Finite Group Databasebeta

← C107×#24469 #41050433

Subgroups — C107×#24469 #41050433

Order 27392.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3489C211yesmaximal, characteristic, complemented
2C107×#3055C211yesmaximal, characteristic, complemented
3C2×#454×C107C211yesmaximal, characteristic, complemented
4C107×#3006C211yesmaximal, characteristic, complemented
5C2×#421×C107C211yesmaximal, characteristic, complemented
6C107×#2620C211yesmaximal, characteristic, complemented
7C107×#2039C211yesmaximal, characteristic, complemented
8C107×#2038C211yesmaximal, characteristic, complemented
9C107×#2006C211yesmaximal, characteristic, complemented
10C107×#2003C211yesmaximal, characteristic, complemented
11C107×#1901C211yesmaximal, characteristic, complemented
12C107×#1897C211yesmaximal, characteristic, complemented
13C107×#1883C211yesmaximal, characteristic, complemented
14C107×#1859C211yesmaximal, characteristic, complemented
15C107×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C107C2211yescharacteristic, complemented
21C22×M16×C107C2211yescharacteristic
22D4×Q8×C107—21no—
23#548×C107—21no—
24#547×C107—21no—
25#547×C107—22no—
26#546×C107—21no—
27#546×C107—22no—
28#537×C107—21no—
29#537×C107C2211yescharacteristic
30#536×C107—21no—
31#536×C107C2211yescharacteristic
32C2×#124×C107C2211yescharacteristic, complemented
33#525×C107—21no—
34#525×C107C2211yescharacteristic
35C2×C22⋊Q8×C107—21no—
36C2×C22⋊Q8×C107C2211yescharacteristic
37C2×#121×C107C2211yescharacteristic
38#520×C107C2211yescharacteristic
39C2×#117×C107C2211yescharacteristic
40#469×C107—21no—
41#468×C107—21no—
42#466×C107—21no—
43#465×C107—21no—
44#454×C107—24no—
45#449×C107—21no—
46#449×C107—21no—
47#448×C107—21no—
48#447×C107—21no—
49#428×C107C2211yescharacteristic, complemented
50#421×C107—24no—
51C2×#104×C107C2211yescharacteristic
52C2×#104×C107C2211yescharacteristic
53C2×#104×C107C2211yescharacteristic
54C2×#104×C107C2211yescharacteristic
55C2×#104×C107C2211yescharacteristic, complemented
56C2×#104×C107C2211yescharacteristic, complemented
57#418×C107C2211yescharacteristic, complemented
58#417×C107C2211yescharacteristic
59#417×C107C2211yescharacteristic
60#417×C107C2211yescharacteristic, complemented
61C2×#101×C107C2211yescharacteristic, complemented
62C2×#101×C107C2211yescharacteristic, complemented
63#407×C107C2211yescharacteristic
64#396×C107—22no—
65#394×C107—22no—
66#391×C107C2211yescharacteristic, complemented
67#390×C107C2211yescharacteristic, complemented
68#384×C107C2211yescharacteristic, complemented
69#343×C107C2211yescharacteristic, complemented
70#343×C107C2211yescharacteristic, complemented
71#339×C107C2211yescharacteristic, complemented
72#339×C107C2211yescharacteristic, complemented
732−1+4×C107—22no—
742−1+4×C107—22no—
752−1+4×C107—41no—
762−1+4×C107—41no—
77C2×#41×C107—21no—
78C2×#41×C107—21no—
79C2×#41×C107—21no—
80C2×#41×C107—22no—
81C2×#41×C107—21no—
82C2×#41×C107—22no—
83C2×#41×C107—22no—
84C2×#41×C107—41no—
85C2×#41×C107—41no—
86C2×#41×C107D411yescharacteristic
87C2×#41×C107D411yescharacteristic
88C2×#41×C107C2311yescharacteristic
89C2×#41×C107C2311yescharacteristic
90C2×#41×C107C2311yescharacteristic
91C22×Q8×C107—21no—
92C22×Q8×C107—21no—
93C22×Q8×C107D411yescharacteristic
94C22×Q8×C107C2311yescharacteristic
95C22×D4×C107—21no—
96C22×D4×C107—21no—
97C22×D4×C107D411yescharacteristic
98C22×D4×C107C2311yescharacteristic
99C23×C4×C107—21no—
100C23×C4×C107C2311yescharacteristic
101AGL(1,ℤ/8)×C107—22no—
102AGL(1,ℤ/8)×C107—22no—
103AGL(1,ℤ/8)×C107—22no—
104AGL(1,ℤ/8)×C107—41no—
105AGL(1,ℤ/8)×C107—41no—
106AGL(1,ℤ/8)×C107—41no—
107C2×SD16×C107—21no—
108C2×SD16×C107—21no—
109C2×SD16×C107—21no—
110C2×D8×C107—21no—
111C2×D8×C107—21no—
112C2×D8×C107—21no—
113C2×M16×C107—21no—
114C2×M16×C107—22no—
115C2×M16×C107—41no—
116C2×M16×C107C2311yescharacteristic
117C2×M16×C107C2311yescharacteristic
118C2×M16×C107C2311yescharacteristic
119C2×M16×C107C2311yescharacteristic
120C22×C8×C107—21no—
121C4⋊Q8×C107—22no—
122C4⋊Q8×C107—21no—
123#124×C107—22no—
124#124×C107—21no—
125#124×C107—22no—
126#124×C107—41no—
127#123×C107—22no—
128#123×C107—22no—
129#123×C107—22no—
130#123×C107—21no—
131#123×C107—22no—
132C22⋊Q8×C107—22no—
133C22⋊Q8×C107—22no—
134C22⋊Q8×C107—22no—
135C22⋊Q8×C107—21no—
136C22⋊Q8×C107—21no—
137C22⋊Q8×C107—21no—
138C22⋊Q8×C107—21no—
139C22⋊Q8×C107—21no—
140C22⋊Q8×C107—21no—
141C22⋊Q8×C107—21no—
142C22⋊Q8×C107—21no—
143C22⋊Q8×C107D411yescharacteristic
144C22⋊Q8×C107D411yescharacteristic
145#121×C107—22no—
146#121×C107—22no—
147#121×C107—22no—
148#121×C107—21no—
149#121×C107—21no—
150#121×C107—22no—
151#121×C107—21no—
152#121×C107—21no—
153#121×C107—21no—
154#121×C107—21no—
155#121×C107D411yescharacteristic
156#121×C107D411yescharacteristic
157#120×C107—22no—
158#120×C107—21no—
159C4×Q8×C107—21no—
160C4×D4×C107—22no—
161C4×D4×C107—22no—
162C4×D4×C107—21no—
163C4×D4×C107—22no—
164C4×D4×C107—21no—
165C4×D4×C107—21no—
166#117×C107—21no—
167#117×C107—22no—
168#117×C107—41no—
169#117×C107C2311yescharacteristic
170C2×C4⋊C4×C107—22no—
171C2×C4⋊C4×C107—21no—
172C2×C4⋊C4×C107—21no—
173C2×C4⋊C4×C107—22no—
174C2×C4⋊C4×C107D412yes—
175C2×C4⋊C4×C107C2311yescharacteristic
176C2×C4⋊C4×C107C2311yescharacteristic
177C2×C22⋊C4×C107—22no—
178C2×C22⋊C4×C107—21no—
179C2×C22⋊C4×C107—22no—
180C2×C22⋊C4×C107—21no—
181C2×C22⋊C4×C107—22no—
182C2×C22⋊C4×C107D412yes—
183C2×C42×C107C2311yescharacteristic
184C2×C42×C107C2311yescharacteristic
185#107×C107—21no—
186#106×C107—21no—
187#104×C107—22no—
188#104×C107—22no—
189#104×C107—22no—
190#104×C107—22no—
191#104×C107—41no—
192#104×C107D414yescomplemented
193#103×C107—21no—
194#103×C107—21no—
195#103×C107—21no—
196#102×C107—21no—
197#102×C107—21no—
198#102×C107—21no—
199#102×C107—21no—
200#102×C107—21no—
201#101×C107—22no—
202#101×C107—41no—
203C22⋊C8×C107—21no—
204C22⋊C8×C107—21no—
205#95×C107—22no—
206C24×C107—21no—
207C24×C107—21no—
208C24×C107C2×D411yescharacteristic
209#41×C107—21no—
210#41×C107—21no—
211#41×C107—22no—
212#41×C107—22no—
213#41×C107—21no—
214#41×C107—21no—
215#41×C107—21no—
216#41×C107—21no—
217#41×C107—21no—
218#41×C107—21no—
219#41×C107—21no—
220#41×C107—21no—
221#41×C107—42no—
222#41×C107—42no—
223#41×C107—41no—
224#41×C107—41no—
225#41×C107—42no—
226#41×C107—42no—
227#41×C107—42no—
228#41×C107—42no—
229#41×C107—44no—
230#41×C107—44no—
231#41×C107—42no—
232#41×C107—42no—
233#41×C107C2×D412yes—
234#41×C107#4112yes—
235C2×Q8×C107—22no—
236C2×Q8×C107—21no—
237C2×Q8×C107—21no—
238C2×Q8×C107—21no—
239C2×Q8×C107—21no—
240C2×Q8×C107—21no—
241C2×Q8×C107—21no—
242C2×Q8×C107—21no—
243C2×Q8×C107—22no—
244C2×Q8×C107—41no—
245C2×Q8×C107—42no—
246C2×Q8×C107—42no—
247C2×Q8×C107—42no—
248C2×Q8×C107—42no—
249C2×Q8×C107C2×D411yescharacteristic
250C2×Q8×C107C2×D411yescharacteristic
251C2×Q8×C107C2×D411yescharacteristic
252C2×D4×C107—21no—
253C2×D4×C107—22no—
254C2×D4×C107—22no—
255C2×D4×C107—21no—
256C2×D4×C107—21no—
257C2×D4×C107—21no—
258C2×D4×C107—21no—
259C2×D4×C107—21no—
260C2×D4×C107—22no—
261C2×D4×C107—21no—
262C2×D4×C107—21no—
263C2×D4×C107—21no—
264C2×D4×C107—21no—
265C2×D4×C107—21no—
266C2×D4×C107—21no—
267C2×D4×C107—21no—
268C2×D4×C107—21no—
269C2×D4×C107—41no—
270C2×D4×C107—42no—
271C2×D4×C107—42no—
272C2×D4×C107—41no—
273C2×D4×C107—41no—
274C2×D4×C107—82no—
275C2×D4×C107C2×D411yescharacteristic
276C2×D4×C107C2×D411yescharacteristic
277C2×D4×C107C2×D411yescharacteristic
278C22×C4×C107—21no—
279C22×C4×C107—21no—
280C22×C4×C107—21no—
281C22×C4×C107—21no—
282C22×C4×C107—21no—
283C22×C4×C107—22no—
284C22×C4×C107—22no—
285C22×C4×C107—21no—
286C22×C4×C107—21no—
287C22×C4×C107—22no—
288C22×C4×C107—21no—
289C22×C4×C107—21no—
290C22×C4×C107—21no—
291C22×C4×C107—21no—
292C22×C4×C107—21no—
293C22×C4×C107—21no—
294C22×C4×C107—42no—
295C22×C4×C107—42no—
296C22×C4×C107C2×D412yes—
297C22×C4×C107C2×D411yescharacteristic
298C22×C4×C107C2×D411yescharacteristic
299C22×C4×C107C2×D411yescharacteristic
300C22×C4×C107C2×D411yescharacteristic
301C22×C4×C107C2×D411yescharacteristic
302C22×C4×C107C2×D412yes—
303C22×C4×C107C2411yescharacteristic
304SD16×C107—42no—
305SD16×C107—42no—
306SD16×C107—42no—
307D8×C107—42no—
308D8×C107—42no—
309D8×C107—42no—
310M16×C107—21no—
311M16×C107—21no—
312M16×C107—21no—
313M16×C107—21no—
314M16×C107—21no—
315M16×C107—21no—
316M16×C107—21no—
317M16×C107—42no—
318M16×C107C2×D412yes—
319C2×C8×C107—21no—
320C2×C8×C107—21no—
321C2×C8×C107—21no—
322C2×C8×C107—21no—
323C2×C8×C107—42no—
324C4⋊C4×C107—22no—
325C4⋊C4×C107—22no—
326C4⋊C4×C107—22no—
327C4⋊C4×C107—22no—
328C4⋊C4×C107—21no—
329C4⋊C4×C107—22no—
330C4⋊C4×C107—22no—
331C4⋊C4×C107—21no—
332C4⋊C4×C107—21no—
333C4⋊C4×C107—21no—
334C4⋊C4×C107—21no—
335C4⋊C4×C107—21no—
336C4⋊C4×C107—42no—
337C4⋊C4×C107—82no—
338C4⋊C4×C107C2×D411yescharacteristic
339C4⋊C4×C107C2×D411yescharacteristic
340C22⋊C4×C107—22no—
341C22⋊C4×C107—22no—
342C22⋊C4×C107—22no—
343C22⋊C4×C107—22no—
344C22⋊C4×C107—22no—
345C22⋊C4×C107—21no—
346C22⋊C4×C107—22no—
347C22⋊C4×C107—22no—
348C22⋊C4×C107—21no—
349C22⋊C4×C107—21no—
350C22⋊C4×C107—21no—
351C22⋊C4×C107—21no—
352C22⋊C4×C107—44no—
353C22⋊C4×C107—42no—
354C22⋊C4×C107—41no—
355C22⋊C4×C107—41no—
356C22⋊C4×C107—82no—
357C42×C107—22no—
358C42×C107—21no—
359C42×C107—21no—
360C42×C107—21no—
361C42×C107—21no—
362C42×C107C2×D412yes—
363C23×C107—21no—
364C23×C107—21no—
365C23×C107—21no—
366C23×C107—21no—
367C23×C107—21no—
368C23×C107—41no—
369C23×C107—41no—
370C23×C107—42no—
371C23×C107—42no—
372C23×C107—42no—
373C23×C107—42no—
374C23×C107—41no—
375C23×C107—41no—
376C23×C107—41no—
377C23×C107—81no—
378C23×C107#12011yescharacteristic
379C23×C107#12011yescharacteristic
380C23×C107C22×D411yescharacteristic
381Q8×C107—21no—
382Q8×C107—21no—
383Q8×C107—21no—
384Q8×C107—21no—
385Q8×C107—21no—
386Q8×C107—42no—
387Q8×C107—44no—
388Q8×C107—41no—
389Q8×C107—41no—
390Q8×C107—41no—
391Q8×C107—41no—
392Q8×C107#12112yes—
393D4×C107—22no—
394D4×C107—22no—
395D4×C107—21no—
396D4×C107—21no—
397D4×C107—21no—
398D4×C107—21no—
399D4×C107—21no—
400D4×C107—42no—
401D4×C107—42no—
402D4×C107—42no—
403D4×C107—42no—
404D4×C107—44no—
405D4×C107—41no—
406D4×C107—41no—
407D4×C107—41no—
408D4×C107—41no—
409D4×C107—41no—
410D4×C107—41no—
411D4×C107—41no—
412D4×C107—41no—
413D4×C107—81no—
414D4×C107—82no—
415D4×C107—82no—
416D4×C107—82no—
417D4×C107#12112yes—
418C2×C4×C107—21no—
419C2×C4×C107—21no—
420C2×C4×C107—21no—
421C2×C4×C107—21no—
422C2×C4×C107—21no—
423C2×C4×C107—21no—
424C2×C4×C107—21no—
425C2×C4×C107—21no—
426C2×C4×C107—21no—
427C2×C4×C107—22no—
428C2×C4×C107—21no—
429C2×C4×C107—21no—
430C2×C4×C107—22no—
431C2×C4×C107—21no—
432C2×C4×C107—22no—
433C2×C4×C107—21no—
434C2×C4×C107—21no—
435C2×C4×C107—22no—
436C2×C4×C107—21no—
437C2×C4×C107—22no—
438C2×C4×C107—22no—
439C2×C4×C107—22no—
440C2×C4×C107—42no—
441C2×C4×C107—42no—
442C2×C4×C107—42no—
443C2×C4×C107—44no—
444C2×C4×C107—41no—
445C2×C4×C107—41no—
446C2×C4×C107—44no—
447C2×C4×C107—41no—
448C2×C4×C107—41no—
449C2×C4×C107—41no—
450C2×C4×C107—41no—
451C2×C4×C107—42no—
452C2×C4×C107—41no—
453C2×C4×C107—42no—
454C2×C4×C107—41no—
455C2×C4×C107—41no—
456C2×C4×C107—41no—
457C2×C4×C107—82no—
458C2×C4×C107#12011yescharacteristic
459C2×C4×C107#12011yescharacteristic
460C2×C4×C107C22×D411yescharacteristic
461C2×C4×C107C22×D411yescharacteristic
462C2×C4×C107C22×D411yescharacteristic
463C2×C4×C107C2×#4111yescharacteristic
464C2×C4×C107H(5,𝔽2)11yescharacteristic
465C2×C4×C107H(5,𝔽2)11yescharacteristic
466C8×C107—22no—
467C8×C107—41no—
468C8×C107—41no—
469C8×C107—41no—
470C22×C107—21no—
471C22×C107—21no—
472C22×C107—21no—
473C22×C107—21no—
474C22×C107—22no—
475C22×C107—21no—
476C22×C107—21no—
477C22×C107—21no—
478C22×C107—21no—
479C22×C107—41no—
480C22×C107—41no—
481C22×C107—41no—
482C22×C107—41no—
483C22×C107—41no—
484C22×C107—41no—
485C22×C107—41no—
486C22×C107—41no—
487C22×C107—81no—
488C22×C107—81no—
489C22×C107—82no—
490C22×C107—82no—
491C22×C107—84no—
492C22×C107—81no—
493C22×C107—81no—
494C22×C107—81no—
495C22×C107C2×#12011yescharacteristic
496C22×C107D4211yescharacteristic
497C22×C107#54611yescharacteristic
498C4×C107—21no—
499C4×C107—21no—
500C4×C107—22no—
501C4×C107—42no—
502C4×C107—42no—
503C4×C107—41no—
504C4×C107—41no—
505C4×C107—41no—
506C4×C107—42no—
507C4×C107—41no—
508C4×C107—81no—
509C4×C107—81no—
510C4×C107C2×#12111yescharacteristic
511C4×C107#53411yescharacteristic
512C4×C107D4211yescharacteristic
513C4×C107#54611yescharacteristic
514#24469C10711yesmaximal, characteristic, direct product factor, Sylow
515C2×C107—21no—
516C2×C107—21no—
517C2×C107—41no—
518C2×C107—41no—
519C2×C107—42no—
520C2×C107—81no—
521C2×C107—81no—
522C2×C107—161no—
523C2×C107#241011yescharacteristic
524C2×C107#302011yescharacteristic
525C2×C107#302111yescharacteristic
526#3489C2×C10711yescharacteristic, complemented
527#3055C2×C10711yescharacteristic, complemented
528C2×#454C2×C10711yescharacteristic, complemented
529#3006C2×C10711yescharacteristic, complemented
530C2×#421C2×C10711yescharacteristic, complemented
531#2620C2×C10711yescharacteristic, complemented
532#2039C2×C10711yescharacteristic, complemented
533#2038C2×C10711yescharacteristic, complemented
534#2006C2×C10711yescharacteristic, complemented
535#2003C2×C10711yescharacteristic, complemented
536#1901C2×C10711yescharacteristic, complemented
537#1897C2×C10711yescharacteristic, complemented
538#1883C2×C10711yescharacteristic, complemented
539#1859C2×C10711yescharacteristic, complemented
540#1793C2×C10711yescharacteristic, complemented
541C107#2446911yescharacteristic, direct product factor, Sylow
542C2×2−1+4C22×C10711yescharacteristic
543C22×#41C22×C10711yescharacteristic
544C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
545C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
546C2×AGL(1,ℤ/8)C22×C10711yescharacteristic, complemented
547C22×M16C22×C10711yescharacteristic
548D4×Q8—21no—
549#548—21no—
550#547—21no—
551#547—22no—
552#546—21no—
553#546—22no—
554#537—21no—
555#537C22×C10711yescharacteristic
556#536—21no—
557#536C22×C10711yescharacteristic
558C2×#124C22×C10711yescharacteristic, complemented
559#525—21no—
560#525C22×C10711yescharacteristic
561C2×C22⋊Q8—21no—
562C2×C22⋊Q8C22×C10711yescharacteristic
563C2×#121C22×C10711yescharacteristic
564#520C22×C10711yescharacteristic
565C2×#117C22×C10711yescharacteristic
566#469—21no—
567#468—21no—
568#466—21no—
569#465—21no—
570#454—24no—
571#449—21no—
572#449—21no—
573#448—21no—
574#447—21no—
575#428C22×C10711yescharacteristic, complemented
576#421—24no—
577C2×#104C22×C10711yescharacteristic
578C2×#104C22×C10711yescharacteristic
579C2×#104C22×C10711yescharacteristic
580C2×#104C22×C10711yescharacteristic
581C2×#104C22×C10711yescharacteristic, complemented
582C2×#104C22×C10711yescharacteristic, complemented
583#418C22×C10711yescharacteristic, complemented
584#417C22×C10711yescharacteristic
585#417C22×C10711yescharacteristic
586#417C22×C10711yescharacteristic, complemented
587C2×#101C22×C10711yescharacteristic, complemented
588C2×#101C22×C10711yescharacteristic, complemented
589#407C22×C10711yescharacteristic
590#396—22no—
591#394—22no—
592#391C22×C10711yescharacteristic, complemented
593#390C22×C10711yescharacteristic, complemented
594#384C22×C10711yescharacteristic, complemented
595#343C22×C10711yescharacteristic, complemented
596#343C22×C10711yescharacteristic, complemented
597#339C22×C10711yescharacteristic, complemented
598#339C22×C10711yescharacteristic, complemented
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C10711yescharacteristic
613C2×#41D4×C10711yescharacteristic
614C2×#41C23×C10711yescharacteristic
615C2×#41C23×C10711yescharacteristic
616C2×#41C23×C10711yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C10711yescharacteristic
620C22×Q8C23×C10711yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C10711yescharacteristic
624C22×D4C23×C10711yescharacteristic
625C23×C4—21no—
626C23×C4C23×C10711yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C10711yescharacteristic
643C2×M16C23×C10711yescharacteristic
644C2×M16C23×C10711yescharacteristic
645C2×M16C23×C10711yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C10711yescharacteristic
670C22⋊Q8D4×C10711yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C10711yescharacteristic
682#121D4×C10711yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C10711yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C10712yes—
701C2×C4⋊C4C23×C10711yescharacteristic
702C2×C4⋊C4C23×C10711yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C10712yes—
709C2×C42C23×C10711yescharacteristic
710C2×C42C23×C10711yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C10714yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C10711yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C10712yes—
760#41#41×C10712yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C10711yescharacteristic
776C2×Q8C2×D4×C10711yescharacteristic
777C2×Q8C2×D4×C10711yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C10711yescharacteristic
802C2×D4C2×D4×C10711yescharacteristic
803C2×D4C2×D4×C10711yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C10712yes—
823C22×C4C2×D4×C10711yescharacteristic
824C22×C4C2×D4×C10711yescharacteristic
825C22×C4C2×D4×C10711yescharacteristic
826C22×C4C2×D4×C10711yescharacteristic
827C22×C4C2×D4×C10711yescharacteristic
828C22×C4C2×D4×C10712yes—
829C22×C4C24×C10711yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C10712yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C10711yescharacteristic
865C4⋊C4C2×D4×C10711yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C10712yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C10711yescharacteristic
905C23#120×C10711yescharacteristic
906C23C22×D4×C10711yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C10712yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C10712yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C10711yescharacteristic
985C2×C4#120×C10711yescharacteristic
986C2×C4C22×D4×C10711yescharacteristic
987C2×C4C22×D4×C10711yescharacteristic
988C2×C4C22×D4×C10711yescharacteristic
989C2×C4C2×#41×C10711yescharacteristic
990C2×C4H(5,𝔽2)×C10711yescharacteristic
991C2×C4H(5,𝔽2)×C10711yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C10711yescharacteristic
1022C22D42×C10711yescharacteristic
1023C22#546×C10711yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C10711yescharacteristic
1037C4#534×C10711yescharacteristic
1038C4D42×C10711yescharacteristic
1039C4#546×C10711yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C107×#241011yescharacteristic
1049C2C107×#302011yescharacteristic
1050C2C107×#302111yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3489C2semidirect
2. C107×#3055C2semidirect
3. C2×#454×C107C2semidirect
4. C107×#3006C2semidirect
5. C2×#421×C107C2semidirect
6. C107×#2620C2semidirect
7. C107×#2039C2semidirect
8. C107×#2038C2semidirect
9. C107×#2006C2semidirect
10. C107×#2003C2semidirect
11. C107×#1901C2semidirect
12. C107×#1897C2semidirect
13. C107×#1883C2semidirect
14. C107×#1859C2semidirect
15. C107×#1793C2semidirect
20. C2×AGL(1,ℤ/8)×C107C22semidirect
32. C2×#124×C107C22semidirect
49. #428×C107C22semidirect
55. C2×#104×C107C22semidirect
56. C2×#104×C107C22semidirect
57. #418×C107C22semidirect
60. #417×C107C22semidirect
61. C2×#101×C107C22semidirect
62. C2×#101×C107C22semidirect
66. #391×C107C22semidirect
67. #390×C107C22semidirect
68. #384×C107C22semidirect
69. #343×C107C22semidirect
70. #343×C107C22semidirect
71. #339×C107C22semidirect
72. #339×C107C22semidirect
192. #104×C107D4semidirect
514. #24469C107direct (N × H)
526. #3489C2×C107semidirect
527. #3055C2×C107semidirect
528. C2×#454C2×C107semidirect
529. #3006C2×C107semidirect
530. C2×#421C2×C107semidirect
531. #2620C2×C107semidirect
532. #2039C2×C107semidirect
533. #2038C2×C107semidirect
534. #2006C2×C107semidirect
535. #2003C2×C107semidirect
536. #1901C2×C107semidirect
537. #1897C2×C107semidirect
538. #1883C2×C107semidirect
539. #1859C2×C107semidirect
540. #1793C2×C107semidirect
541. C107#24469direct (N × H)
546. C2×AGL(1,ℤ/8)C22×C107semidirect
558. C2×#124C22×C107semidirect
575. #428C22×C107semidirect
581. C2×#104C22×C107semidirect
582. C2×#104C22×C107semidirect
583. #418C22×C107semidirect
586. #417C22×C107semidirect
587. C2×#101C22×C107semidirect
588. C2×#101C22×C107semidirect
592. #391C22×C107semidirect
593. #390C22×C107semidirect
594. #384C22×C107semidirect
595. #343C22×C107semidirect
596. #343C22×C107semidirect
597. #339C22×C107semidirect
598. #339C22×C107semidirect
718. #104D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34892
C107×#30552
C2×#454×C1072
C107×#30062
C2×#421×C1072
C107×#26202
C107×#20392
C107×#20382
C107×#20062
C107×#20032
C107×#19012
C107×#18972
C107×#18832
C107×#18592
C107×#17932
#24469107