Finite Group Databasebeta

← C107×#24034 #41049998

Subgroups — C107×#24034 #41049998

Order 27392.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C107C211yesmaximal, characteristic
2C2×#482×C107C211yesmaximal, characteristic, complemented
3C2×#416×C107C211yesmaximal, characteristic, complemented
4C107×#2485C211yesmaximal, characteristic, complemented
5C107×#2041C211yesmaximal, characteristic, complemented
6C107×#2041C211yesmaximal, characteristic, complemented
7C107×#2034C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#1893C211yesmaximal, characteristic, complemented
10C107×#1869C211yesmaximal, characteristic, complemented
11C107×#1865C211yesmaximal, characteristic, complemented
12C107×#1863C211yesmaximal, characteristic, complemented
13C107×#1788C211yesmaximal, characteristic, complemented
14C107×#1788C211yesmaximal, characteristic, complemented
15C107×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic
18C23×C8×C107C2211yescharacteristic
19#550×C107—24no—
20#550×C107—24no—
21C2×#127×C107—21no—
22C2×#127×C107C2211yescharacteristic
23C2×#121×C107—21no—
24C2×#121×C107—21no—
25C2×#121×C107C2211yescharacteristic
26C2×#121×C107C2211yescharacteristic
27C2×C4×Q8×C107C2211yescharacteristic
28C2×C4×D4×C107—21no—
29C2×C4×D4×C107C2211yescharacteristic
30C2×#117×C107C2211yescharacteristic
31#482×C107—24no—
32C2×#107×C107C2211yescharacteristic
33C2×#106×C107C2211yescharacteristic
34#416×C107—24no—
35C2×#103×C107C2211yescharacteristic
36C2×#103×C107C2211yescharacteristic
37C2×#103×C107C2211yescharacteristic
38C2×#103×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic
46C2×#102×C107C2211yescharacteristic
47C2×C22⋊C8×C107C2211yescharacteristic
48C2×C22⋊C8×C107C2211yescharacteristic
49C2×C22⋊C8×C107C2211yescharacteristic
50#397×C107—21no—
51#394×C107—21no—
52#389×C107C2211yescharacteristic
53#389×C107C2211yescharacteristic
54#388×C107—21no—
55#387×C107—21no—
56#380×C107C2211yescharacteristic
57#380×C107C2211yescharacteristic
58#380×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#340×C107C2211yescharacteristic
61#336×C107C2211yescharacteristic
62#336×C107C2211yescharacteristic
63C2×#41×C107—22no—
64C2×#41×C107—22no—
65C2×#41×C107—22no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—22no—
70C2×#41×C107—41no—
71C2×#41×C107—41no—
72C2×#41×C107—41no—
73C2×#41×C107—41no—
74C2×#41×C107D414yes—
75C22×Q8×C107C2311yescharacteristic
76C22×D4×C107—21no—
77C22×D4×C107—21no—
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107D411yescharacteristic
83C22×D4×C107C2311yescharacteristic
84C22×D4×C107C2311yescharacteristic
85C23×C4×C107—21no—
86C23×C4×C107—21no—
87C23×C4×C107C2311yescharacteristic
88C23×C4×C107C2311yescharacteristic
89C22×C8×C107—22no—
90C22×C8×C107—41no—
91C22×C8×C107—41no—
92C22×C8×C107C2311yescharacteristic
93C22×C8×C107C2311yescharacteristic
94C22×C8×C107C2311yescharacteristic
95C22×C8×C107C2311yescharacteristic
96#127×C107—28no—
97#127×C107—22no—
98#127×C107—22no—
99#121×C107—28no—
100#121×C107—28no—
101#121×C107—22no—
102#121×C107—22no—
103#121×C107—22no—
104#121×C107D414yes—
105C4×Q8×C107—22no—
106C4×Q8×C107—22no—
107C4×D4×C107—28no—
108C4×D4×C107—22no—
109C4×D4×C107—22no—
110#117×C107—22no—
111#117×C107—22no—
112C2×C4⋊C4×C107—21no—
113C2×C4⋊C4×C107—21no—
114C2×C4⋊C4×C107—21no—
115C2×C4⋊C4×C107D411yescharacteristic
116C2×C4⋊C4×C107C2311yescharacteristic
117C2×C4⋊C4×C107C2311yescharacteristic
118C2×C4⋊C4×C107C2311yescharacteristic
119C2×C4⋊C4×C107C2311yescharacteristic
120C2×C4⋊C4×C107C2311yescharacteristic
121C2×C22⋊C4×C107—21no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107D411yescharacteristic
128C2×C22⋊C4×C107D411yescharacteristic
129C2×C42×C107—21no—
130C2×C42×C107—21no—
131C2×C42×C107C2311yescharacteristic
132#107×C107—22no—
133#106×C107—22no—
134#103×C107—22no—
135#103×C107—22no—
136#103×C107—22no—
137#103×C107—22no—
138#102×C107—22no—
139#102×C107—22no—
140#102×C107—22no—
141#102×C107—22no—
142#102×C107—41no—
143#102×C107—41no—
144#102×C107—41no—
145#102×C107—41no—
146C22⋊C8×C107—22no—
147C22⋊C8×C107—41no—
148C22⋊C8×C107—41no—
149#95×C107—21no—
150#95×C107—21no—
151#95×C107—21no—
152#95×C107—21no—
153#95×C107—21no—
154C24×C107—21no—
155C24×C107—21no—
156C24×C107C2×D411yescharacteristic
157C24×C107C2×D411yescharacteristic
158#41×C107—28no—
159#41×C107—44no—
160#41×C107—44no—
161#41×C107—44no—
162#41×C107—44no—
163#41×C107—44no—
164#41×C107—44no—
165#41×C107—44no—
166C2×Q8×C107—21no—
167C2×Q8×C107—21no—
168C2×Q8×C107—21no—
169C2×Q8×C107C2×D412yes—
170C2×Q8×C107#4112yes—
171C2×Q8×C107#4112yes—
172C2×D4×C107—24no—
173C2×D4×C107—24no—
174C2×D4×C107—22no—
175C2×D4×C107—24no—
176C2×D4×C107—24no—
177C2×D4×C107—24no—
178C2×D4×C107—24no—
179C2×D4×C107—22no—
180C2×D4×C107—21no—
181C2×D4×C107—21no—
182C2×D4×C107—21no—
183C2×D4×C107—21no—
184C2×D4×C107—21no—
185C2×D4×C107—21no—
186C2×D4×C107—21no—
187C2×D4×C107—21no—
188C2×D4×C107—21no—
189C2×D4×C107—21no—
190C2×D4×C107—41no—
191C2×D4×C107—42no—
192C2×D4×C107—42no—
193C2×D4×C107—42no—
194C2×D4×C107—42no—
195C2×D4×C107—42no—
196C2×D4×C107—42no—
197C2×D4×C107—81no—
198C2×D4×C107—81no—
199C2×D4×C107—81no—
200C2×D4×C107—81no—
201C2×D4×C107—81no—
202C2×D4×C107—81no—
203C2×D4×C107C2×D412yes—
204C2×D4×C107C2×D412yes—
205C22×C4×C107—21no—
206C22×C4×C107—21no—
207C22×C4×C107—21no—
208C22×C4×C107—21no—
209C22×C4×C107—21no—
210C22×C4×C107—24no—
211C22×C4×C107—21no—
212C22×C4×C107—24no—
213C22×C4×C107—21no—
214C22×C4×C107—21no—
215C22×C4×C107—21no—
216C22×C4×C107—21no—
217C22×C4×C107—21no—
218C22×C4×C107—21no—
219C22×C4×C107—21no—
220C22×C4×C107—21no—
221C22×C4×C107—21no—
222C22×C4×C107—21no—
223C22×C4×C107—42no—
224C22×C4×C107—42no—
225C22×C4×C107—42no—
226C22×C4×C107—42no—
227C22×C4×C107C2×D411yescharacteristic
228C22×C4×C107C2×D411yescharacteristic
229C22×C4×C107C2×D411yescharacteristic
230C22×C4×C107C2×D412yes—
231C22×C4×C107C2×D412yes—
232C22×C4×C107C2×D411yescharacteristic
233C22×C4×C107C2411yescharacteristic
234C2×C8×C107—21no—
235C2×C8×C107—21no—
236C2×C8×C107—21no—
237C2×C8×C107—21no—
238C2×C8×C107—21no—
239C2×C8×C107—21no—
240C2×C8×C107—21no—
241C2×C8×C107—21no—
242C2×C8×C107—21no—
243C2×C8×C107—21no—
244C2×C8×C107—21no—
245C2×C8×C107—21no—
246C2×C8×C107—44no—
247C4⋊C4×C107—24no—
248C4⋊C4×C107—22no—
249C4⋊C4×C107—21no—
250C4⋊C4×C107—21no—
251C4⋊C4×C107—21no—
252C4⋊C4×C107—21no—
253C4⋊C4×C107—21no—
254C4⋊C4×C107—21no—
255C4⋊C4×C107—21no—
256C4⋊C4×C107—21no—
257C4⋊C4×C107—21no—
258C4⋊C4×C107—42no—
259C4⋊C4×C107—81no—
260C4⋊C4×C107C2×D412yes—
261C22⋊C4×C107—24no—
262C22⋊C4×C107—22no—
263C22⋊C4×C107—24no—
264C22⋊C4×C107—22no—
265C22⋊C4×C107—42no—
266C22⋊C4×C107—42no—
267C22⋊C4×C107—81no—
268C22⋊C4×C107—81no—
269C42×C107—24no—
270C42×C107—21no—
271C42×C107—21no—
272C42×C107—42no—
273C23×C107—21no—
274C23×C107—21no—
275C23×C107—21no—
276C23×C107—21no—
277C23×C107—21no—
278C23×C107—21no—
279C23×C107—21no—
280C23×C107—22no—
281C23×C107—22no—
282C23×C107—21no—
283C23×C107—21no—
284C23×C107—21no—
285C23×C107—21no—
286C23×C107—21no—
287C23×C107—21no—
288C23×C107—41no—
289C23×C107—41no—
290C23×C107—41no—
291C23×C107—41no—
292C23×C107—41no—
293C23×C107—41no—
294C23×C107—41no—
295C23×C107—41no—
296C23×C107—41no—
297C23×C107—41no—
298C23×C107—41no—
299C23×C107—41no—
300C23×C107#12012yes—
301C23×C107C22×D411yescharacteristic
302Q8×C107—22no—
303Q8×C107—22no—
304Q8×C107—22no—
305Q8×C107#12314yes—
306D4×C107—22no—
307D4×C107—22no—
308D4×C107—22no—
309D4×C107—22no—
310D4×C107—44no—
311D4×C107—48no—
312D4×C107—48no—
313D4×C107—48no—
314D4×C107—41no—
315D4×C107—41no—
316D4×C107—41no—
317D4×C107—41no—
318D4×C107—84no—
319D4×C107—84no—
320D4×C107—84no—
321C2×C4×C107—21no—
322C2×C4×C107—22no—
323C2×C4×C107—21no—
324C2×C4×C107—21no—
325C2×C4×C107—22no—
326C2×C4×C107—22no—
327C2×C4×C107—21no—
328C2×C4×C107—22no—
329C2×C4×C107—22no—
330C2×C4×C107—22no—
331C2×C4×C107—22no—
332C2×C4×C107—21no—
333C2×C4×C107—22no—
334C2×C4×C107—21no—
335C2×C4×C107—21no—
336C2×C4×C107—21no—
337C2×C4×C107—21no—
338C2×C4×C107—21no—
339C2×C4×C107—48no—
340C2×C4×C107—48no—
341C2×C4×C107—41no—
342C2×C4×C107—41no—
343C2×C4×C107—41no—
344C2×C4×C107—41no—
345C2×C4×C107—41no—
346C2×C4×C107—41no—
347C2×C4×C107—41no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—41no—
351C2×C4×C107—41no—
352C2×C4×C107—41no—
353C2×C4×C107—41no—
354C2×C4×C107—41no—
355C2×C4×C107—41no—
356C2×C4×C107—41no—
357C2×C4×C107—41no—
358C2×C4×C107—41no—
359C2×C4×C107#12012yes—
360C2×C4×C107#13512yes—
361C2×C4×C107C22×D411yescharacteristic
362C2×C4×C107C22×D411yescharacteristic
363C2×C4×C107C2×#4111yescharacteristic
364C2×C4×C107C2×#4111yescharacteristic
365C2×C4×C107H(5,𝔽2)11yescharacteristic
366C2×C4×C107H(5,𝔽2)11yescharacteristic
367C8×C107—41no—
368C8×C107—41no—
369C8×C107—41no—
370C8×C107—41no—
371C22×C107—22no—
372C22×C107—22no—
373C22×C107—22no—
374C22×C107—41no—
375C22×C107—41no—
376C22×C107—41no—
377C22×C107—41no—
378C22×C107—42no—
379C22×C107—42no—
380C22×C107—41no—
381C22×C107—41no—
382C22×C107—42no—
383C22×C107—42no—
384C22×C107—41no—
385C22×C107—42no—
386C22×C107—42no—
387C22×C107—41no—
388C22×C107—41no—
389C22×C107—41no—
390C22×C107—41no—
391C22×C107—81no—
392C22×C107—81no—
393C22×C107—81no—
394C22×C107—81no—
395C22×C107—81no—
396C22×C107—81no—
397C22×C107—81no—
398C22×C107—81no—
399C22×C107C2×#12011yescharacteristic
400C22×C107#54611yescharacteristic
401C22×C107#54611yescharacteristic
402C22×C107C2×#13511yescharacteristic
403C22×C107#57511yescharacteristic
404C22×C107#57611yescharacteristic
405C22×C107#57711yescharacteristic
406C4×C107—22no—
407C4×C107—24no—
408C4×C107—22no—
409C4×C107—41no—
410C4×C107—41no—
411C4×C107—42no—
412C4×C107—81no—
413C4×C107—81no—
414C4×C107—81no—
415C4×C107—81no—
416C4×C107C2×#12311yescharacteristic
417C4×C107#53411yescharacteristic
418C4×C107#54611yescharacteristic
419C4×C107#54611yescharacteristic
420#24034C10711yesmaximal, characteristic, direct product factor, Sylow
421C2×C107—42no—
422C2×C107—81no—
423C2×C107—82no—
424C2×C107—82no—
425C2×C107#240511yescharacteristic
426C2×C107#300211yescharacteristic
427C2×C107#301211yescharacteristic
428C2×C107#330411yescharacteristic
429C2×C107#330511yescharacteristic
430C2×C107#330911yescharacteristic
431C2×C107#331711yescharacteristic
432C2×#550C2×C10711yescharacteristic
433C2×#482C2×C10711yescharacteristic, complemented
434C2×#416C2×C10711yescharacteristic, complemented
435#2485C2×C10711yescharacteristic, complemented
436#2041C2×C10711yescharacteristic, complemented
437#2041C2×C10711yescharacteristic, complemented
438#2034C2×C10711yescharacteristic, complemented
439#2033C2×C10711yescharacteristic, complemented
440#1893C2×C10711yescharacteristic, complemented
441#1869C2×C10711yescharacteristic, complemented
442#1865C2×C10711yescharacteristic, complemented
443#1863C2×C10711yescharacteristic, complemented
444#1788C2×C10711yescharacteristic, complemented
445#1788C2×C10711yescharacteristic, complemented
446#1788C2×C10711yescharacteristic, complemented
447C107#2403411yescharacteristic, direct product factor, Sylow
448C22×#41C22×C10711yescharacteristic
449C22×#41C22×C10711yescharacteristic
450C23×C8C22×C10711yescharacteristic
451#550—24no—
452#550—24no—
453C2×#127—21no—
454C2×#127C22×C10711yescharacteristic
455C2×#121—21no—
456C2×#121—21no—
457C2×#121C22×C10711yescharacteristic
458C2×#121C22×C10711yescharacteristic
459C2×C4×Q8C22×C10711yescharacteristic
460C2×C4×D4—21no—
461C2×C4×D4C22×C10711yescharacteristic
462C2×#117C22×C10711yescharacteristic
463#482—24no—
464C2×#107C22×C10711yescharacteristic
465C2×#106C22×C10711yescharacteristic
466#416—24no—
467C2×#103C22×C10711yescharacteristic
468C2×#103C22×C10711yescharacteristic
469C2×#103C22×C10711yescharacteristic
470C2×#103C22×C10711yescharacteristic
471C2×#102C22×C10711yescharacteristic
472C2×#102C22×C10711yescharacteristic
473C2×#102C22×C10711yescharacteristic
474C2×#102C22×C10711yescharacteristic
475C2×#102C22×C10711yescharacteristic
476C2×#102C22×C10711yescharacteristic
477C2×#102C22×C10711yescharacteristic
478C2×#102C22×C10711yescharacteristic
479C2×C22⋊C8C22×C10711yescharacteristic
480C2×C22⋊C8C22×C10711yescharacteristic
481C2×C22⋊C8C22×C10711yescharacteristic
482#397—21no—
483#394—21no—
484#389C22×C10711yescharacteristic
485#389C22×C10711yescharacteristic
486#388—21no—
487#387—21no—
488#380C22×C10711yescharacteristic
489#380C22×C10711yescharacteristic
490#380C22×C10711yescharacteristic
491#340C22×C10711yescharacteristic
492#340C22×C10711yescharacteristic
493#336C22×C10711yescharacteristic
494#336C22×C10711yescharacteristic
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C10714yes—
507C22×Q8C23×C10711yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C10711yescharacteristic
515C22×D4C23×C10711yescharacteristic
516C22×D4C23×C10711yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C10711yescharacteristic
520C23×C4C23×C10711yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C10711yescharacteristic
525C22×C8C23×C10711yescharacteristic
526C22×C8C23×C10711yescharacteristic
527C22×C8C23×C10711yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C10714yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C10711yescharacteristic
548C2×C4⋊C4C23×C10711yescharacteristic
549C2×C4⋊C4C23×C10711yescharacteristic
550C2×C4⋊C4C23×C10711yescharacteristic
551C2×C4⋊C4C23×C10711yescharacteristic
552C2×C4⋊C4C23×C10711yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C10711yescharacteristic
560C2×C22⋊C4D4×C10711yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C10711yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C10711yescharacteristic
589C24C2×D4×C10711yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C10712yes—
602C2×Q8#41×C10712yes—
603C2×Q8#41×C10712yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C10712yes—
636C2×D4C2×D4×C10712yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C10711yescharacteristic
660C22×C4C2×D4×C10711yescharacteristic
661C22×C4C2×D4×C10711yescharacteristic
662C22×C4C2×D4×C10712yes—
663C22×C4C2×D4×C10712yes—
664C22×C4C2×D4×C10711yescharacteristic
665C22×C4C24×C10711yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C10712yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C10712yes—
733C23C22×D4×C10711yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C10714yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#120×C10712yes—
792C2×C4#135×C10712yes—
793C2×C4C22×D4×C10711yescharacteristic
794C2×C4C22×D4×C10711yescharacteristic
795C2×C4C2×#41×C10711yescharacteristic
796C2×C4C2×#41×C10711yescharacteristic
797C2×C4H(5,𝔽2)×C10711yescharacteristic
798C2×C4H(5,𝔽2)×C10711yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C10711yescharacteristic
832C22#546×C10711yescharacteristic
833C22#546×C10711yescharacteristic
834C22C2×#135×C10711yescharacteristic
835C22#575×C10711yescharacteristic
836C22#576×C10711yescharacteristic
837C22#577×C10711yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C10711yescharacteristic
849C4#534×C10711yescharacteristic
850C4#546×C10711yescharacteristic
851C4#546×C10711yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2C107×#240511yescharacteristic
857C2C107×#300211yescharacteristic
858C2C107×#301211yescharacteristic
859C2C107×#330411yescharacteristic
860C2C107×#330511yescharacteristic
861C2C107×#330911yescharacteristic
862C2C107×#331711yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#550×C107C2
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
2. C2×#482×C107C2semidirect
3. C2×#416×C107C2semidirect
4. C107×#2485C2semidirect
5. C107×#2041C2semidirect
6. C107×#2041C2semidirect
7. C107×#2034C2semidirect
8. C107×#2033C2semidirect
9. C107×#1893C2semidirect
10. C107×#1869C2semidirect
11. C107×#1865C2semidirect
12. C107×#1863C2semidirect
13. C107×#1788C2semidirect
14. C107×#1788C2semidirect
15. C107×#1788C2semidirect
420. #24034C107direct (N × H)
433. C2×#482C2×C107semidirect
434. C2×#416C2×C107semidirect
435. #2485C2×C107semidirect
436. #2041C2×C107semidirect
437. #2041C2×C107semidirect
438. #2034C2×C107semidirect
439. #2033C2×C107semidirect
440. #1893C2×C107semidirect
441. #1869C2×C107semidirect
442. #1865C2×C107semidirect
443. #1863C2×C107semidirect
444. #1788C2×C107semidirect
445. #1788C2×C107semidirect
446. #1788C2×C107semidirect
447. C107#24034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#550×C1072
C2×#482×C1072
C2×#416×C1072
C107×#24852
C107×#20412
C107×#20342
C107×#20332
C107×#18932
C107×#18692
C107×#18652
C107×#18632
C107×#17882
#24034107