Finite Group Databasebeta

← C107×#29102 #41055066

Subgroups — C107×#29102 #41055066

Order 27392.

668 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2513C211yesmaximal, characteristic
2C107×#2453C211yesmaximal, characteristic, complemented
3C107×#2088C211yesmaximal, characteristic, complemented
4C107×#2074C211yesmaximal, characteristic, complemented
5C107×#2055C211yesmaximal, characteristic
6C107×#2025C211yesmaximal, characteristic
7C107×#1991C211yesmaximal, characteristic, complemented
8C107×#1968C211yesmaximal, characteristic
9C107×#1936C211yesmaximal, characteristic
10C107×#1936C211yesmaximal, characteristic
11C107×#1935C211yesmaximal, characteristic, complemented
12C107×#1920C211yesmaximal, characteristic, complemented
13C107×#1880C211yesmaximal, characteristic
14C107×#1771C211yesmaximal, characteristic, complemented
15C107×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C107C2211yescharacteristic
17C2×#125×C107C2211yescharacteristic
18C2×C4×Q8×C107C2211yescharacteristic
19C2×#106×C107C2211yescharacteristic
20C2×C4⋊C8×C107C2211yescharacteristic
21C2×#103×C107C2211yescharacteristic
22C2×#103×C107C2211yescharacteristic
23C2×#103×C107C2211yescharacteristic
24C2×#102×C107C2211yescharacteristic
25C2×#102×C107C2211yescharacteristic
26C2×#102×C107C2211yescharacteristic
27C2×#97×C107C2211yescharacteristic
28C2×#97×C107C2211yescharacteristic
29C2×C4×C8×C107C2211yescharacteristic
30#400×C107—21no—
31#398×C107—21no—
32#397×C107—21no—
33#397×C107—21no—
34#391×C107C2211yescharacteristic
35#391×C107C2211yescharacteristic
36#390×C107C2211yescharacteristic
37#390×C107C2211yescharacteristic
38#390×C107C2211yescharacteristic
39#389×C107—21no—
40#389×C107C2211yescharacteristic
41#389×C107C2211yescharacteristic
42#389×C107C2211yescharacteristic
43#388×C107—21no—
44#388×C107—21no—
45#387×C107—21no—
46#382×C107C2211yescharacteristic
47C4×C4⋊C4×C107C2211yescharacteristic
48C4×C4⋊C4×C107C2211yescharacteristic
49#340×C107C2211yescharacteristic
50#340×C107C2211yescharacteristic
51#340×C107C2211yescharacteristic
52#340×C107C2211yescharacteristic
53#340×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59C22×Q8×C107C2311yescharacteristic
60C22×D4×C107C2311yescharacteristic
61C2×SD16×C107—22no—
62C2×SD16×C107—22no—
63C2×SD16×C107—41no—
64C22×C8×C107C2311yescharacteristic
65C22×C8×C107C2311yescharacteristic
66C22×C8×C107C2311yescharacteristic
67C22×C8×C107C2311yescharacteristic
68#125×C107—22no—
69#125×C107—41no—
70C4×Q8×C107—22no—
71C4×Q8×C107—41no—
72C2×C4⋊C4×C107—21no—
73C2×C4⋊C4×C107—21no—
74C2×C4⋊C4×C107—21no—
75C2×C4⋊C4×C107—21no—
76C2×C4⋊C4×C107—21no—
77C2×C4⋊C4×C107—21no—
78C2×C4⋊C4×C107D411yescharacteristic
79C2×C4⋊C4×C107D411yescharacteristic
80C2×C4⋊C4×C107C2311yescharacteristic
81C2×C4⋊C4×C107C2311yescharacteristic
82C2×C4⋊C4×C107C2311yescharacteristic
83C2×C4⋊C4×C107C2311yescharacteristic
84C2×C4⋊C4×C107C2311yescharacteristic
85C2×C4⋊C4×C107C2311yescharacteristic
86C2×C22⋊C4×C107—21no—
87C2×C22⋊C4×C107—21no—
88C2×C22⋊C4×C107—21no—
89C2×C22⋊C4×C107—21no—
90C2×C22⋊C4×C107—21no—
91C2×C22⋊C4×C107—21no—
92C2×C42×C107—21no—
93C2×C42×C107—21no—
94C2×C42×C107C2311yescharacteristic
95C2×C42×C107C2311yescharacteristic
96C2×C42×C107C2311yescharacteristic
97#106×C107—22no—
98C4⋊C8×C107—22no—
99#103×C107—22no—
100#103×C107—22no—
101#103×C107—22no—
102#102×C107—22no—
103#102×C107—22no—
104#102×C107—41no—
105#97×C107—22no—
106#97×C107—41no—
107C4×C8×C107—41no—
108#95×C107—21no—
109#95×C107—21no—
110#95×C107—21no—
111#95×C107—21no—
112#95×C107—21no—
113#95×C107—21no—
114#95×C107—21no—
115#95×C107—21no—
116#95×C107—21no—
117#95×C107—21no—
118#95×C107D411yescharacteristic
119#95×C107D411yescharacteristic
120C24×C107—21no—
121C2×Q8×C107—21no—
122C2×Q8×C107—21no—
123C2×Q8×C107—21no—
124C2×Q8×C107—21no—
125C2×Q8×C107—21no—
126C2×Q8×C107#4112yes—
127C2×D4×C107—21no—
128C2×D4×C107—21no—
129C2×D4×C107—21no—
130C2×D4×C107—21no—
131C2×D4×C107—21no—
132C2×D4×C107—21no—
133C22×C4×C107—21no—
134C22×C4×C107—21no—
135C22×C4×C107—21no—
136C22×C4×C107—21no—
137C22×C4×C107—21no—
138C22×C4×C107—21no—
139C22×C4×C107—21no—
140C22×C4×C107C2×D411yescharacteristic
141C22×C4×C107C2×D411yescharacteristic
142C22×C4×C107C2×D411yescharacteristic
143C22×C4×C107C2×D411yescharacteristic
144C22×C4×C107C2×D411yescharacteristic
145C22×C4×C107C2×D411yescharacteristic
146C22×C4×C107C2411yescharacteristic
147SD16×C107—44no—
148C2×C8×C107—21no—
149C2×C8×C107—21no—
150C2×C8×C107—21no—
151C2×C8×C107—21no—
152C2×C8×C107—21no—
153C2×C8×C107—21no—
154C2×C8×C107—21no—
155C2×C8×C107—21no—
156C2×C8×C107—21no—
157C2×C8×C107—21no—
158C2×C8×C107#4112yes—
159C2×C8×C107#4112yes—
160C4⋊C4×C107—21no—
161C4⋊C4×C107—21no—
162C4⋊C4×C107—21no—
163C4⋊C4×C107—21no—
164C4⋊C4×C107—21no—
165C4⋊C4×C107—21no—
166C4⋊C4×C107—21no—
167C4⋊C4×C107—21no—
168C4⋊C4×C107—21no—
169C4⋊C4×C107—21no—
170C4⋊C4×C107—21no—
171C4⋊C4×C107—41no—
172C4⋊C4×C107—41no—
173C4⋊C4×C107—42no—
174C4⋊C4×C107—42no—
175C4⋊C4×C107—42no—
176C4⋊C4×C107—42no—
177C4⋊C4×C107—42no—
178C4⋊C4×C107—81no—
179C4⋊C4×C107#4112yes—
180C22⋊C4×C107—42no—
181C22⋊C4×C107—42no—
182C22⋊C4×C107—81no—
183C22⋊C4×C107—81no—
184C22⋊C4×C107—81no—
185C22⋊C4×C107—81no—
186C42×C107—21no—
187C42×C107—21no—
188C42×C107—21no—
189C42×C107—21no—
190C42×C107—21no—
191C42×C107—21no—
192C42×C107—42no—
193C42×C107—81no—
194C23×C107—41no—
195C23×C107—41no—
196C23×C107—41no—
197C23×C107—41no—
198C23×C107—41no—
199C23×C107—41no—
200C23×C107—41no—
201C23×C107C22×D411yescharacteristic
202Q8×C107—22no—
203Q8×C107—22no—
204Q8×C107—41no—
205Q8×C107—41no—
206D4×C107—41no—
207D4×C107—41no—
208D4×C107—41no—
209D4×C107—41no—
210C2×C4×C107—21no—
211C2×C4×C107—21no—
212C2×C4×C107—21no—
213C2×C4×C107—21no—
214C2×C4×C107—21no—
215C2×C4×C107—21no—
216C2×C4×C107—22no—
217C2×C4×C107—22no—
218C2×C4×C107—21no—
219C2×C4×C107—21no—
220C2×C4×C107—21no—
221C2×C4×C107—21no—
222C2×C4×C107—21no—
223C2×C4×C107—21no—
224C2×C4×C107—21no—
225C2×C4×C107—21no—
226C2×C4×C107—21no—
227C2×C4×C107—21no—
228C2×C4×C107—21no—
229C2×C4×C107—21no—
230C2×C4×C107—41no—
231C2×C4×C107—41no—
232C2×C4×C107—41no—
233C2×C4×C107—41no—
234C2×C4×C107—41no—
235C2×C4×C107—41no—
236C2×C4×C107—41no—
237C2×C4×C107—41no—
238C2×C4×C107—41no—
239C2×C4×C107—41no—
240C2×C4×C107—41no—
241C2×C4×C107—41no—
242C2×C4×C107—41no—
243C2×C4×C107—41no—
244C2×C4×C107—41no—
245C2×C4×C107—41no—
246C2×C4×C107—41no—
247C2×C4×C107—41no—
248C2×C4×C107—41no—
249C2×C4×C107C2×#4111yescharacteristic
250C2×C4×C107C2×#4111yescharacteristic
251C2×C4×C107C2×#4111yescharacteristic
252C2×C4×C107C2×#4111yescharacteristic
253C2×C4×C107H(5,𝔽2)11yescharacteristic
254C2×C4×C1072−1+411yescharacteristic
255C8×C107—22no—
256C8×C107—22no—
257C8×C107—41no—
258C8×C107—41no—
259C22×C107—81no—
260C22×C107—81no—
261C22×C107—81no—
262C22×C107—81no—
263C22×C107—81no—
264C22×C107—81no—
265C22×C107—81no—
266C22×C107#53211yescharacteristic
267C22×C107#54611yescharacteristic
268C22×C107#54811yescharacteristic
269C22×C107#57511yescharacteristic
270C22×C107#57511yescharacteristic
271C22×C107#57711yescharacteristic
272C22×C107#57711yescharacteristic
273C4×C107—42no—
274C4×C107—41no—
275C4×C107—41no—
276C4×C107—41no—
277C4×C107—41no—
278C4×C107—42no—
279C4×C107—41no—
280C4×C107—41no—
281C4×C107—81no—
282C4×C107—81no—
283C4×C107—81no—
284C4×C107—81no—
285C4×C107—81no—
286C4×C107#52911yescharacteristic
287C4×C107#53911yescharacteristic
288C4×C107#55111yescharacteristic
289C4×C107#55611yescharacteristic
290#29102C10711yesmaximal, characteristic, direct product factor, Sylow
291C2×C107—161no—
292C2×C107#256011yescharacteristic
293C2×C107#317411yescharacteristic
294C2×C107#318311yescharacteristic
295C2×C107#330711yescharacteristic
296C2×C107#332111yescharacteristic
297C2×C107#337111yescharacteristic
298C2×C107#337111yescharacteristic
299#2513C2×C10711yescharacteristic
300#2453C2×C10711yescharacteristic, complemented
301#2088C2×C10711yescharacteristic, complemented
302#2074C2×C10711yescharacteristic, complemented
303#2055C2×C10711yescharacteristic
304#2025C2×C10711yescharacteristic
305#1991C2×C10711yescharacteristic, complemented
306#1968C2×C10711yescharacteristic
307#1936C2×C10711yescharacteristic
308#1936C2×C10711yescharacteristic
309#1935C2×C10711yescharacteristic, complemented
310#1920C2×C10711yescharacteristic, complemented
311#1880C2×C10711yescharacteristic
312#1771C2×C10711yescharacteristic, complemented
313#1763C2×C10711yescharacteristic, complemented
314C107#2910211yescharacteristic, direct product factor, Sylow
315C22×SD16C22×C10711yescharacteristic
316C2×#125C22×C10711yescharacteristic
317C2×C4×Q8C22×C10711yescharacteristic
318C2×#106C22×C10711yescharacteristic
319C2×C4⋊C8C22×C10711yescharacteristic
320C2×#103C22×C10711yescharacteristic
321C2×#103C22×C10711yescharacteristic
322C2×#103C22×C10711yescharacteristic
323C2×#102C22×C10711yescharacteristic
324C2×#102C22×C10711yescharacteristic
325C2×#102C22×C10711yescharacteristic
326C2×#97C22×C10711yescharacteristic
327C2×#97C22×C10711yescharacteristic
328C2×C4×C8C22×C10711yescharacteristic
329#400—21no—
330#398—21no—
331#397—21no—
332#397—21no—
333#391C22×C10711yescharacteristic
334#391C22×C10711yescharacteristic
335#390C22×C10711yescharacteristic
336#390C22×C10711yescharacteristic
337#390C22×C10711yescharacteristic
338#389—21no—
339#389C22×C10711yescharacteristic
340#389C22×C10711yescharacteristic
341#389C22×C10711yescharacteristic
342#388—21no—
343#388—21no—
344#387—21no—
345#382C22×C10711yescharacteristic
346C4×C4⋊C4C22×C10711yescharacteristic
347C4×C4⋊C4C22×C10711yescharacteristic
348#340C22×C10711yescharacteristic
349#340C22×C10711yescharacteristic
350#340C22×C10711yescharacteristic
351#340C22×C10711yescharacteristic
352#340C22×C10711yescharacteristic
353#340C22×C10711yescharacteristic
354#340C22×C10711yescharacteristic
355#340C22×C10711yescharacteristic
356#336C22×C10711yescharacteristic
357#336C22×C10711yescharacteristic
358C22×Q8C23×C10711yescharacteristic
359C22×D4C23×C10711yescharacteristic
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—41no—
363C22×C8C23×C10711yescharacteristic
364C22×C8C23×C10711yescharacteristic
365C22×C8C23×C10711yescharacteristic
366C22×C8C23×C10711yescharacteristic
367#125—22no—
368#125—41no—
369C4×Q8—22no—
370C4×Q8—41no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4D4×C10711yescharacteristic
378C2×C4⋊C4D4×C10711yescharacteristic
379C2×C4⋊C4C23×C10711yescharacteristic
380C2×C4⋊C4C23×C10711yescharacteristic
381C2×C4⋊C4C23×C10711yescharacteristic
382C2×C4⋊C4C23×C10711yescharacteristic
383C2×C4⋊C4C23×C10711yescharacteristic
384C2×C4⋊C4C23×C10711yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C10711yescharacteristic
394C2×C42C23×C10711yescharacteristic
395C2×C42C23×C10711yescharacteristic
396#106—22no—
397C4⋊C8—22no—
398#103—22no—
399#103—22no—
400#103—22no—
401#102—22no—
402#102—22no—
403#102—41no—
404#97—22no—
405#97—41no—
406C4×C8—41no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95D4×C10711yescharacteristic
418#95D4×C10711yescharacteristic
419C24—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8#41×C10712yes—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4C2×D4×C10711yescharacteristic
440C22×C4C2×D4×C10711yescharacteristic
441C22×C4C2×D4×C10711yescharacteristic
442C22×C4C2×D4×C10711yescharacteristic
443C22×C4C2×D4×C10711yescharacteristic
444C22×C4C2×D4×C10711yescharacteristic
445C22×C4C24×C10711yescharacteristic
446SD16—44no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8#41×C10712yes—
458C2×C8#41×C10712yes—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—81no—
478C4⋊C4#41×C10712yes—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—81no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—42no—
492C42—81no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C22×D4×C10711yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—41no—
504Q8—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4C2×#41×C10711yescharacteristic
549C2×C4C2×#41×C10711yescharacteristic
550C2×C4C2×#41×C10711yescharacteristic
551C2×C4C2×#41×C10711yescharacteristic
552C2×C4H(5,𝔽2)×C10711yescharacteristic
553C2×C42−1+4×C10711yescharacteristic
554C8—22no—
555C8—22no—
556C8—41no—
557C8—41no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22#532×C10711yescharacteristic
566C22#546×C10711yescharacteristic
567C22#548×C10711yescharacteristic
568C22#575×C10711yescharacteristic
569C22#575×C10711yescharacteristic
570C22#577×C10711yescharacteristic
571C22#577×C10711yescharacteristic
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—42no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4#529×C10711yescharacteristic
586C4#539×C10711yescharacteristic
587C4#551×C10711yescharacteristic
588C4#556×C10711yescharacteristic
589C2—161no—
590C2C107×#256011yescharacteristic
591C2C107×#317411yescharacteristic
592C2C107×#318311yescharacteristic
593C2C107×#330711yescharacteristic
594C2C107×#332111yescharacteristic
595C2C107×#337111yescharacteristic
596C2C107×#337111yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C4⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2453C2semidirect
3. C107×#2088C2semidirect
4. C107×#2074C2semidirect
7. C107×#1991C2semidirect
11. C107×#1935C2semidirect
12. C107×#1920C2semidirect
14. C107×#1771C2semidirect
15. C107×#1763C2semidirect
290. #29102C107direct (N × H)
300. #2453C2×C107semidirect
301. #2088C2×C107semidirect
302. #2074C2×C107semidirect
305. #1991C2×C107semidirect
309. #1935C2×C107semidirect
310. #1920C2×C107semidirect
312. #1771C2×C107semidirect
313. #1763C2×C107semidirect
314. C107#29102direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#25132
C107×#24532
C107×#20882
C107×#20742
C107×#20552
C107×#20252
C107×#19912
C107×#19682
C107×#19362
C107×#19352
C107×#19202
C107×#18802
C107×#17712
C107×#17632
#29102107