Finite Group Databasebeta

← C107×#23876 #41049840

Subgroups — C107×#23876 #41049840

Order 27392.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C107C211yesmaximal, characteristic, complemented
2C107×#3488C211yesmaximal, characteristic, complemented
3C2×#453×C107C212yesmaximal, complemented
4C107×#3003C211yesmaximal, characteristic, complemented
5C107×#2433C211yesmaximal, characteristic, complemented
6C107×#2006C212yesmaximal, complemented
7C107×#2002C212yesmaximal, complemented
8C107×#1900C211yesmaximal, characteristic, complemented
9C107×#1883C212yesmaximal, complemented
10C107×#1871C211yesmaximal, characteristic, complemented
11C107×#1789C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C107C2211yescharacteristic, complemented
13C22×#41×C107C2211yescharacteristic
14C23×D4×C107C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C107—21no—
16C2×AGL(1,ℤ/8)×C107—21no—
17C2×AGL(1,ℤ/8)×C107—28no—
18C2×AGL(1,ℤ/8)×C107C2212yes—
19C2×AGL(1,ℤ/8)×C107C2212yescomplemented
20C2×AGL(1,ℤ/8)×C107C2212yescomplemented
21C22×SD16×C107—21no—
22C22×D8×C107—21no—
23C22×M16×C107C2211yescharacteristic, complemented
24#550×C107—21no—
25#548×C107—21no—
26#546×C107—21no—
27#546×C107—22no—
28D42×C107—22no—
29D42×C107—21no—
30#537×C107—21no—
31#537×C107C2211yescharacteristic, complemented
32#535×C107—21no—
33#535×C107C2211yescharacteristic, complemented
34C2×#127×C107C2212yescomplemented
35#525×C107—21no—
36#525×C107C2211yescharacteristic
37C2×#121×C107—21no—
38C2×#121×C107C2211yescharacteristic
39C2×#120×C107—22no—
40#520×C107C2211yescharacteristic, complemented
41#453×C107—28no—
42#450×C107—21no—
43#450×C107—21no—
44#447×C107—21no—
45#447×C107—21no—
46C2×#104×C107C2212yescomplemented
47C2×#104×C107C2212yescomplemented
48C2×#104×C107C2212yescomplemented
49#418×C107C2212yescomplemented
50C2×#100×C107C2212yescomplemented
51#407×C107C2211yescharacteristic, complemented
52#392×C107—22no—
53#390×C107C2212yescomplemented
54C4×C22⋊C4×C107C2211yescharacteristic, complemented
55#343×C107C2212yescomplemented
56#339×C107C2212yescomplemented
57C25×C107—21no—
58H(5,𝔽2)×C107—24no—
59H(5,𝔽2)×C107—42no—
60C2×#41×C107—21no—
61C2×#41×C107—21no—
62C2×#41×C107—21no—
63C2×#41×C107—21no—
64C2×#41×C107—24no—
65C2×#41×C107—42no—
66C2×#41×C107D411yescharacteristic, complemented
67C2×#41×C107D411yescharacteristic, complemented
68C2×#41×C107C2311yescharacteristic
69C2×#41×C107C2311yescharacteristic
70C2×#41×C107C2311yescharacteristic
71C22×Q8×C107D411yescharacteristic, complemented
72C22×D4×C107—24no—
73C22×D4×C107—21no—
74C22×D4×C107—22no—
75C22×D4×C107—22no—
76C22×D4×C107—21no—
77C22×D4×C107—21no—
78C22×D4×C107—24no—
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107—21no—
83C22×D4×C107—21no—
84C22×D4×C107—42no—
85C22×D4×C107D412yes—
86C22×D4×C107D411yescharacteristic, complemented
87C22×D4×C107C2311yescharacteristic
88C22×D4×C107C2312yes—
89C23×C4×C107—21no—
90C23×C4×C107C2311yescharacteristic
91AGL(1,ℤ/8)×C107—28no—
92AGL(1,ℤ/8)×C107—28no—
93AGL(1,ℤ/8)×C107—24no—
94AGL(1,ℤ/8)×C107—24no—
95AGL(1,ℤ/8)×C107—24no—
96AGL(1,ℤ/8)×C107—24no—
97AGL(1,ℤ/8)×C107—42no—
98AGL(1,ℤ/8)×C107D418yescomplemented
99C2×SD16×C107—28no—
100C2×SD16×C107—22no—
101C2×SD16×C107—22no—
102C2×SD16×C107—22no—
103C2×D8×C107—28no—
104C2×D8×C107—22no—
105C2×D8×C107—22no—
106C2×D8×C107—22no—
107C2×M16×C107—21no—
108C2×M16×C107—24no—
109C2×M16×C107C2312yes—
110C2×M16×C107C2312yes—
111C22×C8×C107—21no—
112#127×C107—22no—
113#127×C107—21no—
114#127×C107—24no—
115#127×C107—42no—
116#124×C107—22no—
117#124×C107—21no—
118#123×C107—22no—
119#123×C107—21no—
120C22⋊Q8×C107—22no—
121C22⋊Q8×C107—21no—
122C22⋊Q8×C107—21no—
123C22⋊Q8×C107D411yescharacteristic, complemented
124C22⋊Q8×C107D411yescharacteristic, complemented
125#121×C107—22no—
126#121×C107—22no—
127#121×C107—22no—
128#121×C107—22no—
129#121×C107—22no—
130#121×C107—21no—
131#121×C107—21no—
132#121×C107—21no—
133#121×C107—21no—
134#121×C107—21no—
135#121×C107—21no—
136#121×C107—22no—
137#121×C107—21no—
138#121×C107—21no—
139#121×C107D411yescharacteristic, complemented
140#121×C107D411yescharacteristic, complemented
141#120×C107—22no—
142#120×C107—22no—
143#120×C107—22no—
144#120×C107—21no—
145#120×C107—22no—
146#120×C107—48no—
147C4×Q8×C107—21no—
148C4×D4×C107—22no—
149C4×D4×C107—22no—
150C4×D4×C107—21no—
151C4×D4×C107—22no—
152C4×D4×C107—21no—
153C4×D4×C107—21no—
154#117×C107—21no—
155#117×C107C2311yescharacteristic
156C2×C4⋊C4×C107—21no—
157C2×C4⋊C4×C107C2311yescharacteristic
158C2×C22⋊C4×C107—22no—
159C2×C22⋊C4×C107—21no—
160C2×C22⋊C4×C107—24no—
161C2×C22⋊C4×C107D412yes—
162C2×C42×C107C2312yes—
163#104×C107—24no—
164#104×C107—24no—
165#104×C107—42no—
166#102×C107—22no—
167#102×C107—22no—
168#100×C107—24no—
169C22⋊C8×C107—21no—
170C22⋊C8×C107—21no—
171#95×C107—21no—
172C24×C107—22no—
173C24×C107—22no—
174C24×C107—21no—
175C24×C107—44no—
176C24×C107—44no—
177C24×C107—41no—
178C24×C107—41no—
179C24×C107—82no—
180C24×C107C2×D411yescharacteristic
181C24×C107C2×D412yes—
182#41×C107—22no—
183#41×C107—22no—
184#41×C107—22no—
185#41×C107—22no—
186#41×C107—22no—
187#41×C107—22no—
188#41×C107—22no—
189#41×C107—44no—
190#41×C107—41no—
191#41×C107—41no—
192#41×C107—44no—
193#41×C107—44no—
194#41×C107—42no—
195#41×C107—42no—
196#41×C107C2×D414yes—
197C2×Q8×C107—21no—
198C2×Q8×C107—22no—
199C2×Q8×C107—41no—
200C2×Q8×C107C2×D411yescharacteristic
201C2×Q8×C107C2×D411yescharacteristic
202C2×Q8×C107C2×D411yescharacteristic
203C2×D4×C107—21no—
204C2×D4×C107—24no—
205C2×D4×C107—24no—
206C2×D4×C107—22no—
207C2×D4×C107—22no—
208C2×D4×C107—22no—
209C2×D4×C107—22no—
210C2×D4×C107—21no—
211C2×D4×C107—21no—
212C2×D4×C107—21no—
213C2×D4×C107—21no—
214C2×D4×C107—21no—
215C2×D4×C107—22no—
216C2×D4×C107—22no—
217C2×D4×C107—22no—
218C2×D4×C107—21no—
219C2×D4×C107—22no—
220C2×D4×C107—21no—
221C2×D4×C107—22no—
222C2×D4×C107—22no—
223C2×D4×C107—22no—
224C2×D4×C107—22no—
225C2×D4×C107—21no—
226C2×D4×C107—21no—
227C2×D4×C107—22no—
228C2×D4×C107—22no—
229C2×D4×C107—22no—
230C2×D4×C107—41no—
231C2×D4×C107—44no—
232C2×D4×C107—44no—
233C2×D4×C107—44no—
234C2×D4×C107—44no—
235C2×D4×C107—42no—
236C2×D4×C107—42no—
237C2×D4×C107—48no—
238C2×D4×C107—44no—
239C2×D4×C107—48no—
240C2×D4×C107—42no—
241C2×D4×C107—42no—
242C2×D4×C107—44no—
243C2×D4×C107—48no—
244C2×D4×C107—41no—
245C2×D4×C107—41no—
246C2×D4×C107—84no—
247C2×D4×C107—84no—
248C2×D4×C107C2×D411yescharacteristic
249C2×D4×C107C2×D411yescharacteristic
250C2×D4×C107C2×D411yescharacteristic
251C2×D4×C107C2×D414yescomplemented
252C22×C4×C107—21no—
253C22×C4×C107—22no—
254C22×C4×C107—22no—
255C22×C4×C107—22no—
256C22×C4×C107—21no—
257C22×C4×C107—22no—
258C22×C4×C107—22no—
259C22×C4×C107—21no—
260C22×C4×C107—21no—
261C22×C4×C107—21no—
262C22×C4×C107—21no—
263C22×C4×C107—44no—
264C22×C4×C107C2×D411yescharacteristic
265C22×C4×C107C2×D411yescharacteristic
266C22×C4×C107C2×D411yescharacteristic
267C22×C4×C107C2×D411yescharacteristic
268C22×C4×C107C2×D411yescharacteristic
269C22×C4×C107C2×D412yes—
270C22×C4×C107C2411yescharacteristic
271SD16×C107—28no—
272SD16×C107—28no—
273SD16×C107—44no—
274D8×C107—28no—
275D8×C107—28no—
276D8×C107—44no—
277M16×C107—24no—
278M16×C107—22no—
279M16×C107—22no—
280M16×C107—22no—
281M16×C107C2×D414yescomplemented
282C2×C8×C107—24no—
283C2×C8×C107—22no—
284C2×C8×C107—22no—
285C4⋊C4×C107—22no—
286C4⋊C4×C107—22no—
287C4⋊C4×C107—21no—
288C4⋊C4×C107—21no—
289C4⋊C4×C107—21no—
290C4⋊C4×C107—21no—
291C4⋊C4×C107C2×D411yescharacteristic
292C4⋊C4×C107C2×D411yescharacteristic
293C22⋊C4×C107—22no—
294C22⋊C4×C107—22no—
295C22⋊C4×C107—24no—
296C22⋊C4×C107—22no—
297C22⋊C4×C107—22no—
298C22⋊C4×C107—22no—
299C22⋊C4×C107—21no—
300C22⋊C4×C107—21no—
301C22⋊C4×C107—21no—
302C22⋊C4×C107—21no—
303C22⋊C4×C107—22no—
304C22⋊C4×C107—22no—
305C22⋊C4×C107—21no—
306C22⋊C4×C107—48no—
307C42×C107—22no—
308C42×C107—21no—
309C42×C107—22no—
310C42×C107—22no—
311C23×C107—21no—
312C23×C107—22no—
313C23×C107—22no—
314C23×C107—22no—
315C23×C107—21no—
316C23×C107—21no—
317C23×C107—24no—
318C23×C107—24no—
319C23×C107—41no—
320C23×C107—42no—
321C23×C107—44no—
322C23×C107—44no—
323C23×C107—44no—
324C23×C107—44no—
325C23×C107—44no—
326C23×C107—42no—
327C23×C107—42no—
328C23×C107—42no—
329C23×C107—42no—
330C23×C107—42no—
331C23×C107—81no—
332C23×C107—82no—
333C23×C107—82no—
334C23×C107—82no—
335C23×C107—82no—
336C23×C107—82no—
337C23×C107—816no—
338C23×C107—82no—
339C23×C107#12011yescharacteristic
340C23×C107#12011yescharacteristic
341C23×C107C22×D411yescharacteristic
342Q8×C107—21no—
343Q8×C107—21no—
344Q8×C107—21no—
345Q8×C107—22no—
346Q8×C107—42no—
347Q8×C107#12012yescomplemented
348D4×C107—24no—
349D4×C107—21no—
350D4×C107—24no—
351D4×C107—21no—
352D4×C107—21no—
353D4×C107—22no—
354D4×C107—24no—
355D4×C107—42no—
356D4×C107—42no—
357D4×C107—44no—
358D4×C107—44no—
359D4×C107—44no—
360D4×C107—42no—
361D4×C107—44no—
362D4×C107—42no—
363D4×C107—42no—
364D4×C107—44no—
365D4×C107—42no—
366D4×C107—41no—
367D4×C107—42no—
368D4×C107—41no—
369D4×C107—42no—
370D4×C107—42no—
371D4×C107—81no—
372D4×C107—82no—
373D4×C107—82no—
374D4×C107—82no—
375D4×C107—82no—
376D4×C107—816no—
377D4×C107#12012yescomplemented
378C2×C4×C107—21no—
379C2×C4×C107—22no—
380C2×C4×C107—21no—
381C2×C4×C107—21no—
382C2×C4×C107—21no—
383C2×C4×C107—21no—
384C2×C4×C107—22no—
385C2×C4×C107—22no—
386C2×C4×C107—24no—
387C2×C4×C107—24no—
388C2×C4×C107—21no—
389C2×C4×C107—22no—
390C2×C4×C107—21no—
391C2×C4×C107—21no—
392C2×C4×C107—21no—
393C2×C4×C107—42no—
394C2×C4×C107—42no—
395C2×C4×C107—42no—
396C2×C4×C107—44no—
397C2×C4×C107—42no—
398C2×C4×C107—42no—
399C2×C4×C107—41no—
400C2×C4×C107—41no—
401C2×C4×C107—42no—
402C2×C4×C107—42no—
403C2×C4×C107—82no—
404C2×C4×C107#12011yescharacteristic
405C2×C4×C107#12011yescharacteristic
406C2×C4×C107C22×D411yescharacteristic
407C2×C4×C107C22×D412yes—
408C2×C4×C107C22×D411yescharacteristic
409C2×C4×C107H(5,𝔽2)12yes—
410C8×C107—24no—
411C8×C107—42no—
412C22×C107—21no—
413C22×C107—21no—
414C22×C107—21no—
415C22×C107—21no—
416C22×C107—21no—
417C22×C107—22no—
418C22×C107—21no—
419C22×C107—21no—
420C22×C107—44no—
421C22×C107—48no—
422C22×C107—41no—
423C22×C107—41no—
424C22×C107—41no—
425C22×C107—41no—
426C22×C107—42no—
427C22×C107—44no—
428C22×C107—42no—
429C22×C107—41no—
430C22×C107—41no—
431C22×C107—41no—
432C22×C107—42no—
433C22×C107—41no—
434C22×C107—84no—
435C22×C107—84no—
436C22×C107—84no—
437C22×C107—88no—
438C22×C107—88no—
439C22×C107—82no—
440C22×C107—82no—
441C22×C107—164no—
442C22×C107#45312yescomplemented
443C22×C107C2×#12011yescharacteristic
444C22×C107D4212yes—
445C4×C107—21no—
446C4×C107—21no—
447C4×C107—22no—
448C4×C107—44no—
449C4×C107—41no—
450C4×C107—41no—
451C4×C107—42no—
452C4×C107—41no—
453C4×C107—41no—
454C4×C107C2×#12011yescharacteristic
455C4×C107#53411yescharacteristic
456C4×C107D4212yes—
457#23876C10711yesmaximal, characteristic, direct product factor, Sylow
458C2×C107—22no—
459C2×C107—22no—
460C2×C107—41no—
461C2×C107—42no—
462C2×C107—81no—
463C2×C107—84no—
464C2×C107—82no—
465C2×C107—81no—
466C2×C107#240311yescharacteristic
467C2×C107C2×#45311yescharacteristic
468C2×C107#302111yescharacteristic
469C22×AGL(1,ℤ/8)C2×C10711yescharacteristic, complemented
470#3488C2×C10711yescharacteristic, complemented
471C2×#453C2×C10712yescomplemented
472#3003C2×C10711yescharacteristic, complemented
473#2433C2×C10711yescharacteristic, complemented
474#2006C2×C10712yescomplemented
475#2002C2×C10712yescomplemented
476#1900C2×C10711yescharacteristic, complemented
477#1883C2×C10712yescomplemented
478#1871C2×C10711yescharacteristic, complemented
479#1789C2×C10711yescharacteristic, complemented
480C107#2387611yescharacteristic, direct product factor, Sylow
481C2×H(5,𝔽2)C22×C10711yescharacteristic, complemented
482C22×#41C22×C10711yescharacteristic
483C23×D4C22×C10711yescharacteristic, complemented
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—21no—
486C2×AGL(1,ℤ/8)—28no—
487C2×AGL(1,ℤ/8)C22×C10712yes—
488C2×AGL(1,ℤ/8)C22×C10712yescomplemented
489C2×AGL(1,ℤ/8)C22×C10712yescomplemented
490C22×SD16—21no—
491C22×D8—21no—
492C22×M16C22×C10711yescharacteristic, complemented
493#550—21no—
494#548—21no—
495#546—21no—
496#546—22no—
497D42—22no—
498D42—21no—
499#537—21no—
500#537C22×C10711yescharacteristic, complemented
501#535—21no—
502#535C22×C10711yescharacteristic, complemented
503C2×#127C22×C10712yescomplemented
504#525—21no—
505#525C22×C10711yescharacteristic
506C2×#121—21no—
507C2×#121C22×C10711yescharacteristic
508C2×#120—22no—
509#520C22×C10711yescharacteristic, complemented
510#453—28no—
511#450—21no—
512#450—21no—
513#447—21no—
514#447—21no—
515C2×#104C22×C10712yescomplemented
516C2×#104C22×C10712yescomplemented
517C2×#104C22×C10712yescomplemented
518#418C22×C10712yescomplemented
519C2×#100C22×C10712yescomplemented
520#407C22×C10711yescharacteristic, complemented
521#392—22no—
522#390C22×C10712yescomplemented
523C4×C22⋊C4C22×C10711yescharacteristic, complemented
524#343C22×C10712yescomplemented
525#339C22×C10712yescomplemented
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C10711yescharacteristic, complemented
536C2×#41D4×C10711yescharacteristic, complemented
537C2×#41C23×C10711yescharacteristic
538C2×#41C23×C10711yescharacteristic
539C2×#41C23×C10711yescharacteristic
540C22×Q8D4×C10711yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C10712yes—
555C22×D4D4×C10711yescharacteristic, complemented
556C22×D4C23×C10711yescharacteristic
557C22×D4C23×C10712yes—
558C23×C4—21no—
559C23×C4C23×C10711yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C10718yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C10712yes—
579C2×M16C23×C10712yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C10711yescharacteristic, complemented
593C22⋊Q8D4×C10711yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C10711yescharacteristic, complemented
609#121D4×C10711yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C10711yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C10711yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C10712yes—
631C2×C42C23×C10712yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C10711yescharacteristic
650C24C2×D4×C10712yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C10714yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C10711yescharacteristic
670C2×Q8C2×D4×C10711yescharacteristic
671C2×Q8C2×D4×C10711yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C10711yescharacteristic
718C2×D4C2×D4×C10711yescharacteristic
719C2×D4C2×D4×C10711yescharacteristic
720C2×D4C2×D4×C10714yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C10711yescharacteristic
734C22×C4C2×D4×C10711yescharacteristic
735C22×C4C2×D4×C10711yescharacteristic
736C22×C4C2×D4×C10711yescharacteristic
737C22×C4C2×D4×C10711yescharacteristic
738C22×C4C2×D4×C10712yes—
739C22×C4C24×C10711yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C10714yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C10711yescharacteristic
761C4⋊C4C2×D4×C10711yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C10711yescharacteristic
809C23#120×C10711yescharacteristic
810C23C22×D4×C10711yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C10712yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—44no—
832D4—42no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—82no—
841D4—81no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C10712yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C10711yescharacteristic
874C2×C4#120×C10711yescharacteristic
875C2×C4C22×D4×C10711yescharacteristic
876C2×C4C22×D4×C10712yes—
877C2×C4C22×D4×C10711yescharacteristic
878C2×C4H(5,𝔽2)×C10712yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22#453×C10712yescomplemented
912C22C2×#120×C10711yescharacteristic
913C22D42×C10712yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4C2×#120×C10711yescharacteristic
924C4#534×C10711yescharacteristic
925C4D42×C10712yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2C107×#240311yescharacteristic
935C2C2×#453×C10711yescharacteristic
936C2C107×#302111yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C107C2semidirect
2. C107×#3488C2semidirect
3. C2×#453×C107C2semidirect
4. C107×#3003C2semidirect
5. C107×#2433C2semidirect
6. C107×#2006C2semidirect
7. C107×#2002C2semidirect
8. C107×#1900C2semidirect
9. C107×#1883C2semidirect
10. C107×#1871C2semidirect
11. C107×#1789C2semidirect
12. C2×H(5,𝔽2)×C107C22semidirect
14. C23×D4×C107C22semidirect
19. C2×AGL(1,ℤ/8)×C107C22semidirect
20. C2×AGL(1,ℤ/8)×C107C22semidirect
23. C22×M16×C107C22semidirect
31. #537×C107C22semidirect
33. #535×C107C22semidirect
34. C2×#127×C107C22semidirect
40. #520×C107C22semidirect
46. C2×#104×C107C22semidirect
47. C2×#104×C107C22semidirect
48. C2×#104×C107C22semidirect
49. #418×C107C22semidirect
50. C2×#100×C107C22semidirect
51. #407×C107C22semidirect
53. #390×C107C22semidirect
54. C4×C22⋊C4×C107C22semidirect
55. #343×C107C22semidirect
56. #339×C107C22semidirect
66. C2×#41×C107D4semidirect
67. C2×#41×C107D4semidirect
71. C22×Q8×C107D4semidirect
86. C22×D4×C107D4semidirect
98. AGL(1,ℤ/8)×C107D4semidirect
123. C22⋊Q8×C107D4semidirect
124. C22⋊Q8×C107D4semidirect
139. #121×C107D4semidirect
140. #121×C107D4semidirect
251. C2×D4×C107C2×D4semidirect
281. M16×C107C2×D4semidirect
347. Q8×C107#120semidirect
377. D4×C107#120semidirect
442. C22×C107#453semidirect
457. #23876C107direct (N × H)
469. C22×AGL(1,ℤ/8)C2×C107semidirect
470. #3488C2×C107semidirect
471. C2×#453C2×C107semidirect
472. #3003C2×C107semidirect
473. #2433C2×C107semidirect
474. #2006C2×C107semidirect
475. #2002C2×C107semidirect
476. #1900C2×C107semidirect
477. #1883C2×C107semidirect
478. #1871C2×C107semidirect
479. #1789C2×C107semidirect
480. C107#23876direct (N × H)
481. C2×H(5,𝔽2)C22×C107semidirect
483. C23×D4C22×C107semidirect
488. C2×AGL(1,ℤ/8)C22×C107semidirect
489. C2×AGL(1,ℤ/8)C22×C107semidirect
492. C22×M16C22×C107semidirect
500. #537C22×C107semidirect
502. #535C22×C107semidirect
503. C2×#127C22×C107semidirect
509. #520C22×C107semidirect
515. C2×#104C22×C107semidirect
516. C2×#104C22×C107semidirect
517. C2×#104C22×C107semidirect
518. #418C22×C107semidirect
519. C2×#100C22×C107semidirect
520. #407C22×C107semidirect
522. #390C22×C107semidirect
523. C4×C22⋊C4C22×C107semidirect
524. #343C22×C107semidirect
525. #339C22×C107semidirect
535. C2×#41D4×C107semidirect
536. C2×#41D4×C107semidirect
540. C22×Q8D4×C107semidirect
555. C22×D4D4×C107semidirect
567. AGL(1,ℤ/8)D4×C107semidirect
592. C22⋊Q8D4×C107semidirect
593. C22⋊Q8D4×C107semidirect
608. #121D4×C107semidirect
609. #121D4×C107semidirect
720. C2×D4C2×D4×C107semidirect
750. M16C2×D4×C107semidirect
816. Q8#120×C107semidirect
846. D4#120×C107semidirect
911. C22#453×C107semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1072
C107×#34882
C2×#453×C1072
C107×#30032
C107×#24332
C107×#20062
C107×#20022
C107×#19002
C107×#18832
C107×#18712
C107×#17892
#23876107