×C8×C107—21no—
226C2×C8×C107—21no—
227C2×C8×C107—21no—
228C2×C8×C107—21no—
229C2×C8×C107—21no—
230C2×C8×C107—21no—
231C2×C8×C107—21no—
232C2×C8×C107—21no—
233C2×C8×C107C2×D412yes—
234C2×C8×C107#4112yes—
235C4⋊C4×C107—22no—
236C4⋊C4×C107—21no—
237C4⋊C4×C107—21no—
238C4⋊C4×C107—21no—
239C4⋊C4×C107—21no—
240C4⋊C4×C107—21no—
241C4⋊C4×C107—41no—
242C4⋊C4×C107C2×D412yes—
243C22⋊C4×C107—42no—
244C22⋊C4×C107—42no—
245C22⋊C4×C107—42no—
246C22⋊C4×C107—42no—
247C22⋊C4×C107—42no—
248C22⋊C4×C107—42no—
249C22⋊C4×C107—42no—
250C22⋊C4×C107—42no—
251C22⋊C4×C107—42no—
252C22⋊C4×C107—81no—
253C22⋊C4×C107—81no—
254C22⋊C4×C107—81no—
255C22⋊C4×C107—81no—
256C42×C107—21no—
257C42×C107—21no—
258C42×C107—21no—
259C42×C107—21no—
260C42×C107—42no—
261C42×C107C2×D412yes—
262C42×C107#4112yes—
263C23×C107—22no—
264C23×C107—22no—
265C23×C107—22no—
266C23×C107—41no—
267C23×C107—41no—
268C23×C107—41no—
269C23×C107—41no—
270C23×C107—41no—
271C23×C107—41no—
272C23×C107—41no—
273C23×C107—41no—
274C23×C107—41no—
275C23×C107—41no—
276C23×C107—41no—
277C23×C107—41no—
278C23×C107—41no—
279C23×C107—41no—
280C23×C107—41no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—41no—
285C23×C107—41no—
286C23×C107—41no—
287C23×C107—41no—
288C23×C107—41no—
289C23×C107—41no—
290C23×C107—41no—
291C23×C107C22×D411yescharacteristic
292Q8×C107—41no—
293Q8×C107—41no—
294Q8×C107—41no—
295Q8×C107—41no—
296D4×C107—22no—
297D4×C107—22no—
298D4×C107—22no—
299D4×C107—22no—
300D4×C107—22no—
301D4×C107—22no—
302D4×C107—48no—
303D4×C107—41no—
304D4×C107—41no—
305D4×C107—41no—
306D4×C107—41no—
307D4×C107—41no—
308D4×C107—41no—
309D4×C107—41no—
310D4×C107—41no—
311D4×C107—41no—
312D4×C107—41no—
313D4×C107—84no—
314D4×C107—84no—
315D4×C107—84no—
316C2×C4×C107—21no—
317C2×C4×C107—21no—
318C2×C4×C107—21no—
319C2×C4×C107—21no—
320C2×C4×C107—21no—
321C2×C4×C107—21no—
322C2×C4×C107—21no—
323C2×C4×C107—21no—
324C2×C4×C107—21no—
325C2×C4×C107—22no—
326C2×C4×C107—21no—
327C2×C4×C107—21no—
328C2×C4×C107—21no—
329C2×C4×C107—21no—
330C2×C4×C107—21no—
331C2×C4×C107—21no—
332C2×C4×C107—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
335C2×C4×C107—41no—
336C2×C4×C107—41no—
337C2×C4×C107—41no—
338C2×C4×C107—41no—
339C2×C4×C107—41no—
340C2×C4×C107—41no—
341C2×C4×C107—41no—
342C2×C4×C107—41no—
343C2×C4×C107—84no—
344C2×C4×C107—84no—
345C2×C4×C107—84no—
346C2×C4×C107#12112yes—
347C2×C4×C107#12112yes—
348C2×C4×C107AGL(1,ℤ/8)12yes—
349C2×C4×C107C22×D411yescharacteristic
350C2×C4×C107C22×D411yescharacteristic
351C2×C4×C107C2×#4111yescharacteristic
352C2×C4×C107C2×#4111yescharacteristic
353C2×C4×C107H(5,𝔽2)11yescharacteristic
354C2×C4×C107H(5,𝔽2)11yescharacteristic
355C8×C107—22no—
356C8×C107—22no—
357C8×C107—41no—
358C8×C107—41no—
359C22×C107—42no—
360C22×C107—42no—
361C22×C107—42no—
362C22×C107—42no—
363C22×C107—42no—
364C22×C107—42no—
365C22×C107—42no—
366C22×C107—42no—
367C22×C107—42no—
368C22×C107—81no—
369C22×C107—81no—
370C22×C107—81no—
371C22×C107—81no—
372C22×C107—81no—
373C22×C107—81no—
374C22×C107—81no—
375C22×C107—81no—
376C22×C107—81no—
377C22×C107—81no—
378C22×C107—81no—
379C22×C107—81no—
380C22×C107—81no—
381C22×C107—81no—
382C22×C107—81no—
383C22×C107—81no—
384C22×C107—81no—
385C22×C107—81no—
386C22×C107—81no—
387C22×C107C2×#12111yescharacteristic
388C22×C107D4211yescharacteristic
389C22×C107#55011yescharacteristic
390C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
391C22×C107#57511yescharacteristic
392C22×C107#57611yescharacteristic
393C22×C107#57611yescharacteristic
394C4×C107—22no—
395C4×C107—22no—
396C4×C107—22no—
397C4×C107—41no—
398C4×C107—42no—
399C4×C107—41no—
400C4×C107—41no—
401C4×C107—81no—
402C4×C107—81no—
403C4×C107—81no—
404C4×C107#53211yescharacteristic
405C4×C107#54011yescharacteristic
406C4×C107D4211yescharacteristic
407C4×C107#54611yescharacteristic
408#25376C10711yesmaximal, characteristic, direct product factor, Sylow
409C2×C107—82no—
410C2×C107—82no—
411C2×C107—82no—
412C2×C107—161no—
413C2×C107#242811yescharacteristic
414C2×C107#303611yescharacteristic
415C2×C107#304111yescharacteristic
416C2×C107#326411yescharacteristic
417C2×C107#326811yescharacteristic
418C2×C107#339911yescharacteristic
419C2×C107#340311yescharacteristic
420C2×#496C2×C10711yescharacteristic, complemented
421C2×#463C2×C10711yescharacteristic, complemented
422C2×#459C2×C10711yescharacteristic, complemented
423C2×#459C2×C10711yescharacteristic, complemented
424#2544C2×C10711yescharacteristic, complemented
425#2366C2×C10711yescharacteristic, complemented
426#2055C2×C10711yescharacteristic, complemented
427#2054C2×C10711yescharacteristic, complemented
428#2012C2×C10711yescharacteristic, complemented
429#2011C2×C10711yescharacteristic, complemented
430#1983C2×C10711yescharacteristic, complemented
431#1940C2×C10711yescharacteristic, complemented
432#1879C2×C10711yescharacteristic, complemented
433#1877C2×C10711yescharacteristic, complemented
434#1762C2×C10711yescharacteristic, complemented
435C107#2537611yescharacteristic, direct product factor, Sylow
436C22×SD16C22×C10711yescharacteristic
437C22×SD16C22×C10711yescharacteristic
438C22×D8C22×C10711yescharacteristic
439C22×D8C22×C10711yescharacteristic
440C22×D8C22×C10711yescharacteristic
441C22×D8C22×C10711yescharacteristic
442C2×#127C22×C10711yescharacteristic
443C2×#127C22×C10711yescharacteristic
444C2×#124C22×C10711yescharacteristic
445C2×#124C22×C10711yescharacteristic
446C2×C4×D4—21no—
447C2×C4×D4C22×C10711yescharacteristic
448C2×C4×D4C22×C10711yescharacteristic
449C2×C4×D4C22×C10711yescharacteristic
450#496—24no—
451#463—24no—
452#459—24no—
453#459—24no—
454C2×C4⋊C8C22×C10711yescharacteristic
455C2×C4⋊C8C22×C10711yescharacteristic
456C2×C4⋊C8C22×C10711yescharacteristic
457C2×#103C22×C10711yescharacteristic
458C2×#103C22×C10711yescharacteristic
459C2×#102C22×C10711yescharacteristic
460C2×#102C22×C10711yescharacteristic
461C2×#102C22×C10711yescharacteristic
462C2×#102C22×C10711yescharacteristic
463C2×#102C22×C10711yescharacteristic
464C2×#102C22×C10711yescharacteristic
465C2×#97C22×C10711yescharacteristic
466#394—21no—
467#394—21no—
468#391C22×C10711yescharacteristic
469#390—21no—
470#390C22×C10711yescharacteristic
471#390C22×C10711yescharacteristic
472#390C22×C10711yescharacteristic
473#386—21no—
474#386—21no—
475#386—21no—
476#386—21no—
477C4×C4⋊C4C22×C10711yescharacteristic
478C4×C4⋊C4C22×C10711yescharacteristic
479#340C22×C10711yescharacteristic
480#340C22×C10711yescharacteristic
481#336C22×C10711yescharacteristic
482#336C22×C10711yescharacteristic
483C22×Q8C23×C10711yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4C23×C10711yescharacteristic
489C22×D4C23×C10711yescharacteristic
490C22×D4C23×C10711yescharacteristic
491C22×D4C23×C10711yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C2×D8—41no—
512C2×D8—41no—
513C22×C8C23×C10711yescharacteristic
514C22×C8C23×C10711yescharacteristic
515C22×C8C23×C10711yescharacteristic
516C22×C8C23×C10711yescharacteristic
517#127—22no—
518#127—22no—
519#127—41no—
520#127D4×C10714yescomplemented
521#124—22no—
522#124—22no—
523#124—22no—
524#124—41no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—41no—
530C4×D4—41no—
531C4×D4—44no—
532C2×C4⋊C4D4×C10711yescharacteristic
533C2×C4⋊C4D4×C10711yescharacteristic
534C2×C4⋊C4C23×C10711yescharacteristic
535C2×C4⋊C4C23×C10711yescharacteristic
536C2×C4⋊C4C23×C10711yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C42—21no—
551C2×C42C23×C10711yescharacteristic
552C2×C42C23×C10711yescharacteristic
553C2×C42C23×C10711yescharacteristic
554C4⋊C8—22no—
555C4⋊C8—22no—
556C4⋊C8—22no—
557#103—22no—
558#103—41no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C10714yescomplemented
565#97—22no—
566#95—21no—
567#95—21no—
568#95—21no—
569#95D4×C10711yescharacteristic
570#95D4×C10711yescharacteristic
571C24—21no—
572C24—21no—
573C24—21no—
574C24—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C2×D4×C10712yes—
615C2×D4C2×D4×C10712yes—
616C2×D4C2×D4×C10712yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—81no—
627C22×C4—81no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4C2×D4×C10711yescharacteristic
631C22×C4C2×D4×C10711yescharacteristic
632C22×C4C2×D4×C10711yescharacteristic
633C22×C4C2×D4×C10711yescharacteristic
634C22×C4C2×D4×C10711yescharacteristic
635C22×C4C2×D4×C10711yescharacteristic
636C22×C4C24×C10711yescharacteristic
637SD16—44no—
638SD16—44no—
639D8—44no—
640D8—44no—
641D8—44no—
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8C2×D4×C10712yes—
654C2×C8#41×C10712yes—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—41no—
662C4⋊C4C2×D4×C10712yes—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—81no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—42no—
681C42C2×D4×C10712yes—
682C42#41×C10712yes—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23C22×D4×C10711yescharacteristic
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—84no—
734D4—84no—
735D4—84no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4#121×C10712yes—
767C2×C4#121×C10712yes—
768C2×C4AGL(1,ℤ/8)×C10712yes—
769C2×C4C22×D4×C10711yescharacteristic
770C2×C4C22×D4×C10711yescharacteristic
771C2×C4C2×#41×C10711yescharacteristic
772C2×C4C2×#41×C10711yescharacteristic
773C2×C4H(5,𝔽2)×C10711yescharacteristic
774C2×C4H(5,𝔽2)×C10711yescharacteristic
775C8—22no—
776C8—22no—
777C8—41no—
778C8—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C10711yescharacteristic
808C22D42×C10711yescharacteristic
809C22#550×C10711yescharacteristic
810C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
811C22#575×C10711yescharacteristic
812C22#576×C10711yescharacteristic
813C22#576×C10711yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—41no—
818C4—42no—
819C4—41no—
820C4—41no—
821C4—81no—
822C4—81no—
823C4—81no—
824C4#532×C10711yescharacteristic
825C4#540×C10711yescharacteristic
826C4D42×C10711yescharacteristic
827C4#546×C10711yescharacteristic
828C2—82no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C107×#242811yescharacteristic
833C2C107×#303611yescharacteristic
834C2C107×#304111yescharacteristic
835C2C107×#326411yescharacteristic
836C2C107×#326811yescharacteristic
837C2C107×#339911yescharacteristic
838C2C107×#340311yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C4⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#496×C107C2semidirect
2. C2×#463×C107C2semidirect
3. C2×#459×C107C2semidirect
4. C2×#459×C107C2semidirect
5. C107×#2544C2semidirect
6. C107×#2366C2semidirect
7. C107×#2055C2semidirect
8. C107×#2054C2semidirect
9. C107×#2012C2semidirect
10. C107×#2011C2semidirect
11. C107×#1983C2semidirect
12. C107×#1940C2semidirect
13. C107×#1879C2semidirect
14. C107×#1877C2semidirect
15. C107×#1762C2semidirect
100. #127×C107D4semidirect
144. #102×C107D4semidirect
408. #25376C107direct (N × H)
420. C2×#496C2×C107semidirect
421. C2×#463C2×C107semidirect
422. C2×#459C2×C107semidirect
423. C2×#459C2×C107semidirect
424. #2544C2×C107semidirect
425. #2366C2×C107semidirect
426. #2055C2×C107semidirect
427. #2054C2×C107semidirect
428. #2012C2×C107semidirect
429. #2011C2×C107semidirect
430. #1983C2×C107semidirect
431. #1940C2×C107semidirect
432. #1879C2×C107semidirect
433. #1877C2×C107semidirect
434. #1762C2×C107semidirect
435. C107#25376direct (N × H)
520. #127D4×C107semidirect
564. #102D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#496×C1072
C2×#463×C1072
C2×#459×C1072
C107×#25442
C107×#23662
C107×#20552
C107×#20542
C107×#20122
C107×#20112
C107×#19832
C107×#19402
C107×#18792
C107×#18772
C107×#17622
#25376107