Finite Group Databasebeta

← C107×#26984 #41052948

Subgroups — C107×#26984 #41052948

Order 27392.

1050 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C107C211yesmaximal, characteristic, complemented
2C2×#442×C107C211yesmaximal, characteristic, complemented
3C107×#2428C211yesmaximal, characteristic, complemented
4C107×#2422C211yesmaximal, characteristic, complemented
5C107×#2084C211yesmaximal, characteristic, complemented
6C107×#2034C211yesmaximal, characteristic, complemented
7C107×#2011C211yesmaximal, characteristic, complemented
8C107×#1999C211yesmaximal, characteristic, complemented
9C107×#1957C211yesmaximal, characteristic, complemented
10C107×#1936C211yesmaximal, characteristic, complemented
11C107×#1934C211yesmaximal, characteristic, complemented
12C107×#1895C211yesmaximal, characteristic, complemented
13C107×#1879C211yesmaximal, characteristic, complemented
14C107×#1864C211yesmaximal, characteristic, complemented
15C107×#1753C211yesmaximal, characteristic, complemented
16C22×D8×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C22×M16×C107C2211yescharacteristic
19C2×#127×C107C2211yescharacteristic
20C2×#123×C107—21no—
21C2×#121×C107—21no—
22C2×#121×C107C2211yescharacteristic
23C2×#121×C107C2211yescharacteristic
24C2×#121×C107C2211yescharacteristic
25C2×C4×D4×C107C2211yescharacteristic
26C2×C4×D4×C107C2211yescharacteristic
27#469×C107—24no—
28#442×C107—24no—
29C2×#106×C107C2211yescharacteristic
30C2×#106×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#102×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×#102×C107C2211yescharacteristic
39C2×C22⋊C8×C107C2211yescharacteristic
40C2×#97×C107C2211yescharacteristic
41C2×C4×C8×C107C2211yescharacteristic
42#397×C107—21no—
43#394×C107—21no—
44#394×C107—21no—
45#392×C107—21no—
46#390×C107C2211yescharacteristic
47#390×C107C2211yescharacteristic
48#389×C107C2211yescharacteristic
49#389×C107C2211yescharacteristic
50#386×C107—21no—
51#385×C107—21no—
52#384×C107C2211yescharacteristic
53#380×C107C2211yescharacteristic
54C4×C22⋊C4×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60#336×C107C2211yescharacteristic
61C22×D4×C107—21no—
62C22×D4×C107—21no—
63C22×D4×C107—21no—
64C22×D4×C107—21no—
65C22×D4×C107—21no—
66C22×D4×C107C2311yescharacteristic
67C22×D4×C107C2311yescharacteristic
68C22×D4×C107C2311yescharacteristic
69C23×C4×C107—21no—
70C23×C4×C107—21no—
71C23×C4×C107C2311yescharacteristic
72C2×D8×C107—22no—
73C2×D8×C107—22no—
74C2×D8×C107—22no—
75C2×D8×C107—22no—
76C2×D8×C107—22no—
77C2×D8×C107—41no—
78C2×M16×C107—22no—
79C2×M16×C107—22no—
80C2×M16×C107—41no—
81C22×C8×C107C2311yescharacteristic
82C22×C8×C107C2311yescharacteristic
83C22×C8×C107C2311yescharacteristic
84C22×C8×C107C2311yescharacteristic
85#127×C107—22no—
86#127×C107—41no—
87#123×C107—44no—
88#121×C107—22no—
89#121×C107—22no—
90#121×C107—22no—
91#121×C107—44no—
92#121×C107—41no—
93#121×C107—41no—
94#121×C107—41no—
95C4×D4×C107—22no—
96C4×D4×C107—22no—
97C4×D4×C107—41no—
98C4×D4×C107—41no—
99C2×C4⋊C4×C107—21no—
100C2×C4⋊C4×C107—21no—
101C2×C4⋊C4×C107—21no—
102C2×C4⋊C4×C107—21no—
103C2×C4⋊C4×C107C2311yescharacteristic
104C2×C4⋊C4×C107C2311yescharacteristic
105C2×C4⋊C4×C107C2311yescharacteristic
106C2×C4⋊C4×C107C2311yescharacteristic
107C2×C4⋊C4×C107C2311yescharacteristic
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×C107D411yescharacteristic
119C2×C22⋊C4×C107D411yescharacteristic
120C2×C42×C107C2311yescharacteristic
121C2×C42×C107C2311yescharacteristic
122#106×C107—22no—
123#106×C107—22no—
124#102×C107—22no—
125#102×C107—22no—
126#102×C107—22no—
127#102×C107—22no—
128#102×C107—41no—
129#102×C107—41no—
130#102×C107—41no—
131#102×C107D414yescomplemented
132C22⋊C8×C107—22no—
133#97×C107—22no—
134C4×C8×C107—41no—
135#95×C107—21no—
136#95×C107—21no—
137#95×C107—21no—
138#95×C107D411yescharacteristic
139#95×C107D411yescharacteristic
140C24×C107—21no—
141C24×C107—21no—
142C24×C107—21no—
143C24×C107C2×D411yescharacteristic
144C2×D4×C107—21no—
145C2×D4×C107—21no—
146C2×D4×C107—21no—
147C2×D4×C107—21no—
148C2×D4×C107—21no—
149C2×D4×C107—21no—
150C2×D4×C107—21no—
151C2×D4×C107—21no—
152C2×D4×C107—21no—
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—42no—
161C2×D4×C107—42no—
162C2×D4×C107—42no—
163C2×D4×C107—42no—
164C2×D4×C107—42no—
165C2×D4×C107—42no—
166C2×D4×C107—42no—
167C2×D4×C107—42no—
168C2×D4×C107—42no—
169C2×D4×C107—42no—
170C2×D4×C107—81no—
171C2×D4×C107—81no—
172C2×D4×C107—81no—
173C2×D4×C107—81no—
174C2×D4×C107—81no—
175C2×D4×C107C2×D412yes—
176C2×D4×C107#4112yes—
177C22×C4×C107—21no—
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—42no—
189C22×C4×C107—42no—
190C22×C4×C107—42no—
191C22×C4×C107—42no—
192C22×C4×C107—81no—
193C22×C4×C107—81no—
194C22×C4×C107C2×D411yescharacteristic
195C22×C4×C107C2×D411yescharacteristic
196C22×C4×C107C2×D411yescharacteristic
197C22×C4×C107C2×D411yescharacteristic
198C22×C4×C107C2×D411yescharacteristic
199C22×C4×C107C2411yescharacteristic
200D8×C107—28no—
201D8×C107—44no—
202M16×C107—44no—
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×C107C2×D412yes—
213C2×C8×C107#4112yes—
214C2×C8×C107#4112yes—
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—42no—
225C4⋊C4×C107—42no—
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—42no—
239C22⋊C4×C107—42no—
240C22⋊C4×C107—81no—
241C42×C107—21no—
242C42×C107—21no—
243C42×C107—21no—
244C42×C107—21no—
245C23×C107—21no—
246C23×C107—22no—
247C23×C107—21no—
248C23×C107—22no—
249C23×C107—21no—
250C23×C107—21no—
251C23×C107—21no—
252C23×C107—21no—
253C23×C107—21no—
254C23×C107—41no—
255C23×C107—41no—
256C23×C107—41no—
257C23×C107—41no—
258C23×C107—41no—
259C23×C107—41no—
260C23×C107—41no—
261C23×C107—41no—
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×C107C22×D411yescharacteristic
274D4×C107—22no—
275D4×C107—22no—
276D4×C107—22no—
277D4×C107—22no—
278D4×C107—41no—
279D4×C107—41no—
280D4×C107—41no—
281D4×C107—41no—
282D4×C107—41no—
283D4×C107—41no—
284D4×C107—41no—
285D4×C107—41no—
286D4×C107—84no—
287D4×C107—84no—
288D4×C107—84no—
289D4×C107—84no—
290D4×C107—84no—
291C2×C4×C107—21no—
292C2×C4×C107—21no—
293C2×C4×C107—21no—
294C2×C4×C107—21no—
295C2×C4×C107—21no—
296C2×C4×C107—21no—
297C2×C4×C107—21no—
298C2×C4×C107—21no—
299C2×C4×C107—22no—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—41no—
306C2×C4×C107—41no—
307C2×C4×C107—41no—
308C2×C4×C107—41no—
309C2×C4×C107—41no—
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—84no—
324C2×C4×C107—84no—
325C2×C4×C107AGL(1,ℤ/8)12yes—
326C2×C4×C107AGL(1,ℤ/8)12yes—
327C2×C4×C107C22×D411yescharacteristic
328C2×C4×C107C2×#4111yescharacteristic
329C2×C4×C107C2×#4111yescharacteristic
330C2×C4×C107C2×#4111yescharacteristic
331C2×C4×C107H(5,𝔽2)11yescharacteristic
332C2×C4×C107H(5,𝔽2)11yescharacteristic
333C8×C107—22no—
334C8×C107—22no—
335C8×C107—22no—
336C8×C107—41no—
337C22×C107—41no—
338C22×C107—41no—
339C22×C107—41no—
340C22×C107—42no—
341C22×C107—42no—
342C22×C107—41no—
343C22×C107—42no—
344C22×C107—42no—
345C22×C107—41no—
346C22×C107—42no—
347C22×C107—41no—
348C22×C107—41no—
349C22×C107—42no—
350C22×C107—81no—
351C22×C107—81no—
352C22×C107—81no—
353C22×C107—81no—
354C22×C107—81no—
355C22×C107—81no—
356C22×C107—81no—
357C22×C107—81no—
358C22×C107—81no—
359C22×C107—81no—
360C22×C107—81no—
361C22×C107—81no—
362C22×C107—81no—
363C22×C107—81no—
364C22×C107—81no—
365C22×C107#53211yescharacteristic
366C22×C107D4211yescharacteristic
367C22×C107#54611yescharacteristic
368C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C107#57611yescharacteristic
371C22×C107#57711yescharacteristic
372C4×C107—22no—
373C4×C107—22no—
374C4×C107—41no—
375C4×C107—41no—
376C4×C107—42no—
377C4×C107—41no—
378C4×C107—81no—
379C4×C107—81no—
380C4×C107—81no—
381C4×C107—81no—
382C4×C107#52511yescharacteristic
383C4×C107#54011yescharacteristic
384C4×C107#54611yescharacteristic
385C4×C107#55311yescharacteristic
386#26984C10711yesmaximal, characteristic, direct product factor, Sylow
387C2×C107—81no—
388C2×C107—82no—
389C2×C107—82no—
390C2×C107—161no—
391C2×C107#246411yescharacteristic
392C2×C107#317911yescharacteristic
393C2×C107#318411yescharacteristic
394C2×C107#327211yescharacteristic
395C2×C107#327411yescharacteristic
396C2×C107#330611yescharacteristic
397C2×C107#331811yescharacteristic
398C2×#469C2×C10711yescharacteristic, complemented
399C2×#442C2×C10711yescharacteristic, complemented
400#2428C2×C10711yescharacteristic, complemented
401#2422C2×C10711yescharacteristic, complemented
402#2084C2×C10711yescharacteristic, complemented
403#2034C2×C10711yescharacteristic, complemented
404#2011C2×C10711yescharacteristic, complemented
405#1999C2×C10711yescharacteristic, complemented
406#1957C2×C10711yescharacteristic, complemented
407#1936C2×C10711yescharacteristic, complemented
408#1934C2×C10711yescharacteristic, complemented
409#1895C2×C10711yescharacteristic, complemented
410#1879C2×C10711yescharacteristic, complemented
411#1864C2×C10711yescharacteristic, complemented
412#1753C2×C10711yescharacteristic, complemented
413C107#2698411yescharacteristic, direct product factor, Sylow
414C22×D8C22×C10711yescharacteristic
415C22×D8C22×C10711yescharacteristic
416C22×M16C22×C10711yescharacteristic
417C2×#127C22×C10711yescharacteristic
418C2×#123—21no—
419C2×#121—21no—
420C2×#121C22×C10711yescharacteristic
421C2×#121C22×C10711yescharacteristic
422C2×#121C22×C10711yescharacteristic
423C2×C4×D4C22×C10711yescharacteristic
424C2×C4×D4C22×C10711yescharacteristic
425#469—24no—
426#442—24no—
427C2×#106C22×C10711yescharacteristic
428C2×#106C22×C10711yescharacteristic
429C2×#102C22×C10711yescharacteristic
430C2×#102C22×C10711yescharacteristic
431C2×#102C22×C10711yescharacteristic
432C2×#102C22×C10711yescharacteristic
433C2×#102C22×C10711yescharacteristic
434C2×#102C22×C10711yescharacteristic
435C2×#102C22×C10711yescharacteristic
436C2×#102C22×C10711yescharacteristic
437C2×C22⋊C8C22×C10711yescharacteristic
438C2×#97C22×C10711yescharacteristic
439C2×C4×C8C22×C10711yescharacteristic
440#397—21no—
441#394—21no—
442#394—21no—
443#392—21no—
444#390C22×C10711yescharacteristic
445#390C22×C10711yescharacteristic
446#389C22×C10711yescharacteristic
447#389C22×C10711yescharacteristic
448#386—21no—
449#385—21no—
450#384C22×C10711yescharacteristic
451#380C22×C10711yescharacteristic
452C4×C22⋊C4C22×C10711yescharacteristic
453#340C22×C10711yescharacteristic
454#340C22×C10711yescharacteristic
455#340C22×C10711yescharacteristic
456#340C22×C10711yescharacteristic
457#336C22×C10711yescharacteristic
458#336C22×C10711yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C23×C10711yescharacteristic
465C22×D4C23×C10711yescharacteristic
466C22×D4C23×C10711yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C10711yescharacteristic
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—41no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—41no—
479C22×C8C23×C10711yescharacteristic
480C22×C8C23×C10711yescharacteristic
481C22×C8C23×C10711yescharacteristic
482C22×C8C23×C10711yescharacteristic
483#127—22no—
484#127—41no—
485#123—44no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—44no—
490#121—41no—
491#121—41no—
492#121—41no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—41no—
496C4×D4—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4C23×C10711yescharacteristic
502C2×C4⋊C4C23×C10711yescharacteristic
503C2×C4⋊C4C23×C10711yescharacteristic
504C2×C4⋊C4C23×C10711yescharacteristic
505C2×C4⋊C4C23×C10711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
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⋊C4D4×C10711yescharacteristic
517C2×C22⋊C4D4×C10711yescharacteristic
518C2×C42C23×C10711yescharacteristic
519C2×C42C23×C10711yescharacteristic
520#106—22no—
521#106—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102D4×C10714yescomplemented
530C22⋊C8—22no—
531#97—22no—
532C4×C8—41no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95D4×C10711yescharacteristic
537#95D4×C10711yescharacteristic
538C24—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C10711yescharacteristic
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4C2×D4×C10712yes—
574C2×D4#41×C10712yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C2×D4×C10711yescharacteristic
593C22×C4C2×D4×C10711yescharacteristic
594C22×C4C2×D4×C10711yescharacteristic
595C22×C4C2×D4×C10711yescharacteristic
596C22×C4C2×D4×C10711yescharacteristic
597C22×C4C24×C10711yescharacteristic
598D8—28no—
599D8—44no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×D4×C10712yes—
611C2×C8#41×C10712yes—
612C2×C8#41×C10712yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C10712yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C23—21no—
644C23—22no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C22×D4×C10711yescharacteristic
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—84no—
687D4—84no—
688D4—84no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4AGL(1,ℤ/8)×C10712yes—
724C2×C4AGL(1,ℤ/8)×C10712yes—
725C2×C4C22×D4×C10711yescharacteristic
726C2×C4C2×#41×C10711yescharacteristic
727C2×C4C2×#41×C10711yescharacteristic
728C2×C4C2×#41×C10711yescharacteristic
729C2×C4H(5,𝔽2)×C10711yescharacteristic
730C2×C4H(5,𝔽2)×C10711yescharacteristic
731C8—22no—
732C8—22no—
733C8—22no—
734C8—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22#532×C10711yescharacteristic
764C22D42×C10711yescharacteristic
765C22#546×C10711yescharacteristic
766C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
767C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
768C22#576×C10711yescharacteristic
769C22#577×C10711yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4#525×C10711yescharacteristic
781C4#540×C10711yescharacteristic
782C4#546×C10711yescharacteristic
783C4#553×C10711yescharacteristic
784C2—81no—
785C2—82no—
786C2—82no—
787C2—161no—
788C2C107×#246411yescharacteristic
789C2C107×#317911yescharacteristic
790C2C107×#318411yescharacteristic
791C2C107×#327211yescharacteristic
792C2C107×#327411yescharacteristic
793C2C107×#330611yescharacteristic
794C2C107×#331811yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×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
1. C2×#469×C107C2semidirect
2. C2×#442×C107C2semidirect
3. C107×#2428C2semidirect
4. C107×#2422C2semidirect
5. C107×#2084C2semidirect
6. C107×#2034C2semidirect
7. C107×#2011C2semidirect
8. C107×#1999C2semidirect
9. C107×#1957C2semidirect
10. C107×#1936C2semidirect
11. C107×#1934C2semidirect
12. C107×#1895C2semidirect
13. C107×#1879C2semidirect
14. C107×#1864C2semidirect
15. C107×#1753C2semidirect
131. #102×C107D4semidirect
386. #26984C107direct (N × H)
398. C2×#469C2×C107semidirect
399. C2×#442C2×C107semidirect
400. #2428C2×C107semidirect
401. #2422C2×C107semidirect
402. #2084C2×C107semidirect
403. #2034C2×C107semidirect
404. #2011C2×C107semidirect
405. #1999C2×C107semidirect
406. #1957C2×C107semidirect
407. #1936C2×C107semidirect
408. #1934C2×C107semidirect
409. #1895C2×C107semidirect
410. #1879C2×C107semidirect
411. #1864C2×C107semidirect
412. #1753C2×C107semidirect
413. C107#26984direct (N × H)
529. #102D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1072
C2×#442×C1072
C107×#24282
C107×#24222
C107×#20842
C107×#20342
C107×#20112
C107×#19992
C107×#19572
C107×#19362
C107×#19342
C107×#18952
C107×#18792
C107×#18642
C107×#17532
#26984107