Finite Group Databasebeta

← C107×#24404 #41050368

Subgroups — C107×#24404 #41050368

Order 27392.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3484C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C107C211yesmaximal, characteristic, complemented
3C22×#99×C107C211yesmaximal, characteristic, complemented
4C107×#2410C212yesmaximal, complemented
5C107×#2403C211yesmaximal, characteristic, complemented
6C107×#2044C212yesmaximal, complemented
7C107×#2021C212yesmaximal, complemented
8C107×#1898C212yesmaximal, complemented
9C107×#1889C211yesmaximal, characteristic, complemented
10C107×#1867C211yesmaximal, characteristic, complemented
11C107×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C107C2211yescharacteristic
13C23×D4×C107C2211yescharacteristic
14C23×D4×C107C2211yescharacteristic, complemented
15#546×C107—22no—
16#546×C107—22no—
17D42×C107—22no—
18D42×C107—22no—
19#535×C107—21no—
20#534×C107—21no—
21#534×C107C2212yes—
22#525×C107—21no—
23C2×#121×C107—22no—
24C2×#120×C107—21no—
25C2×#120×C107—21no—
26C2×#120×C107C2211yescharacteristic
27C2×#120×C107C2212yes—
28C2×#120×C107C2212yescomplemented
29C2×#120×C107C2211yescharacteristic, complemented
30#518×C107C2211yescharacteristic
31C22×C22⋊C4×C107C2212yescomplemented
32B(4,𝔽2)×C107—24no—
33C2×#99×C107—24no—
34C2×#99×C107C2211yescharacteristic
35C2×#99×C107C2211yescharacteristic
36C2×#99×C107C2212yescomplemented
37C2×#99×C107C2212yescomplemented
38C2×#99×C107C2212yescomplemented
39#394×C107—22no—
40#392×C107—21no—
41#392×C107—21no—
42#392×C107—22no—
43#386×C107—21no—
44#386×C107—22no—
45#386×C107C2211yescharacteristic
46#386×C107C2211yescharacteristic, complemented
47#386×C107C2212yescomplemented
48#385×C107C2212yescomplemented
49#379×C107C2212yescomplemented
50#379×C107C2211yescharacteristic, complemented
51#342×C107C2212yescomplemented
52#342×C107C2212yescomplemented
53C25×C107D411yescharacteristic, complemented
54C25×C107C2311yescharacteristic
55C25×C107C2311yescharacteristic
56H(5,𝔽2)×C107—22no—
57H(5,𝔽2)×C107—22no—
58H(5,𝔽2)×C107—42no—
59C2×#41×C107—21no—
60C2×#41×C107—22no—
61C22×D4×C107—21no—
62C22×D4×C107—22no—
63C22×D4×C107—21no—
64C22×D4×C107—22no—
65C22×D4×C107—22no—
66C22×D4×C107—22no—
67C22×D4×C107—21no—
68C22×D4×C107—21no—
69C22×D4×C107—22no—
70C22×D4×C107—22no—
71C22×D4×C107—21no—
72C22×D4×C107—22no—
73C22×D4×C107—21no—
74C22×D4×C107—21no—
75C22×D4×C107—22no—
76C22×D4×C107—44no—
77C22×D4×C107—42no—
78C22×D4×C107D411yescharacteristic, complemented
79C22×D4×C107D411yescharacteristic, complemented
80C22×D4×C107D412yescomplemented
81C22×D4×C107D412yescomplemented
82C22×D4×C107C2312yes—
83C22×D4×C107C2311yescharacteristic
84C22×D4×C107C2311yescharacteristic
85C23×C4×C107—22no—
86C23×C4×C107D411yescharacteristic, complemented
87C23×C4×C107C2311yescharacteristic
88#127×C107—22no—
89#124×C107—22no—
90#123×C107—22no—
91#123×C107—22no—
92#123×C107—22no—
93C22⋊Q8×C107—21no—
94C22⋊Q8×C107—21no—
95#121×C107—21no—
96#121×C107—21no—
97#121×C107—22no—
98#121×C107—22no—
99#121×C107—22no—
100#121×C107—22no—
101#121×C107—22no—
102#121×C107—22no—
103#121×C107—48no—
104#120×C107—22no—
105#120×C107—22no—
106#120×C107—22no—
107#120×C107—22no—
108#120×C107—22no—
109#120×C107—22no—
110#120×C107—22no—
111#120×C107—22no—
112#120×C107—22no—
113#120×C107—22no—
114#120×C107—22no—
115#120×C107—24no—
116#120×C107—42no—
117#120×C107—42no—
118#120×C107—44no—
119C4×D4×C107—22no—
120C4×D4×C107—22no—
121C4×D4×C107—22no—
122C4×D4×C107—22no—
123#117×C107—21no—
124C2×C4⋊C4×C107—22no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—21no—
128C2×C22⋊C4×C107—24no—
129C2×C22⋊C4×C107—21no—
130C2×C22⋊C4×C107—21no—
131C2×C22⋊C4×C107—21no—
132C2×C22⋊C4×C107—22no—
133C2×C22⋊C4×C107—22no—
134C2×C22⋊C4×C107—22no—
135C2×C22⋊C4×C107—21no—
136C2×C22⋊C4×C107—21no—
137C2×C22⋊C4×C107—22no—
138C2×C22⋊C4×C107—21no—
139C2×C22⋊C4×C107—22no—
140C2×C22⋊C4×C107—42no—
141C2×C22⋊C4×C107D412yescomplemented
142C2×C22⋊C4×C107D412yescomplemented
143C2×C22⋊C4×C107C2311yescharacteristic
144C2×C22⋊C4×C107C2311yescharacteristic
145C2×C22⋊C4×C107C2312yes—
146C2×C22⋊C4×C107C2312yes—
147C2×C22⋊C4×C107C2312yes—
148#99×C107—22no—
149#99×C107—24no—
150#99×C107—24no—
151#99×C107—42no—
152#99×C107D414yescomplemented
153#95×C107—22no—
154#95×C107—21no—
155#95×C107—21no—
156#95×C107—22no—
157C24×C107—21no—
158C24×C107—21no—
159C24×C107—22no—
160C24×C107—21no—
161C24×C107—22no—
162C24×C107—21no—
163C24×C107—21no—
164C24×C107—21no—
165C24×C107—22no—
166C24×C107—21no—
167C24×C107—21no—
168C24×C107—22no—
169C24×C107—41no—
170C24×C107—42no—
171C24×C107—42no—
172C24×C107—42no—
173C24×C107—81no—
174C24×C107—81no—
175C24×C107—81no—
176C24×C107C2×D411yescharacteristic
177C24×C107C2×D412yes—
178C24×C107C2×D411yescharacteristic
179C24×C107C2×D412yes—
180C24×C107C2×D412yes—
181C24×C107C2×D411yescharacteristic
182C24×C107C2×D411yescharacteristic
183C24×C107C2411yescharacteristic
184#41×C107—44no—
185#41×C107—44no—
186#41×C107—42no—
187#41×C107—42no—
188C2×Q8×C107—21no—
189C2×D4×C107—22no—
190C2×D4×C107—22no—
191C2×D4×C107—22no—
192C2×D4×C107—24no—
193C2×D4×C107—21no—
194C2×D4×C107—28no—
195C2×D4×C107—22no—
196C2×D4×C107—22no—
197C2×D4×C107—22no—
198C2×D4×C107—22no—
199C2×D4×C107—22no—
200C2×D4×C107—21no—
201C2×D4×C107—22no—
202C2×D4×C107—22no—
203C2×D4×C107—22no—
204C2×D4×C107—22no—
205C2×D4×C107—21no—
206C2×D4×C107—22no—
207C2×D4×C107—22no—
208C2×D4×C107—22no—
209C2×D4×C107—22no—
210C2×D4×C107—22no—
211C2×D4×C107—22no—
212C2×D4×C107—22no—
213C2×D4×C107—22no—
214C2×D4×C107—22no—
215C2×D4×C107—41no—
216C2×D4×C107—41no—
217C2×D4×C107—42no—
218C2×D4×C107—44no—
219C2×D4×C107—44no—
220C2×D4×C107—44no—
221C2×D4×C107—44no—
222C2×D4×C107—44no—
223C2×D4×C107—44no—
224C2×D4×C107—44no—
225C2×D4×C107—44no—
226C2×D4×C107—44no—
227C2×D4×C107—42no—
228C2×D4×C107—42no—
229C2×D4×C107—44no—
230C2×D4×C107—42no—
231C2×D4×C107—41no—
232C2×D4×C107—42no—
233C2×D4×C107—41no—
234C2×D4×C107—42no—
235C2×D4×C107—44no—
236C2×D4×C107—42no—
237C2×D4×C107—42no—
238C2×D4×C107—42no—
239C2×D4×C107—44no—
240C2×D4×C107—42no—
241C2×D4×C107—82no—
242C2×D4×C107—82no—
243C2×D4×C107—81no—
244C2×D4×C107—81no—
245C2×D4×C107—82no—
246C2×D4×C107—82no—
247C2×D4×C107C2×D412yes—
248C2×D4×C107#4112yes—
249C22×C4×C107—21no—
250C22×C4×C107—22no—
251C22×C4×C107—21no—
252C22×C4×C107—21no—
253C22×C4×C107—21no—
254C22×C4×C107—22no—
255C22×C4×C107—22no—
256C22×C4×C107—21no—
257C22×C4×C107—21no—
258C22×C4×C107—22no—
259C22×C4×C107—22no—
260C22×C4×C107—21no—
261C22×C4×C107—21no—
262C22×C4×C107—42no—
263C22×C4×C107—41no—
264C22×C4×C107—44no—
265C22×C4×C107—44no—
266C22×C4×C107—82no—
267C22×C4×C107C2×D412yes—
268C22×C4×C107C2×D411yescharacteristic
269C22×C4×C107C2×D411yescharacteristic
270C22×C4×C107C2×D412yes—
271C22×C4×C107C2×D412yes—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—22no—
275C4⋊C4×C107—22no—
276C4⋊C4×C107—44no—
277C22⋊C4×C107—22no—
278C22⋊C4×C107—22no—
279C22⋊C4×C107—22no—
280C22⋊C4×C107—22no—
281C22⋊C4×C107—22no—
282C22⋊C4×C107—22no—
283C22⋊C4×C107—22no—
284C22⋊C4×C107—22no—
285C22⋊C4×C107—22no—
286C22⋊C4×C107—22no—
287C22⋊C4×C107—22no—
288C22⋊C4×C107—22no—
289C22⋊C4×C107—22no—
290C22⋊C4×C107—21no—
291C22⋊C4×C107—21no—
292C22⋊C4×C107—22no—
293C22⋊C4×C107—22no—
294C22⋊C4×C107—44no—
295C22⋊C4×C107—44no—
296C22⋊C4×C107—42no—
297C22⋊C4×C107—42no—
298C22⋊C4×C107—42no—
299C22⋊C4×C107—44no—
300C22⋊C4×C107—42no—
301C22⋊C4×C107—44no—
302C22⋊C4×C107—42no—
303C22⋊C4×C107—82no—
304C22⋊C4×C107—81no—
305C22⋊C4×C107C2×D414yescomplemented
306C42×C107—22no—
307C23×C107—21no—
308C23×C107—21no—
309C23×C107—21no—
310C23×C107—22no—
311C23×C107—22no—
312C23×C107—22no—
313C23×C107—24no—
314C23×C107—21no—
315C23×C107—21no—
316C23×C107—21no—
317C23×C107—22no—
318C23×C107—22no—
319C23×C107—24no—
320C23×C107—22no—
321C23×C107—21no—
322C23×C107—22no—
323C23×C107—21no—
324C23×C107—21no—
325C23×C107—22no—
326C23×C107—22no—
327C23×C107—41no—
328C23×C107—42no—
329C23×C107—41no—
330C23×C107—41no—
331C23×C107—41no—
332C23×C107—42no—
333C23×C107—41no—
334C23×C107—42no—
335C23×C107—42no—
336C23×C107—42no—
337C23×C107—41no—
338C23×C107—41no—
339C23×C107—41no—
340C23×C107—41no—
341C23×C107—42no—
342C23×C107—42no—
343C23×C107—41no—
344C23×C107—42no—
345C23×C107—41no—
346C23×C107—41no—
347C23×C107—42no—
348C23×C107—42no—
349C23×C107—42no—
350C23×C107—42no—
351C23×C107—41no—
352C23×C107—41no—
353C23×C107—41no—
354C23×C107—42no—
355C23×C107—42no—
356C23×C107—42no—
357C23×C107—81no—
358C23×C107—81no—
359C23×C107—82no—
360C23×C107—82no—
361C23×C107—82no—
362C23×C107—82no—
363C23×C107—84no—
364C23×C107—84no—
365C23×C107—81no—
366C23×C107—81no—
367C23×C107—84no—
368C23×C107—84no—
369C23×C107#12011yescharacteristic
370C23×C107#12012yes—
371C23×C107#12011yescharacteristic
372C23×C107#12112yescomplemented
373C23×C107C22×D411yescharacteristic
374C23×C107C22×D412yes—
375C23×C107C22×D411yescharacteristic
376C23×C107C2×#4111yescharacteristic
377C23×C107H(5,𝔽2)12yes—
378Q8×C107—42no—
379D4×C107—24no—
380D4×C107—24no—
381D4×C107—44no—
382D4×C107—42no—
383D4×C107—44no—
384D4×C107—48no—
385D4×C107—44no—
386D4×C107—44no—
387D4×C107—44no—
388D4×C107—42no—
389D4×C107—42no—
390D4×C107—42no—
391D4×C107—42no—
392D4×C107—42no—
393D4×C107—42no—
394D4×C107—44no—
395D4×C107—44no—
396D4×C107—82no—
397D4×C107—82no—
398D4×C107—82no—
399D4×C107—82no—
400D4×C107—88no—
401D4×C107—84no—
402D4×C107—84no—
403C2×C4×C107—21no—
404C2×C4×C107—21no—
405C2×C4×C107—22no—
406C2×C4×C107—24no—
407C2×C4×C107—22no—
408C2×C4×C107—22no—
409C2×C4×C107—22no—
410C2×C4×C107—21no—
411C2×C4×C107—21no—
412C2×C4×C107—21no—
413C2×C4×C107—24no—
414C2×C4×C107—22no—
415C2×C4×C107—22no—
416C2×C4×C107—42no—
417C2×C4×C107—42no—
418C2×C4×C107—44no—
419C2×C4×C107—42no—
420C2×C4×C107—42no—
421C2×C4×C107—41no—
422C2×C4×C107—42no—
423C2×C4×C107—42no—
424C2×C4×C107—41no—
425C2×C4×C107—42no—
426C2×C4×C107—42no—
427C2×C4×C107—42no—
428C2×C4×C107—41no—
429C2×C4×C107—41no—
430C2×C4×C107—42no—
431C2×C4×C107—41no—
432C2×C4×C107—41no—
433C2×C4×C107—41no—
434C2×C4×C107—41no—
435C2×C4×C107—42no—
436C2×C4×C107—81no—
437C2×C4×C107—81no—
438C2×C4×C107—88no—
439C2×C4×C107#12112yescomplemented
440C22×C107—21no—
441C22×C107—22no—
442C22×C107—21no—
443C22×C107—22no—
444C22×C107—21no—
445C22×C107—21no—
446C22×C107—21no—
447C22×C107—22no—
448C22×C107—22no—
449C22×C107—22no—
450C22×C107—21no—
451C22×C107—21no—
452C22×C107—22no—
453C22×C107—41no—
454C22×C107—41no—
455C22×C107—42no—
456C22×C107—44no—
457C22×C107—44no—
458C22×C107—42no—
459C22×C107—42no—
460C22×C107—42no—
461C22×C107—44no—
462C22×C107—42no—
463C22×C107—42no—
464C22×C107—42no—
465C22×C107—44no—
466C22×C107—41no—
467C22×C107—41no—
468C22×C107—42no—
469C22×C107—41no—
470C22×C107—42no—
471C22×C107—42no—
472C22×C107—41no—
473C22×C107—42no—
474C22×C107—41no—
475C22×C107—82no—
476C22×C107—81no—
477C22×C107—81no—
478C22×C107—81no—
479C22×C107—82no—
480C22×C107—84no—
481C22×C107—82no—
482C22×C107—82no—
483C22×C107—81no—
484C22×C107—82no—
485C22×C107—81no—
486C22×C107—81no—
487C22×C107—82no—
488C22×C107—84no—
489C22×C107—81no—
490C22×C107—81no—
491C22×C107—162no—
492C22×C107B(4,𝔽2)12yescomplemented
493C22×C107C2×#12011yescharacteristic
494C22×C107C2×#12111yescharacteristic
495C22×C107#53411yescharacteristic
496C22×C107D4212yes—
497C22×C107#54612yes—
498C4×C107—22no—
499C4×C107—44no—
500C4×C107—41no—
501C4×C107—42no—
502C4×C107—42no—
503C4×C107—42no—
504C4×C107—42no—
505C4×C107—82no—
506C4×C107—81no—
507C4×C107—81no—
508#24404C10711yesmaximal, characteristic, direct product factor, Sylow
509C2×C107—22no—
510C2×C107—21no—
511C2×C107—21no—
512C2×C107—22no—
513C2×C107—22no—
514C2×C107—42no—
515C2×C107—41no—
516C2×C107—42no—
517C2×C107—82no—
518C2×C107—81no—
519C2×C107—82no—
520C2×C107#241011yescharacteristic
521C2×C107C2×B(4,𝔽2)11yescharacteristic
522C2×C107#302611yescharacteristic
523#3484C2×C10711yescharacteristic, complemented
524C2×B(4,𝔽2)C2×C10711yescharacteristic, complemented
525C22×#99C2×C10711yescharacteristic, complemented
526#2410C2×C10712yescomplemented
527#2403C2×C10711yescharacteristic, complemented
528#2044C2×C10712yescomplemented
529#2021C2×C10712yescomplemented
530#1898C2×C10712yescomplemented
531#1889C2×C10711yescharacteristic, complemented
532#1867C2×C10711yescharacteristic, complemented
533#1790C2×C10711yescharacteristic, complemented
534C107#2440411yescharacteristic, direct product factor, Sylow
535C2×H(5,𝔽2)C22×C10711yescharacteristic
536C23×D4C22×C10711yescharacteristic
537C23×D4C22×C10711yescharacteristic, complemented
538#546—22no—
539#546—22no—
540D42—22no—
541D42—22no—
542#535—21no—
543#534—21no—
544#534C22×C10712yes—
545#525—21no—
546C2×#121—22no—
547C2×#120—21no—
548C2×#120—21no—
549C2×#120C22×C10711yescharacteristic
550C2×#120C22×C10712yes—
551C2×#120C22×C10712yescomplemented
552C2×#120C22×C10711yescharacteristic, complemented
553#518C22×C10711yescharacteristic
554C22×C22⋊C4C22×C10712yescomplemented
555B(4,𝔽2)—24no—
556C2×#99—24no—
557C2×#99C22×C10711yescharacteristic
558C2×#99C22×C10711yescharacteristic
559C2×#99C22×C10712yescomplemented
560C2×#99C22×C10712yescomplemented
561C2×#99C22×C10712yescomplemented
562#394—22no—
563#392—21no—
564#392—21no—
565#392—22no—
566#386—21no—
567#386—22no—
568#386C22×C10711yescharacteristic
569#386C22×C10711yescharacteristic, complemented
570#386C22×C10712yescomplemented
571#385C22×C10712yescomplemented
572#379C22×C10712yescomplemented
573#379C22×C10711yescharacteristic, complemented
574#342C22×C10712yescomplemented
575#342C22×C10712yescomplemented
576C25D4×C10711yescharacteristic, complemented
577C25C23×C10711yescharacteristic
578C25C23×C10711yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C10711yescharacteristic, complemented
602C22×D4D4×C10711yescharacteristic, complemented
603C22×D4D4×C10712yescomplemented
604C22×D4D4×C10712yescomplemented
605C22×D4C23×C10712yes—
606C22×D4C23×C10711yescharacteristic
607C22×D4C23×C10711yescharacteristic
608C23×C4—22no—
609C23×C4D4×C10711yescharacteristic, complemented
610C23×C4C23×C10711yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C10712yescomplemented
665C2×C22⋊C4D4×C10712yescomplemented
666C2×C22⋊C4C23×C10712yes—
667C2×C22⋊C4C23×C10711yescharacteristic
668C2×C22⋊C4C23×C10711yescharacteristic
669C2×C22⋊C4C23×C10712yes—
670C2×C22⋊C4C23×C10712yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C10714yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C10711yescharacteristic
700C24C2×D4×C10712yes—
701C24C2×D4×C10711yescharacteristic
702C24C2×D4×C10712yes—
703C24C2×D4×C10712yes—
704C24C2×D4×C10711yescharacteristic
705C24C2×D4×C10711yescharacteristic
706C24C24×C10711yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C10712yes—
771C2×D4#41×C10712yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C10712yes—
791C22×C4C2×D4×C10711yescharacteristic
792C22×C4C2×D4×C10711yescharacteristic
793C22×C4C2×D4×C10712yes—
794C22×C4C2×D4×C10712yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C10714yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C10711yescharacteristic
893C23#120×C10712yes—
894C23#120×C10711yescharacteristic
895C23#121×C10712yescomplemented
896C23C22×D4×C10711yescharacteristic
897C23C22×D4×C10712yes—
898C23C22×D4×C10711yescharacteristic
899C23C2×#41×C10711yescharacteristic
900C23H(5,𝔽2)×C10712yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C10712yescomplemented
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22B(4,𝔽2)×C10712yescomplemented
1016C22C2×#120×C10711yescharacteristic
1017C22C2×#121×C10711yescharacteristic
1018C22#534×C10711yescharacteristic
1019C22D42×C10712yes—
1020C22#546×C10712yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C107×#241011yescharacteristic
1043C2C2×B(4,𝔽2)×C10711yescharacteristic
1044C2C107×#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×#3484C2semidirect
2. C2×B(4,𝔽2)×C107C2semidirect
3. C22×#99×C107C2semidirect
4. C107×#2410C2semidirect
5. C107×#2403C2semidirect
6. C107×#2044C2semidirect
7. C107×#2021C2semidirect
8. C107×#1898C2semidirect
9. C107×#1889C2semidirect
10. C107×#1867C2semidirect
11. C107×#1790C2semidirect
14. C23×D4×C107C22semidirect
28. C2×#120×C107C22semidirect
29. C2×#120×C107C22semidirect
31. C22×C22⋊C4×C107C22semidirect
36. C2×#99×C107C22semidirect
37. C2×#99×C107C22semidirect
38. C2×#99×C107C22semidirect
46. #386×C107C22semidirect
47. #386×C107C22semidirect
48. #385×C107C22semidirect
49. #379×C107C22semidirect
50. #379×C107C22semidirect
51. #342×C107C22semidirect
52. #342×C107C22semidirect
53. C25×C107D4semidirect
78. C22×D4×C107D4semidirect
79. C22×D4×C107D4semidirect
80. C22×D4×C107D4semidirect
81. C22×D4×C107D4semidirect
86. C23×C4×C107D4semidirect
141. C2×C22⋊C4×C107D4semidirect
142. C2×C22⋊C4×C107D4semidirect
152. #99×C107D4semidirect
305. C22⋊C4×C107C2×D4semidirect
372. C23×C107#121semidirect
439. C2×C4×C107#121semidirect
492. C22×C107B(4,𝔽2)semidirect
508. #24404C107direct (N × H)
523. #3484C2×C107semidirect
524. C2×B(4,𝔽2)C2×C107semidirect
525. C22×#99C2×C107semidirect
526. #2410C2×C107semidirect
527. #2403C2×C107semidirect
528. #2044C2×C107semidirect
529. #2021C2×C107semidirect
530. #1898C2×C107semidirect
531. #1889C2×C107semidirect
532. #1867C2×C107semidirect
533. #1790C2×C107semidirect
534. C107#24404direct (N × H)
537. C23×D4C22×C107semidirect
551. C2×#120C22×C107semidirect
552. C2×#120C22×C107semidirect
554. C22×C22⋊C4C22×C107semidirect
559. C2×#99C22×C107semidirect
560. C2×#99C22×C107semidirect
561. C2×#99C22×C107semidirect
569. #386C22×C107semidirect
570. #386C22×C107semidirect
571. #385C22×C107semidirect
572. #379C22×C107semidirect
573. #379C22×C107semidirect
574. #342C22×C107semidirect
575. #342C22×C107semidirect
576. C25D4×C107semidirect
601. C22×D4D4×C107semidirect
602. C22×D4D4×C107semidirect
603. C22×D4D4×C107semidirect
604. C22×D4D4×C107semidirect
609. C23×C4D4×C107semidirect
664. C2×C22⋊C4D4×C107semidirect
665. C2×C22⋊C4D4×C107semidirect
675. #99D4×C107semidirect
828. C22⋊C4C2×D4×C107semidirect
895. C23#121×C107semidirect
962. C2×C4#121×C107semidirect
1015. C22B(4,𝔽2)×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34842
C2×B(4,𝔽2)×C1072
C22×#99×C1072
C107×#24102
C107×#24032
C107×#20442
C107×#20212
C107×#18982
C107×#18892
C107×#18672
C107×#17902
#24404107