Finite Group Databasebeta

← C107×#22233 #41048197

Subgroups — C107×#22233 #41048197

Order 27392.

782 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#489×C107C211yesmaximal, characteristic
2C107×#2331C211yesmaximal, characteristic, complemented
3C107×#2326C211yesmaximal, characteristic
4C107×#1990C211yesmaximal, characteristic, complemented
5C107×#1958C211yesmaximal, characteristic
6C107×#1928C211yesmaximal, characteristic, complemented
7C107×#1927C211yesmaximal, characteristic, complemented
8C107×#1926C211yesmaximal, characteristic
9C107×#1925C211yesmaximal, characteristic
10C107×#1865C211yesmaximal, characteristic, complemented
11C107×#1864C211yesmaximal, characteristic
12C107×#1863C211yesmaximal, characteristic, complemented
13C107×#1862C211yesmaximal, characteristic
14C107×#1847C211yesmaximal, characteristic, complemented
15C107×#1746C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C107C2211yescharacteristic
17C2×#124×C107C2211yescharacteristic
18C2×C4×Q8×C107C2211yescharacteristic
19C2×C4×D4×C107C2211yescharacteristic
20#489×C107C418yescomplemented
21C2×#107×C107C2211yescharacteristic
22C2×#107×C107C2211yescharacteristic
23C2×#106×C107C2211yescharacteristic
24C2×#106×C107C2211yescharacteristic
25C2×#103×C107C2211yescharacteristic
26C2×#103×C107C2211yescharacteristic
27C2×#103×C107C2211yescharacteristic
28C2×#103×C107C2211yescharacteristic
29C2×#102×C107C2211yescharacteristic
30C2×#102×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#97×C107C2211yescharacteristic
34C2×C4×C8×C107C2211yescharacteristic
35#391×C107—21no—
36#391×C107—21no—
37#391×C107C2211yescharacteristic
38#390×C107C2211yescharacteristic
39#389×C107C2211yescharacteristic
40#389×C107C2211yescharacteristic
41#388×C107—21no—
42#388×C107—21no—
43#387×C107—21no—
44#387×C107—21no—
45#385×C107—21no—
46#385×C107—21no—
47#384×C107C2211yescharacteristic
48#382×C107C2211yescharacteristic
49C4×C4⋊C4×C107C2211yescharacteristic
50C4×C4⋊C4×C107C2211yescharacteristic
51#376×C107C2211yescharacteristic
52#340×C107C2211yescharacteristic
53#340×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#336×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60C22×Q8×C107—21no—
61C22×Q8×C107C2311yescharacteristic
62C22×D4×C107C2311yescharacteristic
63C23×C4×C107—21no—
64C22×C8×C107C2311yescharacteristic
65C22×C8×C107C2311yescharacteristic
66C22×C8×C107C2311yescharacteristic
67C22×C8×C107C2311yescharacteristic
68C4⋊Q8×C107—22no—
69C4⋊Q8×C107C2×C414yescomplemented
70#124×C107—22no—
71#124×C107C2×C414yes—
72C4×Q8×C107—41no—
73C4×Q8×C107—41no—
74C4×D4×C107—41no—
75C4×D4×C107—41no—
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×C107—21no—
82C2×C4⋊C4×C107C2311yescharacteristic
83C2×C4⋊C4×C107C2311yescharacteristic
84C2×C4⋊C4×C107C2311yescharacteristic
85C2×C4⋊C4×C107C2311yescharacteristic
86C2×C4⋊C4×C107C2311yescharacteristic
87C2×C4⋊C4×C107C2311yescharacteristic
88C2×C22⋊C4×C107—21no—
89C2×C22⋊C4×C107—21no—
90C2×C22⋊C4×C107—21no—
91C2×C22⋊C4×C107—21no—
92C2×C22⋊C4×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—41no—
100#107×C107—41no—
101#106×C107—41no—
102#106×C107—41no—
103#103×C107—41no—
104#103×C107—41no—
105#103×C107C2×C414yescomplemented
106#103×C107C2×C414yescomplemented
107#102×C107—41no—
108#102×C107—41no—
109#102×C107C2×C414yes—
110#102×C107C2×C414yes—
111#97×C107C2×C414yescomplemented
112C4×C8×C107—22no—
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—24no—
127C2×Q8×C107—21no—
128C2×Q8×C107—21no—
129C2×Q8×C107—21no—
130C2×Q8×C107—21no—
131C2×Q8×C107—21no—
132C2×Q8×C107—81no—
133C2×Q8×C107—81no—
134C2×Q8×C107C22×C412yes—
135C2×D4×C107—21no—
136C2×D4×C107—21no—
137C2×D4×C107—21no—
138C2×D4×C107—21no—
139C2×D4×C107—21no—
140C2×D4×C107C22×C412yes—
141C22×C4×C107—21no—
142C22×C4×C107—21no—
143C22×C4×C107—21no—
144C22×C4×C107—21no—
145C22×C4×C107—21no—
146C22×C4×C107—21no—
147C22×C4×C107—21no—
148C22×C4×C107—42no—
149C22×C4×C107—81no—
150C22×C4×C107—81no—
151C22×C4×C107C2×D411yescharacteristic
152C22×C4×C107C2×D411yescharacteristic
153C22×C4×C107C2×D411yescharacteristic
154C22×C4×C107C2×D411yescharacteristic
155C22×C4×C107C2×D411yescharacteristic
156C22×C4×C107C2×D411yescharacteristic
157C22×C4×C107C2411yescharacteristic
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×C107—21no—
166C2×C8×C107—21no—
167C2×C8×C107—21no—
168C2×C8×C107C22×C412yes—
169C2×C8×C107C22×C412yes—
170C4⋊C4×C107—24no—
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—42no—
182C4⋊C4×C107—81no—
183C4⋊C4×C107—81no—
184C4⋊C4×C107—81no—
185C4⋊C4×C107—81no—
186C4⋊C4×C107C22×C412yes—
187C4⋊C4×C107C22×C412yes—
188C22⋊C4×C107—24no—
189C22⋊C4×C107—24no—
190C22⋊C4×C107—42no—
191C22⋊C4×C107—81no—
192C22⋊C4×C107—81no—
193C42×C107—21no—
194C42×C107—21no—
195C42×C107—21no—
196C42×C107—21no—
197C42×C107—42no—
198C42×C107—81no—
199C42×C107—81no—
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—
214Q8×C107—84no—
215D4×C107—22no—
216D4×C107—22no—
217D4×C107—41no—
218D4×C107—41no—
219C2×C4×C107—21no—
220C2×C4×C107—21no—
221C2×C4×C107—21no—
222C2×C4×C107—21no—
223C2×C4×C107—22no—
224C2×C4×C107—22no—
225C2×C4×C107—22no—
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—21no—
235C2×C4×C107—21no—
236C2×C4×C107—21no—
237C2×C4×C107—21no—
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×C107—41no—
256C2×C4×C107—84no—
257C2×C4×C107C4×D412yes—
258C2×C4×C107C4×D412yes—
259C2×C4×C107C23×C411yescharacteristic
260C2×C4×C107C2×#4111yescharacteristic
261C2×C4×C107H(5,𝔽2)11yescharacteristic
262C2×C4×C107H(5,𝔽2)11yescharacteristic
263C2×C4×C1072−1+411yescharacteristic
264C2×C4×C1072−1+411yescharacteristic
265C8×C107—22no—
266C8×C107—22no—
267C8×C107—41no—
268C8×C107—41no—
269C22×C107—42no—
270C22×C107—42no—
271C22×C107—42no—
272C22×C107—81no—
273C22×C107—81no—
274C22×C107—81no—
275C22×C107—81no—
276C22×C107C2×C4×D411yescharacteristic
277C22×C107#53511yescharacteristic
278C22×C107#53611yescharacteristic
279C22×C107#57611yescharacteristic
280C22×C107#57711yescharacteristic
281C22×C107#57711yescharacteristic
282C22×C107#57811yescharacteristic
283C4×C107—22no—
284C4×C107—22no—
285C4×C107—42no—
286C4×C107—42no—
287C4×C107—42no—
288C4×C107—41no—
289C4×C107—41no—
290C4×C107—41no—
291C4×C107—41no—
292C4×C107—81no—
293C4×C107—81no—
294C4×C107—81no—
295C4×C107—81no—
296C4×C107#52011yescharacteristic
297C4×C107#52011yescharacteristic
298C4×C107#54211yescharacteristic
299C4×C107#54211yescharacteristic
300#22233C10711yesmaximal, characteristic, direct product factor, Sylow
301C2×C107—82no—
302C2×C107#232611yescharacteristic
303C2×C107#294611yescharacteristic
304C2×C107#294711yescharacteristic
305C2×C107#322411yescharacteristic
306C2×C107#322511yescharacteristic
307C2×C107#324311yescharacteristic
308C2×C107#324411yescharacteristic
309C2×#489C2×C10711yescharacteristic
310#2331C2×C10711yescharacteristic, complemented
311#2326C2×C10711yescharacteristic
312#1990C2×C10711yescharacteristic, complemented
313#1958C2×C10711yescharacteristic
314#1928C2×C10711yescharacteristic, complemented
315#1927C2×C10711yescharacteristic, complemented
316#1926C2×C10711yescharacteristic
317#1925C2×C10711yescharacteristic
318#1865C2×C10711yescharacteristic, complemented
319#1864C2×C10711yescharacteristic
320#1863C2×C10711yescharacteristic, complemented
321#1862C2×C10711yescharacteristic
322#1847C2×C10711yescharacteristic, complemented
323#1746C2×C10711yescharacteristic, complemented
324C107#2223311yescharacteristic, direct product factor, Sylow
325C2×C4⋊Q8C22×C10711yescharacteristic
326C2×#124C22×C10711yescharacteristic
327C2×C4×Q8C22×C10711yescharacteristic
328C2×C4×D4C22×C10711yescharacteristic
329#489C4×C10718yescomplemented
330C2×#107C22×C10711yescharacteristic
331C2×#107C22×C10711yescharacteristic
332C2×#106C22×C10711yescharacteristic
333C2×#106C22×C10711yescharacteristic
334C2×#103C22×C10711yescharacteristic
335C2×#103C22×C10711yescharacteristic
336C2×#103C22×C10711yescharacteristic
337C2×#103C22×C10711yescharacteristic
338C2×#102C22×C10711yescharacteristic
339C2×#102C22×C10711yescharacteristic
340C2×#102C22×C10711yescharacteristic
341C2×#102C22×C10711yescharacteristic
342C2×#97C22×C10711yescharacteristic
343C2×C4×C8C22×C10711yescharacteristic
344#391—21no—
345#391—21no—
346#391C22×C10711yescharacteristic
347#390C22×C10711yescharacteristic
348#389C22×C10711yescharacteristic
349#389C22×C10711yescharacteristic
350#388—21no—
351#388—21no—
352#387—21no—
353#387—21no—
354#385—21no—
355#385—21no—
356#384C22×C10711yescharacteristic
357#382C22×C10711yescharacteristic
358C4×C4⋊C4C22×C10711yescharacteristic
359C4×C4⋊C4C22×C10711yescharacteristic
360#376C22×C10711yescharacteristic
361#340C22×C10711yescharacteristic
362#340C22×C10711yescharacteristic
363#340C22×C10711yescharacteristic
364#340C22×C10711yescharacteristic
365#336C22×C10711yescharacteristic
366#336C22×C10711yescharacteristic
367#336C22×C10711yescharacteristic
368#336C22×C10711yescharacteristic
369C22×Q8—21no—
370C22×Q8C23×C10711yescharacteristic
371C22×D4C23×C10711yescharacteristic
372C23×C4—21no—
373C22×C8C23×C10711yescharacteristic
374C22×C8C23×C10711yescharacteristic
375C22×C8C23×C10711yescharacteristic
376C22×C8C23×C10711yescharacteristic
377C4⋊Q8—22no—
378C4⋊Q8C2×C4×C10714yescomplemented
379#124—22no—
380#124C2×C4×C10714yes—
381C4×Q8—41no—
382C4×Q8—41no—
383C4×D4—41no—
384C4×D4—41no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C23×C10711yescharacteristic
392C2×C4⋊C4C23×C10711yescharacteristic
393C2×C4⋊C4C23×C10711yescharacteristic
394C2×C4⋊C4C23×C10711yescharacteristic
395C2×C4⋊C4C23×C10711yescharacteristic
396C2×C4⋊C4C23×C10711yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42C23×C10711yescharacteristic
406C2×C42C23×C10711yescharacteristic
407C2×C42C23×C10711yescharacteristic
408#107—41no—
409#107—41no—
410#106—41no—
411#106—41no—
412#103—41no—
413#103—41no—
414#103C2×C4×C10714yescomplemented
415#103C2×C4×C10714yescomplemented
416#102—41no—
417#102—41no—
418#102C2×C4×C10714yes—
419#102C2×C4×C10714yes—
420#97C2×C4×C10714yescomplemented
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#95D4×C10711yescharacteristic
431#95D4×C10711yescharacteristic
432#95D4×C10711yescharacteristic
433#95D4×C10711yescharacteristic
434C24—21no—
435C2×Q8—24no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—81no—
442C2×Q8—81no—
443C2×Q8C22×C4×C10712yes—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C22×C4×C10712yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—42no—
458C22×C4—81no—
459C22×C4—81no—
460C22×C4C2×D4×C10711yescharacteristic
461C22×C4C2×D4×C10711yescharacteristic
462C22×C4C2×D4×C10711yescharacteristic
463C22×C4C2×D4×C10711yescharacteristic
464C22×C4C2×D4×C10711yescharacteristic
465C22×C4C2×D4×C10711yescharacteristic
466C22×C4C24×C10711yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8C22×C4×C10712yes—
478C2×C8C22×C4×C10712yes—
479C4⋊C4—24no—
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—21no—
490C4⋊C4—42no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4C22×C4×C10712yes—
496C4⋊C4C22×C4×C10712yes—
497C22⋊C4—24no—
498C22⋊C4—24no—
499C22⋊C4—42no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—81no—
508C42—81no—
509C42C22×C4×C10712yes—
510C42#41×C10712yes—
511C23—22no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23C22×D4×C10711yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—41no—
522Q8—41no—
523Q8—84no—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
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—21no—
545C2×C4—21no—
546C2×C4—21no—
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×C4—41no—
564C2×C4—41no—
565C2×C4—84no—
566C2×C4C4×D4×C10712yes—
567C2×C4C4×D4×C10712yes—
568C2×C4C23×C4×C10711yescharacteristic
569C2×C4C2×#41×C10711yescharacteristic
570C2×C4H(5,𝔽2)×C10711yescharacteristic
571C2×C4H(5,𝔽2)×C10711yescharacteristic
572C2×C42−1+4×C10711yescharacteristic
573C2×C42−1+4×C10711yescharacteristic
574C8—22no—
575C8—22no—
576C8—41no—
577C8—41no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22C2×C4×D4×C10711yescharacteristic
586C22#535×C10711yescharacteristic
587C22#536×C10711yescharacteristic
588C22#576×C10711yescharacteristic
589C22#577×C10711yescharacteristic
590C22#577×C10711yescharacteristic
591C22#578×C10711yescharacteristic
592C4—22no—
593C4—22no—
594C4—42no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4#520×C10711yescharacteristic
606C4#520×C10711yescharacteristic
607C4#542×C10711yescharacteristic
608C4#542×C10711yescharacteristic
609C2—82no—
610C2C107×#232611yescharacteristic
611C2C107×#294611yescharacteristic
612C2C107×#294711yescharacteristic
613C2C107×#322411yescharacteristic
614C2C107×#322511yescharacteristic
615C2C107×#324311yescharacteristic
616C2C107×#324411yescharacteristic
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×#2331C2semidirect
4. C107×#1990C2semidirect
6. C107×#1928C2semidirect
7. C107×#1927C2semidirect
10. C107×#1865C2semidirect
12. C107×#1863C2semidirect
14. C107×#1847C2semidirect
15. C107×#1746C2semidirect
20. #489×C107C4semidirect
69. C4⋊Q8×C107C2×C4semidirect
105. #103×C107C2×C4semidirect
106. #103×C107C2×C4semidirect
111. #97×C107C2×C4semidirect
300. #22233C107direct (N × H)
310. #2331C2×C107semidirect
312. #1990C2×C107semidirect
314. #1928C2×C107semidirect
315. #1927C2×C107semidirect
318. #1865C2×C107semidirect
320. #1863C2×C107semidirect
322. #1847C2×C107semidirect
323. #1746C2×C107semidirect
324. C107#22233direct (N × H)
329. #489C4×C107semidirect
378. C4⋊Q8C2×C4×C107semidirect
414. #103C2×C4×C107semidirect
415. #103C2×C4×C107semidirect
420. #97C2×C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#489×C1072
C107×#23312
C107×#23262
C107×#19902
C107×#19582
C107×#19282
C107×#19272
C107×#19262
C107×#19252
C107×#18652
C107×#18642
C107×#18632
C107×#18622
C107×#18472
C107×#17462
#22233107