Finite Group Databasebeta

← C107×#22868 #41048832

Subgroups — C107×#22868 #41048832

Order 27392.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C107C211yesmaximal, characteristic
2C2×#442×C107C211yesmaximal, characteristic, complemented
3C2×#418×C107C211yesmaximal, characteristic, complemented
4C107×#2363C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C107C211yesmaximal, characteristic, complemented
6C107×#1970C211yesmaximal, characteristic, complemented
7C107×#1936C211yesmaximal, characteristic, complemented
8C107×#1926C211yesmaximal, characteristic, complemented
9C107×#1895C211yesmaximal, characteristic, complemented
10C107×#1879C211yesmaximal, characteristic, complemented
11C107×#1879C211yesmaximal, characteristic, complemented
12C107×#1862C211yesmaximal, characteristic, complemented
13C107×#1854C211yesmaximal, characteristic, complemented
14C4×#102×C107C211yesmaximal, characteristic, complemented
15C107×#1753C211yesmaximal, characteristic, complemented
16C23×D4×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C22×D8×C107C2211yescharacteristic
19C22×M16×C107C2211yescharacteristic
20C2×#121×C107C2211yescharacteristic
21C2×C4×D4×C107C2211yescharacteristic
22C2×C4×D4×C107C2211yescharacteristic
23C2×C4×D4×C107C2211yescharacteristic, complemented
24C2×#117×C107C2211yescharacteristic
25C22×C22⋊C4×C107—21no—
26#447×C107C418yescomplemented
27#442×C107—24no—
28C2×#107×C107C2211yescharacteristic, complemented
29C2×#106×C107C2211yescharacteristic, complemented
30#418×C107—24no—
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#102×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic, complemented
38C2×#102×C107C2211yescharacteristic, complemented
39C2×C22⋊C8×C107C2211yescharacteristic
40C2×#97×C107C2211yescharacteristic, complemented
41C2×C4×C8×C107C2211yescharacteristic, complemented
42#390×C107—21no—
43#390×C107C2211yescharacteristic
44#390×C107C2211yescharacteristic
45#390×C107C2211yescharacteristic, complemented
46#389×C107C2211yescharacteristic, complemented
47#388×C107—21no—
48#386×C107—21no—
49#386×C107—21no—
50#386×C107—21no—
51#380×C107C2211yescharacteristic
52#379×C107—21no—
53C4×C4⋊C4×C107C2211yescharacteristic, complemented
54C4×C22⋊C4×C107—21no—
55C4×C22⋊C4×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic, complemented
57#340×C107C2211yescharacteristic, complemented
58#340×C107C2211yescharacteristic, complemented
59#340×C107C2211yescharacteristic, complemented
60#336×C107C2211yescharacteristic, complemented
61#336×C107C2211yescharacteristic, complemented
62C25×C107—21no—
63C22×D4×C107—22no—
64C22×D4×C107—22no—
65C22×D4×C107—21no—
66C22×D4×C107—21no—
67C22×D4×C107—22no—
68C22×D4×C107—41no—
69C22×D4×C107—41no—
70C22×D4×C107C2×C414yescomplemented
71C22×D4×C107C2311yescharacteristic
72C22×D4×C107C2311yescharacteristic
73C22×D4×C107C2311yescharacteristic
74C23×C4×C107—21no—
75C23×C4×C107—21no—
76C23×C4×C107—21no—
77C23×C4×C107C2311yescharacteristic
78C2×D8×C107—22no—
79C2×D8×C107—22no—
80C2×D8×C107—41no—
81C2×D8×C107—41no—
82C2×D8×C107C2×C414yes—
83C2×D8×C107C2×C414yescomplemented
84C2×M16×C107—22no—
85C2×M16×C107—22no—
86C2×M16×C107—41no—
87C22×C8×C107C2311yescharacteristic
88C22×C8×C107C2311yescharacteristic
89C22×C8×C107C2311yescharacteristic
90C22×C8×C107C2311yescharacteristic
91#121×C107—22no—
92#121×C107C2×C414yescomplemented
93C4×D4×C107—22no—
94C4×D4×C107—22no—
95C4×D4×C107—22no—
96C4×D4×C107—41no—
97C4×D4×C107—41no—
98C4×D4×C107—41no—
99#117×C107—22no—
100#117×C107—41no—
101C2×C4⋊C4×C107—21no—
102C2×C4⋊C4×C107C2311yescharacteristic
103C2×C4⋊C4×C107C2311yescharacteristic
104C2×C4⋊C4×C107C2311yescharacteristic
105C2×C4⋊C4×C107C2311yescharacteristic
106C2×C4⋊C4×C107C2311yescharacteristic
107C2×C22⋊C4×C107—21no—
108C2×C22⋊C4×C107—21no—
109C2×C22⋊C4×C107—21no—
110C2×C22⋊C4×C107—21no—
111C2×C22⋊C4×C107—21no—
112C2×C22⋊C4×C107—21no—
113C2×C22⋊C4×C107—21no—
114C2×C22⋊C4×C107—21no—
115C2×C22⋊C4×C107—21no—
116C2×C22⋊C4×C107—21no—
117C2×C22⋊C4×C107—21no—
118C2×C22⋊C4×C107—21no—
119C2×C22⋊C4×C107—44no—
120C2×C22⋊C4×C107D411yescharacteristic
121C2×C22⋊C4×C107D411yescharacteristic
122C2×C42×C107—21no—
123C2×C42×C107—21no—
124C2×C42×C107C2311yescharacteristic
125C2×C42×C107C2311yescharacteristic
126#107×C107—41no—
127#106×C107—22no—
128#102×C107—22no—
129#102×C107—22no—
130#102×C107—22no—
131#102×C107—22no—
132#102×C107—41no—
133#102×C107C2×C414yescomplemented
134#102×C107C2×C414yescomplemented
135#102×C107D414yescomplemented
136C22⋊C8×C107C2×C414yescomplemented
137#97×C107—22no—
138C4×C8×C107—41no—
139#95×C107—21no—
140#95×C107—21no—
141#95×C107—21no—
142#95×C107D411yescharacteristic
143#95×C107D411yescharacteristic
144C24×C107—21no—
145C24×C107—21no—
146C24×C107—21no—
147C24×C107—24no—
148C24×C107—42no—
149C24×C107—42no—
150C24×C107—42no—
151C24×C107—42no—
152C24×C107—81no—
153C24×C107—81no—
154C24×C107C2×D411yescharacteristic
155C2×D4×C107—28no—
156C2×D4×C107—24no—
157C2×D4×C107—24no—
158C2×D4×C107—21no—
159C2×D4×C107—21no—
160C2×D4×C107—21no—
161C2×D4×C107—21no—
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—44no—
172C2×D4×C107—44no—
173C2×D4×C107—44no—
174C2×D4×C107—42no—
175C2×D4×C107—42no—
176C2×D4×C107—81no—
177C2×D4×C107—81no—
178C2×D4×C107C22×C412yes—
179C2×D4×C107C22×C412yes—
180C2×D4×C107C22×C412yes—
181C2×D4×C107C2×D412yes—
182C2×D4×C107#4112yes—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—21no—
186C22×C4×C107—21no—
187C22×C4×C107—21no—
188C22×C4×C107—21no—
189C22×C4×C107—21no—
190C22×C4×C107—21no—
191C22×C4×C107—21no—
192C22×C4×C107—42no—
193C22×C4×C107—42no—
194C22×C4×C107—42no—
195C22×C4×C107—42no—
196C22×C4×C107—42no—
197C22×C4×C107—42no—
198C22×C4×C107—81no—
199C22×C4×C107—81no—
200C22×C4×C107—81no—
201C22×C4×C107C22×C412yes—
202C22×C4×C107C2×D411yescharacteristic
203C22×C4×C107C2×D411yescharacteristic
204C22×C4×C107C2×D411yescharacteristic
205C22×C4×C107C2×D411yescharacteristic
206C22×C4×C107C2×D411yescharacteristic
207C22×C4×C107#4112yes—
208C22×C4×C107C2411yescharacteristic
209D8×C107—28no—
210D8×C107—44no—
211M16×C107—44no—
212C2×C8×C107—21no—
213C2×C8×C107—21no—
214C2×C8×C107—21no—
215C2×C8×C107—21no—
216C2×C8×C107—21no—
217C2×C8×C107—21no—
218C2×C8×C107—21no—
219C2×C8×C107—21no—
220C2×C8×C107—21no—
221C2×C8×C107C22×C412yes—
222C2×C8×C107C22×C412yes—
223C2×C8×C107C2×D412yes—
224C4⋊C4×C107—21no—
225C4⋊C4×C107—21no—
226C4⋊C4×C107—21no—
227C4⋊C4×C107—21no—
228C4⋊C4×C107—21no—
229C4⋊C4×C107—21no—
230C4⋊C4×C107—21no—
231C4⋊C4×C107—21no—
232C4⋊C4×C107—81no—
233C4⋊C4×C107C22×C412yes—
234C4⋊C4×C107C2×D412yes—
235C22⋊C4×C107—24no—
236C22⋊C4×C107—22no—
237C22⋊C4×C107—41no—
238C22⋊C4×C107—42no—
239C22⋊C4×C107—42no—
240C22⋊C4×C107—42no—
241C22⋊C4×C107—42no—
242C22⋊C4×C107—42no—
243C22⋊C4×C107—42no—
244C22⋊C4×C107—42no—
245C22⋊C4×C107—42no—
246C22⋊C4×C107—81no—
247C22⋊C4×C107—81no—
248C22⋊C4×C107—81no—
249C42×C107—21no—
250C42×C107—21no—
251C42×C107—21no—
252C42×C107—21no—
253C42×C107—42no—
254C42×C107—81no—
255C23×C107—22no—
256C23×C107—21no—
257C23×C107—22no—
258C23×C107—22no—
259C23×C107—21no—
260C23×C107—21no—
261C23×C107—21no—
262C23×C107—21no—
263C23×C107—21no—
264C23×C107—22no—
265C23×C107—22no—
266C23×C107—48no—
267C23×C107—48no—
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—84no—
285C23×C107—84no—
286C23×C107—84no—
287C23×C107—84no—
288C23×C107—84no—
289C23×C107C4×D412yes—
290C23×C107C22×D411yescharacteristic
291D4×C107—22no—
292D4×C107—22no—
293D4×C107—22no—
294D4×C107—22no—
295D4×C107—22no—
296D4×C107—22no—
297D4×C107—22no—
298D4×C107—48no—
299D4×C107—41no—
300D4×C107—41no—
301D4×C107—41no—
302D4×C107—41no—
303D4×C107—84no—
304D4×C107C4×D414yes—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—22no—
310C2×C4×C107—22no—
311C2×C4×C107—22no—
312C2×C4×C107—22no—
313C2×C4×C107—22no—
314C2×C4×C107—21no—
315C2×C4×C107—21no—
316C2×C4×C107—22no—
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—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107—41no—
329C2×C4×C107—41no—
330C2×C4×C107—41no—
331C2×C4×C107—41no—
332C2×C4×C107—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
335C2×C4×C107—41no—
336C2×C4×C107—41no—
337C2×C4×C107—84no—
338C2×C4×C107—84no—
339C2×C4×C107—84no—
340C2×C4×C107C4×D412yes—
341C2×C4×C107AGL(1,ℤ/8)12yes—
342C2×C4×C107C23×C411yescharacteristic
343C2×C4×C107C22×D411yescharacteristic
344C2×C4×C107C2×#4111yescharacteristic
345C2×C4×C107C2×#4111yescharacteristic
346C2×C4×C107H(5,𝔽2)11yescharacteristic
347C2×C4×C107H(5,𝔽2)11yescharacteristic
348C8×C107—22no—
349C8×C107—22no—
350C8×C107—22no—
351C8×C107—41no—
352C22×C107—22no—
353C22×C107—24no—
354C22×C107—22no—
355C22×C107—22no—
356C22×C107—42no—
357C22×C107—42no—
358C22×C107—41no—
359C22×C107—42no—
360C22×C107—42no—
361C22×C107—41no—
362C22×C107—42no—
363C22×C107—41no—
364C22×C107—41no—
365C22×C107—42no—
366C22×C107—42no—
367C22×C107—42no—
368C22×C107—42no—
369C22×C107—42no—
370C22×C107—42no—
371C22×C107—42no—
372C22×C107—816no—
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×C107C2×C4×D411yescharacteristic
382C22×C107D4211yescharacteristic
383C22×C107#54611yescharacteristic
384C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C107#57511yescharacteristic
386C22×C107#57611yescharacteristic
387C22×C107#57611yescharacteristic
388C4×C107—22no—
389C4×C107—22no—
390C4×C107—42no—
391C4×C107—41no—
392C4×C107—42no—
393C4×C107—41no—
394C4×C107—41no—
395C4×C107—81no—
396C4×C107—81no—
397C4×C107—81no—
398C4×C107C2×C4×D411yescharacteristic
399C4×C107#51811yescharacteristic
400C4×C107#54611yescharacteristic
401C4×C107#55111yescharacteristic
402#22868C10711yesmaximal, characteristic, direct product factor, Sylow
403C2×C107—42no—
404C2×C107—44no—
405C2×C107—82no—
406C2×C107—82no—
407C2×C107#235811yescharacteristic
408C2×C107C4×AGL(1,ℤ/8)11yescharacteristic
409C2×C107#294811yescharacteristic
410C2×C107#327311yescharacteristic
411C2×C107#327411yescharacteristic
412C2×C107#331811yescharacteristic
413C2×C107#331911yescharacteristic
414C2×#447C2×C10711yescharacteristic
415C2×#442C2×C10711yescharacteristic, complemented
416C2×#418C2×C10711yescharacteristic, complemented
417#2363C2×C10711yescharacteristic, complemented
418D4×C22⋊C4C2×C10711yescharacteristic, complemented
419#1970C2×C10711yescharacteristic, complemented
420#1936C2×C10711yescharacteristic, complemented
421#1926C2×C10711yescharacteristic, complemented
422#1895C2×C10711yescharacteristic, complemented
423#1879C2×C10711yescharacteristic, complemented
424#1879C2×C10711yescharacteristic, complemented
425#1862C2×C10711yescharacteristic, complemented
426#1854C2×C10711yescharacteristic, complemented
427C4×#102C2×C10711yescharacteristic, complemented
428#1753C2×C10711yescharacteristic, complemented
429C107#2286811yescharacteristic, direct product factor, Sylow
430C23×D4C22×C10711yescharacteristic
431C22×D8C22×C10711yescharacteristic
432C22×D8C22×C10711yescharacteristic
433C22×M16C22×C10711yescharacteristic
434C2×#121C22×C10711yescharacteristic
435C2×C4×D4C22×C10711yescharacteristic
436C2×C4×D4C22×C10711yescharacteristic
437C2×C4×D4C22×C10711yescharacteristic, complemented
438C2×#117C22×C10711yescharacteristic
439C22×C22⋊C4—21no—
440#447C4×C10718yescomplemented
441#442—24no—
442C2×#107C22×C10711yescharacteristic, complemented
443C2×#106C22×C10711yescharacteristic, complemented
444#418—24no—
445C2×#102C22×C10711yescharacteristic
446C2×#102C22×C10711yescharacteristic
447C2×#102C22×C10711yescharacteristic
448C2×#102C22×C10711yescharacteristic
449C2×#102C22×C10711yescharacteristic
450C2×#102C22×C10711yescharacteristic
451C2×#102C22×C10711yescharacteristic, complemented
452C2×#102C22×C10711yescharacteristic, complemented
453C2×C22⋊C8C22×C10711yescharacteristic
454C2×#97C22×C10711yescharacteristic, complemented
455C2×C4×C8C22×C10711yescharacteristic, complemented
456#390—21no—
457#390C22×C10711yescharacteristic
458#390C22×C10711yescharacteristic
459#390C22×C10711yescharacteristic, complemented
460#389C22×C10711yescharacteristic, complemented
461#388—21no—
462#386—21no—
463#386—21no—
464#386—21no—
465#380C22×C10711yescharacteristic
466#379—21no—
467C4×C4⋊C4C22×C10711yescharacteristic, complemented
468C4×C22⋊C4—21no—
469C4×C22⋊C4C22×C10711yescharacteristic
470#340C22×C10711yescharacteristic, complemented
471#340C22×C10711yescharacteristic, complemented
472#340C22×C10711yescharacteristic, complemented
473#340C22×C10711yescharacteristic, complemented
474#336C22×C10711yescharacteristic, complemented
475#336C22×C10711yescharacteristic, complemented
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—22no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×C4×C10714yescomplemented
485C22×D4C23×C10711yescharacteristic
486C22×D4C23×C10711yescharacteristic
487C22×D4C23×C10711yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C23×C10711yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×C4×C10714yes—
497C2×D8C2×C4×C10714yescomplemented
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8C23×C10711yescharacteristic
502C22×C8C23×C10711yescharacteristic
503C22×C8C23×C10711yescharacteristic
504C22×C8C23×C10711yescharacteristic
505#121—22no—
506#121C2×C4×C10714yescomplemented
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4C23×C10711yescharacteristic
517C2×C4⋊C4C23×C10711yescharacteristic
518C2×C4⋊C4C23×C10711yescharacteristic
519C2×C4⋊C4C23×C10711yescharacteristic
520C2×C4⋊C4C23×C10711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—44no—
534C2×C22⋊C4D4×C10711yescharacteristic
535C2×C22⋊C4D4×C10711yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42C23×C10711yescharacteristic
539C2×C42C23×C10711yescharacteristic
540#107—41no—
541#106—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—41no—
547#102C2×C4×C10714yescomplemented
548#102C2×C4×C10714yescomplemented
549#102D4×C10714yescomplemented
550C22⋊C8C2×C4×C10714yescomplemented
551#97—22no—
552C4×C8—41no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95D4×C10711yescharacteristic
557#95D4×C10711yescharacteristic
558C24—21no—
559C24—21no—
560C24—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24C2×D4×C10711yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C22×C4×C10712yes—
593C2×D4C22×C4×C10712yes—
594C2×D4C22×C4×C10712yes—
595C2×D4C2×D4×C10712yes—
596C2×D4#41×C10712yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C22×C4×C10712yes—
616C22×C4C2×D4×C10711yescharacteristic
617C22×C4C2×D4×C10711yescharacteristic
618C22×C4C2×D4×C10711yescharacteristic
619C22×C4C2×D4×C10711yescharacteristic
620C22×C4C2×D4×C10711yescharacteristic
621C22×C4#41×C10712yes—
622C22×C4C24×C10711yescharacteristic
623D8—28no—
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8C22×C4×C10712yes—
636C2×C8C22×C4×C10712yes—
637C2×C8C2×D4×C10712yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C22×C4×C10712yes—
648C4⋊C4C2×D4×C10712yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
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—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23C4×D4×C10712yes—
704C23C22×D4×C10711yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4C4×D4×C10714yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4C4×D4×C10712yes—
755C2×C4AGL(1,ℤ/8)×C10712yes—
756C2×C4C23×C4×C10711yescharacteristic
757C2×C4C22×D4×C10711yescharacteristic
758C2×C4C2×#41×C10711yescharacteristic
759C2×C4C2×#41×C10711yescharacteristic
760C2×C4H(5,𝔽2)×C10711yescharacteristic
761C2×C4H(5,𝔽2)×C10711yescharacteristic
762C8—22no—
763C8—22no—
764C8—22no—
765C8—41no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—24no—
770C22—42no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C4×D4×C10711yescharacteristic
796C22D42×C10711yescharacteristic
797C22#546×C10711yescharacteristic
798C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
799C22#575×C10711yescharacteristic
800C22#576×C10711yescharacteristic
801C22#576×C10711yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—41no—
806C4—42no—
807C4—41no—
808C4—41no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C2×C4×D4×C10711yescharacteristic
813C4#518×C10711yescharacteristic
814C4#546×C10711yescharacteristic
815C4#551×C10711yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2C107×#235811yescharacteristic
821C2C4×AGL(1,ℤ/8)×C10711yescharacteristic
822C2C107×#294811yescharacteristic
823C2C107×#327311yescharacteristic
824C2C107×#327411yescharacteristic
825C2C107×#331811yescharacteristic
826C2C107×#331911yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC2×#447×C107C2
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. C2×#442×C107C2semidirect
3. C2×#418×C107C2semidirect
4. C107×#2363C2semidirect
5. D4×C22⋊C4×C107C2semidirect
6. C107×#1970C2semidirect
7. C107×#1936C2semidirect
8. C107×#1926C2semidirect
9. C107×#1895C2semidirect
10. C107×#1879C2semidirect
11. C107×#1879C2semidirect
12. C107×#1862C2semidirect
13. C107×#1854C2semidirect
14. C4×#102×C107C2semidirect
15. C107×#1753C2semidirect
23. C2×C4×D4×C107C22semidirect
26. #447×C107C4semidirect
28. C2×#107×C107C22semidirect
29. C2×#106×C107C22semidirect
37. C2×#102×C107C22semidirect
38. C2×#102×C107C22semidirect
40. C2×#97×C107C22semidirect
41. C2×C4×C8×C107C22semidirect
45. #390×C107C22semidirect
46. #389×C107C22semidirect
53. C4×C4⋊C4×C107C22semidirect
56. #340×C107C22semidirect
57. #340×C107C22semidirect
58. #340×C107C22semidirect
59. #340×C107C22semidirect
60. #336×C107C22semidirect
61. #336×C107C22semidirect
70. C22×D4×C107C2×C4semidirect
83. C2×D8×C107C2×C4semidirect
92. #121×C107C2×C4semidirect
133. #102×C107C2×C4semidirect
134. #102×C107C2×C4semidirect
135. #102×C107D4semidirect
136. C22⋊C8×C107C2×C4semidirect
402. #22868C107direct (N × H)
415. C2×#442C2×C107semidirect
416. C2×#418C2×C107semidirect
417. #2363C2×C107semidirect
418. D4×C22⋊C4C2×C107semidirect
419. #1970C2×C107semidirect
420. #1936C2×C107semidirect
421. #1926C2×C107semidirect
422. #1895C2×C107semidirect
423. #1879C2×C107semidirect
424. #1879C2×C107semidirect
425. #1862C2×C107semidirect
426. #1854C2×C107semidirect
427. C4×#102C2×C107semidirect
428. #1753C2×C107semidirect
429. C107#22868direct (N × H)
437. C2×C4×D4C22×C107semidirect
440. #447C4×C107semidirect
442. C2×#107C22×C107semidirect
443. C2×#106C22×C107semidirect
451. C2×#102C22×C107semidirect
452. C2×#102C22×C107semidirect
454. C2×#97C22×C107semidirect
455. C2×C4×C8C22×C107semidirect
459. #390C22×C107semidirect
460. #389C22×C107semidirect
467. C4×C4⋊C4C22×C107semidirect
470. #340C22×C107semidirect
471. #340C22×C107semidirect
472. #340C22×C107semidirect
473. #340C22×C107semidirect
474. #336C22×C107semidirect
475. #336C22×C107semidirect
484. C22×D4C2×C4×C107semidirect
497. C2×D8C2×C4×C107semidirect
506. #121C2×C4×C107semidirect
547. #102C2×C4×C107semidirect
548. #102C2×C4×C107semidirect
549. #102D4×C107semidirect
550. C22⋊C8C2×C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1072
C2×#442×C1072
C2×#418×C1072
C107×#23632
D4×C22⋊C4×C1072
C107×#19702
C107×#19362
C107×#19262
C107×#18952
C107×#18792
C107×#18622
C107×#18542
C4×#102×C1072
C107×#17532
#22868107