Finite Group Databasebeta

← C107×#21291 #41047255

Subgroups — C107×#21291 #41047255

Order 27392.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#440×C107C211yesmaximal, characteristic
2C107×#2320C211yesmaximal, characteristic, complemented
3C107×#2319C211yesmaximal, characteristic
4C107×#1973C211yesmaximal, characteristic
5C107×#1968C211yesmaximal, characteristic
6C107×#1943C211yesmaximal, characteristic, complemented
7C107×#1942C211yesmaximal, characteristic, complemented
8C107×#1936C211yesmaximal, characteristic
9C107×#1935C211yesmaximal, characteristic, complemented
10C107×#1934C211yesmaximal, characteristic
11C107×#1933C211yesmaximal, characteristic, complemented
12C107×#1776C211yesmaximal, characteristic, complemented
13C4×#103×C107C211yesmaximal, characteristic, complemented
14C4×#102×C107C211yesmaximal, characteristic
15C107×#1726C211yesmaximal, characteristic, complemented
16C22×SD16×C107C2211yescharacteristic
17C2×C4×Q8×C107C2211yescharacteristic
18C2×C4×D4×C107C2211yescharacteristic
19#440×C107C418yescomplemented
20C2×#107×C107C2211yescharacteristic
21C2×#107×C107C2211yescharacteristic
22C2×#106×C107C2211yescharacteristic
23C2×#103×C107C2211yescharacteristic
24C2×#103×C107C2211yescharacteristic
25C2×#103×C107C2211yescharacteristic
26C2×#102×C107C2211yescharacteristic
27C2×#102×C107C2211yescharacteristic
28C2×#102×C107C2211yescharacteristic
29C2×#97×C107C2211yescharacteristic
30C2×#97×C107C2211yescharacteristic
31C2×#97×C107C2211yescharacteristic
32C2×C4×C8×C107C2211yescharacteristic
33C2×C4×C8×C107C2211yescharacteristic
34C2×C4×C8×C107C2211yescharacteristic
35#391×C107C2211yescharacteristic
36#391×C107C2211yescharacteristic
37#390×C107C2211yescharacteristic
38#390×C107C2211yescharacteristic
39#389×C107C2211yescharacteristic
40#389×C107C2211yescharacteristic
41#389×C107C2211yescharacteristic
42#389×C107C2211yescharacteristic
43#388×C107—21no—
44#388×C107—21no—
45#387×C107—21no—
46#387×C107—21no—
47#383×C107—21no—
48#382×C107—21no—
49#381×C107—21no—
50#380×C107—21no—
51C4×C4⋊C4×C107C2211yescharacteristic
52C4×C4⋊C4×C107C2211yescharacteristic
53#376×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60C22×Q8×C107C2311yescharacteristic
61C22×D4×C107C2311yescharacteristic
62C23×C4×C107—21no—
63C2×SD16×C107—22no—
64C2×SD16×C107—22no—
65C2×SD16×C107C2×C414yes—
66C22×C8×C107C2311yescharacteristic
67C22×C8×C107C2311yescharacteristic
68C22×C8×C107C2311yescharacteristic
69C22×C8×C107C2311yescharacteristic
70C4×Q8×C107—22no—
71C4×Q8×C107C2×C414yes—
72C4×D4×C107—22no—
73C4×D4×C107C2×C414yes—
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×C107C2311yescharacteristic
80C2×C4⋊C4×C107C2311yescharacteristic
81C2×C4⋊C4×C107C2311yescharacteristic
82C2×C4⋊C4×C107C2311yescharacteristic
83C2×C4⋊C4×C107C2311yescharacteristic
84C2×C4⋊C4×C107C2311yescharacteristic
85C2×C22⋊C4×C107—21no—
86C2×C22⋊C4×C107—21no—
87C2×C22⋊C4×C107—21no—
88C2×C22⋊C4×C107—21no—
89C2×C22⋊C4×C107—21no—
90C2×C42×C107—21no—
91C2×C42×C107—21no—
92C2×C42×C107—21no—
93C2×C42×C107C2311yescharacteristic
94C2×C42×C107C2311yescharacteristic
95C2×C42×C107C2311yescharacteristic
96#107×C107—22no—
97#107×C107C2×C414yes—
98#106×C107—22no—
99#103×C107—22no—
100#103×C107—22no—
101#103×C107C2×C414yes—
102#102×C107—22no—
103#102×C107—22no—
104#102×C107C2×C414yes—
105#97×C107—22no—
106#97×C107—22no—
107#97×C107C2×C414yes—
108C4×C8×C107—22no—
109C4×C8×C107—22no—
110C4×C8×C107—22no—
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×C107—21no—
119#95×C107—21no—
120#95×C107—21no—
121#95×C107D411yescharacteristic
122#95×C107D411yescharacteristic
123#95×C107D411yescharacteristic
124#95×C107D411yescharacteristic
125C24×C107—21no—
126C2×Q8×C107—21no—
127C2×Q8×C107—21no—
128C2×Q8×C107—21no—
129C2×Q8×C107—21no—
130C2×Q8×C107—21no—
131C2×Q8×C107C22×C412yes—
132C2×D4×C107—21no—
133C2×D4×C107—21no—
134C2×D4×C107—21no—
135C2×D4×C107—21no—
136C2×D4×C107—21no—
137C2×D4×C107C22×C412yes—
138C22×C4×C107—21no—
139C22×C4×C107—21no—
140C22×C4×C107—21no—
141C22×C4×C107—24no—
142C22×C4×C107—21no—
143C22×C4×C107—21no—
144C22×C4×C107—21no—
145C22×C4×C107—21no—
146C22×C4×C107—81no—
147C22×C4×C107—81no—
148C22×C4×C107C2×D411yescharacteristic
149C22×C4×C107C2×D411yescharacteristic
150C22×C4×C107C2×D411yescharacteristic
151C22×C4×C107C2×D411yescharacteristic
152C22×C4×C107C2×D411yescharacteristic
153C22×C4×C107C2×D411yescharacteristic
154C22×C4×C107C2411yescharacteristic
155SD16×C107—28no—
156C2×C8×C107—21no—
157C2×C8×C107—21no—
158C2×C8×C107—21no—
159C2×C8×C107—21no—
160C2×C8×C107—21no—
161C2×C8×C107—21no—
162C2×C8×C107C22×C412yes—
163C2×C8×C107C22×C412yes—
164C2×C8×C107#4112yes—
165C2×C8×C107#4112yes—
166C2×C8×C107#4112yes—
167C2×C8×C107#4112yes—
168C4⋊C4×C107—24no—
169C4⋊C4×C107—21no—
170C4⋊C4×C107—21no—
171C4⋊C4×C107—21no—
172C4⋊C4×C107—21no—
173C4⋊C4×C107—21no—
174C4⋊C4×C107—21no—
175C4⋊C4×C107—21no—
176C4⋊C4×C107—21no—
177C4⋊C4×C107—21no—
178C4⋊C4×C107—21no—
179C4⋊C4×C107—81no—
180C4⋊C4×C107—81no—
181C4⋊C4×C107—81no—
182C4⋊C4×C107—81no—
183C4⋊C4×C107C22×C412yes—
184C4⋊C4×C107C22×C412yes—
185C22⋊C4×C107—24no—
186C22⋊C4×C107—81no—
187C22⋊C4×C107—81no—
188C22⋊C4×C107—81no—
189C22⋊C4×C107—81no—
190C42×C107—24no—
191C42×C107—21no—
192C42×C107—21no—
193C42×C107—21no—
194C42×C107—21no—
195C42×C107—81no—
196C42×C107—81no—
197C42×C107C22×C412yes—
198C42×C107#4112yes—
199C23×C107—22no—
200C23×C107—41no—
201C23×C107—41no—
202C23×C107—41no—
203C23×C107—41no—
204C23×C107—41no—
205C23×C107—41no—
206C23×C107C22×D411yescharacteristic
207Q8×C107—22no—
208Q8×C107—22no—
209Q8×C107—41no—
210Q8×C107—41no—
211D4×C107—22no—
212D4×C107—22no—
213D4×C107—41no—
214D4×C107—41no—
215C2×C4×C107—21no—
216C2×C4×C107—21no—
217C2×C4×C107—21no—
218C2×C4×C107—21no—
219C2×C4×C107—22no—
220C2×C4×C107—22no—
221C2×C4×C107—22no—
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—21no—
231C2×C4×C107—21no—
232C2×C4×C107—21no—
233C2×C4×C107—21no—
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×C107—41no—
250C2×C4×C107—41no—
251C2×C4×C107—41no—
252C2×C4×C107—84no—
253C2×C4×C107C4×D412yes—
254C2×C4×C107C4×D412yes—
255C2×C4×C107C23×C411yescharacteristic
256C2×C4×C107C2×#4111yescharacteristic
257C2×C4×C107C2×#4111yescharacteristic
258C2×C4×C107C2×#4111yescharacteristic
259C2×C4×C107C2×#4111yescharacteristic
260C2×C4×C107C2×#4111yescharacteristic
261C8×C107—22no—
262C8×C107—22no—
263C8×C107—22no—
264C8×C107#11714yes—
265C22×C107—42no—
266C22×C107—42no—
267C22×C107—42no—
268C22×C107—81no—
269C22×C107—81no—
270C22×C107—81no—
271C22×C107—81no—
272C22×C107C2×C4×D411yescharacteristic
273C22×C107#53211yescharacteristic
274C22×C107#53211yescharacteristic
275C22×C107#57611yescharacteristic
276C22×C107#57711yescharacteristic
277C22×C107#57711yescharacteristic
278C22×C107#57811yescharacteristic
279C4×C107—22no—
280C4×C107—22no—
281C4×C107—41no—
282C4×C107—41no—
283C4×C107—41no—
284C4×C107—41no—
285C4×C107—42no—
286C4×C107—42no—
287C4×C107—42no—
288C4×C107—81no—
289C4×C107—81no—
290C4×C107—81no—
291C4×C107—81no—
292C4×C107C2×#11711yescharacteristic
293C4×C107C4×#4111yescharacteristic
294C4×C107#52911yescharacteristic
295C4×C107#52911yescharacteristic
296#21291C10711yesmaximal, characteristic, direct product factor, Sylow
297C2×C107—82no—
298C2×C107#229311yescharacteristic
299C2×C107#294611yescharacteristic
300C2×C107#294711yescharacteristic
301C2×C107#317411yescharacteristic
302C2×C107#317511yescharacteristic
303C2×C107#317811yescharacteristic
304C2×C107#317911yescharacteristic
305C2×#440C2×C10711yescharacteristic
306#2320C2×C10711yescharacteristic, complemented
307#2319C2×C10711yescharacteristic
308#1973C2×C10711yescharacteristic
309#1968C2×C10711yescharacteristic
310#1943C2×C10711yescharacteristic, complemented
311#1942C2×C10711yescharacteristic, complemented
312#1936C2×C10711yescharacteristic
313#1935C2×C10711yescharacteristic, complemented
314#1934C2×C10711yescharacteristic
315#1933C2×C10711yescharacteristic, complemented
316#1776C2×C10711yescharacteristic, complemented
317C4×#103C2×C10711yescharacteristic, complemented
318C4×#102C2×C10711yescharacteristic
319#1726C2×C10711yescharacteristic, complemented
320C107#2129111yescharacteristic, direct product factor, Sylow
321C22×SD16C22×C10711yescharacteristic
322C2×C4×Q8C22×C10711yescharacteristic
323C2×C4×D4C22×C10711yescharacteristic
324#440C4×C10718yescomplemented
325C2×#107C22×C10711yescharacteristic
326C2×#107C22×C10711yescharacteristic
327C2×#106C22×C10711yescharacteristic
328C2×#103C22×C10711yescharacteristic
329C2×#103C22×C10711yescharacteristic
330C2×#103C22×C10711yescharacteristic
331C2×#102C22×C10711yescharacteristic
332C2×#102C22×C10711yescharacteristic
333C2×#102C22×C10711yescharacteristic
334C2×#97C22×C10711yescharacteristic
335C2×#97C22×C10711yescharacteristic
336C2×#97C22×C10711yescharacteristic
337C2×C4×C8C22×C10711yescharacteristic
338C2×C4×C8C22×C10711yescharacteristic
339C2×C4×C8C22×C10711yescharacteristic
340#391C22×C10711yescharacteristic
341#391C22×C10711yescharacteristic
342#390C22×C10711yescharacteristic
343#390C22×C10711yescharacteristic
344#389C22×C10711yescharacteristic
345#389C22×C10711yescharacteristic
346#389C22×C10711yescharacteristic
347#389C22×C10711yescharacteristic
348#388—21no—
349#388—21no—
350#387—21no—
351#387—21no—
352#383—21no—
353#382—21no—
354#381—21no—
355#380—21no—
356C4×C4⋊C4C22×C10711yescharacteristic
357C4×C4⋊C4C22×C10711yescharacteristic
358#376C22×C10711yescharacteristic
359#340C22×C10711yescharacteristic
360#340C22×C10711yescharacteristic
361#340C22×C10711yescharacteristic
362#340C22×C10711yescharacteristic
363#340C22×C10711yescharacteristic
364#340C22×C10711yescharacteristic
365C22×Q8C23×C10711yescharacteristic
366C22×D4C23×C10711yescharacteristic
367C23×C4—21no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16C2×C4×C10714yes—
371C22×C8C23×C10711yescharacteristic
372C22×C8C23×C10711yescharacteristic
373C22×C8C23×C10711yescharacteristic
374C22×C8C23×C10711yescharacteristic
375C4×Q8—22no—
376C4×Q8C2×C4×C10714yes—
377C4×D4—22no—
378C4×D4C2×C4×C10714yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4C23×C10711yescharacteristic
385C2×C4⋊C4C23×C10711yescharacteristic
386C2×C4⋊C4C23×C10711yescharacteristic
387C2×C4⋊C4C23×C10711yescharacteristic
388C2×C4⋊C4C23×C10711yescharacteristic
389C2×C4⋊C4C23×C10711yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C10711yescharacteristic
399C2×C42C23×C10711yescharacteristic
400C2×C42C23×C10711yescharacteristic
401#107—22no—
402#107C2×C4×C10714yes—
403#106—22no—
404#103—22no—
405#103—22no—
406#103C2×C4×C10714yes—
407#102—22no—
408#102—22no—
409#102C2×C4×C10714yes—
410#97—22no—
411#97—22no—
412#97C2×C4×C10714yes—
413C4×C8—22no—
414C4×C8—22no—
415C4×C8—22no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95D4×C10711yescharacteristic
427#95D4×C10711yescharacteristic
428#95D4×C10711yescharacteristic
429#95D4×C10711yescharacteristic
430C24—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C22×C4×C10712yes—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C22×C4×C10712yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4C2×D4×C10711yescharacteristic
454C22×C4C2×D4×C10711yescharacteristic
455C22×C4C2×D4×C10711yescharacteristic
456C22×C4C2×D4×C10711yescharacteristic
457C22×C4C2×D4×C10711yescharacteristic
458C22×C4C2×D4×C10711yescharacteristic
459C22×C4C24×C10711yescharacteristic
460SD16—28no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8C22×C4×C10712yes—
468C2×C8C22×C4×C10712yes—
469C2×C8#41×C10712yes—
470C2×C8#41×C10712yes—
471C2×C8#41×C10712yes—
472C2×C8#41×C10712yes—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4C22×C4×C10712yes—
489C4⋊C4C22×C4×C10712yes—
490C22⋊C4—24no—
491C22⋊C4—81no—
492C22⋊C4—81no—
493C22⋊C4—81no—
494C22⋊C4—81no—
495C42—24no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—81no—
501C42—81no—
502C42C22×C4×C10712yes—
503C42#41×C10712yes—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×D4×C10711yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
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—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—84no—
558C2×C4C4×D4×C10712yes—
559C2×C4C4×D4×C10712yes—
560C2×C4C23×C4×C10711yescharacteristic
561C2×C4C2×#41×C10711yescharacteristic
562C2×C4C2×#41×C10711yescharacteristic
563C2×C4C2×#41×C10711yescharacteristic
564C2×C4C2×#41×C10711yescharacteristic
565C2×C4C2×#41×C10711yescharacteristic
566C8—22no—
567C8—22no—
568C8—22no—
569C8#117×C10714yes—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×C4×D4×C10711yescharacteristic
578C22#532×C10711yescharacteristic
579C22#532×C10711yescharacteristic
580C22#576×C10711yescharacteristic
581C22#577×C10711yescharacteristic
582C22#577×C10711yescharacteristic
583C22#578×C10711yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4C2×#117×C10711yescharacteristic
598C4C4×#41×C10711yescharacteristic
599C4#529×C10711yescharacteristic
600C4#529×C10711yescharacteristic
601C2—82no—
602C2C107×#229311yescharacteristic
603C2C107×#294611yescharacteristic
604C2C107×#294711yescharacteristic
605C2C107×#317411yescharacteristic
606C2C107×#317511yescharacteristic
607C2C107×#317811yescharacteristic
608C2C107×#317911yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ #376×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2320C2semidirect
6. C107×#1943C2semidirect
7. C107×#1942C2semidirect
9. C107×#1935C2semidirect
11. C107×#1933C2semidirect
12. C107×#1776C2semidirect
13. C4×#103×C107C2semidirect
15. C107×#1726C2semidirect
19. #440×C107C4semidirect
296. #21291C107direct (N × H)
306. #2320C2×C107semidirect
310. #1943C2×C107semidirect
311. #1942C2×C107semidirect
313. #1935C2×C107semidirect
315. #1933C2×C107semidirect
316. #1776C2×C107semidirect
317. C4×#103C2×C107semidirect
319. #1726C2×C107semidirect
320. C107#21291direct (N × H)
324. #440C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#440×C1072
C107×#23202
C107×#23192
C107×#19732
C107×#19682
C107×#19432
C107×#19422
C107×#19362
C107×#19352
C107×#19342
C107×#19332
C107×#17762
C4×#103×C1072
C4×#102×C1072
C107×#17262
#21291107