Finite Group Databasebeta

← C107×#22820 #41048784

Subgroups — C107×#22820 #41048784

Order 27392.

838 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#440×C107C211yesmaximal, characteristic
2C107×#2356C211yesmaximal, characteristic, complemented
3C107×#2354C211yesmaximal, characteristic
4C107×#1973C211yesmaximal, characteristic
5C107×#1968C211yesmaximal, characteristic
6C107×#1928C211yesmaximal, characteristic, complemented
7C107×#1927C211yesmaximal, characteristic, complemented
8C107×#1926C211yesmaximal, characteristic
9C107×#1925C211yesmaximal, characteristic
10C107×#1847C211yesmaximal, characteristic, complemented
11C107×#1804C211yesmaximal, characteristic
12C107×#1803C211yesmaximal, characteristic, complemented
13C107×#1776C211yesmaximal, characteristic, complemented
14C4×#107×C107C211yesmaximal, characteristic, complemented
15C107×#1771C211yesmaximal, characteristic, complemented
16C22×SD16×C107C2211yescharacteristic
17C2×C4×Q8×C107C2211yescharacteristic
18C2×C4×D4×C107C2211yescharacteristic
19C2×#117×C107—21no—
20#440×C107C418yescomplemented
21C2×#107×C107C2211yescharacteristic
22C2×#107×C107C2211yescharacteristic
23C2×#107×C107C2211yescharacteristic
24C2×#106×C107C2211yescharacteristic
25C2×#106×C107C2211yescharacteristic
26C2×C4⋊C8×C107C2211yescharacteristic
27C2×#103×C107C2211yescharacteristic
28C2×#103×C107C2211yescharacteristic
29C2×#103×C107C2211yescharacteristic
30C2×#102×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#97×C107C2211yescharacteristic
34C2×#97×C107C2211yescharacteristic
35C2×C4×C8×C107C2211yescharacteristic
36#391×C107C2211yescharacteristic
37#391×C107C2211yescharacteristic
38#390×C107C2211yescharacteristic
39#390×C107C2211yescharacteristic
40#388×C107—21no—
41#388×C107—21no—
42#387×C107—21no—
43#387×C107—21no—
44#384×C107C2211yescharacteristic
45#383×C107—21no—
46#382×C107C2211yescharacteristic
47#380×C107—21no—
48C4×C4⋊C4×C107C2211yescharacteristic
49C4×C4⋊C4×C107C2211yescharacteristic
50C4×C4⋊C4×C107C2211yescharacteristic
51C4×C4⋊C4×C107C2211yescharacteristic
52C4×C4⋊C4×C107C2211yescharacteristic
53#376×C107—21no—
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59#336×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—
74#117×C107—44no—
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×C42×C107—21no—
92C2×C42×C107—21no—
93C2×C42×C107—21no—
94C2×C42×C107—21no—
95C2×C42×C107—21no—
96C2×C42×C107C2311yescharacteristic
97C2×C42×C107C2311yescharacteristic
98C2×C42×C107C2311yescharacteristic
99#107×C107—22no—
100#107×C107—41no—
101#107×C107C2×C414yes—
102#106×C107—22no—
103#106×C107—41no—
104C4⋊C8×C107—22no—
105#103×C107—41no—
106#103×C107—41no—
107#103×C107C2×C414yes—
108#102×C107—41no—
109#102×C107—41no—
110#102×C107C2×C414yes—
111#97×C107—22no—
112#97×C107C2×C414yes—
113C4×C8×C107—22no—
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×C107—21no—
122#95×C107—21no—
123#95×C107—21no—
124#95×C107D411yescharacteristic
125#95×C107D411yescharacteristic
126C24×C107—21no—
127C2×Q8×C107—21no—
128C2×Q8×C107—21no—
129C2×Q8×C107—21no—
130C2×Q8×C107—21no—
131C2×Q8×C107—21no—
132C2×Q8×C107C22×C412yes—
133C2×D4×C107—21no—
134C2×D4×C107—21no—
135C2×D4×C107—21no—
136C2×D4×C107—21no—
137C2×D4×C107—21no—
138C2×D4×C107C22×C412yes—
139C22×C4×C107—21no—
140C22×C4×C107—21no—
141C22×C4×C107—21no—
142C22×C4×C107—24no—
143C22×C4×C107—21no—
144C22×C4×C107—21no—
145C22×C4×C107—21no—
146C22×C4×C107—21no—
147C22×C4×C107—42no—
148C22×C4×C107—42no—
149C22×C4×C107C2×D411yescharacteristic
150C22×C4×C107C2×D411yescharacteristic
151C22×C4×C107C2×D411yescharacteristic
152C22×C4×C107C2×D411yescharacteristic
153C22×C4×C107C2×D411yescharacteristic
154C22×C4×C107C2×D411yescharacteristic
155C22×C4×C107C2411yescharacteristic
156SD16×C107—28no—
157C2×C8×C107—21no—
158C2×C8×C107—21no—
159C2×C8×C107—21no—
160C2×C8×C107—21no—
161C2×C8×C107—21no—
162C2×C8×C107—21no—
163C2×C8×C107—21no—
164C2×C8×C107—21no—
165C2×C8×C107C22×C412yes—
166C2×C8×C107C22×C412yes—
167C2×C8×C107#4112yes—
168C2×C8×C107#4112yes—
169C4⋊C4×C107—24no—
170C4⋊C4×C107—22no—
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—21no—
180C4⋊C4×C107—21no—
181C4⋊C4×C107—41no—
182C4⋊C4×C107—42no—
183C4⋊C4×C107—81no—
184C4⋊C4×C107C22×C412yes—
185C4⋊C4×C107C22×C412yes—
186C22⋊C4×C107—24no—
187C22⋊C4×C107—42no—
188C22⋊C4×C107—42no—
189C22⋊C4×C107—81no—
190C22⋊C4×C107—81no—
191C42×C107—24no—
192C42×C107—21no—
193C42×C107—21no—
194C42×C107—21no—
195C42×C107—21no—
196C42×C107—42no—
197C42×C107—42no—
198C42×C107—42no—
199C42×C107—42no—
200C42×C107C22×C412yes—
201C42×C107#4112yes—
202C23×C107—22no—
203C23×C107—41no—
204C23×C107—41no—
205C23×C107—41no—
206C23×C107—41no—
207C23×C107—41no—
208C23×C107—41no—
209C23×C107C22×D411yescharacteristic
210Q8×C107—22no—
211Q8×C107—22no—
212Q8×C107—41no—
213Q8×C107—41no—
214D4×C107—22no—
215D4×C107—22no—
216D4×C107—41no—
217D4×C107—41no—
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—22no—
225C2×C4×C107—22no—
226C2×C4×C107—22no—
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—21no—
235C2×C4×C107—21no—
236C2×C4×C107—48no—
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—41no—
253C2×C4×C107—41no—
254C2×C4×C107—41no—
255C2×C4×C107C4×D412yes—
256C2×C4×C107C4×D412yes—
257C2×C4×C107AGL(1,ℤ/8)12yes—
258C2×C4×C107C23×C411yescharacteristic
259C2×C4×C107C2×#4111yescharacteristic
260C2×C4×C107C2×#4111yescharacteristic
261C2×C4×C107C2×#4111yescharacteristic
262C2×C4×C107H(5,𝔽2)11yescharacteristic
263C2×C4×C1072−1+411yescharacteristic
264C8×C107—22no—
265C8×C107—41no—
266C8×C107—41no—
267C8×C107#11714yescomplemented
268C22×C107—42no—
269C22×C107—42no—
270C22×C107—42no—
271C22×C107—81no—
272C22×C107—81no—
273C22×C107—81no—
274C22×C107—81no—
275C22×C107C2×C4×D411yescharacteristic
276C22×C107#54711yescharacteristic
277C22×C107#55011yescharacteristic
278C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C107#57511yescharacteristic
280C22×C107#57711yescharacteristic
281C22×C107#57811yescharacteristic
282C4×C107—22no—
283C4×C107—22no—
284C4×C107—22no—
285C4×C107—41no—
286C4×C107—41no—
287C4×C107—41no—
288C4×C107—42no—
289C4×C107—42no—
290C4×C107—42no—
291C4×C107—81no—
292C4×C107—81no—
293C4×C107—81no—
294C4×C107—81no—
295C4×C107C2×#11711yescharacteristic
296C4×C107#52011yescharacteristic
297C4×C107#55511yescharacteristic
298C4×C107#55611yescharacteristic
299#22820C10711yesmaximal, characteristic, direct product factor, Sylow
300C2×C107—82no—
301C2×C107#235411yescharacteristic
302C2×C107C4×AGL(1,ℤ/8)11yescharacteristic
303C2×C107#294711yescharacteristic
304C2×C107#334311yescharacteristic
305C2×C107#334811yescharacteristic
306C2×C107#339711yescharacteristic
307C2×C107#340211yescharacteristic
308C2×#440C2×C10711yescharacteristic
309#2356C2×C10711yescharacteristic, complemented
310#2354C2×C10711yescharacteristic
311#1973C2×C10711yescharacteristic
312#1968C2×C10711yescharacteristic
313#1928C2×C10711yescharacteristic, complemented
314#1927C2×C10711yescharacteristic, complemented
315#1926C2×C10711yescharacteristic
316#1925C2×C10711yescharacteristic
317#1847C2×C10711yescharacteristic, complemented
318#1804C2×C10711yescharacteristic
319#1803C2×C10711yescharacteristic, complemented
320#1776C2×C10711yescharacteristic, complemented
321C4×#107C2×C10711yescharacteristic, complemented
322#1771C2×C10711yescharacteristic, complemented
323C107#2282011yescharacteristic, direct product factor, Sylow
324C22×SD16C22×C10711yescharacteristic
325C2×C4×Q8C22×C10711yescharacteristic
326C2×C4×D4C22×C10711yescharacteristic
327C2×#117—21no—
328#440C4×C10718yescomplemented
329C2×#107C22×C10711yescharacteristic
330C2×#107C22×C10711yescharacteristic
331C2×#107C22×C10711yescharacteristic
332C2×#106C22×C10711yescharacteristic
333C2×#106C22×C10711yescharacteristic
334C2×C4⋊C8C22×C10711yescharacteristic
335C2×#103C22×C10711yescharacteristic
336C2×#103C22×C10711yescharacteristic
337C2×#103C22×C10711yescharacteristic
338C2×#102C22×C10711yescharacteristic
339C2×#102C22×C10711yescharacteristic
340C2×#102C22×C10711yescharacteristic
341C2×#97C22×C10711yescharacteristic
342C2×#97C22×C10711yescharacteristic
343C2×C4×C8C22×C10711yescharacteristic
344#391C22×C10711yescharacteristic
345#391C22×C10711yescharacteristic
346#390C22×C10711yescharacteristic
347#390C22×C10711yescharacteristic
348#388—21no—
349#388—21no—
350#387—21no—
351#387—21no—
352#384C22×C10711yescharacteristic
353#383—21no—
354#382C22×C10711yescharacteristic
355#380—21no—
356C4×C4⋊C4C22×C10711yescharacteristic
357C4×C4⋊C4C22×C10711yescharacteristic
358C4×C4⋊C4C22×C10711yescharacteristic
359C4×C4⋊C4C22×C10711yescharacteristic
360C4×C4⋊C4C22×C10711yescharacteristic
361#376—21no—
362#340C22×C10711yescharacteristic
363#340C22×C10711yescharacteristic
364#340C22×C10711yescharacteristic
365#340C22×C10711yescharacteristic
366#336C22×C10711yescharacteristic
367#336C22×C10711yescharacteristic
368C22×Q8C23×C10711yescharacteristic
369C22×D4C23×C10711yescharacteristic
370C23×C4—21no—
371C2×SD16—22no—
372C2×SD16—22no—
373C2×SD16C2×C4×C10714yes—
374C22×C8C23×C10711yescharacteristic
375C22×C8C23×C10711yescharacteristic
376C22×C8C23×C10711yescharacteristic
377C22×C8C23×C10711yescharacteristic
378C4×Q8—22no—
379C4×Q8C2×C4×C10714yes—
380C4×D4—22no—
381C4×D4C2×C4×C10714yes—
382#117—44no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4D4×C10711yescharacteristic
387C2×C4⋊C4D4×C10711yescharacteristic
388C2×C4⋊C4C23×C10711yescharacteristic
389C2×C4⋊C4C23×C10711yescharacteristic
390C2×C4⋊C4C23×C10711yescharacteristic
391C2×C4⋊C4C23×C10711yescharacteristic
392C2×C4⋊C4C23×C10711yescharacteristic
393C2×C4⋊C4C23×C10711yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42C23×C10711yescharacteristic
405C2×C42C23×C10711yescharacteristic
406C2×C42C23×C10711yescharacteristic
407#107—22no—
408#107—41no—
409#107C2×C4×C10714yes—
410#106—22no—
411#106—41no—
412C4⋊C8—22no—
413#103—41no—
414#103—41no—
415#103C2×C4×C10714yes—
416#102—41no—
417#102—41no—
418#102C2×C4×C10714yes—
419#97—22no—
420#97C2×C4×C10714yes—
421C4×C8—22no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95D4×C10711yescharacteristic
433#95D4×C10711yescharacteristic
434C24—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C22×C4×C10712yes—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C22×C4×C10712yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4C2×D4×C10711yescharacteristic
458C22×C4C2×D4×C10711yescharacteristic
459C22×C4C2×D4×C10711yescharacteristic
460C22×C4C2×D4×C10711yescharacteristic
461C22×C4C2×D4×C10711yescharacteristic
462C22×C4C2×D4×C10711yescharacteristic
463C22×C4C24×C10711yescharacteristic
464SD16—28no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8C22×C4×C10712yes—
474C2×C8C22×C4×C10712yes—
475C2×C8#41×C10712yes—
476C2×C8#41×C10712yes—
477C4⋊C4—24no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—42no—
491C4⋊C4—81no—
492C4⋊C4C22×C4×C10712yes—
493C4⋊C4C22×C4×C10712yes—
494C22⋊C4—24no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—81no—
498C22⋊C4—81no—
499C42—24no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—42no—
505C42—42no—
506C42—42no—
507C42—42no—
508C42C22×C4×C10712yes—
509C42#41×C10712yes—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C22×D4×C10711yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—48no—
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—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4C4×D4×C10712yes—
564C2×C4C4×D4×C10712yes—
565C2×C4AGL(1,ℤ/8)×C10712yes—
566C2×C4C23×C4×C10711yescharacteristic
567C2×C4C2×#41×C10711yescharacteristic
568C2×C4C2×#41×C10711yescharacteristic
569C2×C4C2×#41×C10711yescharacteristic
570C2×C4H(5,𝔽2)×C10711yescharacteristic
571C2×C42−1+4×C10711yescharacteristic
572C8—22no—
573C8—41no—
574C8—41no—
575C8#117×C10714yescomplemented
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C2×C4×D4×C10711yescharacteristic
584C22#547×C10711yescharacteristic
585C22#550×C10711yescharacteristic
586C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
587C22#575×C10711yescharacteristic
588C22#577×C10711yescharacteristic
589C22#578×C10711yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—42no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C2×#117×C10711yescharacteristic
604C4#520×C10711yescharacteristic
605C4#555×C10711yescharacteristic
606C4#556×C10711yescharacteristic
607C2—82no—
608C2C107×#235411yescharacteristic
609C2C4×AGL(1,ℤ/8)×C10711yescharacteristic
610C2C107×#294711yescharacteristic
611C2C107×#334311yescharacteristic
612C2C107×#334811yescharacteristic
613C2C107×#339711yescharacteristic
614C2C107×#340211yescharacteristic
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 ◁ C4×C4⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2356C2semidirect
6. C107×#1928C2semidirect
7. C107×#1927C2semidirect
10. C107×#1847C2semidirect
12. C107×#1803C2semidirect
13. C107×#1776C2semidirect
14. C4×#107×C107C2semidirect
15. C107×#1771C2semidirect
20. #440×C107C4semidirect
267. C8×C107#117semidirect
299. #22820C107direct (N × H)
309. #2356C2×C107semidirect
313. #1928C2×C107semidirect
314. #1927C2×C107semidirect
317. #1847C2×C107semidirect
319. #1803C2×C107semidirect
320. #1776C2×C107semidirect
321. C4×#107C2×C107semidirect
322. #1771C2×C107semidirect
323. C107#22820direct (N × H)
328. #440C4×C107semidirect
575. C8#117×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×#23562
C107×#23542
C107×#19732
C107×#19682
C107×#19282
C107×#19272
C107×#19262
C107×#19252
C107×#18472
C107×#18042
C107×#18032
C107×#17762
C4×#107×C1072
C107×#17712
#22820107