Finite Group Databasebeta

← C107×#22583 #41048547

Subgroups — C107×#22583 #41048547

Order 27392.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#417×C107C211yesmaximal, characteristic
2C107×#2344C211yesmaximal, characteristic, complemented
3C107×#2341C211yesmaximal, characteristic
4C107×#1936C211yesmaximal, characteristic, complemented
5C107×#1934C211yesmaximal, characteristic, complemented
6C107×#1926C211yesmaximal, characteristic, complemented
7C107×#1925C211yesmaximal, characteristic, complemented
8C107×#1865C211yesmaximal, characteristic, complemented
9C107×#1863C211yesmaximal, characteristic, complemented
10C107×#1824C211yesmaximal, characteristic, complemented
11C107×#1809C211yesmaximal, characteristic, complemented
12C107×#1788C211yesmaximal, characteristic
13C107×#1763C211yesmaximal, characteristic, complemented
14C4×#103×C107C211yesmaximal, characteristic, complemented
15C107×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×M16×C107C2211yescharacteristic
18C2×C4×Q8×C107C2211yescharacteristic
19C2×C4×Q8×C107C2211yescharacteristic
20C2×#117×C107—21no—
21C22×C4⋊C4×C107C2211yescharacteristic
22C2×#107×C107C2211yescharacteristic
23C2×#106×C107C2211yescharacteristic
24#417×C107C418yescomplemented
25C2×#103×C107C2211yescharacteristic
26C2×#103×C107C2211yescharacteristic
27C2×#103×C107C2211yescharacteristic
28C2×#103×C107C2211yescharacteristic
29C2×#102×C107C2211yescharacteristic
30C2×#102×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×C22⋊C8×C107C2211yescharacteristic
34C2×#97×C107C2211yescharacteristic
35C2×C4×C8×C107C2211yescharacteristic
36#390×C107—21no—
37#390×C107—21no—
38#390×C107C2211yescharacteristic
39#390×C107C2211yescharacteristic
40#389×C107C2211yescharacteristic
41#389×C107C2211yescharacteristic
42#387×C107—21no—
43#387×C107—21no—
44#381×C107—21no—
45#380×C107—21no—
46#380×C107C2211yescharacteristic
47#380×C107C2211yescharacteristic
48C4×C4⋊C4×C107C2211yescharacteristic
49C4×C4⋊C4×C107C2211yescharacteristic
50C4×C22⋊C4×C107—21no—
51C4×C22⋊C4×C107C2211yescharacteristic
52#340×C107C2211yescharacteristic
53#340×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60C2×#41×C107—22no—
61C2×#41×C107—22no—
62C2×#41×C107—22no—
63C2×#41×C107—41no—
64C2×#41×C107—41no—
65C2×#41×C107C2×C414yes—
66C22×Q8×C107C2311yescharacteristic
67C22×D4×C107—21no—
68C22×D4×C107C2311yescharacteristic
69C23×C4×C107—21no—
70C23×C4×C107—21no—
71C23×C4×C107C2311yescharacteristic
72C2×M16×C107—41no—
73C2×M16×C107—41no—
74C2×M16×C107C2×C414yes—
75C22×C8×C107C2311yescharacteristic
76C22×C8×C107C2311yescharacteristic
77C22×C8×C107C2311yescharacteristic
78C22×C8×C107C2311yescharacteristic
79C4×Q8×C107—22no—
80C4×Q8×C107—22no—
81C4×Q8×C107—41no—
82C4×Q8×C107—41no—
83#117×C107—44no—
84C2×C4⋊C4×C107—21no—
85C2×C4⋊C4×C107—22no—
86C2×C4⋊C4×C107—21no—
87C2×C4⋊C4×C107—21no—
88C2×C4⋊C4×C107—21no—
89C2×C4⋊C4×C107—21no—
90C2×C4⋊C4×C107C2×C414yes—
91C2×C4⋊C4×C107C2311yescharacteristic
92C2×C4⋊C4×C107C2311yescharacteristic
93C2×C4⋊C4×C107C2311yescharacteristic
94C2×C4⋊C4×C107C2311yescharacteristic
95C2×C4⋊C4×C107C2311yescharacteristic
96C2×C4⋊C4×C107C2311yescharacteristic
97C2×C22⋊C4×C107—21no—
98C2×C22⋊C4×C107—21no—
99C2×C22⋊C4×C107—21no—
100C2×C22⋊C4×C107—21no—
101C2×C22⋊C4×C107—21no—
102C2×C22⋊C4×C107—21no—
103C2×C22⋊C4×C107D411yescharacteristic
104C2×C22⋊C4×C107D411yescharacteristic
105C2×C42×C107—21no—
106C2×C42×C107—21no—
107C2×C42×C107—21no—
108C2×C42×C107—21no—
109C2×C42×C107C2311yescharacteristic
110C2×C42×C107C2311yescharacteristic
111#107×C107—41no—
112#106×C107—41no—
113#103×C107—22no—
114#103×C107—22no—
115#103×C107C2×C414yes—
116#103×C107C2×C414yes—
117#102×C107—41no—
118#102×C107—41no—
119#102×C107C2×C414yes—
120#102×C107C2×C414yes—
121C22⋊C8×C107—22no—
122#97×C107—41no—
123C4×C8×C107—41no—
124#95×C107—21no—
125#95×C107—21no—
126#95×C107—21no—
127#95×C107—21no—
128#95×C107—21no—
129#95×C107—21no—
130#95×C107D411yescharacteristic
131#95×C107D411yescharacteristic
132C24×C107—21no—
133C24×C107C2×D411yescharacteristic
134#41×C107—28no—
135#41×C107—44no—
136#41×C107—44no—
137#41×C107—44no—
138C2×Q8×C107—21no—
139C2×Q8×C107—21no—
140C2×Q8×C107—21no—
141C2×Q8×C107C22×C412yes—
142C2×Q8×C107#4112yes—
143C2×Q8×C107#4112yes—
144C2×D4×C107—24no—
145C2×D4×C107—21no—
146C2×D4×C107—21no—
147C2×D4×C107—21no—
148C2×D4×C107—21no—
149C2×D4×C107—21no—
150C2×D4×C107—42no—
151C2×D4×C107—42no—
152C2×D4×C107C22×C412yes—
153C22×C4×C107—21no—
154C22×C4×C107—21no—
155C22×C4×C107—21no—
156C22×C4×C107—21no—
157C22×C4×C107—21no—
158C22×C4×C107—24no—
159C22×C4×C107—21no—
160C22×C4×C107—21no—
161C22×C4×C107—24no—
162C22×C4×C107—21no—
163C22×C4×C107—21no—
164C22×C4×C107—21no—
165C22×C4×C107—21no—
166C22×C4×C107—42no—
167C22×C4×C107—42no—
168C22×C4×C107—42no—
169C22×C4×C107—42no—
170C22×C4×C107C22×C412yes—
171C22×C4×C107C2×D411yescharacteristic
172C22×C4×C107C2×D411yescharacteristic
173C22×C4×C107C2×D411yescharacteristic
174C22×C4×C107C2×D411yescharacteristic
175C22×C4×C107C2×D411yescharacteristic
176C22×C4×C107#4112yes—
177C22×C4×C107C2411yescharacteristic
178M16×C107—44no—
179C2×C8×C107—21no—
180C2×C8×C107—21no—
181C2×C8×C107—21no—
182C2×C8×C107—21no—
183C2×C8×C107—21no—
184C2×C8×C107—21no—
185C2×C8×C107—21no—
186C2×C8×C107—21no—
187C2×C8×C107—21no—
188C2×C8×C107—21no—
189C2×C8×C107C22×C412yes—
190C2×C8×C107C22×C412yes—
191C4⋊C4×C107—24no—
192C4⋊C4×C107—21no—
193C4⋊C4×C107—21no—
194C4⋊C4×C107—21no—
195C4⋊C4×C107—21no—
196C4⋊C4×C107—21no—
197C4⋊C4×C107—21no—
198C4⋊C4×C107—21no—
199C4⋊C4×C107—21no—
200C4⋊C4×C107—21no—
201C4⋊C4×C107—21no—
202C4⋊C4×C107—42no—
203C4⋊C4×C107—42no—
204C4⋊C4×C107—42no—
205C4⋊C4×C107—42no—
206C4⋊C4×C107C22×C412yes—
207C4⋊C4×C107C22×C412yes—
208C22⋊C4×C107—22no—
209C22⋊C4×C107—41no—
210C22⋊C4×C107—42no—
211C22⋊C4×C107—42no—
212C22⋊C4×C107—42no—
213C22⋊C4×C107—81no—
214C22⋊C4×C107—81no—
215C22⋊C4×C107—81no—
216C42×C107—21no—
217C42×C107—21no—
218C42×C107—21no—
219C42×C107—21no—
220C42×C107—42no—
221C42×C107—42no—
222C42×C107—42no—
223C42×C107—42no—
224C23×C107—21no—
225C23×C107—21no—
226C23×C107—21no—
227C23×C107—21no—
228C23×C107—21no—
229C23×C107—21no—
230C23×C107—22no—
231C23×C107—41no—
232C23×C107—41no—
233C23×C107—41no—
234C23×C107—41no—
235C23×C107—41no—
236C23×C107—41no—
237C23×C107C4×D412yes—
238C23×C107C22×D411yescharacteristic
239Q8×C107—22no—
240Q8×C107—22no—
241Q8×C107—22no—
242Q8×C107#11714yescomplemented
243D4×C107—22no—
244D4×C107—22no—
245D4×C107—48no—
246D4×C107—41no—
247D4×C107—41no—
248C2×C4×C107—22no—
249C2×C4×C107—21no—
250C2×C4×C107—22no—
251C2×C4×C107—22no—
252C2×C4×C107—21no—
253C2×C4×C107—21no—
254C2×C4×C107—21no—
255C2×C4×C107—22no—
256C2×C4×C107—22no—
257C2×C4×C107—22no—
258C2×C4×C107—22no—
259C2×C4×C107—22no—
260C2×C4×C107—22no—
261C2×C4×C107—21no—
262C2×C4×C107—21no—
263C2×C4×C107—21no—
264C2×C4×C107—21no—
265C2×C4×C107—21no—
266C2×C4×C107—21no—
267C2×C4×C107—21no—
268C2×C4×C107—21no—
269C2×C4×C107—21no—
270C2×C4×C107—48no—
271C2×C4×C107—48no—
272C2×C4×C107—41no—
273C2×C4×C107—41no—
274C2×C4×C107—41no—
275C2×C4×C107—41no—
276C2×C4×C107—41no—
277C2×C4×C107—41no—
278C2×C4×C107—41no—
279C2×C4×C107—41no—
280C2×C4×C107—41no—
281C2×C4×C107—41no—
282C2×C4×C107—41no—
283C2×C4×C107—41no—
284C2×C4×C107—41no—
285C2×C4×C107—41no—
286C2×C4×C107—41no—
287C2×C4×C107—41no—
288C2×C4×C107C4×D412yes—
289C2×C4×C107AGL(1,ℤ/8)12yes—
290C2×C4×C107C23×C411yescharacteristic
291C2×C4×C107C2×#4111yescharacteristic
292C2×C4×C107C2×#4111yescharacteristic
293C2×C4×C107C2×#4111yescharacteristic
294C2×C4×C107H(5,𝔽2)11yescharacteristic
295C2×C4×C107H(5,𝔽2)11yescharacteristic
296C8×C107—22no—
297C8×C107—22no—
298C8×C107—41no—
299C8×C107—41no—
300C22×C107—22no—
301C22×C107—22no—
302C22×C107—22no—
303C22×C107—41no—
304C22×C107—41no—
305C22×C107—41no—
306C22×C107—41no—
307C22×C107—42no—
308C22×C107—42no—
309C22×C107—42no—
310C22×C107—81no—
311C22×C107—81no—
312C22×C107—81no—
313C22×C107—81no—
314C22×C107C2×C4×D411yescharacteristic
315C22×C107#54611yescharacteristic
316C22×C107#54611yescharacteristic
317C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C107#57511yescharacteristic
319C22×C107#57711yescharacteristic
320C22×C107#57811yescharacteristic
321C4×C107—22no—
322C4×C107—24no—
323C4×C107—22no—
324C4×C107—41no—
325C4×C107—42no—
326C4×C107—42no—
327C4×C107—41no—
328C4×C107—41no—
329C4×C107—81no—
330C4×C107—81no—
331C4×C107—81no—
332C4×C107—81no—
333C4×C107C2×#11711yescharacteristic
334C4×C107#51811yescharacteristic
335C4×C107#55111yescharacteristic
336C4×C107#55111yescharacteristic
337#22583C10711yesmaximal, characteristic, direct product factor, Sylow
338C2×C107—42no—
339C2×C107—82no—
340C2×C107#234211yescharacteristic
341C2×C107C4×AGL(1,ℤ/8)11yescharacteristic
342C2×C107#294711yescharacteristic
343C2×C107#330811yescharacteristic
344C2×C107#331711yescharacteristic
345C2×C107#332711yescharacteristic
346C2×C107#333211yescharacteristic
347C2×#417C2×C10711yescharacteristic
348#2344C2×C10711yescharacteristic, complemented
349#2341C2×C10711yescharacteristic
350#1936C2×C10711yescharacteristic, complemented
351#1934C2×C10711yescharacteristic, complemented
352#1926C2×C10711yescharacteristic, complemented
353#1925C2×C10711yescharacteristic, complemented
354#1865C2×C10711yescharacteristic, complemented
355#1863C2×C10711yescharacteristic, complemented
356#1824C2×C10711yescharacteristic, complemented
357#1809C2×C10711yescharacteristic, complemented
358#1788C2×C10711yescharacteristic
359#1763C2×C10711yescharacteristic, complemented
360C4×#103C2×C10711yescharacteristic, complemented
361#1753C2×C10711yescharacteristic, complemented
362C107#2258311yescharacteristic, direct product factor, Sylow
363C22×#41C22×C10711yescharacteristic
364C22×M16C22×C10711yescharacteristic
365C2×C4×Q8C22×C10711yescharacteristic
366C2×C4×Q8C22×C10711yescharacteristic
367C2×#117—21no—
368C22×C4⋊C4C22×C10711yescharacteristic
369C2×#107C22×C10711yescharacteristic
370C2×#106C22×C10711yescharacteristic
371#417C4×C10718yescomplemented
372C2×#103C22×C10711yescharacteristic
373C2×#103C22×C10711yescharacteristic
374C2×#103C22×C10711yescharacteristic
375C2×#103C22×C10711yescharacteristic
376C2×#102C22×C10711yescharacteristic
377C2×#102C22×C10711yescharacteristic
378C2×#102C22×C10711yescharacteristic
379C2×#102C22×C10711yescharacteristic
380C2×C22⋊C8C22×C10711yescharacteristic
381C2×#97C22×C10711yescharacteristic
382C2×C4×C8C22×C10711yescharacteristic
383#390—21no—
384#390—21no—
385#390C22×C10711yescharacteristic
386#390C22×C10711yescharacteristic
387#389C22×C10711yescharacteristic
388#389C22×C10711yescharacteristic
389#387—21no—
390#387—21no—
391#381—21no—
392#380—21no—
393#380C22×C10711yescharacteristic
394#380C22×C10711yescharacteristic
395C4×C4⋊C4C22×C10711yescharacteristic
396C4×C4⋊C4C22×C10711yescharacteristic
397C4×C22⋊C4—21no—
398C4×C22⋊C4C22×C10711yescharacteristic
399#340C22×C10711yescharacteristic
400#340C22×C10711yescharacteristic
401#340C22×C10711yescharacteristic
402#340C22×C10711yescharacteristic
403#340C22×C10711yescharacteristic
404#340C22×C10711yescharacteristic
405#336C22×C10711yescharacteristic
406#336C22×C10711yescharacteristic
407C2×#41—22no—
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—41no—
411C2×#41—41no—
412C2×#41C2×C4×C10714yes—
413C22×Q8C23×C10711yescharacteristic
414C22×D4—21no—
415C22×D4C23×C10711yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C23×C4C23×C10711yescharacteristic
419C2×M16—41no—
420C2×M16—41no—
421C2×M16C2×C4×C10714yes—
422C22×C8C23×C10711yescharacteristic
423C22×C8C23×C10711yescharacteristic
424C22×C8C23×C10711yescharacteristic
425C22×C8C23×C10711yescharacteristic
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—41no—
429C4×Q8—41no—
430#117—44no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4C2×C4×C10714yes—
438C2×C4⋊C4C23×C10711yescharacteristic
439C2×C4⋊C4C23×C10711yescharacteristic
440C2×C4⋊C4C23×C10711yescharacteristic
441C2×C4⋊C4C23×C10711yescharacteristic
442C2×C4⋊C4C23×C10711yescharacteristic
443C2×C4⋊C4C23×C10711yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4D4×C10711yescharacteristic
451C2×C22⋊C4D4×C10711yescharacteristic
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42C23×C10711yescharacteristic
457C2×C42C23×C10711yescharacteristic
458#107—41no—
459#106—41no—
460#103—22no—
461#103—22no—
462#103C2×C4×C10714yes—
463#103C2×C4×C10714yes—
464#102—41no—
465#102—41no—
466#102C2×C4×C10714yes—
467#102C2×C4×C10714yes—
468C22⋊C8—22no—
469#97—41no—
470C4×C8—41no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95D4×C10711yescharacteristic
478#95D4×C10711yescharacteristic
479C24—21no—
480C24C2×D4×C10711yescharacteristic
481#41—28no—
482#41—44no—
483#41—44no—
484#41—44no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8C22×C4×C10712yes—
489C2×Q8#41×C10712yes—
490C2×Q8#41×C10712yes—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4C22×C4×C10712yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4C22×C4×C10712yes—
518C22×C4C2×D4×C10711yescharacteristic
519C22×C4C2×D4×C10711yescharacteristic
520C22×C4C2×D4×C10711yescharacteristic
521C22×C4C2×D4×C10711yescharacteristic
522C22×C4C2×D4×C10711yescharacteristic
523C22×C4#41×C10712yes—
524C22×C4C24×C10711yescharacteristic
525M16—44no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8C22×C4×C10712yes—
537C2×C8C22×C4×C10712yes—
538C4⋊C4—24no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4C22×C4×C10712yes—
554C4⋊C4C22×C4×C10712yes—
555C22⋊C4—22no—
556C22⋊C4—41no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—42no—
568C42—42no—
569C42—42no—
570C42—42no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—22no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23C4×D4×C10712yes—
585C23C22×D4×C10711yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—22no—
589Q8#117×C10714yescomplemented
590D4—22no—
591D4—22no—
592D4—48no—
593D4—41no—
594D4—41no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—48no—
618C2×C4—48no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4C4×D4×C10712yes—
636C2×C4AGL(1,ℤ/8)×C10712yes—
637C2×C4C23×C4×C10711yescharacteristic
638C2×C4C2×#41×C10711yescharacteristic
639C2×C4C2×#41×C10711yescharacteristic
640C2×C4C2×#41×C10711yescharacteristic
641C2×C4H(5,𝔽2)×C10711yescharacteristic
642C2×C4H(5,𝔽2)×C10711yescharacteristic
643C8—22no—
644C8—22no—
645C8—41no—
646C8—41no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×C4×D4×C10711yescharacteristic
662C22#546×C10711yescharacteristic
663C22#546×C10711yescharacteristic
664C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
665C22#575×C10711yescharacteristic
666C22#577×C10711yescharacteristic
667C22#578×C10711yescharacteristic
668C4—22no—
669C4—22no—
670C4—24no—
671C4—42no—
672C4—42no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4C2×#117×C10711yescharacteristic
681C4#518×C10711yescharacteristic
682C4#551×C10711yescharacteristic
683C4#551×C10711yescharacteristic
684C2—42no—
685C2—82no—
686C2C107×#234211yescharacteristic
687C2C4×AGL(1,ℤ/8)×C10711yescharacteristic
688C2C107×#294711yescharacteristic
689C2C107×#330811yescharacteristic
690C2C107×#331711yescharacteristic
691C2C107×#332711yescharacteristic
692C2C107×#333211yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC22×#41×C107C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C22⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2344C2semidirect
4. C107×#1936C2semidirect
5. C107×#1934C2semidirect
6. C107×#1926C2semidirect
7. C107×#1925C2semidirect
8. C107×#1865C2semidirect
9. C107×#1863C2semidirect
10. C107×#1824C2semidirect
11. C107×#1809C2semidirect
13. C107×#1763C2semidirect
14. C4×#103×C107C2semidirect
15. C107×#1753C2semidirect
24. #417×C107C4semidirect
242. Q8×C107#117semidirect
337. #22583C107direct (N × H)
348. #2344C2×C107semidirect
350. #1936C2×C107semidirect
351. #1934C2×C107semidirect
352. #1926C2×C107semidirect
353. #1925C2×C107semidirect
354. #1865C2×C107semidirect
355. #1863C2×C107semidirect
356. #1824C2×C107semidirect
357. #1809C2×C107semidirect
359. #1763C2×C107semidirect
360. C4×#103C2×C107semidirect
361. #1753C2×C107semidirect
362. C107#22583direct (N × H)
371. #417C4×C107semidirect
589. Q8#117×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#417×C1072
C107×#23442
C107×#23412
C107×#19362
C107×#19342
C107×#19262
C107×#19252
C107×#18652
C107×#18632
C107×#18242
C107×#18092
C107×#17882
C107×#17632
C4×#103×C1072
C107×#17532
#22583107