Finite Group Databasebeta

← C107×#24886 #41050850

Subgroups — C107×#24886 #41050850

Order 27392.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C107C211yesmaximal, characteristic, complemented
2C2×#418×C107C211yesmaximal, characteristic, complemented
3C107×#2408C211yesmaximal, characteristic
4C107×#2354C211yesmaximal, characteristic, complemented
5C107×#2094C211yesmaximal, characteristic, complemented
6C107×#2071C211yesmaximal, characteristic, complemented
7C107×#2034C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#1925C211yesmaximal, characteristic, complemented
10C107×#1925C211yesmaximal, characteristic, complemented
11C107×#1875C211yesmaximal, 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
23C2×#117×C107C2211yescharacteristic, complemented
24#482×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×C107—21no—
44#390×C107C2211yescharacteristic
45#390×C107C2211yescharacteristic
46#388×C107—21no—
47#388×C107—21no—
48#384×C107C2211yescharacteristic, complemented
49#380×C107C2211yescharacteristic
50#380×C107C2211yescharacteristic
51#380×C107C2211yescharacteristic, complemented
52#379×C107—21no—
53C4×C4⋊C4×C107—21no—
54C4×C4⋊C4×C107C2211yescharacteristic, complemented
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×C107C2311yescharacteristic
75C23×C4×C107C2311yescharacteristic
76C2×M16×C107—22no—
77C2×M16×C107—22no—
78C2×M16×C107—41no—
79C22×C8×C107C2311yescharacteristic
80C22×C8×C107C2311yescharacteristic
81C22×C8×C107C2311yescharacteristic
82C22×C8×C107C2311yescharacteristic
83#121×C107—22no—
84#121×C107—22no—
85#121×C107—41no—
86#121×C107—41no—
87#120×C107—44no—
88C4×D4×C107—22no—
89C4×D4×C107—22no—
90#117×C107—22no—
91#117×C107—22no—
92#117×C107—41no—
93#117×C107—41no—
94C2×C4⋊C4×C107—21no—
95C2×C4⋊C4×C107—21no—
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×C107—21no—
114C2×C22⋊C4×C107D411yescharacteristic
115C2×C22⋊C4×C107D411yescharacteristic
116C2×C42×C107—21no—
117C2×C42×C107—21no—
118C2×C42×C107—21no—
119C2×C42×C107C2311yescharacteristic
120#107×C107—22no—
121#107×C107—41no—
122#106×C107—22no—
123#106×C107—41no—
124#102×C107—22no—
125#102×C107—22no—
126#102×C107—22no—
127#102×C107—22no—
128#102×C107—22no—
129#102×C107—41no—
130#102×C107—41no—
131#102×C107D414yescomplemented
132C22⋊C8×C107—22no—
133C22⋊C8×C107—22no—
134C22⋊C8×C107—41no—
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×C107C2×D411yescharacteristic
195C22×C4×C107C2×D411yescharacteristic
196C22×C4×C107C2×D411yescharacteristic
197C22×C4×C107C2×D411yescharacteristic
198C22×C4×C107#4112yes—
199C22×C4×C107#4112yes—
200C22×C4×C107C2411yescharacteristic
201M16×C107—44no—
202C2×C8×C107—21no—
203C2×C8×C107—21no—
204C2×C8×C107—21no—
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×C107C2×D412yes—
214C4⋊C4×C107—22no—
215C4⋊C4×C107—21no—
216C4⋊C4×C107—21no—
217C4⋊C4×C107—21no—
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—42no—
227C4⋊C4×C107—81no—
228C4⋊C4×C107C2×D412yes—
229C22⋊C4×C107—22no—
230C22⋊C4×C107—22no—
231C22⋊C4×C107—42no—
232C22⋊C4×C107—42no—
233C22⋊C4×C107—42no—
234C22⋊C4×C107—42no—
235C22⋊C4×C107—42no—
236C22⋊C4×C107—42no—
237C22⋊C4×C107—42no—
238C22⋊C4×C107—81no—
239C22⋊C4×C107—81no—
240C22⋊C4×C107—81no—
241C22⋊C4×C107—81no—
242C42×C107—21no—
243C42×C107—21no—
244C42×C107—42no—
245C42×C107—42no—
246C42×C107—42no—
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—22no—
256C23×C107—22no—
257C23×C107—21no—
258C23×C107—21no—
259C23×C107—21no—
260C23×C107—21no—
261C23×C107—21no—
262C23×C107—48no—
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—41no—
275C23×C107—84no—
276C23×C107—84no—
277C23×C107—84no—
278C23×C107—84no—
279C23×C107—84no—
280C23×C107—84no—
281C23×C107#12312yes—
282C23×C107C22×D411yescharacteristic
283D4×C107—22no—
284D4×C107—22no—
285D4×C107—22no—
286D4×C107—22no—
287D4×C107—44no—
288D4×C107—48no—
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—21no—
298C2×C4×C107—21no—
299C2×C4×C107—22no—
300C2×C4×C107—22no—
301C2×C4×C107—22no—
302C2×C4×C107—22no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—22no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—41no—
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#12312yes—
332C2×C4×C107AGL(1,ℤ/8)12yes—
333C2×C4×C107C22×D411yescharacteristic
334C2×C4×C107C2×#4111yescharacteristic
335C2×C4×C107C2×#4111yescharacteristic
336C2×C4×C107C2×#4111yescharacteristic
337C2×C4×C107H(5,𝔽2)11yescharacteristic
338C2×C4×C107H(5,𝔽2)11yescharacteristic
339C8×C107—22no—
340C8×C107—41no—
341C8×C107—41no—
342C8×C107—41no—
343C22×C107—22no—
344C22×C107—22no—
345C22×C107—22no—
346C22×C107—41no—
347C22×C107—41no—
348C22×C107—41no—
349C22×C107—41no—
350C22×C107—41no—
351C22×C107—41no—
352C22×C107—41no—
353C22×C107—42no—
354C22×C107—42no—
355C22×C107—41no—
356C22×C107—42no—
357C22×C107—41no—
358C22×C107—42no—
359C22×C107—41no—
360C22×C107—42no—
361C22×C107—41no—
362C22×C107—42no—
363C22×C107—816no—
364C22×C107—81no—
365C22×C107—81no—
366C22×C107—81no—
367C22×C107—81no—
368C22×C107—81no—
369C22×C107—81no—
370C22×C107—81no—
371C22×C107—81no—
372C22×C107C2×#12311yescharacteristic
373C22×C107D4211yescharacteristic
374C22×C107#54611yescharacteristic
375C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C107#57511yescharacteristic
377C22×C107#57611yescharacteristic
378C22×C107#57711yescharacteristic
379C4×C107—22no—
380C4×C107—22no—
381C4×C107—41no—
382C4×C107—41no—
383C4×C107—42no—
384C4×C107—81no—
385C4×C107—81no—
386C4×C107—81no—
387C4×C107—81no—
388C4×C107—81no—
389C4×C107#52511yescharacteristic
390C4×C107#53811yescharacteristic
391C4×C107#54611yescharacteristic
392C4×C107#55111yescharacteristic
393#24886C10711yesmaximal, characteristic, direct product factor, Sylow
394C2×C107—42no—
395C2×C107—81no—
396C2×C107—82no—
397C2×C107—82no—
398C2×C107#241811yescharacteristic
399C2×C107#309411yescharacteristic
400C2×C107#309611yescharacteristic
401C2×C107#326811yescharacteristic
402C2×C107#327211yescharacteristic
403C2×C107#331111yescharacteristic
404C2×C107#332511yescharacteristic
405C2×#482C2×C10711yescharacteristic, complemented
406C2×#418C2×C10711yescharacteristic, complemented
407#2408C2×C10711yescharacteristic
408#2354C2×C10711yescharacteristic, complemented
409#2094C2×C10711yescharacteristic, complemented
410#2071C2×C10711yescharacteristic, complemented
411#2034C2×C10711yescharacteristic, complemented
412#2033C2×C10711yescharacteristic, complemented
413#1925C2×C10711yescharacteristic, complemented
414#1925C2×C10711yescharacteristic, complemented
415#1875C2×C10711yescharacteristic, complemented
416#1870C2×C10711yescharacteristic, complemented
417#1854C2×C10711yescharacteristic, complemented
418#1809C2×C10711yescharacteristic, complemented
419#1786C2×C10711yescharacteristic, complemented
420C107#2488611yescharacteristic, direct product factor, Sylow
421C23×D4C22×C10711yescharacteristic
422C22×M16C22×C10711yescharacteristic
423C2×#121C22×C10711yescharacteristic
424C2×#121C22×C10711yescharacteristic
425C2×#120—21no—
426C2×C4×D4C22×C10711yescharacteristic
427C2×#117C22×C10711yescharacteristic
428C2×#117C22×C10711yescharacteristic, complemented
429#482—24no—
430C2×#107C22×C10711yescharacteristic, complemented
431C2×#107C22×C10711yescharacteristic, complemented
432C2×#106C22×C10711yescharacteristic, complemented
433C2×#106C22×C10711yescharacteristic, complemented
434#418—24no—
435C2×#102C22×C10711yescharacteristic
436C2×#102C22×C10711yescharacteristic
437C2×#102C22×C10711yescharacteristic
438C2×#102C22×C10711yescharacteristic
439C2×#102C22×C10711yescharacteristic
440C2×#102C22×C10711yescharacteristic
441C2×#102C22×C10711yescharacteristic
442C2×#102C22×C10711yescharacteristic
443C2×C22⋊C8C22×C10711yescharacteristic
444C2×C22⋊C8C22×C10711yescharacteristic, complemented
445C2×C22⋊C8C22×C10711yescharacteristic, complemented
446#394—21no—
447#392—21no—
448#390—21no—
449#390C22×C10711yescharacteristic
450#390C22×C10711yescharacteristic
451#388—21no—
452#388—21no—
453#384C22×C10711yescharacteristic, complemented
454#380C22×C10711yescharacteristic
455#380C22×C10711yescharacteristic
456#380C22×C10711yescharacteristic, complemented
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C22×C10711yescharacteristic, complemented
460#340C22×C10711yescharacteristic, complemented
461#340C22×C10711yescharacteristic, complemented
462#340C22×C10711yescharacteristic, complemented
463#340C22×C10711yescharacteristic, complemented
464#336C22×C10711yescharacteristic, complemented
465#336C22×C10711yescharacteristic, complemented
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4D4×C10711yescharacteristic
477C22×D4C23×C10711yescharacteristic
478C22×D4C23×C10711yescharacteristic
479C23×C4C23×C10711yescharacteristic
480C23×C4C23×C10711yescharacteristic
481C2×M16—22no—
482C2×M16—22no—
483C2×M16—41no—
484C22×C8C23×C10711yescharacteristic
485C22×C8C23×C10711yescharacteristic
486C22×C8C23×C10711yescharacteristic
487C22×C8C23×C10711yescharacteristic
488#121—22no—
489#121—22no—
490#121—41no—
491#121—41no—
492#120—44no—
493C4×D4—22no—
494C4×D4—22no—
495#117—22no—
496#117—22no—
497#117—41no—
498#117—41no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C10711yescharacteristic
502C2×C4⋊C4C23×C10711yescharacteristic
503C2×C4⋊C4C23×C10711yescharacteristic
504C2×C4⋊C4C23×C10711yescharacteristic
505C2×C4⋊C4C23×C10711yescharacteristic
506C2×C4⋊C4C23×C10711yescharacteristic
507C2×C4⋊C4C23×C10711yescharacteristic
508C2×C22⋊C4—21no—
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×C42—21no—
524C2×C42C23×C10711yescharacteristic
525#107—22no—
526#107—41no—
527#106—22no—
528#106—41no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—41no—
535#102—41no—
536#102D4×C10714yescomplemented
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—41no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24C2×D4×C10711yescharacteristic
554C24C2×D4×C10711yescharacteristic
555C2×D4—28no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
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—44no—
569C2×D4—44no—
570C2×D4—41no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4C2×D4×C10712yes—
582C2×D4#41×C10712yes—
583C22×C4—21no—
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×C4C2×D4×C10711yescharacteristic
600C22×C4C2×D4×C10711yescharacteristic
601C22×C4C2×D4×C10711yescharacteristic
602C22×C4C2×D4×C10711yescharacteristic
603C22×C4#41×C10712yes—
604C22×C4#41×C10712yes—
605C22×C4C24×C10711yescharacteristic
606M16—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8C2×D4×C10712yes—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—81no—
633C4⋊C4C2×D4×C10712yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C42—42no—
651C42—42no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
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—
687C23C22×D4×C10711yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
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#123×C10712yes—
737C2×C4AGL(1,ℤ/8)×C10712yes—
738C2×C4C22×D4×C10711yescharacteristic
739C2×C4C2×#41×C10711yescharacteristic
740C2×C4C2×#41×C10711yescharacteristic
741C2×C4C2×#41×C10711yescharacteristic
742C2×C4H(5,𝔽2)×C10711yescharacteristic
743C2×C4H(5,𝔽2)×C10711yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#123×C10711yescharacteristic
778C22D42×C10711yescharacteristic
779C22#546×C10711yescharacteristic
780C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
781C22#575×C10711yescharacteristic
782C22#576×C10711yescharacteristic
783C22#577×C10711yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—42no—
788C4—41no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4#525×C10711yescharacteristic
795C4#538×C10711yescharacteristic
796C4#546×C10711yescharacteristic
797C4#551×C10711yescharacteristic
798C2—42no—
799C2—81no—
800C2—82no—
801C2—82no—
802C2C107×#241811yescharacteristic
803C2C107×#309411yescharacteristic
804C2C107×#309611yescharacteristic
805C2C107×#326811yescharacteristic
806C2C107×#327211yescharacteristic
807C2C107×#331111yescharacteristic
808C2C107×#332511yescharacteristic
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×#482×C107C2semidirect
2. C2×#418×C107C2semidirect
4. C107×#2354C2semidirect
5. C107×#2094C2semidirect
6. C107×#2071C2semidirect
7. C107×#2034C2semidirect
8. C107×#2033C2semidirect
9. C107×#1925C2semidirect
10. C107×#1925C2semidirect
11. C107×#1875C2semidirect
12. C107×#1870C2semidirect
13. C107×#1854C2semidirect
14. C107×#1809C2semidirect
15. C107×#1786C2semidirect
23. C2×#117×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. #384×C107C22semidirect
51. #380×C107C22semidirect
54. C4×C4⋊C4×C107C22semidirect
55. #340×C107C22semidirect
56. #340×C107C22semidirect
57. #340×C107C22semidirect
58. #340×C107C22semidirect
59. #336×C107C22semidirect
60. #336×C107C22semidirect
131. #102×C107D4semidirect
393. #24886C107direct (N × H)
405. C2×#482C2×C107semidirect
406. C2×#418C2×C107semidirect
408. #2354C2×C107semidirect
409. #2094C2×C107semidirect
410. #2071C2×C107semidirect
411. #2034C2×C107semidirect
412. #2033C2×C107semidirect
413. #1925C2×C107semidirect
414. #1925C2×C107semidirect
415. #1875C2×C107semidirect
416. #1870C2×C107semidirect
417. #1854C2×C107semidirect
418. #1809C2×C107semidirect
419. #1786C2×C107semidirect
420. C107#24886direct (N × H)
428. C2×#117C22×C107semidirect
430. C2×#107C22×C107semidirect
431. C2×#107C22×C107semidirect
432. C2×#106C22×C107semidirect
433. C2×#106C22×C107semidirect
444. C2×C22⋊C8C22×C107semidirect
445. C2×C22⋊C8C22×C107semidirect
453. #384C22×C107semidirect
456. #380C22×C107semidirect
459. C4×C4⋊C4C22×C107semidirect
460. #340C22×C107semidirect
461. #340C22×C107semidirect
462. #340C22×C107semidirect
463. #340C22×C107semidirect
464. #336C22×C107semidirect
465. #336C22×C107semidirect
536. #102D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1072
C2×#418×C1072
C107×#24082
C107×#23542
C107×#20942
C107×#20712
C107×#20342
C107×#20332
C107×#19252
C107×#18752
C107×#18702
C107×#18542
C107×#18092
C107×#17862
#24886107