Finite Group Databasebeta

← C107×#25380 #41051344

Subgroups — C107×#25380 #41051344

Order 27392.

1184 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#496×C107C211yesmaximal, characteristic, complemented
2C2×#460×C107C211yesmaximal, characteristic, complemented
3C2×#463×C107C211yesmaximal, characteristic, complemented
4C2×#459×C107C211yesmaximal, characteristic, complemented
5C107×#2541C211yesmaximal, characteristic, complemented
6C107×#2367C211yesmaximal, characteristic, complemented
7C107×#2055C211yesmaximal, characteristic, complemented
8C107×#2054C211yesmaximal, characteristic, complemented
9C107×#2014C211yesmaximal, characteristic, complemented
10C107×#2011C211yesmaximal, characteristic, complemented
11C107×#1982C211yesmaximal, characteristic, complemented
12C107×#1940C211yesmaximal, characteristic, complemented
13C107×#1880C211yesmaximal, characteristic, complemented
14C107×#1879C211yesmaximal, characteristic, complemented
15C107×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C22×D8×C107C2211yescharacteristic
20C22×D8×C107C2211yescharacteristic
21C22×D8×C107C2211yescharacteristic
22C2×#127×C107C2211yescharacteristic
23C2×#127×C107C2211yescharacteristic
24C2×#127×C107C2211yescharacteristic
25C2×#124×C107C2211yescharacteristic
26C2×#121×C107—21no—
27C2×#121×C107—21no—
28C2×C4×Q8×C107C2211yescharacteristic
29C2×C4×D4×C107C2211yescharacteristic
30C2×C4×D4×C107C2211yescharacteristic
31#496×C107—24no—
32#463×C107—24no—
33#460×C107—24no—
34#459×C107—24no—
35C2×C4⋊C8×C107C2211yescharacteristic
36C2×C4⋊C8×C107C2211yescharacteristic
37C2×C4⋊C8×C107C2211yescharacteristic
38C2×#103×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic
46C2×#97×C107C2211yescharacteristic
47#392×C107—21no—
48#392×C107—21no—
49#391×C107C2211yescharacteristic
50#390×C107C2211yescharacteristic
51#390×C107C2211yescharacteristic
52#390×C107C2211yescharacteristic
53#388×C107—21no—
54#388×C107—21no—
55#385×C107—21no—
56C4×C4⋊C4×C107C2211yescharacteristic
57C4×C4⋊C4×C107C2211yescharacteristic
58C4×C22⋊C4×C107—21no—
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×C107—21no—
69C22×D4×C107—21no—
70C22×D4×C107C2311yescharacteristic
71C22×D4×C107C2311yescharacteristic
72C22×D4×C107C2311yescharacteristic
73C22×D4×C107C2311yescharacteristic
74C23×C4×C107—21no—
75C23×C4×C107—21no—
76C2×SD16×C107—22no—
77C2×SD16×C107—22no—
78C2×SD16×C107—22no—
79C2×SD16×C107—22no—
80C2×SD16×C107—22no—
81C2×SD16×C107—22no—
82C2×SD16×C107—41no—
83C2×SD16×C107—41no—
84C2×SD16×C107—41no—
85C2×D8×C107—22no—
86C2×D8×C107—22no—
87C2×D8×C107—22no—
88C2×D8×C107—22no—
89C2×D8×C107—22no—
90C2×D8×C107—22no—
91C2×D8×C107—41no—
92C2×D8×C107—41no—
93C2×D8×C107—41no—
94C22×C8×C107C2311yescharacteristic
95C22×C8×C107C2311yescharacteristic
96C22×C8×C107C2311yescharacteristic
97C22×C8×C107C2311yescharacteristic
98#127×C107—22no—
99#127×C107—22no—
100#127×C107—22no—
101#127×C107—22no—
102#127×C107—41no—
103#127×C107—41no—
104#124×C107—22no—
105#124×C107D414yescomplemented
106#121×C107—44no—
107#121×C107—44no—
108C4×Q8×C107—22no—
109C4×Q8×C107—41no—
110C4×D4×C107—22no—
111C4×D4×C107—22no—
112C4×D4×C107—22no—
113C4×D4×C107—41no—
114C2×C4⋊C4×C107—21no—
115C2×C4⋊C4×C107D411yescharacteristic
116C2×C4⋊C4×C107D411yescharacteristic
117C2×C4⋊C4×C107C2311yescharacteristic
118C2×C4⋊C4×C107C2311yescharacteristic
119C2×C4⋊C4×C107C2311yescharacteristic
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×C107—21no—
132C2×C42×C107C2311yescharacteristic
133C2×C42×C107C2311yescharacteristic
134C2×C42×C107C2311yescharacteristic
135C4⋊C8×C107—22no—
136C4⋊C8×C107—22no—
137C4⋊C8×C107—22no—
138#103×C107—22no—
139#102×C107—22no—
140#102×C107—22no—
141#102×C107—22no—
142#102×C107—22no—
143#102×C107—41no—
144#102×C107—41no—
145#102×C107D414yescomplemented
146#97×C107—22no—
147#95×C107—21no—
148#95×C107—21no—
149#95×C107—21no—
150#95×C107D411yescharacteristic
151#95×C107D411yescharacteristic
152C24×C107—21no—
153C24×C107—21no—
154C24×C107—21no—
155C24×C107—21no—
156C2×Q8×C107—21no—
157C2×Q8×C107—21no—
158C2×Q8×C107—21no—
159C2×Q8×C107—21no—
160C2×Q8×C107—21no—
161C2×Q8×C107C2×D412yes—
162C2×D4×C107—21no—
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—42no—
191C2×D4×C107—42no—
192C2×D4×C107—42no—
193C2×D4×C107—42no—
194C2×D4×C107—42no—
195C2×D4×C107—42no—
196C2×D4×C107—81no—
197C2×D4×C107—81no—
198C2×D4×C107—81no—
199C2×D4×C107—81no—
200C2×D4×C107—81no—
201C2×D4×C107—81no—
202C2×D4×C107C2×D412yes—
203C2×D4×C107C2×D412yes—
204C22×C4×C107—21no—
205C22×C4×C107—21no—
206C22×C4×C107—21no—
207C22×C4×C107—21no—
208C22×C4×C107—42no—
209C22×C4×C107—42no—
210C22×C4×C107—42no—
211C22×C4×C107—42no—
212C22×C4×C107—42no—
213C22×C4×C107—81no—
214C22×C4×C107C2×D411yescharacteristic
215C22×C4×C107C2×D411yescharacteristic
216C22×C4×C107C2×D411yescharacteristic
217C22×C4×C107C2×D411yescharacteristic
218C22×C4×C107C2×D411yescharacteristic
219C22×C4×C107C2×D411yescharacteristic
220C22×C4×C107C2411yescharacteristic
221SD16×C107—44no—
222SD16×C107—44no—
223SD16×C107—44no—
224D8×C107—44no—
225D8×C107—44no—
226D8×C107—44no—
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×C107—21no—
234C2×C8×C107—21no—
235C2×C8×C107—21no—
236C2×C8×C107—21no—
237C2×C8×C107C2×D412yes—
238C2×C8×C107#4112yes—
239C4⋊C4×C107—22no—
240C4⋊C4×C107—22no—
241C4⋊C4×C107—21no—
242C4⋊C4×C107—21no—
243C4⋊C4×C107—21no—
244C4⋊C4×C107—21no—
245C4⋊C4×C107—21no—
246C4⋊C4×C107—42no—
247C4⋊C4×C107C2×D412yes—
248C22⋊C4×C107—24no—
249C22⋊C4×C107—24no—
250C22⋊C4×C107—42no—
251C22⋊C4×C107—42no—
252C22⋊C4×C107—42no—
253C22⋊C4×C107—42no—
254C22⋊C4×C107—42no—
255C22⋊C4×C107—42no—
256C22⋊C4×C107—42no—
257C22⋊C4×C107—81no—
258C42×C107—21no—
259C42×C107—21no—
260C42×C107—21no—
261C42×C107—21no—
262C42×C107—42no—
263C42×C107—81no—
264C42×C107C2×D412yes—
265C42×C107#4112yes—
266C23×C107—22no—
267C23×C107—22no—
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×C107—41no—
292C23×C107—41no—
293C23×C107—41no—
294C23×C107C22×D411yescharacteristic
295Q8×C107—22no—
296Q8×C107—22no—
297Q8×C107—41no—
298Q8×C107—41no—
299D4×C107—22no—
300D4×C107—22no—
301D4×C107—22no—
302D4×C107—22no—
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—41no—
314D4×C107—41no—
315D4×C107—84no—
316D4×C107—84no—
317D4×C107—84no—
318D4×C107—84no—
319D4×C107—84no—
320D4×C107—84no—
321C2×C4×C107—21no—
322C2×C4×C107—21no—
323C2×C4×C107—21no—
324C2×C4×C107—21no—
325C2×C4×C107—21no—
326C2×C4×C107—21no—
327C2×C4×C107—21no—
328C2×C4×C107—21no—
329C2×C4×C107—22no—
330C2×C4×C107—21no—
331C2×C4×C107—21no—
332C2×C4×C107—22no—
333C2×C4×C107—21no—
334C2×C4×C107—21no—
335C2×C4×C107—21no—
336C2×C4×C107—21no—
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—41no—
344C2×C4×C107—41no—
345C2×C4×C107—41no—
346C2×C4×C107—41no—
347C2×C4×C107—84no—
348C2×C4×C107—84no—
349C2×C4×C107#12112yes—
350C2×C4×C107#12112yes—
351C2×C4×C107AGL(1,ℤ/8)12yes—
352C2×C4×C107AGL(1,ℤ/8)12yes—
353C2×C4×C107C22×D411yescharacteristic
354C2×C4×C107C22×D411yescharacteristic
355C2×C4×C107C2×#4111yescharacteristic
356C2×C4×C107C2×#4111yescharacteristic
357C2×C4×C107H(5,𝔽2)11yescharacteristic
358C2×C4×C107H(5,𝔽2)11yescharacteristic
359C8×C107—22no—
360C8×C107—22no—
361C8×C107—41no—
362C8×C107—41no—
363C22×C107—42no—
364C22×C107—42no—
365C22×C107—42no—
366C22×C107—42no—
367C22×C107—42no—
368C22×C107—42no—
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×C107—81no—
388C22×C107—81no—
389C22×C107—81no—
390C22×C107—81no—
391C22×C107C2×#12111yescharacteristic
392C22×C107D4211yescharacteristic
393C22×C107#55011yescharacteristic
394C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C107#57611yescharacteristic
397C22×C107#57711yescharacteristic
398C4×C107—22no—
399C4×C107—22no—
400C4×C107—22no—
401C4×C107—22no—
402C4×C107—42no—
403C4×C107—41no—
404C4×C107—42no—
405C4×C107—41no—
406C4×C107—81no—
407C4×C107—81no—
408C4×C107#53211yescharacteristic
409C4×C107#54011yescharacteristic
410C4×C107D4211yescharacteristic
411C4×C107#54611yescharacteristic
412#25380C10711yesmaximal, characteristic, direct product factor, Sylow
413C2×C107—82no—
414C2×C107—82no—
415C2×C107—161no—
416C2×C107—161no—
417C2×C107#242811yescharacteristic
418C2×C107#303811yescharacteristic
419C2×C107#304511yescharacteristic
420C2×C107#326411yescharacteristic
421C2×C107#326511yescharacteristic
422C2×C107#339711yescharacteristic
423C2×C107#339911yescharacteristic
424C2×#496C2×C10711yescharacteristic, complemented
425C2×#460C2×C10711yescharacteristic, complemented
426C2×#463C2×C10711yescharacteristic, complemented
427C2×#459C2×C10711yescharacteristic, complemented
428#2541C2×C10711yescharacteristic, complemented
429#2367C2×C10711yescharacteristic, complemented
430#2055C2×C10711yescharacteristic, complemented
431#2054C2×C10711yescharacteristic, complemented
432#2014C2×C10711yescharacteristic, complemented
433#2011C2×C10711yescharacteristic, complemented
434#1982C2×C10711yescharacteristic, complemented
435#1940C2×C10711yescharacteristic, complemented
436#1880C2×C10711yescharacteristic, complemented
437#1879C2×C10711yescharacteristic, complemented
438#1762C2×C10711yescharacteristic, complemented
439C107#2538011yescharacteristic, direct product factor, Sylow
440C22×SD16C22×C10711yescharacteristic
441C22×SD16C22×C10711yescharacteristic
442C22×SD16C22×C10711yescharacteristic
443C22×D8C22×C10711yescharacteristic
444C22×D8C22×C10711yescharacteristic
445C22×D8C22×C10711yescharacteristic
446C2×#127C22×C10711yescharacteristic
447C2×#127C22×C10711yescharacteristic
448C2×#127C22×C10711yescharacteristic
449C2×#124C22×C10711yescharacteristic
450C2×#121—21no—
451C2×#121—21no—
452C2×C4×Q8C22×C10711yescharacteristic
453C2×C4×D4C22×C10711yescharacteristic
454C2×C4×D4C22×C10711yescharacteristic
455#496—24no—
456#463—24no—
457#460—24no—
458#459—24no—
459C2×C4⋊C8C22×C10711yescharacteristic
460C2×C4⋊C8C22×C10711yescharacteristic
461C2×C4⋊C8C22×C10711yescharacteristic
462C2×#103C22×C10711yescharacteristic
463C2×#102C22×C10711yescharacteristic
464C2×#102C22×C10711yescharacteristic
465C2×#102C22×C10711yescharacteristic
466C2×#102C22×C10711yescharacteristic
467C2×#102C22×C10711yescharacteristic
468C2×#102C22×C10711yescharacteristic
469C2×#102C22×C10711yescharacteristic
470C2×#97C22×C10711yescharacteristic
471#392—21no—
472#392—21no—
473#391C22×C10711yescharacteristic
474#390C22×C10711yescharacteristic
475#390C22×C10711yescharacteristic
476#390C22×C10711yescharacteristic
477#388—21no—
478#388—21no—
479#385—21no—
480C4×C4⋊C4C22×C10711yescharacteristic
481C4×C4⋊C4C22×C10711yescharacteristic
482C4×C22⋊C4—21no—
483#340C22×C10711yescharacteristic
484#340C22×C10711yescharacteristic
485#336C22×C10711yescharacteristic
486#336C22×C10711yescharacteristic
487C22×Q8C23×C10711yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4C23×C10711yescharacteristic
495C22×D4C23×C10711yescharacteristic
496C22×D4C23×C10711yescharacteristic
497C22×D4C23×C10711yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—41no—
516C2×D8—41no—
517C2×D8—41no—
518C22×C8C23×C10711yescharacteristic
519C22×C8C23×C10711yescharacteristic
520C22×C8C23×C10711yescharacteristic
521C22×C8C23×C10711yescharacteristic
522#127—22no—
523#127—22no—
524#127—22no—
525#127—22no—
526#127—41no—
527#127—41no—
528#124—22no—
529#124D4×C10714yescomplemented
530#121—44no—
531#121—44no—
532C4×Q8—22no—
533C4×Q8—41no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—41no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4D4×C10711yescharacteristic
540C2×C4⋊C4D4×C10711yescharacteristic
541C2×C4⋊C4C23×C10711yescharacteristic
542C2×C4⋊C4C23×C10711yescharacteristic
543C2×C4⋊C4C23×C10711yescharacteristic
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×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C42—21no—
555C2×C42—21no—
556C2×C42C23×C10711yescharacteristic
557C2×C42C23×C10711yescharacteristic
558C2×C42C23×C10711yescharacteristic
559C4⋊C8—22no—
560C4⋊C8—22no—
561C4⋊C8—22no—
562#103—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—41no—
568#102—41no—
569#102D4×C10714yescomplemented
570#97—22no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C10711yescharacteristic
575#95D4×C10711yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C10712yes—
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—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4—81no—
625C2×D4—81no—
626C2×D4C2×D4×C10712yes—
627C2×D4C2×D4×C10712yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C10711yescharacteristic
639C22×C4C2×D4×C10711yescharacteristic
640C22×C4C2×D4×C10711yescharacteristic
641C22×C4C2×D4×C10711yescharacteristic
642C22×C4C2×D4×C10711yescharacteristic
643C22×C4C2×D4×C10711yescharacteristic
644C22×C4C24×C10711yescharacteristic
645SD16—44no—
646SD16—44no—
647SD16—44no—
648D8—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C10712yes—
662C2×C8#41×C10712yes—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4C2×D4×C10712yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—81no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—42no—
687C42—81no—
688C42C2×D4×C10712yes—
689C42#41×C10712yes—
690C23—22no—
691C23—22no—
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—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23C22×D4×C10711yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—84no—
741D4—84no—
742D4—84no—
743D4—84no—
744D4—84no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4#121×C10712yes—
774C2×C4#121×C10712yes—
775C2×C4AGL(1,ℤ/8)×C10712yes—
776C2×C4AGL(1,ℤ/8)×C10712yes—
777C2×C4C22×D4×C10711yescharacteristic
778C2×C4C22×D4×C10711yescharacteristic
779C2×C4C2×#41×C10711yescharacteristic
780C2×C4C2×#41×C10711yescharacteristic
781C2×C4H(5,𝔽2)×C10711yescharacteristic
782C2×C4H(5,𝔽2)×C10711yescharacteristic
783C8—22no—
784C8—22no—
785C8—41no—
786C8—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
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—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C10711yescharacteristic
816C22D42×C10711yescharacteristic
817C22#550×C10711yescharacteristic
818C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
819C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
820C22#576×C10711yescharacteristic
821C22#577×C10711yescharacteristic
822C4—22no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—42no—
827C4—41no—
828C4—42no—
829C4—41no—
830C4—81no—
831C4—81no—
832C4#532×C10711yescharacteristic
833C4#540×C10711yescharacteristic
834C4D42×C10711yescharacteristic
835C4#546×C10711yescharacteristic
836C2—82no—
837C2—82no—
838C2—161no—
839C2—161no—
840C2C107×#242811yescharacteristic
841C2C107×#303811yescharacteristic
842C2C107×#304511yescharacteristic
843C2C107×#326411yescharacteristic
844C2C107×#326511yescharacteristic
845C2C107×#339711yescharacteristic
846C2C107×#339911yescharacteristic
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×#460×C107C2semidirect
3. C2×#463×C107C2semidirect
4. C2×#459×C107C2semidirect
5. C107×#2541C2semidirect
6. C107×#2367C2semidirect
7. C107×#2055C2semidirect
8. C107×#2054C2semidirect
9. C107×#2014C2semidirect
10. C107×#2011C2semidirect
11. C107×#1982C2semidirect
12. C107×#1940C2semidirect
13. C107×#1880C2semidirect
14. C107×#1879C2semidirect
15. C107×#1762C2semidirect
105. #124×C107D4semidirect
145. #102×C107D4semidirect
412. #25380C107direct (N × H)
424. C2×#496C2×C107semidirect
425. C2×#460C2×C107semidirect
426. C2×#463C2×C107semidirect
427. C2×#459C2×C107semidirect
428. #2541C2×C107semidirect
429. #2367C2×C107semidirect
430. #2055C2×C107semidirect
431. #2054C2×C107semidirect
432. #2014C2×C107semidirect
433. #2011C2×C107semidirect
434. #1982C2×C107semidirect
435. #1940C2×C107semidirect
436. #1880C2×C107semidirect
437. #1879C2×C107semidirect
438. #1762C2×C107semidirect
439. C107#25380direct (N × H)
529. #124D4×C107semidirect
569. #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×#460×C1072
C2×#463×C1072
C2×#459×C1072
C107×#25412
C107×#23672
C107×#20552
C107×#20542
C107×#20142
C107×#20112
C107×#19822
C107×#19402
C107×#18802
C107×#18792
C107×#17622
#25380107