Finite Group Databasebeta

← C107×#26926 #41052890

Subgroups — C107×#26926 #41052890

Order 27392.

1082 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C107C211yesmaximal, characteristic, complemented
2C2×#459×C107C211yesmaximal, characteristic, complemented
3C107×#2428C211yesmaximal, characteristic, complemented
4C107×#2361C211yesmaximal, characteristic, complemented
5C107×#2086C211yesmaximal, characteristic, complemented
6C107×#2041C211yesmaximal, characteristic, complemented
7C107×#1999C211yesmaximal, characteristic, complemented
8C107×#1999C211yesmaximal, characteristic, complemented
9C107×#1970C211yesmaximal, characteristic, complemented
10C107×#1925C211yesmaximal, characteristic, complemented
11C107×#1923C211yesmaximal, characteristic, complemented
12C107×#1879C211yesmaximal, characteristic, complemented
13C107×#1874C211yesmaximal, characteristic, complemented
14C107×#1862C211yesmaximal, characteristic, complemented
15C4×#102×C107C211yesmaximal, characteristic, complemented
16C22×D8×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C2×#127×C107C2211yescharacteristic
19C2×#121×C107—21no—
20C2×#121×C107C2211yescharacteristic
21C2×#121×C107C2211yescharacteristic
22C2×#121×C107C2211yescharacteristic
23C2×C4×D4×C107—21no—
24C2×C4×D4×C107C2211yescharacteristic
25C2×C4×D4×C107C2211yescharacteristic
26C22×C4⋊C4×C107C2211yescharacteristic
27#480×C107—24no—
28#459×C107—24no—
29C2×#107×C107C2211yescharacteristic
30C2×#107×C107C2211yescharacteristic
31C2×C4⋊C8×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#102×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×#102×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic
40C2×C22⋊C8×C107C2211yescharacteristic
41C2×C22⋊C8×C107C2211yescharacteristic
42C2×C4×C8×C107C2211yescharacteristic
43#394×C107—21no—
44#392×C107—21no—
45#390×C107C2211yescharacteristic
46#390×C107C2211yescharacteristic
47#389×C107C2211yescharacteristic
48#389×C107C2211yescharacteristic
49#388×C107—21no—
50#386×C107—21no—
51#386×C107—21no—
52#385×C107—21no—
53C4×C4⋊C4×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×C107—21no—
72C23×C4×C107C2311yescharacteristic
73C2×D8×C107—22no—
74C2×D8×C107—22no—
75C2×D8×C107—22no—
76C2×D8×C107—22no—
77C2×D8×C107—41no—
78C2×D8×C107—41no—
79C22×C8×C107C2311yescharacteristic
80C22×C8×C107C2311yescharacteristic
81C22×C8×C107C2311yescharacteristic
82C22×C8×C107C2311yescharacteristic
83#127×C107—22no—
84#127×C107—41no—
85#121×C107—22no—
86#121×C107—22no—
87#121×C107—22no—
88#121×C107—22no—
89#121×C107—41no—
90#121×C107—41no—
91#121×C107—44no—
92C4×D4×C107—22no—
93C4×D4×C107—22no—
94C4×D4×C107—41no—
95C4×D4×C107—41no—
96C4×D4×C107—44no—
97C2×C4⋊C4×C107—22no—
98C2×C4⋊C4×C107—21no—
99C2×C4⋊C4×C107—21no—
100C2×C4⋊C4×C107—21no—
101C2×C4⋊C4×C107—41no—
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×C107D411yescharacteristic
117C2×C22⋊C4×C107D411yescharacteristic
118C2×C42×C107—21no—
119C2×C42×C107C2311yescharacteristic
120C2×C42×C107C2311yescharacteristic
121#107×C107—22no—
122#107×C107—22no—
123C4⋊C8×C107—22no—
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—41no—
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—24no—
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—21no—
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—42no—
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—42no—
193C22×C4×C107—42no—
194C22×C4×C107—81no—
195C22×C4×C107—81no—
196C22×C4×C107—81no—
197C22×C4×C107C2×D411yescharacteristic
198C22×C4×C107C2×D411yescharacteristic
199C22×C4×C107C2×D411yescharacteristic
200C22×C4×C107C2×D411yescharacteristic
201C22×C4×C107C2×D411yescharacteristic
202C22×C4×C107C2411yescharacteristic
203D8×C107—44no—
204D8×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—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×C107C2×D412yes—
228C4⋊C4×C107#4112yes—
229C4⋊C4×C107#4112yes—
230C22⋊C4×C107—24no—
231C22⋊C4×C107—41no—
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×C107D814yescomplemented
241C42×C107—21no—
242C42×C107—21no—
243C42×C107—21no—
244C42×C107—21no—
245C42×C107—42no—
246C23×C107—21no—
247C23×C107—21no—
248C23×C107—21no—
249C23×C107—21no—
250C23×C107—21no—
251C23×C107—21no—
252C23×C107—22no—
253C23×C107—22no—
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×C107C2×D812yes—
274C23×C107C22×D411yescharacteristic
275D4×C107—22no—
276D4×C107—22no—
277D4×C107—22no—
278D4×C107—22no—
279D4×C107—48no—
280D4×C107—41no—
281D4×C107—41no—
282D4×C107—41no—
283D4×C107—41no—
284D4×C107—41no—
285D4×C107—41no—
286D4×C107—41no—
287D4×C107—41no—
288D4×C107—84no—
289D4×C107—84no—
290D4×C107—84no—
291D4×C107—84no—
292C2×C4×C107—21no—
293C2×C4×C107—21no—
294C2×C4×C107—21no—
295C2×C4×C107—21no—
296C2×C4×C107—21no—
297C2×C4×C107—22no—
298C2×C4×C107—21no—
299C2×C4×C107—21no—
300C2×C4×C107—22no—
301C2×C4×C107—21no—
302C2×C4×C107—22no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
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—41no—
324C2×C4×C107—84no—
325C2×C4×C107—84no—
326C2×C4×C107—84no—
327C2×C4×C107C2×D812yes—
328C2×C4×C107C2×D812yes—
329C2×C4×C107C22×D411yescharacteristic
330C2×C4×C107C2×#4111yescharacteristic
331C2×C4×C107C2×#4111yescharacteristic
332C2×C4×C107C2×#4111yescharacteristic
333C2×C4×C107H(5,𝔽2)11yescharacteristic
334C2×C4×C107H(5,𝔽2)11yescharacteristic
335C8×C107—22no—
336C8×C107—41no—
337C8×C107—41no—
338C8×C107—41no—
339C22×C107—22no—
340C22×C107—22no—
341C22×C107—22no—
342C22×C107—41no—
343C22×C107—41no—
344C22×C107—41no—
345C22×C107—41no—
346C22×C107—42no—
347C22×C107—42no—
348C22×C107—42no—
349C22×C107—42no—
350C22×C107—42no—
351C22×C107—42no—
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—81no—
366C22×C107—81no—
367C22×C107#52511yescharacteristic
368C22×C107D4211yescharacteristic
369C22×C107#54611yescharacteristic
370C22×C107C22×D811yescharacteristic
371C22×C107#57511yescharacteristic
372C22×C107#57611yescharacteristic
373C22×C107#57711yescharacteristic
374C4×C107—22no—
375C4×C107—22no—
376C4×C107—42no—
377C4×C107—41no—
378C4×C107—41no—
379C4×C107—42no—
380C4×C107—42no—
381C4×C107—41no—
382C4×C107—81no—
383C4×C107—81no—
384C4×C107#53211yescharacteristic
385C4×C107#54011yescharacteristic
386C4×C107#54611yescharacteristic
387C4×C107#55311yescharacteristic
388#26926C10711yesmaximal, characteristic, direct product factor, Sylow
389C2×C107—42no—
390C2×C107—82no—
391C2×C107—82no—
392C2×C107—161no—
393C2×C107#246411yescharacteristic
394C2×C107#310011yescharacteristic
395C2×C107#311911yescharacteristic
396C2×C107#327511yescharacteristic
397C2×C107D4×D811yescharacteristic
398C2×C107#329411yescharacteristic
399C2×C107#330911yescharacteristic
400C2×#480C2×C10711yescharacteristic, complemented
401C2×#459C2×C10711yescharacteristic, complemented
402#2428C2×C10711yescharacteristic, complemented
403#2361C2×C10711yescharacteristic, complemented
404#2086C2×C10711yescharacteristic, complemented
405#2041C2×C10711yescharacteristic, complemented
406#1999C2×C10711yescharacteristic, complemented
407#1999C2×C10711yescharacteristic, complemented
408#1970C2×C10711yescharacteristic, complemented
409#1925C2×C10711yescharacteristic, complemented
410#1923C2×C10711yescharacteristic, complemented
411#1879C2×C10711yescharacteristic, complemented
412#1874C2×C10711yescharacteristic, complemented
413#1862C2×C10711yescharacteristic, complemented
414C4×#102C2×C10711yescharacteristic, complemented
415C107#2692611yescharacteristic, direct product factor, Sylow
416C22×D8C22×C10711yescharacteristic
417C22×D8C22×C10711yescharacteristic
418C2×#127C22×C10711yescharacteristic
419C2×#121—21no—
420C2×#121C22×C10711yescharacteristic
421C2×#121C22×C10711yescharacteristic
422C2×#121C22×C10711yescharacteristic
423C2×C4×D4—21no—
424C2×C4×D4C22×C10711yescharacteristic
425C2×C4×D4C22×C10711yescharacteristic
426C22×C4⋊C4C22×C10711yescharacteristic
427#480—24no—
428#459—24no—
429C2×#107C22×C10711yescharacteristic
430C2×#107C22×C10711yescharacteristic
431C2×C4⋊C8C22×C10711yescharacteristic
432C2×#102C22×C10711yescharacteristic
433C2×#102C22×C10711yescharacteristic
434C2×#102C22×C10711yescharacteristic
435C2×#102C22×C10711yescharacteristic
436C2×#102C22×C10711yescharacteristic
437C2×#102C22×C10711yescharacteristic
438C2×#102C22×C10711yescharacteristic
439C2×#102C22×C10711yescharacteristic
440C2×C22⋊C8C22×C10711yescharacteristic
441C2×C22⋊C8C22×C10711yescharacteristic
442C2×C4×C8C22×C10711yescharacteristic
443#394—21no—
444#392—21no—
445#390C22×C10711yescharacteristic
446#390C22×C10711yescharacteristic
447#389C22×C10711yescharacteristic
448#389C22×C10711yescharacteristic
449#388—21no—
450#386—21no—
451#386—21no—
452#385—21no—
453C4×C4⋊C4C22×C10711yescharacteristic
454C4×C22⋊C4C22×C10711yescharacteristic
455#340C22×C10711yescharacteristic
456#340C22×C10711yescharacteristic
457#340C22×C10711yescharacteristic
458#340C22×C10711yescharacteristic
459#336C22×C10711yescharacteristic
460#336C22×C10711yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4C23×C10711yescharacteristic
467C22×D4C23×C10711yescharacteristic
468C22×D4C23×C10711yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C23×C10711yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
479C22×C8C23×C10711yescharacteristic
480C22×C8C23×C10711yescharacteristic
481C22×C8C23×C10711yescharacteristic
482C22×C8C23×C10711yescharacteristic
483#127—22no—
484#127—41no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—41no—
490#121—41no—
491#121—44no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C4×D4—44no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C23×C10711yescharacteristic
503C2×C4⋊C4C23×C10711yescharacteristic
504C2×C4⋊C4C23×C10711yescharacteristic
505C2×C4⋊C4C23×C10711yescharacteristic
506C2×C4⋊C4C23×C10711yescharacteristic
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×C42—21no—
519C2×C42C23×C10711yescharacteristic
520C2×C42C23×C10711yescharacteristic
521#107—22no—
522#107—22no—
523C4⋊C8—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—41no—
530#102—41no—
531#102D4×C10714yescomplemented
532C22⋊C8—22no—
533C22⋊C8—41no—
534C4×C8—41no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95D4×C10711yescharacteristic
539#95D4×C10711yescharacteristic
540C24—21no—
541C24—21no—
542C24—21no—
543C24C2×D4×C10711yescharacteristic
544C2×D4—24no—
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—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C2×D4×C10712yes—
576C2×D4#41×C10712yes—
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—21no—
587C22×C4—21no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C10711yescharacteristic
598C22×C4C2×D4×C10711yescharacteristic
599C22×C4C2×D4×C10711yescharacteristic
600C22×C4C2×D4×C10711yescharacteristic
601C22×C4C2×D4×C10711yescharacteristic
602C22×C4C24×C10711yescharacteristic
603D8—44no—
604D8—44no—
605C2×C8—21no—
606C2×C8—21no—
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×C8C2×D4×C10712yes—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4C2×D4×C10712yes—
628C4⋊C4#41×C10712yes—
629C4⋊C4#41×C10712yes—
630C22⋊C4—24no—
631C22⋊C4—41no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4D8×C10714yescomplemented
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—22no—
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—
671C23—41no—
672C23—41no—
673C23C2×D8×C10712yes—
674C23C22×D4×C10711yescharacteristic
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—48no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—84no—
689D4—84no—
690D4—84no—
691D4—84no—
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—22no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
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—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4C2×D8×C10712yes—
728C2×C4C2×D8×C10712yes—
729C2×C4C22×D4×C10711yescharacteristic
730C2×C4C2×#41×C10711yescharacteristic
731C2×C4C2×#41×C10711yescharacteristic
732C2×C4C2×#41×C10711yescharacteristic
733C2×C4H(5,𝔽2)×C10711yescharacteristic
734C2×C4H(5,𝔽2)×C10711yescharacteristic
735C8—22no—
736C8—41no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22#525×C10711yescharacteristic
768C22D42×C10711yescharacteristic
769C22#546×C10711yescharacteristic
770C22C22×D8×C10711yescharacteristic
771C22#575×C10711yescharacteristic
772C22#576×C10711yescharacteristic
773C22#577×C10711yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
778C4—42no—
779C4—42no—
780C4—41no—
781C4—42no—
782C4—81no—
783C4—81no—
784C4#532×C10711yescharacteristic
785C4#540×C10711yescharacteristic
786C4#546×C10711yescharacteristic
787C4#553×C10711yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C107×#246411yescharacteristic
793C2C107×#310011yescharacteristic
794C2C107×#311911yescharacteristic
795C2C107×#327511yescharacteristic
796C2D4×D8×C10711yescharacteristic
797C2C107×#329411yescharacteristic
798C2C107×#330911yescharacteristic
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×#480×C107C2semidirect
2. C2×#459×C107C2semidirect
3. C107×#2428C2semidirect
4. C107×#2361C2semidirect
5. C107×#2086C2semidirect
6. C107×#2041C2semidirect
7. C107×#1999C2semidirect
8. C107×#1999C2semidirect
9. C107×#1970C2semidirect
10. C107×#1925C2semidirect
11. C107×#1923C2semidirect
12. C107×#1879C2semidirect
13. C107×#1874C2semidirect
14. C107×#1862C2semidirect
15. C4×#102×C107C2semidirect
131. #102×C107D4semidirect
240. C22⋊C4×C107D8semidirect
388. #26926C107direct (N × H)
400. C2×#480C2×C107semidirect
401. C2×#459C2×C107semidirect
402. #2428C2×C107semidirect
403. #2361C2×C107semidirect
404. #2086C2×C107semidirect
405. #2041C2×C107semidirect
406. #1999C2×C107semidirect
407. #1999C2×C107semidirect
408. #1970C2×C107semidirect
409. #1925C2×C107semidirect
410. #1923C2×C107semidirect
411. #1879C2×C107semidirect
412. #1874C2×C107semidirect
413. #1862C2×C107semidirect
414. C4×#102C2×C107semidirect
415. C107#26926direct (N × H)
531. #102D4×C107semidirect
640. C22⋊C4D8×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×#459×C1072
C107×#24282
C107×#23612
C107×#20862
C107×#20412
C107×#19992
C107×#19702
C107×#19252
C107×#19232
C107×#18792
C107×#18742
C107×#18622
C4×#102×C1072
#26926107