Finite Group Databasebeta

← C107×#24471 #41050435

Subgroups — C107×#24471 #41050435

Order 27392.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 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
5C2×#421×C107C211yesmaximal, characteristic, complemented
6C107×#2620C211yesmaximal, characteristic, complemented
7C107×#2039C211yesmaximal, characteristic, complemented
8C107×#2037C211yesmaximal, characteristic, complemented
9C107×#2007C211yesmaximal, characteristic, complemented
10C107×#2004C211yesmaximal, characteristic, complemented
11C107×#1900C211yesmaximal, characteristic, complemented
12C107×#1897C211yesmaximal, characteristic, complemented
13C107×#1882C211yesmaximal, characteristic, complemented
14C107×#1859C211yesmaximal, 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
39C2×#117×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
50#421×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#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
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×C107C2311yescharacteristic
102#137×C107—22no—
103#137×C107—22no—
104#137×C107—22no—
105#137×C107—41no—
106#137×C107—41no—
107#137×C107—41no—
108C2×Q16×C107—21no—
109C2×Q16×C107—21no—
110C2×Q16×C107—21no—
111C2×SD16×C107—21no—
112C2×SD16×C107—21no—
113C2×SD16×C107—21no—
114C2×M16×C107—21no—
115C2×M16×C107—22no—
116C2×M16×C107—41no—
117C2×M16×C107C2311yescharacteristic
118C2×M16×C107C2311yescharacteristic
119C2×M16×C107C2311yescharacteristic
120C2×M16×C107C2311yescharacteristic
121C22×C8×C107—21no—
122#127×C107—22no—
123#127×C107—21no—
124#124×C107—22no—
125#124×C107—21no—
126#124×C107—22no—
127#124×C107—41no—
128#123×C107—22no—
129#123×C107—21no—
130C22⋊Q8×C107—22no—
131C22⋊Q8×C107—21no—
132C22⋊Q8×C107—21no—
133C22⋊Q8×C107—21no—
134C22⋊Q8×C107—21no—
135C22⋊Q8×C107—21no—
136C22⋊Q8×C107—21no—
137C22⋊Q8×C107D411yescharacteristic
138C22⋊Q8×C107D411yescharacteristic
139#121×C107—22no—
140#121×C107—22no—
141#121×C107—22no—
142#121×C107—22no—
143#121×C107—22no—
144#121×C107—21no—
145#121×C107—21no—
146#121×C107—21no—
147#121×C107—21no—
148#121×C107—21no—
149#121×C107—21no—
150#121×C107—22no—
151#121×C107—21no—
152#121×C107—21no—
153#121×C107D411yescharacteristic
154#121×C107D411yescharacteristic
155#120×C107—22no—
156#120×C107—22no—
157#120×C107—22no—
158#120×C107—21no—
159#120×C107—22no—
160C4×Q8×C107—21no—
161C4×D4×C107—22no—
162C4×D4×C107—22no—
163C4×D4×C107—21no—
164C4×D4×C107—22no—
165C4×D4×C107—21no—
166C4×D4×C107—21no—
167#117×C107—21no—
168#117×C107—22no—
169#117×C107—41no—
170#117×C107C2311yescharacteristic
171C2×C4⋊C4×C107—21no—
172C2×C4⋊C4×C107—21no—
173C2×C4⋊C4×C107—21no—
174C2×C4⋊C4×C107—22no—
175C2×C4⋊C4×C107C2311yescharacteristic
176C2×C4⋊C4×C107C2311yescharacteristic
177C2×C22⋊C4×C107—22no—
178C2×C22⋊C4×C107—21no—
179C2×C22⋊C4×C107—21no—
180C2×C22⋊C4×C107—22no—
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#103×C107—21no—
197#103×C107—21no—
198#102×C107—21no—
199#102×C107—21no—
200#102×C107—21no—
201#100×C107—22no—
202#100×C107—41no—
203C22⋊C8×C107—21no—
204C22⋊C8×C107—21no—
205#95×C107—22no—
206C24×C107—22no—
207C24×C107—21no—
208C24×C107C2×D412yes—
209C24×C107C2×D411yescharacteristic
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—82no—
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—22no—
291C22×C4×C107—21no—
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×C107C2×D411yescharacteristic
301C22×C4×C107C2×D411yescharacteristic
302C22×C4×C107C2×D411yescharacteristic
303C22×C4×C107C2×D411yescharacteristic
304C22×C4×C107C2×D411yescharacteristic
305C22×C4×C107C2×D412yes—
306C22×C4×C107C2411yescharacteristic
307Q16×C107—42no—
308Q16×C107—42no—
309Q16×C107—42no—
310SD16×C107—42no—
311SD16×C107—42no—
312SD16×C107—42no—
313M16×C107—21no—
314M16×C107—21no—
315M16×C107—21no—
316M16×C107—21no—
317M16×C107—21no—
318M16×C107—21no—
319M16×C107—21no—
320M16×C107—42no—
321M16×C107C2×D412yescomplemented
322C2×C8×C107—21no—
323C2×C8×C107—21no—
324C2×C8×C107—21no—
325C2×C8×C107—21no—
326C2×C8×C107—42no—
327C4⋊C4×C107—22no—
328C4⋊C4×C107—22no—
329C4⋊C4×C107—21no—
330C4⋊C4×C107—21no—
331C4⋊C4×C107—21no—
332C4⋊C4×C107—21no—
333C4⋊C4×C107—21no—
334C4⋊C4×C107—21no—
335C4⋊C4×C107—42no—
336C4⋊C4×C107—41no—
337C4⋊C4×C107—41no—
338C4⋊C4×C107—82no—
339C4⋊C4×C107C2×D411yescharacteristic
340C4⋊C4×C107C2×D411yescharacteristic
341C22⋊C4×C107—22no—
342C22⋊C4×C107—22no—
343C22⋊C4×C107—22no—
344C22⋊C4×C107—22no—
345C22⋊C4×C107—22no—
346C22⋊C4×C107—21no—
347C22⋊C4×C107—21no—
348C22⋊C4×C107—21no—
349C22⋊C4×C107—21no—
350C22⋊C4×C107—22no—
351C22⋊C4×C107—22no—
352C22⋊C4×C107—21no—
353C22⋊C4×C107—42no—
354C22⋊C4×C107—44no—
355C22⋊C4×C107—41no—
356C22⋊C4×C107—41no—
357C22⋊C4×C107—82no—
358C42×C107—22no—
359C42×C107—21no—
360C42×C107—21no—
361C42×C107—21no—
362C42×C107—21no—
363C42×C107C2×D412yescomplemented
364C23×C107—21no—
365C23×C107—21no—
366C23×C107—21no—
367C23×C107—22no—
368C23×C107—21no—
369C23×C107—21no—
370C23×C107—22no—
371C23×C107—22no—
372C23×C107—41no—
373C23×C107—41no—
374C23×C107—42no—
375C23×C107—42no—
376C23×C107—44no—
377C23×C107—42no—
378C23×C107—42no—
379C23×C107—81no—
380C23×C107—82no—
381C23×C107—82no—
382C23×C107#12011yescharacteristic
383C23×C107#12011yescharacteristic
384C23×C107C22×D411yescharacteristic
385Q8×C107—21no—
386Q8×C107—21no—
387Q8×C107—21no—
388Q8×C107—21no—
389Q8×C107—21no—
390Q8×C107—42no—
391Q8×C107—41no—
392Q8×C107—41no—
393Q8×C107—41no—
394Q8×C107—41no—
395Q8×C107#12112yes—
396D4×C107—22no—
397D4×C107—22no—
398D4×C107—21no—
399D4×C107—21no—
400D4×C107—21no—
401D4×C107—21no—
402D4×C107—21no—
403D4×C107—42no—
404D4×C107—42no—
405D4×C107—44no—
406D4×C107—42no—
407D4×C107—44no—
408D4×C107—44no—
409D4×C107—42no—
410D4×C107—41no—
411D4×C107—41no—
412D4×C107—41no—
413D4×C107—41no—
414D4×C107—41no—
415D4×C107—41no—
416D4×C107—41no—
417D4×C107—41no—
418D4×C107—81no—
419D4×C107—82no—
420D4×C107—82no—
421D4×C107—82no—
422D4×C107—82no—
423D4×C107#12112yes—
424C2×C4×C107—21no—
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—22no—
434C2×C4×C107—21no—
435C2×C4×C107—21no—
436C2×C4×C107—22no—
437C2×C4×C107—21no—
438C2×C4×C107—22no—
439C2×C4×C107—21no—
440C2×C4×C107—21no—
441C2×C4×C107—21no—
442C2×C4×C107—22no—
443C2×C4×C107—42no—
444C2×C4×C107—42no—
445C2×C4×C107—42no—
446C2×C4×C107—44no—
447C2×C4×C107—41no—
448C2×C4×C107—41no—
449C2×C4×C107—41no—
450C2×C4×C107—41no—
451C2×C4×C107—41no—
452C2×C4×C107—41no—
453C2×C4×C107—42no—
454C2×C4×C107—41no—
455C2×C4×C107—42no—
456C2×C4×C107—41no—
457C2×C4×C107—41no—
458C2×C4×C107—41no—
459C2×C4×C107—41no—
460C2×C4×C107—41no—
461C2×C4×C107—41no—
462C2×C4×C107—82no—
463C2×C4×C107#12011yescharacteristic
464C2×C4×C107#12011yescharacteristic
465C2×C4×C107C22×D411yescharacteristic
466C2×C4×C107C22×D411yescharacteristic
467C2×C4×C107C22×D411yescharacteristic
468C2×C4×C107C2×#4111yescharacteristic
469C2×C4×C107H(5,𝔽2)11yescharacteristic
470C2×C4×C107H(5,𝔽2)11yescharacteristic
471C8×C107—22no—
472C8×C107—41no—
473C8×C107—41no—
474C8×C107—41no—
475C22×C107—21no—
476C22×C107—21no—
477C22×C107—21no—
478C22×C107—21no—
479C22×C107—22no—
480C22×C107—21no—
481C22×C107—21no—
482C22×C107—21no—
483C22×C107—21no—
484C22×C107—41no—
485C22×C107—41no—
486C22×C107—41no—
487C22×C107—41no—
488C22×C107—42no—
489C22×C107—42no—
490C22×C107—41no—
491C22×C107—41no—
492C22×C107—41no—
493C22×C107—42no—
494C22×C107—41no—
495C22×C107—81no—
496C22×C107—81no—
497C22×C107—82no—
498C22×C107—82no—
499C22×C107—84no—
500C22×C107—164no—
501C22×C107C2×#12011yescharacteristic
502C22×C107D4211yescharacteristic
503C22×C107#54611yescharacteristic
504C4×C107—21no—
505C4×C107—21no—
506C4×C107—22no—
507C4×C107—42no—
508C4×C107—41no—
509C4×C107—41no—
510C4×C107—42no—
511C4×C107—41no—
512C4×C107—41no—
513C4×C107—81no—
514C4×C107—81no—
515C4×C107—81no—
516C4×C107C2×#12111yescharacteristic
517C4×C107#53411yescharacteristic
518C4×C107D4211yescharacteristic
519C4×C107#54611yescharacteristic
520#24471C10711yesmaximal, characteristic, direct product factor, Sylow
521C2×C107—21no—
522C2×C107—21no—
523C2×C107—41no—
524C2×C107—41no—
525C2×C107—42no—
526C2×C107—81no—
527C2×C107—82no—
528C2×C107—81no—
529C2×C107#241011yescharacteristic
530C2×C107#301911yescharacteristic
531C2×C107#302211yescharacteristic
532#3488C2×C10711yescharacteristic
533#3056C2×C10711yescharacteristic, complemented
534C2×#455C2×C10711yescharacteristic, complemented
535#3007C2×C10711yescharacteristic, complemented
536C2×#421C2×C10711yescharacteristic, complemented
537#2620C2×C10711yescharacteristic, complemented
538#2039C2×C10711yescharacteristic, complemented
539#2037C2×C10711yescharacteristic, complemented
540#2007C2×C10711yescharacteristic, complemented
541#2004C2×C10711yescharacteristic, complemented
542#1900C2×C10711yescharacteristic, complemented
543#1897C2×C10711yescharacteristic, complemented
544#1882C2×C10711yescharacteristic, complemented
545#1859C2×C10711yescharacteristic, complemented
546#1792C2×C10711yescharacteristic, complemented
547C107#2447111yescharacteristic, direct product factor, Sylow
548C2×H(5,𝔽2)C22×C10711yescharacteristic
549C22×#41C22×C10711yescharacteristic
550C2×#137C22×C10711yescharacteristic
551C2×#137C22×C10711yescharacteristic, complemented
552C2×#137C22×C10711yescharacteristic, complemented
553C22×M16C22×C10711yescharacteristic, complemented
554#550—21no—
555#548—21no—
556#546—21no—
557#546—22no—
558D42—22no—
559D42—21no—
560#537—21no—
561#537C22×C10711yescharacteristic
562#535—21no—
563#535C22×C10711yescharacteristic
564C2×#124C22×C10711yescharacteristic, complemented
565#525—21no—
566#525C22×C10711yescharacteristic
567C2×C22⋊Q8C22×C10711yescharacteristic, complemented
568C2×#121—21no—
569C2×#121C22×C10711yescharacteristic
570#520C22×C10711yescharacteristic
571C2×#117C22×C10711yescharacteristic, complemented
572#470—21no—
573#468—21no—
574#467—21no—
575#465—21no—
576#455—24no—
577#452—21no—
578#452—21no—
579#451—21no—
580#450—21no—
581#428C22×C10711yescharacteristic, complemented
582#421—24no—
583C2×#104C22×C10711yescharacteristic
584C2×#104C22×C10711yescharacteristic
585C2×#104C22×C10711yescharacteristic, complemented
586C2×#104C22×C10711yescharacteristic, complemented
587C2×#104C22×C10711yescharacteristic, complemented
588C2×#104C22×C10711yescharacteristic, complemented
589#419C22×C10711yescharacteristic, complemented
590#417C22×C10711yescharacteristic
591#417C22×C10711yescharacteristic, complemented
592#417C22×C10711yescharacteristic, complemented
593C2×#100C22×C10711yescharacteristic, complemented
594C2×#100C22×C10711yescharacteristic, complemented
595#407C22×C10711yescharacteristic, complemented
596#396—22no—
597#394—22no—
598#391C22×C10711yescharacteristic, complemented
599#390C22×C10711yescharacteristic, complemented
600#384C22×C10711yescharacteristic, complemented
601#343C22×C10711yescharacteristic, complemented
602#343C22×C10711yescharacteristic, complemented
603#339C22×C10711yescharacteristic, complemented
604#339C22×C10711yescharacteristic, complemented
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C10711yescharacteristic
618C2×#41D4×C10711yescharacteristic
619C2×#41C23×C10711yescharacteristic
620C2×#41C23×C10711yescharacteristic
621C2×#41C23×C10711yescharacteristic
622C22×Q8D4×C10711yescharacteristic
623C22×Q8C23×C10711yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C10711yescharacteristic
630C22×D4D4×C10712yes—
631C22×D4C23×C10711yescharacteristic
632C23×C4—21no—
633C23×C4C23×C10711yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C10711yescharacteristic
650C2×M16C23×C10711yescharacteristic
651C2×M16C23×C10711yescharacteristic
652C2×M16C23×C10711yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
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—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C10711yescharacteristic
686#121D4×C10711yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C10711yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C10711yescharacteristic
708C2×C4⋊C4C23×C10711yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C10712yes—
715C2×C42C23×C10711yescharacteristic
716C2×C42C23×C10711yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C10714yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C10712yes—
741C24C2×D4×C10711yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C10712yes—
765#41#41×C10712yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C10711yescharacteristic
776C2×Q8C2×D4×C10711yescharacteristic
777C2×Q8C2×D4×C10711yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C10711yescharacteristic
812C2×D4C2×D4×C10711yescharacteristic
813C2×D4C2×D4×C10711yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C10711yescharacteristic
833C22×C4C2×D4×C10711yescharacteristic
834C22×C4C2×D4×C10711yescharacteristic
835C22×C4C2×D4×C10711yescharacteristic
836C22×C4C2×D4×C10711yescharacteristic
837C22×C4C2×D4×C10712yes—
838C22×C4C24×C10711yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C10712yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C10711yescharacteristic
872C4⋊C4C2×D4×C10711yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C10712yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C10711yescharacteristic
915C23#120×C10711yescharacteristic
916C23C22×D4×C10711yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C10712yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C10712yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C10711yescharacteristic
996C2×C4#120×C10711yescharacteristic
997C2×C4C22×D4×C10711yescharacteristic
998C2×C4C22×D4×C10711yescharacteristic
999C2×C4C22×D4×C10711yescharacteristic
1000C2×C4C2×#41×C10711yescharacteristic
1001C2×C4H(5,𝔽2)×C10711yescharacteristic
1002C2×C4H(5,𝔽2)×C10711yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C10711yescharacteristic
1034C22D42×C10711yescharacteristic
1035C22#546×C10711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C10711yescharacteristic
1049C4#534×C10711yescharacteristic
1050C4D42×C10711yescharacteristic
1051C4#546×C10711yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C107×#241011yescharacteristic
1061C2C107×#301911yescharacteristic
1062C2C107×#302211yescharacteristic
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. C2×#421×C107C2semidirect
6. C107×#2620C2semidirect
7. C107×#2039C2semidirect
8. C107×#2037C2semidirect
9. C107×#2007C2semidirect
10. C107×#2004C2semidirect
11. C107×#1900C2semidirect
12. C107×#1897C2semidirect
13. C107×#1882C2semidirect
14. C107×#1859C2semidirect
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. C2×#117×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
66. #391×C107C22semidirect
67. #390×C107C22semidirect
68. #384×C107C22semidirect
69. #343×C107C22semidirect
70. #343×C107C22semidirect
71. #339×C107C22semidirect
72. #339×C107C22semidirect
192. #104×C107D4semidirect
321. M16×C107C2×D4semidirect
363. C42×C107C2×D4semidirect
520. #24471C107direct (N × H)
533. #3056C2×C107semidirect
534. C2×#455C2×C107semidirect
535. #3007C2×C107semidirect
536. C2×#421C2×C107semidirect
537. #2620C2×C107semidirect
538. #2039C2×C107semidirect
539. #2037C2×C107semidirect
540. #2007C2×C107semidirect
541. #2004C2×C107semidirect
542. #1900C2×C107semidirect
543. #1897C2×C107semidirect
544. #1882C2×C107semidirect
545. #1859C2×C107semidirect
546. #1792C2×C107semidirect
547. C107#24471direct (N × H)
551. C2×#137C22×C107semidirect
552. C2×#137C22×C107semidirect
553. C22×M16C22×C107semidirect
564. C2×#124C22×C107semidirect
567. C2×C22⋊Q8C22×C107semidirect
571. C2×#117C22×C107semidirect
581. #428C22×C107semidirect
585. C2×#104C22×C107semidirect
586. C2×#104C22×C107semidirect
587. C2×#104C22×C107semidirect
588. C2×#104C22×C107semidirect
589. #419C22×C107semidirect
591. #417C22×C107semidirect
592. #417C22×C107semidirect
593. C2×#100C22×C107semidirect
594. C2×#100C22×C107semidirect
595. #407C22×C107semidirect
598. #391C22×C107semidirect
599. #390C22×C107semidirect
600. #384C22×C107semidirect
601. #343C22×C107semidirect
602. #343C22×C107semidirect
603. #339C22×C107semidirect
604. #339C22×C107semidirect
724. #104D4×C107semidirect
853. M16C2×D4×C107semidirect
895. C42C2×D4×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
C2×#421×C1072
C107×#26202
C107×#20392
C107×#20372
C107×#20072
C107×#20042
C107×#19002
C107×#18972
C107×#18822
C107×#18592
C107×#17922
#24471107