Finite Group Databasebeta

← C107×#29134 #41055098

Subgroups — C107×#29134 #41055098

Order 27392.

690 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2647C211yesmaximal, characteristic, complemented
2C107×#2326C211yesmaximal, characteristic
3C107×#2100C211yesmaximal, characteristic, complemented
4C107×#2099C211yesmaximal, characteristic, complemented
5C107×#2042C211yesmaximal, characteristic
6C107×#2042C211yesmaximal, characteristic
7C107×#1936C211yesmaximal, characteristic
8C107×#1935C211yesmaximal, characteristic, complemented
9C107×#1934C211yesmaximal, characteristic
10C107×#1933C211yesmaximal, characteristic, complemented
11C107×#1805C211yesmaximal, characteristic, complemented
12C107×#1804C211yesmaximal, characteristic
13C107×#1803C211yesmaximal, characteristic, complemented
14C107×#1802C211yesmaximal, characteristic
15C107×#1768C211yesmaximal, characteristic, complemented
16C2×#124×C107C2211yescharacteristic
17C2×C4×Q8×C107C2211yescharacteristic
18C2×C4×D4×C107C2211yescharacteristic
19C2×C4⋊C8×C107C2211yescharacteristic
20C2×C4⋊C8×C107C2211yescharacteristic
21C2×#103×C107C2211yescharacteristic
22C2×#103×C107C2211yescharacteristic
23C2×#103×C107C2211yescharacteristic
24C2×#103×C107C2211yescharacteristic
25C2×#102×C107C2211yescharacteristic
26C2×#102×C107C2211yescharacteristic
27C2×#102×C107C2211yescharacteristic
28C2×#102×C107C2211yescharacteristic
29C2×#97×C107C2211yescharacteristic
30C2×C4×C8×C107C2211yescharacteristic
31#400×C107—21no—
32#400×C107—21no—
33#398×C107—21no—
34#398×C107—21no—
35#391×C107C2211yescharacteristic
36#390×C107C2211yescharacteristic
37#389×C107C2211yescharacteristic
38#389×C107C2211yescharacteristic
39#389×C107C2211yescharacteristic
40#389×C107C2211yescharacteristic
41#388×C107—21no—
42#388×C107—21no—
43#385×C107—21no—
44#385×C107—21no—
45#384×C107C2211yescharacteristic
46#384×C107C2211yescharacteristic
47#382×C107C2211yescharacteristic
48#376×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
61C23×C4×C107—21no—
62C22×C8×C107C2311yescharacteristic
63C22×C8×C107C2311yescharacteristic
64C22×C8×C107C2311yescharacteristic
65C22×C8×C107C2311yescharacteristic
66#124×C107—22no—
67#124×C107—22no—
68C4×Q8×C107—22no—
69C4×Q8×C107—22no—
70C4×D4×C107—22no—
71C4×D4×C107—22no—
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×C107—21no—
79C2×C4⋊C4×C107—21no—
80C2×C4⋊C4×C107—21no—
81C2×C4⋊C4×C107C2311yescharacteristic
82C2×C4⋊C4×C107C2311yescharacteristic
83C2×C4⋊C4×C107C2311yescharacteristic
84C2×C4⋊C4×C107C2311yescharacteristic
85C2×C4⋊C4×C107C2311yescharacteristic
86C2×C4⋊C4×C107C2311yescharacteristic
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×C107C2311yescharacteristic
94C2×C42×C107C2311yescharacteristic
95C2×C42×C107C2311yescharacteristic
96C4⋊C8×C107—22no—
97C4⋊C8×C107—22no—
98#103×C107—22no—
99#103×C107—22no—
100#103×C107—41no—
101#103×C107—41no—
102#102×C107—22no—
103#102×C107—22no—
104#102×C107—41no—
105#102×C107—41no—
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×C107D411yescharacteristic
117#95×C107D411yescharacteristic
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#4112yes—
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×C107—42no—
141C22×C4×C107—81no—
142C22×C4×C107—81no—
143C22×C4×C107C2×D411yescharacteristic
144C22×C4×C107C2×D411yescharacteristic
145C22×C4×C107C2×D411yescharacteristic
146C22×C4×C107C2×D411yescharacteristic
147C22×C4×C107C2×D411yescharacteristic
148C22×C4×C107C2×D411yescharacteristic
149C22×C4×C107C2411yescharacteristic
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—21no—
159C2×C8×C107—21no—
160C2×C8×C107—21no—
161C2×C8×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—21no—
172C4⋊C4×C107—21no—
173C4⋊C4×C107—21no—
174C4⋊C4×C107—42no—
175C4⋊C4×C107—81no—
176C4⋊C4×C107—81no—
177C4⋊C4×C107—81no—
178C4⋊C4×C107—81no—
179C4⋊C4×C107—81no—
180C4⋊C4×C107—81no—
181C4⋊C4×C107—81no—
182C4⋊C4×C107—81no—
183C22⋊C4×C107—24no—
184C22⋊C4×C107—24no—
185C22⋊C4×C107—42no—
186C22⋊C4×C107—81no—
187C22⋊C4×C107—81no—
188C42×C107—21no—
189C42×C107—21no—
190C42×C107—21no—
191C42×C107—21no—
192C42×C107—42no—
193C42×C107#4112yes—
194C42×C107#4112yes—
195C23×C107—22no—
196C23×C107—41no—
197C23×C107—41no—
198C23×C107—41no—
199C23×C107—41no—
200C23×C107—41no—
201C23×C107—41no—
202C23×C107C22×D411yescharacteristic
203Q8×C107—22no—
204Q8×C107—22no—
205Q8×C107—41no—
206Q8×C107—41no—
207D4×C107—22no—
208D4×C107—22no—
209D4×C107—41no—
210D4×C107—41no—
211C2×C4×C107—21no—
212C2×C4×C107—21no—
213C2×C4×C107—21no—
214C2×C4×C107—21no—
215C2×C4×C107—21no—
216C2×C4×C107—21no—
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—41no—
229C2×C4×C107—41no—
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—84no—
249C2×C4×C107#12412yes—
250C2×C4×C107#12412yes—
251C2×C4×C107C2×#4111yescharacteristic
252C2×C4×C107C2×#4111yescharacteristic
253C2×C4×C107C2×#4111yescharacteristic
254C2×C4×C107C2×#4111yescharacteristic
255C2×C4×C107H(5,𝔽2)11yescharacteristic
256C2×C4×C1072−1+411yescharacteristic
257C8×C107—41no—
258C8×C107—41no—
259C8×C107—41no—
260C8×C107—41no—
261C22×C107—42no—
262C22×C107—42no—
263C22×C107—42no—
264C22×C107—81no—
265C22×C107—81no—
266C22×C107—81no—
267C22×C107—81no—
268C22×C107#52511yescharacteristic
269C22×C107C2×#12411yescharacteristic
270C22×C107#53711yescharacteristic
271C22×C107#57611yescharacteristic
272C22×C107#57711yescharacteristic
273C22×C107#57711yescharacteristic
274C22×C107#57811yescharacteristic
275C4×C107—22no—
276C4×C107—22no—
277C4×C107—42no—
278C4×C107—41no—
279C4×C107—41no—
280C4×C107—41no—
281C4×C107—41no—
282C4×C107—81no—
283C4×C107—81no—
284C4×C107—81no—
285C4×C107—81no—
286C4×C107—81no—
287C4×C107—81no—
288C4×C107#55211yescharacteristic
289C4×C107#55211yescharacteristic
290C4×C107#55311yescharacteristic
291C4×C107#55311yescharacteristic
292#29134C10711yesmaximal, characteristic, direct product factor, Sylow
293C2×C107—82no—
294C2×C107#256211yescharacteristic
295C2×C107#311911yescharacteristic
296C2×C107#312011yescharacteristic
297C2×C107#313611yescharacteristic
298C2×C107#313711yescharacteristic
299C2×C107#326211yescharacteristic
300C2×C107#326311yescharacteristic
301#2647C2×C10711yescharacteristic, complemented
302#2326C2×C10711yescharacteristic
303#2100C2×C10711yescharacteristic, complemented
304#2099C2×C10711yescharacteristic, complemented
305#2042C2×C10711yescharacteristic
306#2042C2×C10711yescharacteristic
307#1936C2×C10711yescharacteristic
308#1935C2×C10711yescharacteristic, complemented
309#1934C2×C10711yescharacteristic
310#1933C2×C10711yescharacteristic, complemented
311#1805C2×C10711yescharacteristic, complemented
312#1804C2×C10711yescharacteristic
313#1803C2×C10711yescharacteristic, complemented
314#1802C2×C10711yescharacteristic
315#1768C2×C10711yescharacteristic, complemented
316C107#2913411yescharacteristic, direct product factor, Sylow
317C2×#124C22×C10711yescharacteristic
318C2×C4×Q8C22×C10711yescharacteristic
319C2×C4×D4C22×C10711yescharacteristic
320C2×C4⋊C8C22×C10711yescharacteristic
321C2×C4⋊C8C22×C10711yescharacteristic
322C2×#103C22×C10711yescharacteristic
323C2×#103C22×C10711yescharacteristic
324C2×#103C22×C10711yescharacteristic
325C2×#103C22×C10711yescharacteristic
326C2×#102C22×C10711yescharacteristic
327C2×#102C22×C10711yescharacteristic
328C2×#102C22×C10711yescharacteristic
329C2×#102C22×C10711yescharacteristic
330C2×#97C22×C10711yescharacteristic
331C2×C4×C8C22×C10711yescharacteristic
332#400—21no—
333#400—21no—
334#398—21no—
335#398—21no—
336#391C22×C10711yescharacteristic
337#390C22×C10711yescharacteristic
338#389C22×C10711yescharacteristic
339#389C22×C10711yescharacteristic
340#389C22×C10711yescharacteristic
341#389C22×C10711yescharacteristic
342#388—21no—
343#388—21no—
344#385—21no—
345#385—21no—
346#384C22×C10711yescharacteristic
347#384C22×C10711yescharacteristic
348#382C22×C10711yescharacteristic
349#376C22×C10711yescharacteristic
350#340C22×C10711yescharacteristic
351#340C22×C10711yescharacteristic
352#340C22×C10711yescharacteristic
353#340C22×C10711yescharacteristic
354#340C22×C10711yescharacteristic
355#340C22×C10711yescharacteristic
356#340C22×C10711yescharacteristic
357#340C22×C10711yescharacteristic
358#336C22×C10711yescharacteristic
359#336C22×C10711yescharacteristic
360C22×Q8C23×C10711yescharacteristic
361C22×D4C23×C10711yescharacteristic
362C23×C4—21no—
363C22×C8C23×C10711yescharacteristic
364C22×C8C23×C10711yescharacteristic
365C22×C8C23×C10711yescharacteristic
366C22×C8C23×C10711yescharacteristic
367#124—22no—
368#124—22no—
369C4×Q8—22no—
370C4×Q8—22no—
371C4×D4—22no—
372C4×D4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4C23×C10711yescharacteristic
383C2×C4⋊C4C23×C10711yescharacteristic
384C2×C4⋊C4C23×C10711yescharacteristic
385C2×C4⋊C4C23×C10711yescharacteristic
386C2×C4⋊C4C23×C10711yescharacteristic
387C2×C4⋊C4C23×C10711yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42—21no—
394C2×C42C23×C10711yescharacteristic
395C2×C42C23×C10711yescharacteristic
396C2×C42C23×C10711yescharacteristic
397C4⋊C8—22no—
398C4⋊C8—22no—
399#103—22no—
400#103—22no—
401#103—41no—
402#103—41no—
403#102—22no—
404#102—22no—
405#102—41no—
406#102—41no—
407#97—41no—
408C4×C8—41no—
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
419#95D4×C10711yescharacteristic
420#95D4×C10711yescharacteristic
421C24—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8#41×C10712yes—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4#41×C10712yes—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—81no—
443C22×C4—81no—
444C22×C4C2×D4×C10711yescharacteristic
445C22×C4C2×D4×C10711yescharacteristic
446C22×C4C2×D4×C10711yescharacteristic
447C22×C4C2×D4×C10711yescharacteristic
448C22×C4C2×D4×C10711yescharacteristic
449C22×C4C2×D4×C10711yescharacteristic
450C22×C4C24×C10711yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42#41×C10712yes—
495C42#41×C10712yes—
496C23—22no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C22×D4×C10711yescharacteristic
504Q8—22no—
505Q8—22no—
506Q8—41no—
507Q8—41no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
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×C4—41no—
549C2×C4—84no—
550C2×C4#124×C10712yes—
551C2×C4#124×C10712yes—
552C2×C4C2×#41×C10711yescharacteristic
553C2×C4C2×#41×C10711yescharacteristic
554C2×C4C2×#41×C10711yescharacteristic
555C2×C4C2×#41×C10711yescharacteristic
556C2×C4H(5,𝔽2)×C10711yescharacteristic
557C2×C42−1+4×C10711yescharacteristic
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#525×C10711yescharacteristic
570C22C2×#124×C10711yescharacteristic
571C22#537×C10711yescharacteristic
572C22#576×C10711yescharacteristic
573C22#577×C10711yescharacteristic
574C22#577×C10711yescharacteristic
575C22#578×C10711yescharacteristic
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—42no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4#552×C10711yescharacteristic
590C4#552×C10711yescharacteristic
591C4#553×C10711yescharacteristic
592C4#553×C10711yescharacteristic
593C2—82no—
594C2C107×#256211yescharacteristic
595C2C107×#311911yescharacteristic
596C2C107×#312011yescharacteristic
597C2C107×#313611yescharacteristic
598C2C107×#313711yescharacteristic
599C2C107×#326211yescharacteristic
600C2C107×#326311yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ #376×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2647C2semidirect
3. C107×#2100C2semidirect
4. C107×#2099C2semidirect
8. C107×#1935C2semidirect
10. C107×#1933C2semidirect
11. C107×#1805C2semidirect
13. C107×#1803C2semidirect
15. C107×#1768C2semidirect
292. #29134C107direct (N × H)
301. #2647C2×C107semidirect
303. #2100C2×C107semidirect
304. #2099C2×C107semidirect
308. #1935C2×C107semidirect
310. #1933C2×C107semidirect
311. #1805C2×C107semidirect
313. #1803C2×C107semidirect
315. #1768C2×C107semidirect
316. C107#29134direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#26472
C107×#23262
C107×#21002
C107×#20992
C107×#20422
C107×#19362
C107×#19352
C107×#19342
C107×#19332
C107×#18052
C107×#18042
C107×#18032
C107×#18022
C107×#17682
#29134107