Finite Group Databasebeta

← C107×#26977 #41052941

Subgroups — C107×#26977 #41052941

Order 27392.

1028 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C107C211yesmaximal, characteristic, complemented
2C2×#442×C107C211yesmaximal, characteristic, complemented
3C107×#2428C211yesmaximal, characteristic, complemented
4C107×#2420C211yesmaximal, characteristic, complemented
5C107×#2085C211yesmaximal, characteristic, complemented
6C107×#2034C211yesmaximal, characteristic, complemented
7C107×#2011C211yesmaximal, characteristic, complemented
8C107×#1999C211yesmaximal, characteristic, complemented
9C107×#1961C211yesmaximal, characteristic, complemented
10C107×#1936C211yesmaximal, characteristic, complemented
11C107×#1936C211yesmaximal, characteristic, complemented
12C107×#1893C211yesmaximal, characteristic, complemented
13C107×#1879C211yesmaximal, characteristic, complemented
14C107×#1862C211yesmaximal, characteristic, complemented
15C107×#1752C211yesmaximal, characteristic, complemented
16C22×D8×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C23×C8×C107C2211yescharacteristic
19C2×#127×C107C2211yescharacteristic
20C2×#121×C107—21no—
21C2×#121×C107C2211yescharacteristic
22C2×#121×C107C2211yescharacteristic
23C2×#121×C107C2211yescharacteristic
24C2×C4×D4×C107C2211yescharacteristic
25C2×C4×D4×C107C2211yescharacteristic
26#466×C107—24no—
27#442×C107—24no—
28C2×#107×C107C2211yescharacteristic
29C2×#106×C107C2211yescharacteristic
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×#97×C107C2211yescharacteristic
40C2×#97×C107C2211yescharacteristic
41#397×C107—21no—
42#394×C107—21no—
43#394×C107—21no—
44#392×C107—21no—
45#390×C107C2211yescharacteristic
46#390×C107C2211yescharacteristic
47#389×C107C2211yescharacteristic
48#389×C107C2211yescharacteristic
49#386×C107—21no—
50#386×C107—21no—
51#382×C107C2211yescharacteristic
52#381×C107—21no—
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—
78C22×C8×C107—22no—
79C22×C8×C107—22no—
80C22×C8×C107—41no—
81C22×C8×C107C2311yescharacteristic
82C22×C8×C107C2311yescharacteristic
83C22×C8×C107C2311yescharacteristic
84C22×C8×C107C2311yescharacteristic
85#127×C107—22no—
86#127×C107—41no—
87#121×C107—22no—
88#121×C107—22no—
89#121×C107—22no—
90#121×C107—44no—
91#121×C107—41no—
92#121×C107—41no—
93#121×C107—41no—
94C4×D4×C107—22no—
95C4×D4×C107—22no—
96C4×D4×C107—41no—
97C4×D4×C107—41no—
98C2×C4⋊C4×C107—21no—
99C2×C4⋊C4×C107—21no—
100C2×C4⋊C4×C107C2311yescharacteristic
101C2×C4⋊C4×C107C2311yescharacteristic
102C2×C4⋊C4×C107C2311yescharacteristic
103C2×C4⋊C4×C107C2311yescharacteristic
104C2×C4⋊C4×C107C2311yescharacteristic
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×C107—21no—
115C2×C22⋊C4×C107D411yescharacteristic
116C2×C22⋊C4×C107D411yescharacteristic
117C2×C42×C107C2311yescharacteristic
118C2×C42×C107C2311yescharacteristic
119#107×C107—22no—
120#106×C107—22no—
121#102×C107—22no—
122#102×C107—22no—
123#102×C107—22no—
124#102×C107—22no—
125#102×C107—41no—
126#102×C107—41no—
127#102×C107—41no—
128#102×C107D414yescomplemented
129C22⋊C8×C107—22no—
130#97×C107—22no—
131#97×C107—41no—
132#95×C107—21no—
133#95×C107—21no—
134#95×C107—21no—
135#95×C107—21no—
136#95×C107—21no—
137#95×C107D411yescharacteristic
138#95×C107D411yescharacteristic
139C24×C107—21no—
140C24×C107—21no—
141C24×C107—21no—
142C24×C107C2×D411yescharacteristic
143C2×D4×C107—21no—
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—42no—
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—81no—
170C2×D4×C107—81no—
171C2×D4×C107—81no—
172C2×D4×C107—81no—
173C2×D4×C107—81no—
174C2×D4×C107C2×D412yes—
175C2×D4×C107#4112yes—
176C22×C4×C107—21no—
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—42no—
188C22×C4×C107—42no—
189C22×C4×C107—42no—
190C22×C4×C107—42no—
191C22×C4×C107—81no—
192C22×C4×C107—81no—
193C22×C4×C107C2×D411yescharacteristic
194C22×C4×C107C2×D411yescharacteristic
195C22×C4×C107C2×D411yescharacteristic
196C22×C4×C107C2×D411yescharacteristic
197C22×C4×C107C2×D411yescharacteristic
198C22×C4×C107C2411yescharacteristic
199D8×C107—28no—
200D8×C107—44no—
201C2×C8×C107—21no—
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—44no—
211C2×C8×C107C2×D412yes—
212C2×C8×C107#4112yes—
213C2×C8×C107#4112yes—
214C4⋊C4×C107—21no—
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—42no—
224C4⋊C4×C107—81no—
225C4⋊C4×C107C2×D412yes—
226C22⋊C4×C107—22no—
227C22⋊C4×C107—41no—
228C22⋊C4×C107—42no—
229C22⋊C4×C107—42no—
230C22⋊C4×C107—42no—
231C22⋊C4×C107—42no—
232C22⋊C4×C107—42no—
233C22⋊C4×C107—42no—
234C22⋊C4×C107—81no—
235C22⋊C4×C107—81no—
236C22⋊C4×C107—81no—
237C22⋊C4×C107—81no—
238C42×C107—21no—
239C42×C107—21no—
240C42×C107—21no—
241C42×C107—21no—
242C23×C107—21no—
243C23×C107—21no—
244C23×C107—21no—
245C23×C107—21no—
246C23×C107—21no—
247C23×C107—21no—
248C23×C107—22no—
249C23×C107—22no—
250C23×C107—41no—
251C23×C107—41no—
252C23×C107—41no—
253C23×C107—41no—
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×C107AGL(1,ℤ/8)12yes—
270C23×C107C22×D411yescharacteristic
271D4×C107—22no—
272D4×C107—22no—
273D4×C107—22no—
274D4×C107—22no—
275D4×C107—41no—
276D4×C107—41no—
277D4×C107—41no—
278D4×C107—41no—
279D4×C107—41no—
280D4×C107—41no—
281D4×C107—41no—
282D4×C107—41no—
283D4×C107—84no—
284D4×C107—84no—
285D4×C107—84no—
286D4×C107—84no—
287D4×C107—84no—
288C2×C4×C107—21no—
289C2×C4×C107—21no—
290C2×C4×C107—21no—
291C2×C4×C107—21no—
292C2×C4×C107—22no—
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—21no—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—41no—
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—84no—
323C2×C4×C107—84no—
324C2×C4×C107C22×D411yescharacteristic
325C2×C4×C107C2×#4111yescharacteristic
326C2×C4×C107C2×#4111yescharacteristic
327C2×C4×C107C2×#4111yescharacteristic
328C2×C4×C107H(5,𝔽2)11yescharacteristic
329C2×C4×C107H(5,𝔽2)11yescharacteristic
330C8×C107—22no—
331C8×C107—22no—
332C8×C107—22no—
333C8×C107—41no—
334C22×C107—22no—
335C22×C107—22no—
336C22×C107—22no—
337C22×C107—41no—
338C22×C107—41no—
339C22×C107—41no—
340C22×C107—41no—
341C22×C107—42no—
342C22×C107—42no—
343C22×C107—42no—
344C22×C107—42no—
345C22×C107—42no—
346C22×C107—42no—
347C22×C107—81no—
348C22×C107—81no—
349C22×C107—81no—
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#53211yescharacteristic
363C22×C107D4211yescharacteristic
364C22×C107#54611yescharacteristic
365C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C107#57511yescharacteristic
367C22×C107#57611yescharacteristic
368C22×C107#57611yescharacteristic
369C4×C107—41no—
370C4×C107—41no—
371C4×C107—42no—
372C4×C107—41no—
373C4×C107—41no—
374C4×C107—41no—
375C4×C107—81no—
376C4×C107—81no—
377C4×C107—81no—
378C4×C107—81no—
379C4×C107#52511yescharacteristic
380C4×C107#54011yescharacteristic
381C4×C107#54611yescharacteristic
382C4×C107#55311yescharacteristic
383#26977C10711yesmaximal, characteristic, direct product factor, Sylow
384C2×C107—42no—
385C2×C107—82no—
386C2×C107—82no—
387C2×C107—161no—
388C2×C107#246411yescharacteristic
389C2×C107#317611yescharacteristic
390C2×C107#318011yescharacteristic
391C2×C107#326411yescharacteristic
392C2×C107#326811yescharacteristic
393C2×C107#331811yescharacteristic
394C2×C107#331911yescharacteristic
395C2×#466C2×C10711yescharacteristic, complemented
396C2×#442C2×C10711yescharacteristic, complemented
397#2428C2×C10711yescharacteristic, complemented
398#2420C2×C10711yescharacteristic, complemented
399#2085C2×C10711yescharacteristic, complemented
400#2034C2×C10711yescharacteristic, complemented
401#2011C2×C10711yescharacteristic, complemented
402#1999C2×C10711yescharacteristic, complemented
403#1961C2×C10711yescharacteristic, complemented
404#1936C2×C10711yescharacteristic, complemented
405#1936C2×C10711yescharacteristic, complemented
406#1893C2×C10711yescharacteristic, complemented
407#1879C2×C10711yescharacteristic, complemented
408#1862C2×C10711yescharacteristic, complemented
409#1752C2×C10711yescharacteristic, complemented
410C107#2697711yescharacteristic, direct product factor, Sylow
411C22×D8C22×C10711yescharacteristic
412C22×D8C22×C10711yescharacteristic
413C23×C8C22×C10711yescharacteristic
414C2×#127C22×C10711yescharacteristic
415C2×#121—21no—
416C2×#121C22×C10711yescharacteristic
417C2×#121C22×C10711yescharacteristic
418C2×#121C22×C10711yescharacteristic
419C2×C4×D4C22×C10711yescharacteristic
420C2×C4×D4C22×C10711yescharacteristic
421#466—24no—
422#442—24no—
423C2×#107C22×C10711yescharacteristic
424C2×#106C22×C10711yescharacteristic
425C2×#102C22×C10711yescharacteristic
426C2×#102C22×C10711yescharacteristic
427C2×#102C22×C10711yescharacteristic
428C2×#102C22×C10711yescharacteristic
429C2×#102C22×C10711yescharacteristic
430C2×#102C22×C10711yescharacteristic
431C2×#102C22×C10711yescharacteristic
432C2×#102C22×C10711yescharacteristic
433C2×C22⋊C8C22×C10711yescharacteristic
434C2×#97C22×C10711yescharacteristic
435C2×#97C22×C10711yescharacteristic
436#397—21no—
437#394—21no—
438#394—21no—
439#392—21no—
440#390C22×C10711yescharacteristic
441#390C22×C10711yescharacteristic
442#389C22×C10711yescharacteristic
443#389C22×C10711yescharacteristic
444#386—21no—
445#386—21no—
446#382C22×C10711yescharacteristic
447#381—21no—
448#380C22×C10711yescharacteristic
449C4×C22⋊C4C22×C10711yescharacteristic
450#340C22×C10711yescharacteristic
451#340C22×C10711yescharacteristic
452#340C22×C10711yescharacteristic
453#340C22×C10711yescharacteristic
454#336C22×C10711yescharacteristic
455#336C22×C10711yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C23×C10711yescharacteristic
462C22×D4C23×C10711yescharacteristic
463C22×D4C23×C10711yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4C23×C10711yescharacteristic
467C2×D8—22no—
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C22×C8—22no—
474C22×C8—22no—
475C22×C8—41no—
476C22×C8C23×C10711yescharacteristic
477C22×C8C23×C10711yescharacteristic
478C22×C8C23×C10711yescharacteristic
479C22×C8C23×C10711yescharacteristic
480#127—22no—
481#127—41no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—44no—
486#121—41no—
487#121—41no—
488#121—41no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—41no—
492C4×D4—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C10711yescharacteristic
496C2×C4⋊C4C23×C10711yescharacteristic
497C2×C4⋊C4C23×C10711yescharacteristic
498C2×C4⋊C4C23×C10711yescharacteristic
499C2×C4⋊C4C23×C10711yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C10711yescharacteristic
511C2×C22⋊C4D4×C10711yescharacteristic
512C2×C42C23×C10711yescharacteristic
513C2×C42C23×C10711yescharacteristic
514#107—22no—
515#106—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102D4×C10714yescomplemented
524C22⋊C8—22no—
525#97—22no—
526#97—41no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95D4×C10711yescharacteristic
533#95D4×C10711yescharacteristic
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C10711yescharacteristic
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
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—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4C2×D4×C10712yes—
570C2×D4#41×C10712yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4C2×D4×C10711yescharacteristic
589C22×C4C2×D4×C10711yescharacteristic
590C22×C4C2×D4×C10711yescharacteristic
591C22×C4C2×D4×C10711yescharacteristic
592C22×C4C2×D4×C10711yescharacteristic
593C22×C4C24×C10711yescharacteristic
594D8—28no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—44no—
606C2×C8C2×D4×C10712yes—
607C2×C8#41×C10712yes—
608C2×C8#41×C10712yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—81no—
620C4⋊C4C2×D4×C10712yes—
621C22⋊C4—22no—
622C22⋊C4—41no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23AGL(1,ℤ/8)×C10712yes—
665C23C22×D4×C10711yescharacteristic
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682D4—84no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
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—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
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—84no—
718C2×C4—84no—
719C2×C4C22×D4×C10711yescharacteristic
720C2×C4C2×#41×C10711yescharacteristic
721C2×C4C2×#41×C10711yescharacteristic
722C2×C4C2×#41×C10711yescharacteristic
723C2×C4H(5,𝔽2)×C10711yescharacteristic
724C2×C4H(5,𝔽2)×C10711yescharacteristic
725C8—22no—
726C8—22no—
727C8—22no—
728C8—41no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22#532×C10711yescharacteristic
758C22D42×C10711yescharacteristic
759C22#546×C10711yescharacteristic
760C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
761C22#575×C10711yescharacteristic
762C22#576×C10711yescharacteristic
763C22#576×C10711yescharacteristic
764C4—41no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4#525×C10711yescharacteristic
775C4#540×C10711yescharacteristic
776C4#546×C10711yescharacteristic
777C4#553×C10711yescharacteristic
778C2—42no—
779C2—82no—
780C2—82no—
781C2—161no—
782C2C107×#246411yescharacteristic
783C2C107×#317611yescharacteristic
784C2C107×#318011yescharacteristic
785C2C107×#326411yescharacteristic
786C2C107×#326811yescharacteristic
787C2C107×#331811yescharacteristic
788C2C107×#331911yescharacteristic
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×#466×C107C2semidirect
2. C2×#442×C107C2semidirect
3. C107×#2428C2semidirect
4. C107×#2420C2semidirect
5. C107×#2085C2semidirect
6. C107×#2034C2semidirect
7. C107×#2011C2semidirect
8. C107×#1999C2semidirect
9. C107×#1961C2semidirect
10. C107×#1936C2semidirect
11. C107×#1936C2semidirect
12. C107×#1893C2semidirect
13. C107×#1879C2semidirect
14. C107×#1862C2semidirect
15. C107×#1752C2semidirect
128. #102×C107D4semidirect
383. #26977C107direct (N × H)
395. C2×#466C2×C107semidirect
396. C2×#442C2×C107semidirect
397. #2428C2×C107semidirect
398. #2420C2×C107semidirect
399. #2085C2×C107semidirect
400. #2034C2×C107semidirect
401. #2011C2×C107semidirect
402. #1999C2×C107semidirect
403. #1961C2×C107semidirect
404. #1936C2×C107semidirect
405. #1936C2×C107semidirect
406. #1893C2×C107semidirect
407. #1879C2×C107semidirect
408. #1862C2×C107semidirect
409. #1752C2×C107semidirect
410. C107#26977direct (N × H)
523. #102D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1072
C2×#442×C1072
C107×#24282
C107×#24202
C107×#20852
C107×#20342
C107×#20112
C107×#19992
C107×#19612
C107×#19362
C107×#18932
C107×#18792
C107×#18622
C107×#17522
#26977107