Finite Group Databasebeta

← C107×#24467 #41050431

Subgroups — C107×#24467 #41050431

Order 27392.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3488C211yesmaximal, characteristic
2C107×#3056C211yesmaximal, characteristic, complemented
3C2×#455×C107C211yesmaximal, characteristic, complemented
4C107×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C107C211yesmaximal, characteristic, complemented
6C107×#2850C211yesmaximal, characteristic, complemented
7C107×#2040C211yesmaximal, characteristic, complemented
8C107×#2037C211yesmaximal, characteristic, complemented
9C107×#2007C211yesmaximal, characteristic, complemented
10C107×#2004C211yesmaximal, characteristic, complemented
11C107×#1900C211yesmaximal, characteristic, complemented
12C107×#1896C211yesmaximal, characteristic, complemented
13C107×#1882C211yesmaximal, characteristic, complemented
14C107×#1860C211yesmaximal, characteristic, complemented
15C107×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic
18C2×#137×C107C2211yescharacteristic
19C2×#137×C107C2211yescharacteristic, complemented
20C2×#137×C107C2211yescharacteristic, complemented
21C22×M16×C107C2211yescharacteristic, complemented
22#550×C107—21no—
23#548×C107—21no—
24#546×C107—21no—
25#546×C107—22no—
26D42×C107—22no—
27D42×C107—21no—
28#537×C107—21no—
29#537×C107C2211yescharacteristic
30#535×C107—21no—
31#535×C107C2211yescharacteristic
32C2×#124×C107C2211yescharacteristic, complemented
33#525×C107—21no—
34#525×C107C2211yescharacteristic
35C2×C22⋊Q8×C107C2211yescharacteristic, complemented
36C2×#121×C107—21no—
37C2×#121×C107C2211yescharacteristic
38#520×C107C2211yescharacteristic
39C22×C42×C107C2211yescharacteristic, complemented
40#470×C107—21no—
41#468×C107—21no—
42#467×C107—21no—
43#465×C107—21no—
44#455×C107—24no—
45#452×C107—21no—
46#452×C107—21no—
47#451×C107—21no—
48#450×C107—21no—
49#428×C107C2211yescharacteristic, complemented
50C2×#104×C107—24no—
51C2×#104×C107C2211yescharacteristic
52C2×#104×C107C2211yescharacteristic
53C2×#104×C107C2211yescharacteristic, complemented
54C2×#104×C107C2211yescharacteristic, complemented
55C2×#104×C107C2211yescharacteristic, complemented
56C2×#104×C107C2211yescharacteristic, complemented
57#419×C107C2211yescharacteristic, complemented
58#417×C107C2211yescharacteristic
59#417×C107C2211yescharacteristic, complemented
60#417×C107C2211yescharacteristic, complemented
61C2×#100×C107C2211yescharacteristic, complemented
62C2×#100×C107C2211yescharacteristic, complemented
63#407×C107C2211yescharacteristic, complemented
64#391×C107C2211yescharacteristic, complemented
65#390×C107C2211yescharacteristic, complemented
66#388×C107—22no—
67#386×C107—22no—
68#382×C107C2211yescharacteristic, complemented
69#343×C107C2211yescharacteristic, complemented
70#343×C107C2211yescharacteristic, complemented
71#339×C107C2211yescharacteristic, complemented
72#339×C107C2211yescharacteristic, complemented
73H(5,𝔽2)×C107—22no—
74H(5,𝔽2)×C107—22no—
75H(5,𝔽2)×C107—41no—
76H(5,𝔽2)×C107—41no—
77C2×#41×C107—21no—
78C2×#41×C107—21no—
79C2×#41×C107—21no—
80C2×#41×C107—21no—
81C2×#41×C107—22no—
82C2×#41×C107—22no—
83C2×#41×C107—41no—
84C2×#41×C107—41no—
85C2×#41×C107D411yescharacteristic
86C2×#41×C107D411yescharacteristic
87C2×#41×C107C2311yescharacteristic
88C2×#41×C107C2311yescharacteristic
89C2×#41×C107C2311yescharacteristic
90C22×Q8×C107D411yescharacteristic
91C22×Q8×C107C2311yescharacteristic
92C22×D4×C107—21no—
93C22×D4×C107—22no—
94C22×D4×C107—22no—
95C22×D4×C107—21no—
96C22×D4×C107—21no—
97C22×D4×C107D411yescharacteristic
98C22×D4×C107D412yes—
99C22×D4×C107C2311yescharacteristic
100C23×C4×C107—21no—
101C23×C4×C107—21no—
102C23×C4×C107C2311yescharacteristic
103#137×C107—22no—
104#137×C107—22no—
105#137×C107—22no—
106#137×C107—41no—
107#137×C107—41no—
108#137×C107—41no—
109C2×Q16×C107—21no—
110C2×Q16×C107—21no—
111C2×Q16×C107—21no—
112C2×SD16×C107—21no—
113C2×SD16×C107—21no—
114C2×SD16×C107—21no—
115C2×M16×C107—21no—
116C2×M16×C107—22no—
117C2×M16×C107—41no—
118C2×M16×C107C2311yescharacteristic
119C2×M16×C107C2311yescharacteristic
120C2×M16×C107C2311yescharacteristic
121C2×M16×C107C2311yescharacteristic
122C22×C8×C107—21no—
123#127×C107—22no—
124#127×C107—21no—
125#124×C107—22no—
126#124×C107—21no—
127#124×C107—22no—
128#124×C107—41no—
129#123×C107—22no—
130#123×C107—21no—
131C22⋊Q8×C107—22no—
132C22⋊Q8×C107—21no—
133C22⋊Q8×C107—21no—
134C22⋊Q8×C107—21no—
135C22⋊Q8×C107—21no—
136C22⋊Q8×C107—21no—
137C22⋊Q8×C107—21no—
138C22⋊Q8×C107D411yescharacteristic
139C22⋊Q8×C107D411yescharacteristic
140#121×C107—22no—
141#121×C107—22no—
142#121×C107—22no—
143#121×C107—22no—
144#121×C107—22no—
145#121×C107—21no—
146#121×C107—21no—
147#121×C107—21no—
148#121×C107—21no—
149#121×C107—21no—
150#121×C107—21no—
151#121×C107—22no—
152#121×C107—21no—
153#121×C107—21no—
154#121×C107D411yescharacteristic
155#121×C107D411yescharacteristic
156#120×C107—22no—
157#120×C107—22no—
158#120×C107—22no—
159#120×C107—21no—
160#120×C107—22no—
161C4×Q8×C107—21no—
162C4×D4×C107—22no—
163C4×D4×C107—22no—
164C4×D4×C107—21no—
165C4×D4×C107—22no—
166C4×D4×C107—21no—
167C4×D4×C107—21no—
168#117×C107—21no—
169#117×C107C2311yescharacteristic
170C2×C4⋊C4×C107—21no—
171C2×C4⋊C4×C107—21no—
172C2×C4⋊C4×C107C2311yescharacteristic
173C2×C4⋊C4×C107C2311yescharacteristic
174C2×C22⋊C4×C107—22no—
175C2×C22⋊C4×C107—21no—
176C2×C22⋊C4×C107—22no—
177C2×C22⋊C4×C107—22no—
178C2×C22⋊C4×C107D412yes—
179C2×C42×C107—22no—
180C2×C42×C107—21no—
181C2×C42×C107—41no—
182C2×C42×C107C2311yescharacteristic
183C2×C42×C107C2311yescharacteristic
184#107×C107—21no—
185#106×C107—21no—
186#104×C107—22no—
187#104×C107—22no—
188#104×C107—22no—
189#104×C107—22no—
190#104×C107—41no—
191#104×C107D414yescomplemented
192#103×C107—21no—
193#103×C107—21no—
194#103×C107—21no—
195#103×C107—21no—
196#103×C107—21no—
197#102×C107—21no—
198#102×C107—21no—
199#102×C107—21no—
200#100×C107—22no—
201#100×C107—41no—
202C22⋊C8×C107—21no—
203C22⋊C8×C107—21no—
204#95×C107—22no—
205#95×C107—22no—
206C24×C107—22no—
207C24×C107—21no—
208C24×C107C2×D411yescharacteristic
209C24×C107C2×D412yes—
210#41×C107—21no—
211#41×C107—21no—
212#41×C107—22no—
213#41×C107—22no—
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—21no—
222#41×C107—42no—
223#41×C107—42no—
224#41×C107—41no—
225#41×C107—41no—
226#41×C107—42no—
227#41×C107—42no—
228#41×C107—42no—
229#41×C107—42no—
230#41×C107—42no—
231#41×C107—42no—
232#41×C107C2×D412yes—
233#41×C107#4112yes—
234C2×Q8×C107—21no—
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—41no—
243C2×Q8×C107C2×D411yescharacteristic
244C2×Q8×C107C2×D411yescharacteristic
245C2×Q8×C107C2×D411yescharacteristic
246C2×D4×C107—21no—
247C2×D4×C107—22no—
248C2×D4×C107—22no—
249C2×D4×C107—22no—
250C2×D4×C107—22no—
251C2×D4×C107—21no—
252C2×D4×C107—21no—
253C2×D4×C107—21no—
254C2×D4×C107—21no—
255C2×D4×C107—21no—
256C2×D4×C107—22no—
257C2×D4×C107—22no—
258C2×D4×C107—22no—
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—41no—
269C2×D4×C107—42no—
270C2×D4×C107—42no—
271C2×D4×C107—42no—
272C2×D4×C107—42no—
273C2×D4×C107—44no—
274C2×D4×C107—44no—
275C2×D4×C107—42no—
276C2×D4×C107—42no—
277C2×D4×C107—44no—
278C2×D4×C107—84no—
279C2×D4×C107C2×D411yescharacteristic
280C2×D4×C107C2×D411yescharacteristic
281C2×D4×C107C2×D411yescharacteristic
282C22×C4×C107—21no—
283C22×C4×C107—21no—
284C22×C4×C107—21no—
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—22no—
292C22×C4×C107—21no—
293C22×C4×C107—21no—
294C22×C4×C107—21no—
295C22×C4×C107—21no—
296C22×C4×C107—21no—
297C22×C4×C107—21no—
298C22×C4×C107—42no—
299C22×C4×C107—42no—
300C22×C4×C107—42no—
301C22×C4×C107—42no—
302C22×C4×C107—42no—
303C22×C4×C107C2×D411yescharacteristic
304C22×C4×C107C2×D411yescharacteristic
305C22×C4×C107C2×D411yescharacteristic
306C22×C4×C107C2×D411yescharacteristic
307C22×C4×C107C2×D411yescharacteristic
308C22×C4×C107C2×D412yes—
309C22×C4×C107C2411yescharacteristic
310Q16×C107—42no—
311Q16×C107—42no—
312Q16×C107—42no—
313SD16×C107—42no—
314SD16×C107—42no—
315SD16×C107—42no—
316M16×C107—21no—
317M16×C107—21no—
318M16×C107—21no—
319M16×C107—21no—
320M16×C107—21no—
321M16×C107—21no—
322M16×C107—21no—
323M16×C107—42no—
324M16×C107C2×D412yescomplemented
325C2×C8×C107—21no—
326C2×C8×C107—21no—
327C2×C8×C107—21no—
328C2×C8×C107—21no—
329C2×C8×C107—42no—
330C4⋊C4×C107—22no—
331C4⋊C4×C107—22no—
332C4⋊C4×C107—21no—
333C4⋊C4×C107—21no—
334C4⋊C4×C107—21no—
335C4⋊C4×C107—21no—
336C4⋊C4×C107—21no—
337C4⋊C4×C107—21no—
338C4⋊C4×C107—41no—
339C4⋊C4×C107—41no—
340C4⋊C4×C107C2×D411yescharacteristic
341C4⋊C4×C107C2×D411yescharacteristic
342C22⋊C4×C107—22no—
343C22⋊C4×C107—22no—
344C22⋊C4×C107—22no—
345C22⋊C4×C107—22no—
346C22⋊C4×C107—22no—
347C22⋊C4×C107—21no—
348C22⋊C4×C107—21no—
349C22⋊C4×C107—21no—
350C22⋊C4×C107—21no—
351C22⋊C4×C107—22no—
352C22⋊C4×C107—22no—
353C22⋊C4×C107—21no—
354C22⋊C4×C107—44no—
355C22⋊C4×C107—44no—
356C22⋊C4×C107—41no—
357C22⋊C4×C107—41no—
358C42×C107—22no—
359C42×C107—21no—
360C42×C107—21no—
361C42×C107—21no—
362C42×C107—21no—
363C42×C107—42no—
364C42×C107C2×D412yescomplemented
365C23×C107—21no—
366C23×C107—21no—
367C23×C107—21no—
368C23×C107—22no—
369C23×C107—22no—
370C23×C107—21no—
371C23×C107—21no—
372C23×C107—22no—
373C23×C107—22no—
374C23×C107—41no—
375C23×C107—42no—
376C23×C107—44no—
377C23×C107—42no—
378C23×C107—42no—
379C23×C107—42no—
380C23×C107—81no—
381C23×C107—82no—
382C23×C107—82no—
383C23×C107#12011yescharacteristic
384C23×C107#12011yescharacteristic
385C23×C107C22×D411yescharacteristic
386Q8×C107—21no—
387Q8×C107—21no—
388Q8×C107—21no—
389Q8×C107—21no—
390Q8×C107—21no—
391Q8×C107—42no—
392Q8×C107—41no—
393Q8×C107—41no—
394Q8×C107—41no—
395Q8×C107—41no—
396Q8×C107#12112yes—
397D4×C107—22no—
398D4×C107—22no—
399D4×C107—21no—
400D4×C107—21no—
401D4×C107—21no—
402D4×C107—21no—
403D4×C107—21no—
404D4×C107—42no—
405D4×C107—42no—
406D4×C107—44no—
407D4×C107—42no—
408D4×C107—44no—
409D4×C107—41no—
410D4×C107—41no—
411D4×C107—41no—
412D4×C107—41no—
413D4×C107—44no—
414D4×C107—42no—
415D4×C107—41no—
416D4×C107—41no—
417D4×C107—41no—
418D4×C107—41no—
419D4×C107—81no—
420D4×C107—82no—
421D4×C107—82no—
422D4×C107—82no—
423D4×C107—82no—
424D4×C107#12112yes—
425C2×C4×C107—21no—
426C2×C4×C107—21no—
427C2×C4×C107—21no—
428C2×C4×C107—21no—
429C2×C4×C107—21no—
430C2×C4×C107—21no—
431C2×C4×C107—21no—
432C2×C4×C107—21no—
433C2×C4×C107—21no—
434C2×C4×C107—22no—
435C2×C4×C107—21no—
436C2×C4×C107—21no—
437C2×C4×C107—22no—
438C2×C4×C107—22no—
439C2×C4×C107—21no—
440C2×C4×C107—22no—
441C2×C4×C107—21no—
442C2×C4×C107—21no—
443C2×C4×C107—21no—
444C2×C4×C107—22no—
445C2×C4×C107—42no—
446C2×C4×C107—42no—
447C2×C4×C107—42no—
448C2×C4×C107—44no—
449C2×C4×C107—41no—
450C2×C4×C107—41no—
451C2×C4×C107—41no—
452C2×C4×C107—48no—
453C2×C4×C107—41no—
454C2×C4×C107—41no—
455C2×C4×C107—41no—
456C2×C4×C107—41no—
457C2×C4×C107—41no—
458C2×C4×C107—42no—
459C2×C4×C107—42no—
460C2×C4×C107—41no—
461C2×C4×C107—41no—
462C2×C4×C107—41no—
463C2×C4×C107—41no—
464C2×C4×C107—82no—
465C2×C4×C107#12011yescharacteristic
466C2×C4×C107#12011yescharacteristic
467C2×C4×C107C22×D411yescharacteristic
468C2×C4×C107C22×D411yescharacteristic
469C2×C4×C107C22×D411yescharacteristic
470C2×C4×C107C2×#4111yescharacteristic
471C2×C4×C107H(5,𝔽2)11yescharacteristic
472C2×C4×C107H(5,𝔽2)11yescharacteristic
473C8×C107—22no—
474C8×C107—41no—
475C8×C107—41no—
476C8×C107—41no—
477C22×C107—21no—
478C22×C107—21no—
479C22×C107—21no—
480C22×C107—21no—
481C22×C107—21no—
482C22×C107—22no—
483C22×C107—21no—
484C22×C107—21no—
485C22×C107—42no—
486C22×C107—42no—
487C22×C107—41no—
488C22×C107—41no—
489C22×C107—41no—
490C22×C107—41no—
491C22×C107—42no—
492C22×C107—42no—
493C22×C107—41no—
494C22×C107—41no—
495C22×C107—41no—
496C22×C107—42no—
497C22×C107—41no—
498C22×C107—84no—
499C22×C107—82no—
500C22×C107—82no—
501C22×C107—164no—
502C22×C107#45512yescomplemented
503C22×C107C2×#12011yescharacteristic
504C22×C107D4211yescharacteristic
505C22×C107#54611yescharacteristic
506C4×C107—21no—
507C4×C107—21no—
508C4×C107—22no—
509C4×C107—42no—
510C4×C107—42no—
511C4×C107—41no—
512C4×C107—41no—
513C4×C107—42no—
514C4×C107—41no—
515C4×C107—41no—
516C4×C107—81no—
517C4×C107—81no—
518C4×C107C2×#12111yescharacteristic
519C4×C107#53411yescharacteristic
520C4×C107D4211yescharacteristic
521C4×C107#54611yescharacteristic
522#24467C10711yesmaximal, characteristic, direct product factor, Sylow
523C2×C107—21no—
524C2×C107—21no—
525C2×C107—22no—
526C2×C107—41no—
527C2×C107—42no—
528C2×C107—81no—
529C2×C107—82no—
530C2×C107—81no—
531C2×C107#241011yescharacteristic
532C2×C107C2×#45511yescharacteristic
533C2×C107#301811yescharacteristic
534#3488C2×C10711yescharacteristic
535#3056C2×C10711yescharacteristic, complemented
536C2×#455C2×C10711yescharacteristic, complemented
537#3007C2×C10711yescharacteristic, complemented
538C22×#104C2×C10711yescharacteristic, complemented
539#2850C2×C10711yescharacteristic, complemented
540#2040C2×C10711yescharacteristic, complemented
541#2037C2×C10711yescharacteristic, complemented
542#2007C2×C10711yescharacteristic, complemented
543#2004C2×C10711yescharacteristic, complemented
544#1900C2×C10711yescharacteristic, complemented
545#1896C2×C10711yescharacteristic, complemented
546#1882C2×C10711yescharacteristic, complemented
547#1860C2×C10711yescharacteristic, complemented
548#1792C2×C10711yescharacteristic, complemented
549C107#2446711yescharacteristic, direct product factor, Sylow
550C2×H(5,𝔽2)C22×C10711yescharacteristic
551C22×#41C22×C10711yescharacteristic
552C2×#137C22×C10711yescharacteristic
553C2×#137C22×C10711yescharacteristic, complemented
554C2×#137C22×C10711yescharacteristic, complemented
555C22×M16C22×C10711yescharacteristic, complemented
556#550—21no—
557#548—21no—
558#546—21no—
559#546—22no—
560D42—22no—
561D42—21no—
562#537—21no—
563#537C22×C10711yescharacteristic
564#535—21no—
565#535C22×C10711yescharacteristic
566C2×#124C22×C10711yescharacteristic, complemented
567#525—21no—
568#525C22×C10711yescharacteristic
569C2×C22⋊Q8C22×C10711yescharacteristic, complemented
570C2×#121—21no—
571C2×#121C22×C10711yescharacteristic
572#520C22×C10711yescharacteristic
573C22×C42C22×C10711yescharacteristic, complemented
574#470—21no—
575#468—21no—
576#467—21no—
577#465—21no—
578#455—24no—
579#452—21no—
580#452—21no—
581#451—21no—
582#450—21no—
583#428C22×C10711yescharacteristic, complemented
584C2×#104—24no—
585C2×#104C22×C10711yescharacteristic
586C2×#104C22×C10711yescharacteristic
587C2×#104C22×C10711yescharacteristic, complemented
588C2×#104C22×C10711yescharacteristic, complemented
589C2×#104C22×C10711yescharacteristic, complemented
590C2×#104C22×C10711yescharacteristic, complemented
591#419C22×C10711yescharacteristic, complemented
592#417C22×C10711yescharacteristic
593#417C22×C10711yescharacteristic, complemented
594#417C22×C10711yescharacteristic, complemented
595C2×#100C22×C10711yescharacteristic, complemented
596C2×#100C22×C10711yescharacteristic, complemented
597#407C22×C10711yescharacteristic, complemented
598#391C22×C10711yescharacteristic, complemented
599#390C22×C10711yescharacteristic, complemented
600#388—22no—
601#386—22no—
602#382C22×C10711yescharacteristic, complemented
603#343C22×C10711yescharacteristic, complemented
604#343C22×C10711yescharacteristic, complemented
605#339C22×C10711yescharacteristic, complemented
606#339C22×C10711yescharacteristic, complemented
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C10711yescharacteristic
620C2×#41D4×C10711yescharacteristic
621C2×#41C23×C10711yescharacteristic
622C2×#41C23×C10711yescharacteristic
623C2×#41C23×C10711yescharacteristic
624C22×Q8D4×C10711yescharacteristic
625C22×Q8C23×C10711yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C10711yescharacteristic
632C22×D4D4×C10712yes—
633C22×D4C23×C10711yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C10711yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C10711yescharacteristic
653C2×M16C23×C10711yescharacteristic
654C2×M16C23×C10711yescharacteristic
655C2×M16C23×C10711yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C10711yescharacteristic
673C22⋊Q8D4×C10711yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C10711yescharacteristic
689#121D4×C10711yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C10711yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C10711yescharacteristic
707C2×C4⋊C4C23×C10711yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C10712yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C10711yescharacteristic
717C2×C42C23×C10711yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C10714yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C10711yescharacteristic
743C24C2×D4×C10712yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C10712yes—
767#41#41×C10712yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C10711yescharacteristic
778C2×Q8C2×D4×C10711yescharacteristic
779C2×Q8C2×D4×C10711yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C10711yescharacteristic
814C2×D4C2×D4×C10711yescharacteristic
815C2×D4C2×D4×C10711yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C10711yescharacteristic
838C22×C4C2×D4×C10711yescharacteristic
839C22×C4C2×D4×C10711yescharacteristic
840C22×C4C2×D4×C10711yescharacteristic
841C22×C4C2×D4×C10711yescharacteristic
842C22×C4C2×D4×C10712yes—
843C22×C4C24×C10711yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C10712yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C10711yescharacteristic
875C4⋊C4C2×D4×C10711yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C10712yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C10711yescharacteristic
918C23#120×C10711yescharacteristic
919C23C22×D4×C10711yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C10712yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C10712yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C10711yescharacteristic
1000C2×C4#120×C10711yescharacteristic
1001C2×C4C22×D4×C10711yescharacteristic
1002C2×C4C22×D4×C10711yescharacteristic
1003C2×C4C22×D4×C10711yescharacteristic
1004C2×C4C2×#41×C10711yescharacteristic
1005C2×C4H(5,𝔽2)×C10711yescharacteristic
1006C2×C4H(5,𝔽2)×C10711yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22#455×C10712yescomplemented
1037C22C2×#120×C10711yescharacteristic
1038C22D42×C10711yescharacteristic
1039C22#546×C10711yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C10711yescharacteristic
1053C4#534×C10711yescharacteristic
1054C4D42×C10711yescharacteristic
1055C4#546×C10711yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C107×#241011yescharacteristic
1065C2C2×#455×C10711yescharacteristic
1066C2C107×#301811yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3488C2
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
2. C107×#3056C2semidirect
3. C2×#455×C107C2semidirect
4. C107×#3007C2semidirect
5. C22×#104×C107C2semidirect
6. C107×#2850C2semidirect
7. C107×#2040C2semidirect
8. C107×#2037C2semidirect
9. C107×#2007C2semidirect
10. C107×#2004C2semidirect
11. C107×#1900C2semidirect
12. C107×#1896C2semidirect
13. C107×#1882C2semidirect
14. C107×#1860C2semidirect
15. C107×#1792C2semidirect
19. C2×#137×C107C22semidirect
20. C2×#137×C107C22semidirect
21. C22×M16×C107C22semidirect
32. C2×#124×C107C22semidirect
35. C2×C22⋊Q8×C107C22semidirect
39. C22×C42×C107C22semidirect
49. #428×C107C22semidirect
53. C2×#104×C107C22semidirect
54. C2×#104×C107C22semidirect
55. C2×#104×C107C22semidirect
56. C2×#104×C107C22semidirect
57. #419×C107C22semidirect
59. #417×C107C22semidirect
60. #417×C107C22semidirect
61. C2×#100×C107C22semidirect
62. C2×#100×C107C22semidirect
63. #407×C107C22semidirect
64. #391×C107C22semidirect
65. #390×C107C22semidirect
68. #382×C107C22semidirect
69. #343×C107C22semidirect
70. #343×C107C22semidirect
71. #339×C107C22semidirect
72. #339×C107C22semidirect
191. #104×C107D4semidirect
324. M16×C107C2×D4semidirect
364. C42×C107C2×D4semidirect
502. C22×C107#455semidirect
522. #24467C107direct (N × H)
535. #3056C2×C107semidirect
536. C2×#455C2×C107semidirect
537. #3007C2×C107semidirect
538. C22×#104C2×C107semidirect
539. #2850C2×C107semidirect
540. #2040C2×C107semidirect
541. #2037C2×C107semidirect
542. #2007C2×C107semidirect
543. #2004C2×C107semidirect
544. #1900C2×C107semidirect
545. #1896C2×C107semidirect
546. #1882C2×C107semidirect
547. #1860C2×C107semidirect
548. #1792C2×C107semidirect
549. C107#24467direct (N × H)
553. C2×#137C22×C107semidirect
554. C2×#137C22×C107semidirect
555. C22×M16C22×C107semidirect
566. C2×#124C22×C107semidirect
569. C2×C22⋊Q8C22×C107semidirect
573. C22×C42C22×C107semidirect
583. #428C22×C107semidirect
587. C2×#104C22×C107semidirect
588. C2×#104C22×C107semidirect
589. C2×#104C22×C107semidirect
590. C2×#104C22×C107semidirect
591. #419C22×C107semidirect
593. #417C22×C107semidirect
594. #417C22×C107semidirect
595. C2×#100C22×C107semidirect
596. C2×#100C22×C107semidirect
597. #407C22×C107semidirect
598. #391C22×C107semidirect
599. #390C22×C107semidirect
602. #382C22×C107semidirect
603. #343C22×C107semidirect
604. #343C22×C107semidirect
605. #339C22×C107semidirect
606. #339C22×C107semidirect
725. #104D4×C107semidirect
858. M16C2×D4×C107semidirect
898. C42C2×D4×C107semidirect
1036. C22#455×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34882
C107×#30562
C2×#455×C1072
C107×#30072
C22×#104×C1072
C107×#28502
C107×#20402
C107×#20372
C107×#20072
C107×#20042
C107×#19002
C107×#18962
C107×#18822
C107×#18602
C107×#17922
#24467107