Finite Group Databasebeta

← C107×#24882 #41050846

Subgroups — C107×#24882 #41050846

Order 27392.

1168 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C107C211yesmaximal, characteristic, complemented
2C2×#418×C107C211yesmaximal, characteristic, complemented
3C107×#2408C211yesmaximal, characteristic
4C107×#2352C211yesmaximal, characteristic, complemented
5C107×#2092C211yesmaximal, characteristic, complemented
6C107×#2073C211yesmaximal, characteristic, complemented
7C107×#2034C211yesmaximal, characteristic, complemented
8C107×#2034C211yesmaximal, characteristic, complemented
9C107×#1926C211yesmaximal, characteristic, complemented
10C107×#1925C211yesmaximal, characteristic, complemented
11C107×#1874C211yesmaximal, characteristic, complemented
12C107×#1870C211yesmaximal, characteristic, complemented
13C107×#1854C211yesmaximal, characteristic, complemented
14C107×#1809C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C107C2211yescharacteristic
17C22×M16×C107C2211yescharacteristic
18C2×#121×C107C2211yescharacteristic
19C2×#121×C107C2211yescharacteristic
20C2×#120×C107—21no—
21C2×C4×D4×C107C2211yescharacteristic
22C2×#117×C107C2211yescharacteristic
23C22×C4⋊C4×C107C2211yescharacteristic, complemented
24#480×C107—24no—
25C2×#107×C107C2211yescharacteristic, complemented
26C2×#107×C107C2211yescharacteristic, complemented
27C2×#106×C107C2211yescharacteristic, complemented
28C2×#106×C107C2211yescharacteristic, complemented
29#418×C107—24no—
30C2×#102×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#102×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×C22⋊C8×C107C2211yescharacteristic
39C2×C22⋊C8×C107C2211yescharacteristic, complemented
40C2×C22⋊C8×C107C2211yescharacteristic, complemented
41#394×C107—21no—
42#392×C107—21no—
43#390×C107C2211yescharacteristic
44#390×C107C2211yescharacteristic
45#388×C107—21no—
46#387×C107—21no—
47#386×C107—21no—
48#382×C107C2211yescharacteristic, complemented
49#380×C107C2211yescharacteristic
50#380×C107C2211yescharacteristic
51#380×C107C2211yescharacteristic, complemented
52#379×C107—21no—
53C4×C4⋊C4×C107C2211yescharacteristic, complemented
54C4×C22⋊C4×C107—21no—
55#340×C107C2211yescharacteristic, complemented
56#340×C107C2211yescharacteristic, complemented
57#340×C107C2211yescharacteristic, complemented
58#340×C107C2211yescharacteristic, complemented
59#336×C107C2211yescharacteristic, complemented
60#336×C107C2211yescharacteristic, complemented
61C25×C107—21no—
62C22×D4×C107—22no—
63C22×D4×C107—22no—
64C22×D4×C107—21no—
65C22×D4×C107—21no—
66C22×D4×C107—21no—
67C22×D4×C107—22no—
68C22×D4×C107—22no—
69C22×D4×C107—41no—
70C22×D4×C107—41no—
71C22×D4×C107D411yescharacteristic
72C22×D4×C107C2311yescharacteristic
73C22×D4×C107C2311yescharacteristic
74C23×C4×C107—21no—
75C23×C4×C107C2311yescharacteristic
76C23×C4×C107C2311yescharacteristic
77C2×M16×C107—22no—
78C2×M16×C107—22no—
79C2×M16×C107—41no—
80C22×C8×C107C2311yescharacteristic
81C22×C8×C107C2311yescharacteristic
82C22×C8×C107C2311yescharacteristic
83C22×C8×C107C2311yescharacteristic
84#121×C107—22no—
85#121×C107—22no—
86#121×C107—41no—
87#121×C107—41no—
88#120×C107—44no—
89C4×D4×C107—22no—
90C4×D4×C107—22no—
91#117×C107—22no—
92#117×C107—41no—
93C2×C4⋊C4×C107—22no—
94C2×C4⋊C4×C107—21no—
95C2×C4⋊C4×C107—41no—
96C2×C4⋊C4×C107D411yescharacteristic
97C2×C4⋊C4×C107C2311yescharacteristic
98C2×C4⋊C4×C107C2311yescharacteristic
99C2×C4⋊C4×C107C2311yescharacteristic
100C2×C4⋊C4×C107C2311yescharacteristic
101C2×C4⋊C4×C107C2311yescharacteristic
102C2×C4⋊C4×C107C2311yescharacteristic
103C2×C22⋊C4×C107—21no—
104C2×C22⋊C4×C107—21no—
105C2×C22⋊C4×C107—21no—
106C2×C22⋊C4×C107—21no—
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×C107D411yescharacteristic
114C2×C22⋊C4×C107D411yescharacteristic
115C2×C42×C107—21no—
116C2×C42×C107—21no—
117C2×C42×C107C2311yescharacteristic
118#107×C107—22no—
119#107×C107—22no—
120#106×C107—41no—
121#106×C107—41no—
122#102×C107—22no—
123#102×C107—22no—
124#102×C107—22no—
125#102×C107—22no—
126#102×C107—22no—
127#102×C107—41no—
128#102×C107—41no—
129#102×C107D414yescomplemented
130C22⋊C8×C107—22no—
131C22⋊C8×C107—22no—
132C22⋊C8×C107—41no—
133#95×C107—21no—
134#95×C107—21no—
135#95×C107—21no—
136#95×C107—21no—
137#95×C107—21no—
138#95×C107—21no—
139C24×C107—21no—
140C24×C107—21no—
141C24×C107—42no—
142C24×C107—42no—
143C24×C107—42no—
144C24×C107—42no—
145C24×C107—42no—
146C24×C107—81no—
147C24×C107—81no—
148C24×C107C2×D411yescharacteristic
149C24×C107C2×D411yescharacteristic
150C2×D4×C107—28no—
151C2×D4×C107—22no—
152C2×D4×C107—22no—
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107—21no—
156C2×D4×C107—21no—
157C2×D4×C107—21no—
158C2×D4×C107—21no—
159C2×D4×C107—21no—
160C2×D4×C107—21no—
161C2×D4×C107—21no—
162C2×D4×C107—21no—
163C2×D4×C107—44no—
164C2×D4×C107—44no—
165C2×D4×C107—41no—
166C2×D4×C107—42no—
167C2×D4×C107—42no—
168C2×D4×C107—44no—
169C2×D4×C107—42no—
170C2×D4×C107—42no—
171C2×D4×C107—42no—
172C2×D4×C107—42no—
173C2×D4×C107—42no—
174C2×D4×C107—81no—
175C2×D4×C107—81no—
176C2×D4×C107C2×D412yes—
177C2×D4×C107#4112yes—
178C22×C4×C107—21no—
179C22×C4×C107—21no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—21no—
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—21no—
193C22×C4×C107—21no—
194C22×C4×C107—42no—
195C22×C4×C107—42no—
196C22×C4×C107—81no—
197C22×C4×C107C2×D411yescharacteristic
198C22×C4×C107C2×D411yescharacteristic
199C22×C4×C107C2×D411yescharacteristic
200C22×C4×C107C2×D411yescharacteristic
201C22×C4×C107#4112yes—
202C22×C4×C107#4112yes—
203C22×C4×C107C2411yescharacteristic
204M16×C107—44no—
205C2×C8×C107—21no—
206C2×C8×C107—21no—
207C2×C8×C107—21no—
208C2×C8×C107—21no—
209C2×C8×C107—21no—
210C2×C8×C107—21no—
211C2×C8×C107—21no—
212C2×C8×C107—21no—
213C2×C8×C107—21no—
214C2×C8×C107—21no—
215C2×C8×C107—21no—
216C2×C8×C107C2×D412yes—
217C4⋊C4×C107—22no—
218C4⋊C4×C107—21no—
219C4⋊C4×C107—21no—
220C4⋊C4×C107—21no—
221C4⋊C4×C107—21no—
222C4⋊C4×C107—21no—
223C4⋊C4×C107—21no—
224C4⋊C4×C107—21no—
225C4⋊C4×C107—21no—
226C4⋊C4×C107—21no—
227C4⋊C4×C107—21no—
228C4⋊C4×C107—21no—
229C4⋊C4×C107—42no—
230C4⋊C4×C107C2×D412yes—
231C22⋊C4×C107—22no—
232C22⋊C4×C107—22no—
233C22⋊C4×C107—42no—
234C22⋊C4×C107—42no—
235C22⋊C4×C107—42no—
236C22⋊C4×C107—42no—
237C22⋊C4×C107—42no—
238C22⋊C4×C107—42no—
239C22⋊C4×C107—42no—
240C22⋊C4×C107—81no—
241C22⋊C4×C107—81no—
242C22⋊C4×C107—81no—
243C42×C107—21no—
244C42×C107—21no—
245C42×C107—42no—
246C42×C107—81no—
247C23×C107—21no—
248C23×C107—21no—
249C23×C107—21no—
250C23×C107—21no—
251C23×C107—21no—
252C23×C107—21no—
253C23×C107—21no—
254C23×C107—21no—
255C23×C107—21no—
256C23×C107—21no—
257C23×C107—21no—
258C23×C107—21no—
259C23×C107—22no—
260C23×C107—22no—
261C23×C107—48no—
262C23×C107—41no—
263C23×C107—41no—
264C23×C107—41no—
265C23×C107—41no—
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—84no—
275C23×C107—84no—
276C23×C107—84no—
277C23×C107—84no—
278C23×C107—84no—
279C23×C107—84no—
280C23×C107#12312yes—
281C23×C107AGL(1,ℤ/8)12yes—
282C23×C107C22×D411yescharacteristic
283D4×C107—22no—
284D4×C107—22no—
285D4×C107—22no—
286D4×C107—22no—
287D4×C107—48no—
288D4×C107—44no—
289D4×C107—41no—
290D4×C107—41no—
291D4×C107—41no—
292D4×C107—41no—
293D4×C107—84no—
294D4×C107—84no—
295C2×C4×C107—21no—
296C2×C4×C107—21no—
297C2×C4×C107—22no—
298C2×C4×C107—22no—
299C2×C4×C107—22no—
300C2×C4×C107—22no—
301C2×C4×C107—21no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—22no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—41no—
312C2×C4×C107—41no—
313C2×C4×C107—41no—
314C2×C4×C107—41no—
315C2×C4×C107—41no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—41no—
321C2×C4×C107—41no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
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—84no—
333C2×C4×C107#12312yes—
334C2×C4×C107C22×D411yescharacteristic
335C2×C4×C107C2×#4111yescharacteristic
336C2×C4×C107C2×#4111yescharacteristic
337C2×C4×C107C2×#4111yescharacteristic
338C2×C4×C107H(5,𝔽2)11yescharacteristic
339C2×C4×C107H(5,𝔽2)11yescharacteristic
340C8×C107—22no—
341C8×C107—41no—
342C8×C107—41no—
343C8×C107—41no—
344C22×C107—22no—
345C22×C107—22no—
346C22×C107—22no—
347C22×C107—22no—
348C22×C107—22no—
349C22×C107—22no—
350C22×C107—41no—
351C22×C107—41no—
352C22×C107—41no—
353C22×C107—41no—
354C22×C107—41no—
355C22×C107—41no—
356C22×C107—41no—
357C22×C107—41no—
358C22×C107—42no—
359C22×C107—42no—
360C22×C107—42no—
361C22×C107—42no—
362C22×C107—42no—
363C22×C107—42no—
364C22×C107—816no—
365C22×C107—81no—
366C22×C107—81no—
367C22×C107—81no—
368C22×C107—81no—
369C22×C107—81no—
370C22×C107—81no—
371C22×C107—81no—
372C22×C107—81no—
373C22×C107C2×#12311yescharacteristic
374C22×C107D4211yescharacteristic
375C22×C107#54611yescharacteristic
376C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C107#57511yescharacteristic
378C22×C107#57611yescharacteristic
379C22×C107#57711yescharacteristic
380C4×C107—22no—
381C4×C107—41no—
382C4×C107—41no—
383C4×C107—41no—
384C4×C107—42no—
385C4×C107—81no—
386C4×C107—81no—
387C4×C107—81no—
388C4×C107—81no—
389C4×C107—81no—
390C4×C107#52511yescharacteristic
391C4×C107#53811yescharacteristic
392C4×C107#54611yescharacteristic
393C4×C107#55111yescharacteristic
394#24882C10711yesmaximal, characteristic, direct product factor, Sylow
395C2×C107—42no—
396C2×C107—42no—
397C2×C107—82no—
398C2×C107—82no—
399C2×C107#241811yescharacteristic
400C2×C107#309411yescharacteristic
401C2×C107#309611yescharacteristic
402C2×C107#326411yescharacteristic
403C2×C107#327511yescharacteristic
404C2×C107#331011yescharacteristic
405C2×C107#332211yescharacteristic
406C2×#480C2×C10711yescharacteristic, complemented
407C2×#418C2×C10711yescharacteristic, complemented
408#2408C2×C10711yescharacteristic
409#2352C2×C10711yescharacteristic, complemented
410#2092C2×C10711yescharacteristic, complemented
411#2073C2×C10711yescharacteristic, complemented
412#2034C2×C10711yescharacteristic, complemented
413#2034C2×C10711yescharacteristic, complemented
414#1926C2×C10711yescharacteristic, complemented
415#1925C2×C10711yescharacteristic, complemented
416#1874C2×C10711yescharacteristic, complemented
417#1870C2×C10711yescharacteristic, complemented
418#1854C2×C10711yescharacteristic, complemented
419#1809C2×C10711yescharacteristic, complemented
420#1786C2×C10711yescharacteristic, complemented
421C107#2488211yescharacteristic, direct product factor, Sylow
422C23×D4C22×C10711yescharacteristic
423C22×M16C22×C10711yescharacteristic
424C2×#121C22×C10711yescharacteristic
425C2×#121C22×C10711yescharacteristic
426C2×#120—21no—
427C2×C4×D4C22×C10711yescharacteristic
428C2×#117C22×C10711yescharacteristic
429C22×C4⋊C4C22×C10711yescharacteristic, complemented
430#480—24no—
431C2×#107C22×C10711yescharacteristic, complemented
432C2×#107C22×C10711yescharacteristic, complemented
433C2×#106C22×C10711yescharacteristic, complemented
434C2×#106C22×C10711yescharacteristic, complemented
435#418—24no—
436C2×#102C22×C10711yescharacteristic
437C2×#102C22×C10711yescharacteristic
438C2×#102C22×C10711yescharacteristic
439C2×#102C22×C10711yescharacteristic
440C2×#102C22×C10711yescharacteristic
441C2×#102C22×C10711yescharacteristic
442C2×#102C22×C10711yescharacteristic
443C2×#102C22×C10711yescharacteristic
444C2×C22⋊C8C22×C10711yescharacteristic
445C2×C22⋊C8C22×C10711yescharacteristic, complemented
446C2×C22⋊C8C22×C10711yescharacteristic, complemented
447#394—21no—
448#392—21no—
449#390C22×C10711yescharacteristic
450#390C22×C10711yescharacteristic
451#388—21no—
452#387—21no—
453#386—21no—
454#382C22×C10711yescharacteristic, complemented
455#380C22×C10711yescharacteristic
456#380C22×C10711yescharacteristic
457#380C22×C10711yescharacteristic, complemented
458#379—21no—
459C4×C4⋊C4C22×C10711yescharacteristic, complemented
460C4×C22⋊C4—21no—
461#340C22×C10711yescharacteristic, complemented
462#340C22×C10711yescharacteristic, complemented
463#340C22×C10711yescharacteristic, complemented
464#340C22×C10711yescharacteristic, complemented
465#336C22×C10711yescharacteristic, complemented
466#336C22×C10711yescharacteristic, complemented
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—41no—
476C22×D4—41no—
477C22×D4D4×C10711yescharacteristic
478C22×D4C23×C10711yescharacteristic
479C22×D4C23×C10711yescharacteristic
480C23×C4—21no—
481C23×C4C23×C10711yescharacteristic
482C23×C4C23×C10711yescharacteristic
483C2×M16—22no—
484C2×M16—22no—
485C2×M16—41no—
486C22×C8C23×C10711yescharacteristic
487C22×C8C23×C10711yescharacteristic
488C22×C8C23×C10711yescharacteristic
489C22×C8C23×C10711yescharacteristic
490#121—22no—
491#121—22no—
492#121—41no—
493#121—41no—
494#120—44no—
495C4×D4—22no—
496C4×D4—22no—
497#117—22no—
498#117—41no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4D4×C10711yescharacteristic
503C2×C4⋊C4C23×C10711yescharacteristic
504C2×C4⋊C4C23×C10711yescharacteristic
505C2×C4⋊C4C23×C10711yescharacteristic
506C2×C4⋊C4C23×C10711yescharacteristic
507C2×C4⋊C4C23×C10711yescharacteristic
508C2×C4⋊C4C23×C10711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C10711yescharacteristic
520C2×C22⋊C4D4×C10711yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42C23×C10711yescharacteristic
524#107—22no—
525#107—22no—
526#106—41no—
527#106—41no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535#102D4×C10714yescomplemented
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545C24—21no—
546C24—21no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24C2×D4×C10711yescharacteristic
555C24C2×D4×C10711yescharacteristic
556C2×D4—28no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—41no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4C2×D4×C10712yes—
583C2×D4#41×C10712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—81no—
603C22×C4C2×D4×C10711yescharacteristic
604C22×C4C2×D4×C10711yescharacteristic
605C22×C4C2×D4×C10711yescharacteristic
606C22×C4C2×D4×C10711yescharacteristic
607C22×C4#41×C10712yes—
608C22×C4#41×C10712yes—
609C22×C4C24×C10711yescharacteristic
610M16—44no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8C2×D4×C10712yes—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—42no—
636C4⋊C4C2×D4×C10712yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—42no—
652C42—81no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—22no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#123×C10712yes—
687C23AGL(1,ℤ/8)×C10712yes—
688C23C22×D4×C10711yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4#123×C10712yes—
740C2×C4C22×D4×C10711yescharacteristic
741C2×C4C2×#41×C10711yescharacteristic
742C2×C4C2×#41×C10711yescharacteristic
743C2×C4C2×#41×C10711yescharacteristic
744C2×C4H(5,𝔽2)×C10711yescharacteristic
745C2×C4H(5,𝔽2)×C10711yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×#123×C10711yescharacteristic
780C22D42×C10711yescharacteristic
781C22#546×C10711yescharacteristic
782C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
783C22#575×C10711yescharacteristic
784C22#576×C10711yescharacteristic
785C22#577×C10711yescharacteristic
786C4—22no—
787C4—41no—
788C4—42no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4#525×C10711yescharacteristic
797C4#538×C10711yescharacteristic
798C4#546×C10711yescharacteristic
799C4#551×C10711yescharacteristic
800C2—42no—
801C2—42no—
802C2—82no—
803C2—82no—
804C2C107×#241811yescharacteristic
805C2C107×#309411yescharacteristic
806C2C107×#309611yescharacteristic
807C2C107×#326411yescharacteristic
808C2C107×#327511yescharacteristic
809C2C107×#331011yescharacteristic
810C2C107×#332211yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#480×C107C2semidirect
2. C2×#418×C107C2semidirect
4. C107×#2352C2semidirect
5. C107×#2092C2semidirect
6. C107×#2073C2semidirect
7. C107×#2034C2semidirect
8. C107×#2034C2semidirect
9. C107×#1926C2semidirect
10. C107×#1925C2semidirect
11. C107×#1874C2semidirect
12. C107×#1870C2semidirect
13. C107×#1854C2semidirect
14. C107×#1809C2semidirect
15. C107×#1786C2semidirect
23. C22×C4⋊C4×C107C22semidirect
25. C2×#107×C107C22semidirect
26. C2×#107×C107C22semidirect
27. C2×#106×C107C22semidirect
28. C2×#106×C107C22semidirect
39. C2×C22⋊C8×C107C22semidirect
40. C2×C22⋊C8×C107C22semidirect
48. #382×C107C22semidirect
51. #380×C107C22semidirect
53. C4×C4⋊C4×C107C22semidirect
55. #340×C107C22semidirect
56. #340×C107C22semidirect
57. #340×C107C22semidirect
58. #340×C107C22semidirect
59. #336×C107C22semidirect
60. #336×C107C22semidirect
129. #102×C107D4semidirect
394. #24882C107direct (N × H)
406. C2×#480C2×C107semidirect
407. C2×#418C2×C107semidirect
409. #2352C2×C107semidirect
410. #2092C2×C107semidirect
411. #2073C2×C107semidirect
412. #2034C2×C107semidirect
413. #2034C2×C107semidirect
414. #1926C2×C107semidirect
415. #1925C2×C107semidirect
416. #1874C2×C107semidirect
417. #1870C2×C107semidirect
418. #1854C2×C107semidirect
419. #1809C2×C107semidirect
420. #1786C2×C107semidirect
421. C107#24882direct (N × H)
429. C22×C4⋊C4C22×C107semidirect
431. C2×#107C22×C107semidirect
432. C2×#107C22×C107semidirect
433. C2×#106C22×C107semidirect
434. C2×#106C22×C107semidirect
445. C2×C22⋊C8C22×C107semidirect
446. C2×C22⋊C8C22×C107semidirect
454. #382C22×C107semidirect
457. #380C22×C107semidirect
459. C4×C4⋊C4C22×C107semidirect
461. #340C22×C107semidirect
462. #340C22×C107semidirect
463. #340C22×C107semidirect
464. #340C22×C107semidirect
465. #336C22×C107semidirect
466. #336C22×C107semidirect
535. #102D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1072
C2×#418×C1072
C107×#24082
C107×#23522
C107×#20922
C107×#20732
C107×#20342
C107×#19262
C107×#19252
C107×#18742
C107×#18702
C107×#18542
C107×#18092
C107×#17862
#24882107