Finite Group Databasebeta

← C107×#18262 #41044226

Subgroups — C107×#18262 #41044226

Order 27392.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3534C211yesmaximal, characteristic
2C107×#3094C211yesmaximal, characteristic, complemented
3C107×#3091C211yesmaximal, characteristic, complemented
4C107×#2498C211yesmaximal, characteristic, complemented
5C107×#1618C211yesmaximal, characteristic, complemented
6C107×#1616C211yesmaximal, characteristic, complemented
7C107×#1615C211yesmaximal, characteristic, complemented
8C107×#1613C211yesmaximal, characteristic, complemented
9C107×#1612C211yesmaximal, characteristic, complemented
10C107×#1610C211yesmaximal, characteristic, complemented
11C107×#1609C211yesmaximal, characteristic, complemented
12C107×#1607C211yesmaximal, characteristic, complemented
13C107×#1504C211yesmaximal, characteristic, complemented
14C2×#327×C107C211yesmaximal, characteristic, complemented
15C107×#1468C211yesmaximal, characteristic, complemented
16#562×C107—21no—
17#560×C107—21no—
18#553×C107—21no—
19#551×C107—21no—
20#546×C107—21no—
21#546×C107—21no—
22#546×C107—21no—
23D42×C107—21no—
24#540×C107—21no—
25#539×C107—21no—
26#539×C107C2211yescharacteristic
27#538×C107—21no—
28#538×C107C2211yescharacteristic
29#537×C107C2211yescharacteristic
30#534×C107—21no—
31#534×C107C2211yescharacteristic
32#525×C107C2211yescharacteristic
33C2×#123×C107C2211yescharacteristic
34C2×#121×C107C2211yescharacteristic
35C2×#117×C107C2211yescharacteristic, complemented
36#485×C107—21no—
37#484×C107C2211yescharacteristic, complemented
38#483×C107C2211yescharacteristic, complemented
39#482×C107—21no—
40#482×C107—21no—
41#482×C107—21no—
42#481×C107C2211yescharacteristic
43#481×C107C2211yescharacteristic, complemented
44#481×C107C2211yescharacteristic, complemented
45#480×C107C2211yescharacteristic
46#480×C107C2211yescharacteristic, complemented
47#480×C107C2211yescharacteristic, complemented
48#428×C107—21no—
49#427×C107—21no—
50#418×C107—21no—
51#416×C107—21no—
52#407×C107C2211yescharacteristic, complemented
53C2×C22⋊C8×C107C2211yescharacteristic, complemented
54#400×C107C2211yescharacteristic, complemented
55#399×C107C2211yescharacteristic, complemented
56#398×C107C2211yescharacteristic, complemented
57#397×C107C2211yescharacteristic, complemented
58#388×C107—21no—
59#387×C107—21no—
60#386×C107—21no—
61#380×C107—21no—
62C2×#95×C107C2211yescharacteristic, complemented
63#328×C107C2211yescharacteristic, complemented
64#328×C107C2211yescharacteristic, complemented
65#327×C107C2211yescharacteristic
66#327×C107C2211yescharacteristic
67#327×C107C2211yescharacteristic, complemented
68#327×C107C2211yescharacteristic, complemented
69#327×C107C2211yescharacteristic, complemented
70#327×C107C2211yescharacteristic, complemented
71#324×C107C2211yescharacteristic, complemented
72#324×C107C2211yescharacteristic, complemented
73#323×C107C2211yescharacteristic, complemented
74#323×C107C2211yescharacteristic, complemented
75C2×#41×C107—21no—
76C2×#41×C107D411yescharacteristic
77C22×D4×C107—21no—
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107D411yescharacteristic
81C22×D4×C107D411yescharacteristic
82C23×C4×C107—21no—
83C23×C4×C107C2311yescharacteristic
84C2×M16×C107—21no—
85C22×C8×C107—21no—
86#127×C107—21no—
87#126×C107—21no—
88#126×C107—21no—
89#126×C107—21no—
90#126×C107—21no—
91#125×C107—21no—
92#125×C107—21no—
93#124×C107—21no—
94#124×C107—21no—
95#124×C107—21no—
96#123×C107—21no—
97#123×C107—21no—
98#123×C107—21no—
99#123×C107—21no—
100#123×C107—21no—
101#123×C107—21no—
102#123×C107—21no—
103#123×C107—21no—
104#123×C107—21no—
105#123×C107—21no—
106#123×C107—21no—
107#123×C107—21no—
108#123×C107—21no—
109#123×C107—21no—
110C22⋊Q8×C107—21no—
111C22⋊Q8×C107—21no—
112C22⋊Q8×C107—21no—
113C22⋊Q8×C107—21no—
114C22⋊Q8×C107—21no—
115C22⋊Q8×C107D411yescharacteristic
116C22⋊Q8×C107C2311yescharacteristic
117#121×C107—21no—
118#121×C107—21no—
119#121×C107—21no—
120#121×C107—21no—
121#121×C107—21no—
122#121×C107—21no—
123#121×C107—21no—
124#121×C107—21no—
125#121×C107—21no—
126#121×C107—21no—
127#121×C107—21no—
128#121×C107—21no—
129#121×C107—21no—
130#121×C107—21no—
131#121×C107—21no—
132#121×C107D411yescharacteristic
133#121×C107D411yescharacteristic
134#121×C107D411yescharacteristic
135#121×C107C2311yescharacteristic
136#121×C107C2311yescharacteristic
137#121×C107C2311yescharacteristic
138#120×C107—21no—
139#120×C107—21no—
140#120×C107—21no—
141#120×C107—21no—
142#120×C107—21no—
143#120×C107—21no—
144#120×C107—21no—
145#120×C107—21no—
146C4×D4×C107—21no—
147C4×D4×C107—21no—
148C4×D4×C107—21no—
149C4×D4×C107—21no—
150C4×D4×C107—21no—
151C4×D4×C107—21no—
152C4×D4×C107—21no—
153C4×D4×C107—21no—
154#117×C107—21no—
155#117×C107—21no—
156#117×C107—21no—
157#117×C107—21no—
158#117×C107—21no—
159#117×C107D411yescharacteristic
160C2×C4⋊C4×C107—21no—
161C2×C4⋊C4×C107—21no—
162C2×C4⋊C4×C107D411yescharacteristic
163C2×C4⋊C4×C107D411yescharacteristic
164C2×C4⋊C4×C107C2311yescharacteristic
165C2×C4⋊C4×C107C2311yescharacteristic
166C2×C4⋊C4×C107C2311yescharacteristic
167C2×C22⋊C4×C107—21no—
168C2×C22⋊C4×C107—21no—
169C2×C22⋊C4×C107—21no—
170C2×C22⋊C4×C107—21no—
171C2×C22⋊C4×C107—21no—
172C2×C22⋊C4×C107—21no—
173C2×C22⋊C4×C107D411yescharacteristic
174C2×C22⋊C4×C107D411yescharacteristic
175C2×C22⋊C4×C107C2311yescharacteristic
176C2×C42×C107—21no—
177#107×C107—21no—
178#107×C107—21no—
179#107×C107—21no—
180#107×C107—21no—
181#106×C107—21no—
182#106×C107—21no—
183#106×C107—21no—
184#106×C107—21no—
185#103×C107—21no—
186#103×C107—21no—
187#102×C107—21no—
188#102×C107—21no—
189#102×C107—21no—
190#102×C107—21no—
191#102×C107—21no—
192#102×C107—21no—
193C22⋊C8×C107—21no—
194C22⋊C8×C107—21no—
195C22⋊C8×C107C2311yescharacteristic
196C22⋊C8×C107C2311yescharacteristic
197C22⋊C8×C107C2311yescharacteristic
198C22⋊C8×C107C2311yescharacteristic
199#95×C107—21no—
200#95×C107—21no—
201#95×C107—21no—
202#95×C107—21no—
203#95×C107—21no—
204#95×C107C2311yescharacteristic
205#95×C107C2311yescharacteristic
206C24×C107—21no—
207C24×C107—21no—
208C24×C107C2×D411yescharacteristic
209C24×C107C2×D411yescharacteristic
210#41×C107—42no—
211#41×C107—81no—
212#41×C107—81no—
213C2×Q8×C107—21no—
214C2×Q8×C107C2×D411yescharacteristic
215C2×D4×C107—21no—
216C2×D4×C107—21no—
217C2×D4×C107—21no—
218C2×D4×C107—21no—
219C2×D4×C107—21no—
220C2×D4×C107—21no—
221C2×D4×C107—21no—
222C2×D4×C107—21no—
223C2×D4×C107—21no—
224C2×D4×C107—21no—
225C2×D4×C107—21no—
226C2×D4×C107—21no—
227C2×D4×C107—21no—
228C2×D4×C107—21no—
229C2×D4×C107—21no—
230C2×D4×C107—21no—
231C2×D4×C107—21no—
232C2×D4×C107—42no—
233C2×D4×C107—42no—
234C2×D4×C107—81no—
235C2×D4×C107—81no—
236C2×D4×C107—81no—
237C2×D4×C107—81no—
238C2×D4×C107—82no—
239C2×D4×C107C2×D411yescharacteristic
240C2×D4×C107C2×D411yescharacteristic
241C2×D4×C107C2×D411yescharacteristic
242C22×C4×C107—21no—
243C22×C4×C107—21no—
244C22×C4×C107—21no—
245C22×C4×C107—21no—
246C22×C4×C107—21no—
247C22×C4×C107—21no—
248C22×C4×C107—21no—
249C22×C4×C107—21no—
250C22×C4×C107—21no—
251C22×C4×C107—21no—
252C22×C4×C107—21no—
253C22×C4×C107—42no—
254C22×C4×C107—42no—
255C22×C4×C107—42no—
256C22×C4×C107—81no—
257C22×C4×C107C2×D411yescharacteristic
258C22×C4×C107C2×D411yescharacteristic
259C22×C4×C107C2×D411yescharacteristic
260C22×C4×C107C2×D411yescharacteristic
261C22×C4×C107C2×D411yescharacteristic
262C22×C4×C107C2×D411yescharacteristic
263C22×C4×C107C2×D411yescharacteristic
264C22×C4×C107C2×D411yescharacteristic
265C22×C4×C107C2411yescharacteristic
266M16×C107—42no—
267C2×C8×C107—21no—
268C2×C8×C107—21no—
269C2×C8×C107—21no—
270C2×C8×C107—21no—
271C2×C8×C107—42no—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—21no—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—21no—
279C4⋊C4×C107—21no—
280C4⋊C4×C107—21no—
281C4⋊C4×C107—21no—
282C4⋊C4×C107—21no—
283C4⋊C4×C107—21no—
284C4⋊C4×C107—21no—
285C4⋊C4×C107—21no—
286C4⋊C4×C107—21no—
287C4⋊C4×C107—21no—
288C4⋊C4×C107—21no—
289C4⋊C4×C107—42no—
290C4⋊C4×C107—81no—
291C4⋊C4×C107C2×D411yescharacteristic
292C4⋊C4×C107C2×D411yescharacteristic
293C4⋊C4×C107C2×D411yescharacteristic
294C4⋊C4×C107C2×D411yescharacteristic
295C22⋊C4×C107—21no—
296C22⋊C4×C107—21no—
297C22⋊C4×C107—21no—
298C22⋊C4×C107—21no—
299C22⋊C4×C107—21no—
300C22⋊C4×C107—21no—
301C22⋊C4×C107—21no—
302C22⋊C4×C107—21no—
303C22⋊C4×C107—21no—
304C22⋊C4×C107—21no—
305C22⋊C4×C107—21no—
306C22⋊C4×C107—21no—
307C22⋊C4×C107—21no—
308C22⋊C4×C107—21no—
309C22⋊C4×C107—21no—
310C22⋊C4×C107—21no—
311C22⋊C4×C107—21no—
312C22⋊C4×C107—21no—
313C22⋊C4×C107—21no—
314C22⋊C4×C107—21no—
315C22⋊C4×C107—21no—
316C22⋊C4×C107—21no—
317C22⋊C4×C107—21no—
318C22⋊C4×C107—21no—
319C22⋊C4×C107—21no—
320C22⋊C4×C107—42no—
321C22⋊C4×C107—41no—
322C22⋊C4×C107—41no—
323C22⋊C4×C107—81no—
324C42×C107—21no—
325C42×C107—21no—
326C42×C107—21no—
327C42×C107—41no—
328C42×C107—41no—
329C23×C107—21no—
330C23×C107—21no—
331C23×C107—22no—
332C23×C107—21no—
333C23×C107—21no—
334C23×C107—21no—
335C23×C107—21no—
336C23×C107—21no—
337C23×C107—21no—
338C23×C107—41no—
339C23×C107—41no—
340C23×C107—41no—
341C23×C107—42no—
342C23×C107—81no—
343C23×C107—81no—
344C23×C107—81no—
345C23×C107—81no—
346C23×C107—81no—
347C23×C107#12011yescharacteristic
348C23×C107#12011yescharacteristic
349C23×C107C22×D411yescharacteristic
350Q8×C107—41no—
351Q8×C107—81no—
352D4×C107—41no—
353D4×C107—41no—
354D4×C107—41no—
355D4×C107—41no—
356D4×C107—41no—
357D4×C107—41no—
358D4×C107—41no—
359D4×C107—41no—
360D4×C107—41no—
361D4×C107—42no—
362D4×C107—42no—
363D4×C107—81no—
364D4×C107—81no—
365D4×C107—81no—
366D4×C107—81no—
367D4×C107—81no—
368D4×C107—81no—
369D4×C107—81no—
370D4×C107—81no—
371D4×C107—81no—
372D4×C107—81no—
373D4×C107—81no—
374D4×C107—81no—
375C2×C4×C107—22no—
376C2×C4×C107—22no—
377C2×C4×C107—22no—
378C2×C4×C107—21no—
379C2×C4×C107—21no—
380C2×C4×C107—21no—
381C2×C4×C107—21no—
382C2×C4×C107—21no—
383C2×C4×C107—21no—
384C2×C4×C107—21no—
385C2×C4×C107—21no—
386C2×C4×C107—21no—
387C2×C4×C107—21no—
388C2×C4×C107—41no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—41no—
392C2×C4×C107—41no—
393C2×C4×C107—41no—
394C2×C4×C107—41no—
395C2×C4×C107—41no—
396C2×C4×C107—41no—
397C2×C4×C107—41no—
398C2×C4×C107—41no—
399C2×C4×C107—41no—
400C2×C4×C107—41no—
401C2×C4×C107—41no—
402C2×C4×C107—41no—
403C2×C4×C107—41no—
404C2×C4×C107—41no—
405C2×C4×C107—81no—
406C2×C4×C107—81no—
407C2×C4×C107—81no—
408C2×C4×C107—81no—
409C2×C4×C107—81no—
410C2×C4×C107—81no—
411C2×C4×C107—81no—
412C2×C4×C107—84no—
413C2×C4×C107#12011yescharacteristic
414C2×C4×C107#12011yescharacteristic
415C2×C4×C107C22×D411yescharacteristic
416C2×C4×C107C22×D411yescharacteristic
417C8×C107—41no—
418C8×C107—41no—
419C8×C107—41no—
420C8×C107—41no—
421C22×C107—21no—
422C22×C107—21no—
423C22×C107—21no—
424C22×C107—21no—
425C22×C107—21no—
426C22×C107—21no—
427C22×C107—21no—
428C22×C107—42no—
429C22×C107—42no—
430C22×C107—41no—
431C22×C107—41no—
432C22×C107—41no—
433C22×C107—41no—
434C22×C107—41no—
435C22×C107—41no—
436C22×C107—41no—
437C22×C107—41no—
438C22×C107—41no—
439C22×C107—41no—
440C22×C107—41no—
441C22×C107—41no—
442C22×C107—81no—
443C22×C107—81no—
444C22×C107—162no—
445C22×C107—162no—
446C22×C107#45812yes—
447C22×C107C2×#12011yescharacteristic
448C22×C107#57611yescharacteristic
449C22×C107#57711yescharacteristic
450C4×C107—21no—
451C4×C107—21no—
452C4×C107—21no—
453C4×C107—21no—
454C4×C107—42no—
455C4×C107—41no—
456C4×C107—41no—
457C4×C107—41no—
458C4×C107—41no—
459C4×C107—41no—
460C4×C107—41no—
461C4×C107—41no—
462C4×C107—41no—
463C4×C107—81no—
464C4×C107—81no—
465C4×C107—81no—
466#18262C10711yesmaximal, characteristic, direct product factor, Sylow
467C2×C107—21no—
468C2×C107—21no—
469C2×C107—22no—
470C2×C107—41no—
471C2×C107—81no—
472C2×C107—81no—
473C2×C107—81no—
474C2×C107—81no—
475C2×C107#301211yescharacteristic
476C2×C107#301811yescharacteristic
477C2×C107C2×#45811yescharacteristic
478#3534C2×C10711yescharacteristic
479#3094C2×C10711yescharacteristic, complemented
480#3091C2×C10711yescharacteristic, complemented
481#2498C2×C10711yescharacteristic, complemented
482#1618C2×C10711yescharacteristic, complemented
483#1616C2×C10711yescharacteristic, complemented
484#1615C2×C10711yescharacteristic, complemented
485#1613C2×C10711yescharacteristic, complemented
486#1612C2×C10711yescharacteristic, complemented
487#1610C2×C10711yescharacteristic, complemented
488#1609C2×C10711yescharacteristic, complemented
489#1607C2×C10711yescharacteristic, complemented
490#1504C2×C10711yescharacteristic, complemented
491C2×#327C2×C10711yescharacteristic, complemented
492#1468C2×C10711yescharacteristic, complemented
493C107#1826211yescharacteristic, direct product factor, Sylow
494#562—21no—
495#560—21no—
496#553—21no—
497#551—21no—
498#546—21no—
499#546—21no—
500#546—21no—
501D42—21no—
502#540—21no—
503#539—21no—
504#539C22×C10711yescharacteristic
505#538—21no—
506#538C22×C10711yescharacteristic
507#537C22×C10711yescharacteristic
508#534—21no—
509#534C22×C10711yescharacteristic
510#525C22×C10711yescharacteristic
511C2×#123C22×C10711yescharacteristic
512C2×#121C22×C10711yescharacteristic
513C2×#117C22×C10711yescharacteristic, complemented
514#485—21no—
515#484C22×C10711yescharacteristic, complemented
516#483C22×C10711yescharacteristic, complemented
517#482—21no—
518#482—21no—
519#482—21no—
520#481C22×C10711yescharacteristic
521#481C22×C10711yescharacteristic, complemented
522#481C22×C10711yescharacteristic, complemented
523#480C22×C10711yescharacteristic
524#480C22×C10711yescharacteristic, complemented
525#480C22×C10711yescharacteristic, complemented
526#428—21no—
527#427—21no—
528#418—21no—
529#416—21no—
530#407C22×C10711yescharacteristic, complemented
531C2×C22⋊C8C22×C10711yescharacteristic, complemented
532#400C22×C10711yescharacteristic, complemented
533#399C22×C10711yescharacteristic, complemented
534#398C22×C10711yescharacteristic, complemented
535#397C22×C10711yescharacteristic, complemented
536#388—21no—
537#387—21no—
538#386—21no—
539#380—21no—
540C2×#95C22×C10711yescharacteristic, complemented
541#328C22×C10711yescharacteristic, complemented
542#328C22×C10711yescharacteristic, complemented
543#327C22×C10711yescharacteristic
544#327C22×C10711yescharacteristic
545#327C22×C10711yescharacteristic, complemented
546#327C22×C10711yescharacteristic, complemented
547#327C22×C10711yescharacteristic, complemented
548#327C22×C10711yescharacteristic, complemented
549#324C22×C10711yescharacteristic, complemented
550#324C22×C10711yescharacteristic, complemented
551#323C22×C10711yescharacteristic, complemented
552#323C22×C10711yescharacteristic, complemented
553C2×#41—21no—
554C2×#41D4×C10711yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C10711yescharacteristic
559C22×D4D4×C10711yescharacteristic
560C23×C4—21no—
561C23×C4C23×C10711yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C10711yescharacteristic
594C22⋊Q8C23×C10711yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C10711yescharacteristic
611#121D4×C10711yescharacteristic
612#121D4×C10711yescharacteristic
613#121C23×C10711yescharacteristic
614#121C23×C10711yescharacteristic
615#121C23×C10711yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C10711yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C10711yescharacteristic
641C2×C4⋊C4D4×C10711yescharacteristic
642C2×C4⋊C4C23×C10711yescharacteristic
643C2×C4⋊C4C23×C10711yescharacteristic
644C2×C4⋊C4C23×C10711yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C10711yescharacteristic
652C2×C22⋊C4D4×C10711yescharacteristic
653C2×C22⋊C4C23×C10711yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C10711yescharacteristic
674C22⋊C8C23×C10711yescharacteristic
675C22⋊C8C23×C10711yescharacteristic
676C22⋊C8C23×C10711yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C10711yescharacteristic
683#95C23×C10711yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C10711yescharacteristic
687C24C2×D4×C10711yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C10711yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C10711yescharacteristic
718C2×D4C2×D4×C10711yescharacteristic
719C2×D4C2×D4×C10711yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C10711yescharacteristic
736C22×C4C2×D4×C10711yescharacteristic
737C22×C4C2×D4×C10711yescharacteristic
738C22×C4C2×D4×C10711yescharacteristic
739C22×C4C2×D4×C10711yescharacteristic
740C22×C4C2×D4×C10711yescharacteristic
741C22×C4C2×D4×C10711yescharacteristic
742C22×C4C2×D4×C10711yescharacteristic
743C22×C4C24×C10711yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C10711yescharacteristic
770C4⋊C4C2×D4×C10711yescharacteristic
771C4⋊C4C2×D4×C10711yescharacteristic
772C4⋊C4C2×D4×C10711yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C10711yescharacteristic
826C23#120×C10711yescharacteristic
827C23C22×D4×C10711yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C10711yescharacteristic
892C2×C4#120×C10711yescharacteristic
893C2×C4C22×D4×C10711yescharacteristic
894C2×C4C22×D4×C10711yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22#458×C10712yes—
925C22C2×#120×C10711yescharacteristic
926C22#576×C10711yescharacteristic
927C22#577×C10711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C107×#301211yescharacteristic
953C2C107×#301811yescharacteristic
954C2C2×#458×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#3094C2semidirect
3. C107×#3091C2semidirect
4. C107×#2498C2semidirect
5. C107×#1618C2semidirect
6. C107×#1616C2semidirect
7. C107×#1615C2semidirect
8. C107×#1613C2semidirect
9. C107×#1612C2semidirect
10. C107×#1610C2semidirect
11. C107×#1609C2semidirect
12. C107×#1607C2semidirect
13. C107×#1504C2semidirect
14. C2×#327×C107C2semidirect
15. C107×#1468C2semidirect
35. C2×#117×C107C22semidirect
37. #484×C107C22semidirect
38. #483×C107C22semidirect
43. #481×C107C22semidirect
44. #481×C107C22semidirect
46. #480×C107C22semidirect
47. #480×C107C22semidirect
52. #407×C107C22semidirect
53. C2×C22⋊C8×C107C22semidirect
54. #400×C107C22semidirect
55. #399×C107C22semidirect
56. #398×C107C22semidirect
57. #397×C107C22semidirect
62. C2×#95×C107C22semidirect
63. #328×C107C22semidirect
64. #328×C107C22semidirect
67. #327×C107C22semidirect
68. #327×C107C22semidirect
69. #327×C107C22semidirect
70. #327×C107C22semidirect
71. #324×C107C22semidirect
72. #324×C107C22semidirect
73. #323×C107C22semidirect
74. #323×C107C22semidirect
466. #18262C107direct (N × H)
479. #3094C2×C107semidirect
480. #3091C2×C107semidirect
481. #2498C2×C107semidirect
482. #1618C2×C107semidirect
483. #1616C2×C107semidirect
484. #1615C2×C107semidirect
485. #1613C2×C107semidirect
486. #1612C2×C107semidirect
487. #1610C2×C107semidirect
488. #1609C2×C107semidirect
489. #1607C2×C107semidirect
490. #1504C2×C107semidirect
491. C2×#327C2×C107semidirect
492. #1468C2×C107semidirect
493. C107#18262direct (N × H)
513. C2×#117C22×C107semidirect
515. #484C22×C107semidirect
516. #483C22×C107semidirect
521. #481C22×C107semidirect
522. #481C22×C107semidirect
524. #480C22×C107semidirect
525. #480C22×C107semidirect
530. #407C22×C107semidirect
531. C2×C22⋊C8C22×C107semidirect
532. #400C22×C107semidirect
533. #399C22×C107semidirect
534. #398C22×C107semidirect
535. #397C22×C107semidirect
540. C2×#95C22×C107semidirect
541. #328C22×C107semidirect
542. #328C22×C107semidirect
545. #327C22×C107semidirect
546. #327C22×C107semidirect
547. #327C22×C107semidirect
548. #327C22×C107semidirect
549. #324C22×C107semidirect
550. #324C22×C107semidirect
551. #323C22×C107semidirect
552. #323C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35342
C107×#30942
C107×#30912
C107×#24982
C107×#16182
C107×#16162
C107×#16152
C107×#16132
C107×#16122
C107×#16102
C107×#16092
C107×#16072
C107×#15042
C2×#327×C1072
C107×#14682
#18262107