Finite Group Databasebeta

← C107×#25563 #41051527

Subgroups — C107×#25563 #41051527

Order 27392.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3490C211yesmaximal, characteristic, complemented
2C107×#2410C212yesmaximal, complemented
3C107×#2405C211yesmaximal, characteristic, complemented
4C107×#2062C211yesmaximal, characteristic, complemented
5C107×#2044C211yesmaximal, characteristic, complemented
6C107×#2029C211yesmaximal, characteristic, complemented
7C107×#2021C211yesmaximal, characteristic, complemented
8C107×#1898C212yesmaximal, complemented
9C107×#1889C212yesmaximal, complemented
10C107×#1867C212yesmaximal, complemented
11C2×#342×C107C211yesmaximal, characteristic, complemented
12C23×D4×C107C2211yescharacteristic
13#551×C107—22no—
14#551×C107—22no—
15#546×C107—22no—
16#546×C107—22no—
17#543×C107C2211yescharacteristic
18#538×C107—21no—
19#538×C107—21no—
20#534×C107C2211yescharacteristic
21#525×C107—21no—
22#525×C107—21no—
23C2×#123×C107—21no—
24C2×#121×C107—22no—
25C2×#120×C107C2212yes—
26C2×#120×C107C2212yes—
27#518×C107C2212yes—
28C22×C22⋊C4×C107C2211yescharacteristic
29C22×C22⋊C4×C107C2212yes—
30C2×#99×C107C2212yes—
31C2×#99×C107C2212yes—
32#394×C107—21no—
33#394×C107—21no—
34#394×C107—22no—
35#392×C107—22no—
36#386×C107—21no—
37#386×C107—22no—
38#386×C107C2212yes—
39#385×C107C2211yescharacteristic
40#385×C107C2212yes—
41#385×C107C2211yescharacteristic
42#379×C107C2211yescharacteristic
43#379×C107C2212yes—
44#379×C107C2211yescharacteristic
45#379×C107C2211yescharacteristic
46#342×C107C2212yes—
47#342×C107C2212yes—
48#342×C107C2212yes—
49#342×C107C2211yescharacteristic
50#342×C107C2211yescharacteristic
51C25×C107C2311yescharacteristic
52C25×C107C2311yescharacteristic
53C2×#41×C107—21no—
54C2×#41×C107—21no—
55C22×D4×C107—22no—
56C22×D4×C107—21no—
57C22×D4×C107—22no—
58C22×D4×C107—21no—
59C22×D4×C107—22no—
60C22×D4×C107—44no—
61C22×D4×C107D412yescomplemented
62C22×D4×C107D412yescomplemented
63C22×D4×C107C2312yes—
64C23×C4×C107—22no—
65C23×C4×C107D411yescharacteristic, complemented
66C23×C4×C107D411yescharacteristic, complemented
67C23×C4×C107C2311yescharacteristic
68#126×C107—22no—
69#126×C107—22no—
70#124×C107—22no—
71#124×C107—22no—
72#123×C107—22no—
73#123×C107—22no—
74#123×C107—22no—
75#123×C107—22no—
76#123×C107—22no—
77#123×C107—44no—
78C22⋊Q8×C107—21no—
79C22⋊Q8×C107—21no—
80C22⋊Q8×C107—21no—
81C22⋊Q8×C107—21no—
82C22⋊Q8×C107—22no—
83C22⋊Q8×C107—22no—
84#121×C107—21no—
85#121×C107—21no—
86#121×C107—22no—
87#121×C107—22no—
88#121×C107—21no—
89#121×C107—21no—
90#121×C107—48no—
91#120×C107—22no—
92#120×C107—22no—
93#120×C107—22no—
94#120×C107—22no—
95#120×C107—22no—
96#120×C107—24no—
97#120×C107—42no—
98C4×D4×C107—22no—
99C4×D4×C107—22no—
100C4×D4×C107—22no—
101C4×D4×C107—22no—
102C4×D4×C107—22no—
103C4×D4×C107—22no—
104#117×C107—21no—
105#117×C107—21no—
106#117×C107—22no—
107C2×C4⋊C4×C107—22no—
108C2×C4⋊C4×C107—21no—
109C2×C4⋊C4×C107—21no—
110C2×C22⋊C4×C107—22no—
111C2×C22⋊C4×C107—22no—
112C2×C22⋊C4×C107—22no—
113C2×C22⋊C4×C107—24no—
114C2×C22⋊C4×C107—21no—
115C2×C22⋊C4×C107—22no—
116C2×C22⋊C4×C107—22no—
117C2×C22⋊C4×C107—22no—
118C2×C22⋊C4×C107—21no—
119C2×C22⋊C4×C107—21no—
120C2×C22⋊C4×C107—22no—
121C2×C22⋊C4×C107—21no—
122C2×C22⋊C4×C107—22no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—42no—
126C2×C22⋊C4×C107D412yescomplemented
127C2×C22⋊C4×C107D411yescharacteristic, complemented
128C2×C22⋊C4×C107D411yescharacteristic, complemented
129C2×C22⋊C4×C107D412yescomplemented
130C2×C22⋊C4×C107C2312yes—
131C2×C22⋊C4×C107C2311yescharacteristic
132C2×C22⋊C4×C107C2311yescharacteristic
133C2×C22⋊C4×C107C2311yescharacteristic
134C2×C22⋊C4×C107C2311yescharacteristic
135C2×C22⋊C4×C107C2312yes—
136C2×C22⋊C4×C107C2312yes—
137#99×C107—24no—
138#99×C107—42no—
139#95×C107—22no—
140#95×C107—21no—
141#95×C107—21no—
142#95×C107—22no—
143C24×C107—22no—
144C24×C107—21no—
145C24×C107—21no—
146C24×C107—21no—
147C24×C107—22no—
148C24×C107—22no—
149C24×C107—21no—
150C24×C107—21no—
151C24×C107—42no—
152C24×C107—42no—
153C24×C107—81no—
154C24×C107—81no—
155C24×C107C2×D412yes—
156C24×C107C2×D411yescharacteristic
157C24×C107C2×D412yes—
158C24×C107C2×D412yes—
159C24×C107C2×D411yescharacteristic
160C24×C107C2411yescharacteristic
161#41×C107—82no—
162#41×C107—82no—
163C2×Q8×C107—21no—
164C2×Q8×C107—21no—
165C2×D4×C107—28no—
166C2×D4×C107—24no—
167C2×D4×C107—22no—
168C2×D4×C107—22no—
169C2×D4×C107—22no—
170C2×D4×C107—22no—
171C2×D4×C107—22no—
172C2×D4×C107—22no—
173C2×D4×C107—22no—
174C2×D4×C107—22no—
175C2×D4×C107—21no—
176C2×D4×C107—21no—
177C2×D4×C107—22no—
178C2×D4×C107—22no—
179C2×D4×C107—44no—
180C2×D4×C107—42no—
181C2×D4×C107—44no—
182C2×D4×C107—42no—
183C2×D4×C107—44no—
184C2×D4×C107—42no—
185C2×D4×C107—44no—
186C2×D4×C107—42no—
187C2×D4×C107—41no—
188C2×D4×C107—41no—
189C2×D4×C107—44no—
190C2×D4×C107—44no—
191C2×D4×C107—82no—
192C2×D4×C107—82no—
193C22×C4×C107—21no—
194C22×C4×C107—21no—
195C22×C4×C107—22no—
196C22×C4×C107—21no—
197C22×C4×C107—22no—
198C22×C4×C107—22no—
199C22×C4×C107—22no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—22no—
205C22×C4×C107—42no—
206C22×C4×C107—44no—
207C22×C4×C107—42no—
208C22×C4×C107—44no—
209C22×C4×C107—81no—
210C22×C4×C107—82no—
211C22×C4×C107C2×D412yes—
212C22×C4×C107C2×D411yescharacteristic
213C22×C4×C107C2×D412yes—
214C22×C4×C107C2×D411yescharacteristic
215C22×C4×C107C2×D411yescharacteristic
216C22×C4×C107C2×D412yes—
217C22×C4×C107C2×D411yescharacteristic
218C4⋊C4×C107—22no—
219C4⋊C4×C107—22no—
220C4⋊C4×C107—21no—
221C4⋊C4×C107—21no—
222C4⋊C4×C107—21no—
223C4⋊C4×C107—21no—
224C4⋊C4×C107—22no—
225C4⋊C4×C107—22no—
226C4⋊C4×C107—44no—
227C4⋊C4×C107—42no—
228C4⋊C4×C107—42no—
229C22⋊C4×C107—22no—
230C22⋊C4×C107—22no—
231C22⋊C4×C107—22no—
232C22⋊C4×C107—22no—
233C22⋊C4×C107—22no—
234C22⋊C4×C107—22no—
235C22⋊C4×C107—22no—
236C22⋊C4×C107—22no—
237C22⋊C4×C107—22no—
238C22⋊C4×C107—22no—
239C22⋊C4×C107—22no—
240C22⋊C4×C107—22no—
241C22⋊C4×C107—22no—
242C22⋊C4×C107—22no—
243C22⋊C4×C107—22no—
244C22⋊C4×C107—22no—
245C22⋊C4×C107—22no—
246C22⋊C4×C107—21no—
247C22⋊C4×C107—22no—
248C22⋊C4×C107—21no—
249C22⋊C4×C107—44no—
250C22⋊C4×C107—44no—
251C22⋊C4×C107—44no—
252C22⋊C4×C107—44no—
253C22⋊C4×C107—42no—
254C22⋊C4×C107—42no—
255C22⋊C4×C107—42no—
256C22⋊C4×C107—81no—
257C22⋊C4×C107—81no—
258C22⋊C4×C107—82no—
259C22⋊C4×C107—81no—
260C22⋊C4×C107#4114yescomplemented
261C42×C107—22no—
262C42×C107—22no—
263C23×C107—21no—
264C23×C107—21no—
265C23×C107—22no—
266C23×C107—22no—
267C23×C107—22no—
268C23×C107—24no—
269C23×C107—21no—
270C23×C107—21no—
271C23×C107—22no—
272C23×C107—22no—
273C23×C107—22no—
274C23×C107—24no—
275C23×C107—22no—
276C23×C107—22no—
277C23×C107—22no—
278C23×C107—41no—
279C23×C107—41no—
280C23×C107—42no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—42no—
285C23×C107—42no—
286C23×C107—41no—
287C23×C107—41no—
288C23×C107—42no—
289C23×C107—41no—
290C23×C107—42no—
291C23×C107—42no—
292C23×C107—42no—
293C23×C107—42no—
294C23×C107—41no—
295C23×C107—41no—
296C23×C107—41no—
297C23×C107—42no—
298C23×C107—42no—
299C23×C107—84no—
300C23×C107—84no—
301C23×C107—82no—
302C23×C107—82no—
303C23×C107—82no—
304C23×C107—82no—
305C23×C107#12012yes—
306C23×C107#12011yescharacteristic
307C23×C107#12011yescharacteristic
308C23×C107C22×D411yescharacteristic
309C23×C107C22×D412yes—
310C23×C107C2×#4112yes—
311C23×C107H(5,𝔽2)11yescharacteristic
312C23×C1072−1+411yescharacteristic
313Q8×C107—81no—
314Q8×C107—81no—
315D4×C107—44no—
316D4×C107—48no—
317D4×C107—44no—
318D4×C107—42no—
319D4×C107—42no—
320D4×C107—42no—
321D4×C107—42no—
322D4×C107—44no—
323D4×C107—44no—
324D4×C107—82no—
325D4×C107—82no—
326D4×C107—81no—
327D4×C107—81no—
328D4×C107—88no—
329C2×C4×C107—24no—
330C2×C4×C107—22no—
331C2×C4×C107—22no—
332C2×C4×C107—21no—
333C2×C4×C107—21no—
334C2×C4×C107—22no—
335C2×C4×C107—22no—
336C2×C4×C107—21no—
337C2×C4×C107—21no—
338C2×C4×C107—24no—
339C2×C4×C107—22no—
340C2×C4×C107—22no—
341C2×C4×C107—42no—
342C2×C4×C107—41no—
343C2×C4×C107—42no—
344C2×C4×C107—42no—
345C2×C4×C107—42no—
346C2×C4×C107—41no—
347C2×C4×C107—42no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—42no—
351C2×C4×C107—41no—
352C2×C4×C107—41no—
353C2×C4×C107—42no—
354C2×C4×C107—41no—
355C2×C4×C107—41no—
356C2×C4×C107—42no—
357C2×C4×C107—41no—
358C2×C4×C107—41no—
359C2×C4×C107—42no—
360C2×C4×C107—41no—
361C2×C4×C107—41no—
362C2×C4×C107—42no—
363C2×C4×C107—81no—
364C2×C4×C107—81no—
365C2×C4×C107—82no—
366C2×C4×C107—82no—
367C2×C4×C107—88no—
368C22×C107—21no—
369C22×C107—21no—
370C22×C107—22no—
371C22×C107—21no—
372C22×C107—22no—
373C22×C107—21no—
374C22×C107—21no—
375C22×C107—22no—
376C22×C107—21no—
377C22×C107—22no—
378C22×C107—21no—
379C22×C107—22no—
380C22×C107—42no—
381C22×C107—41no—
382C22×C107—41no—
383C22×C107—44no—
384C22×C107—42no—
385C22×C107—42no—
386C22×C107—44no—
387C22×C107—44no—
388C22×C107—42no—
389C22×C107—42no—
390C22×C107—44no—
391C22×C107—42no—
392C22×C107—42no—
393C22×C107—42no—
394C22×C107—42no—
395C22×C107—82no—
396C22×C107—81no—
397C22×C107—81no—
398C22×C107—82no—
399C22×C107—82no—
400C22×C107—82no—
401C22×C107—82no—
402C22×C107—81no—
403C22×C107—81no—
404C22×C107—82no—
405C22×C107—81no—
406C22×C107—81no—
407C22×C107B(4,𝔽2)12yes—
408C22×C107C2×#12011yescharacteristic
409C22×C107#53211yescharacteristic
410C22×C107#53711yescharacteristic
411C22×C107#54612yes—
412C22×C107#54712yes—
413C4×C107—44no—
414C4×C107—42no—
415C4×C107—42no—
416C4×C107—41no—
417C4×C107—41no—
418C4×C107—42no—
419C4×C107—41no—
420C4×C107—41no—
421C4×C107—42no—
422C4×C107—81no—
423C4×C107—81no—
424C4×C107—82no—
425#25563C10711yesmaximal, characteristic, direct product factor, Sylow
426C2×C107—22no—
427C2×C107—21no—
428C2×C107—21no—
429C2×C107—22no—
430C2×C107—22no—
431C2×C107—41no—
432C2×C107—42no—
433C2×C107—82no—
434C2×C107—82no—
435C2×C107#243011yescharacteristic
436C2×C107C2×B(4,𝔽2)11yescharacteristic
437C2×C107#302611yescharacteristic
438#3490C2×C10711yescharacteristic, complemented
439#2410C2×C10712yescomplemented
440#2405C2×C10711yescharacteristic, complemented
441#2062C2×C10711yescharacteristic, complemented
442#2044C2×C10711yescharacteristic, complemented
443#2029C2×C10711yescharacteristic, complemented
444#2021C2×C10711yescharacteristic, complemented
445#1898C2×C10712yescomplemented
446#1889C2×C10712yescomplemented
447#1867C2×C10712yescomplemented
448C2×#342C2×C10711yescharacteristic, complemented
449C107#2556311yescharacteristic, direct product factor, Sylow
450C23×D4C22×C10711yescharacteristic
451#551—22no—
452#551—22no—
453#546—22no—
454#546—22no—
455#543C22×C10711yescharacteristic
456#538—21no—
457#538—21no—
458#534C22×C10711yescharacteristic
459#525—21no—
460#525—21no—
461C2×#123—21no—
462C2×#121—22no—
463C2×#120C22×C10712yes—
464C2×#120C22×C10712yes—
465#518C22×C10712yes—
466C22×C22⋊C4C22×C10711yescharacteristic
467C22×C22⋊C4C22×C10712yes—
468C2×#99C22×C10712yes—
469C2×#99C22×C10712yes—
470#394—21no—
471#394—21no—
472#394—22no—
473#392—22no—
474#386—21no—
475#386—22no—
476#386C22×C10712yes—
477#385C22×C10712yes—
478#385C22×C10711yescharacteristic
479#385C22×C10711yescharacteristic
480#379C22×C10711yescharacteristic
481#379C22×C10712yes—
482#379C22×C10711yescharacteristic
483#379C22×C10711yescharacteristic
484#342C22×C10712yes—
485#342C22×C10711yescharacteristic
486#342C22×C10712yes—
487#342C22×C10712yes—
488#342C22×C10711yescharacteristic
489C25C23×C10711yescharacteristic
490C25C23×C10711yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C10712yescomplemented
500C22×D4D4×C10712yescomplemented
501C22×D4C23×C10712yes—
502C23×C4—22no—
503C23×C4D4×C10711yescharacteristic, complemented
504C23×C4D4×C10711yescharacteristic, complemented
505C23×C4C23×C10711yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C10711yescharacteristic, complemented
565C2×C22⋊C4D4×C10711yescharacteristic, complemented
566C2×C22⋊C4D4×C10712yescomplemented
567C2×C22⋊C4D4×C10712yescomplemented
568C2×C22⋊C4C23×C10712yes—
569C2×C22⋊C4C23×C10711yescharacteristic
570C2×C22⋊C4C23×C10711yescharacteristic
571C2×C22⋊C4C23×C10711yescharacteristic
572C2×C22⋊C4C23×C10711yescharacteristic
573C2×C22⋊C4C23×C10712yes—
574C2×C22⋊C4C23×C10712yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C10712yes—
594C24C2×D4×C10711yescharacteristic
595C24C2×D4×C10712yes—
596C24C2×D4×C10712yes—
597C24C2×D4×C10711yescharacteristic
598C24C24×C10711yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C10712yes—
650C22×C4C2×D4×C10711yescharacteristic
651C22×C4C2×D4×C10712yes—
652C22×C4C2×D4×C10711yescharacteristic
653C22×C4C2×D4×C10711yescharacteristic
654C22×C4C2×D4×C10712yes—
655C22×C4C2×D4×C10711yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C10714yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C10712yes—
744C23#120×C10711yescharacteristic
745C23#120×C10711yescharacteristic
746C23C22×D4×C10711yescharacteristic
747C23C22×D4×C10712yes—
748C23C2×#41×C10712yes—
749C23H(5,𝔽2)×C10711yescharacteristic
750C232−1+4×C10711yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22B(4,𝔽2)×C10712yes—
846C22C2×#120×C10711yescharacteristic
847C22#532×C10711yescharacteristic
848C22#537×C10711yescharacteristic
849C22#546×C10712yes—
850C22#547×C10712yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C107×#243011yescharacteristic
873C2C2×B(4,𝔽2)×C10711yescharacteristic
874C2C107×#302611yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC24C24×C107
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C25×C107 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C107×#3490C2semidirect
2. C107×#2410C2semidirect
3. C107×#2405C2semidirect
4. C107×#2062C2semidirect
5. C107×#2044C2semidirect
6. C107×#2029C2semidirect
7. C107×#2021C2semidirect
8. C107×#1898C2semidirect
9. C107×#1889C2semidirect
10. C107×#1867C2semidirect
11. C2×#342×C107C2semidirect
61. C22×D4×C107D4semidirect
62. C22×D4×C107D4semidirect
65. C23×C4×C107D4semidirect
66. C23×C4×C107D4semidirect
126. C2×C22⋊C4×C107D4semidirect
127. C2×C22⋊C4×C107D4semidirect
128. C2×C22⋊C4×C107D4semidirect
129. C2×C22⋊C4×C107D4semidirect
260. C22⋊C4×C107#41semidirect
425. #25563C107direct (N × H)
438. #3490C2×C107semidirect
439. #2410C2×C107semidirect
440. #2405C2×C107semidirect
441. #2062C2×C107semidirect
442. #2044C2×C107semidirect
443. #2029C2×C107semidirect
444. #2021C2×C107semidirect
445. #1898C2×C107semidirect
446. #1889C2×C107semidirect
447. #1867C2×C107semidirect
448. C2×#342C2×C107semidirect
449. C107#25563direct (N × H)
499. C22×D4D4×C107semidirect
500. C22×D4D4×C107semidirect
503. C23×C4D4×C107semidirect
504. C23×C4D4×C107semidirect
564. C2×C22⋊C4D4×C107semidirect
565. C2×C22⋊C4D4×C107semidirect
566. C2×C22⋊C4D4×C107semidirect
567. C2×C22⋊C4D4×C107semidirect
698. C22⋊C4#41×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34902
C107×#24102
C107×#24052
C107×#20622
C107×#20442
C107×#20292
C107×#20212
C107×#18982
C107×#18892
C107×#18672
C2×#342×C1072
#25563107