Finite Group Databasebeta

← C107×#32665 #41058629

Subgroups — C107×#32665 #41058629

Order 27392.

734 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2582C211yesmaximal, characteristic, complemented
2C107×#2538C211yesmaximal, characteristic
3C107×#2095C211yesmaximal, characteristic, complemented
4C107×#2093C211yesmaximal, characteristic
5C107×#2083C211yesmaximal, characteristic, complemented
6C107×#2083C211yesmaximal, characteristic, complemented
7C107×#2068C211yesmaximal, characteristic, complemented
8C107×#2067C211yesmaximal, characteristic
9C107×#1985C211yesmaximal, characteristic, complemented
10C107×#1973C211yesmaximal, characteristic
11C107×#1943C211yesmaximal, characteristic, complemented
12C107×#1880C211yesmaximal, characteristic
13C107×#1877C211yesmaximal, characteristic
14C107×#1865C211yesmaximal, characteristic, complemented
15C107×#1864C211yesmaximal, characteristic
16C22×SD16×C107C2211yescharacteristic
17C2×C22⋊Q8×C107—21no—
18C2×C4×Q8×C107C2211yescharacteristic
19C2×C4×Q8×C107C2211yescharacteristic
20C2×C4×D4×C107C2211yescharacteristic
21C2×#107×C107C2211yescharacteristic
22C2×#107×C107C2211yescharacteristic
23C2×#107×C107C2211yescharacteristic
24C2×#107×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
34#398×C107—21no—
35#398×C107—21no—
36#396×C107—21no—
37#396×C107—21no—
38#391×C107—21no—
39#391×C107C2211yescharacteristic
40#391×C107C2211yescharacteristic
41#390×C107C2211yescharacteristic
42#390×C107C2211yescharacteristic
43#389×C107—21no—
44#389×C107C2211yescharacteristic
45#389×C107C2211yescharacteristic
46#389×C107C2211yescharacteristic
47#389×C107C2211yescharacteristic
48#384×C107C2211yescharacteristic
49#384×C107C2211yescharacteristic
50#380×C107—21no—
51#340×C107C2211yescharacteristic
52#340×C107C2211yescharacteristic
53#340×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#336×C107C2211yescharacteristic
56#336×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59C22×Q8×C107D411yescharacteristic
60C22×Q8×C107C2311yescharacteristic
61C22×D4×C107C2311yescharacteristic
62C23×C4×C107—21no—
63C2×SD16×C107—41no—
64C2×SD16×C107—41no—
65C2×SD16×C107Q814yescomplemented
66C22×C8×C107C2311yescharacteristic
67C22×C8×C107C2311yescharacteristic
68C22×C8×C107C2311yescharacteristic
69C22×C8×C107C2311yescharacteristic
70C22⋊Q8×C107—44no—
71C4×Q8×C107—41no—
72C4×Q8×C107—41no—
73C4×Q8×C107—41no—
74C4×Q8×C107—41no—
75C4×D4×C107—41no—
76C4×D4×C107—41no—
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×C107—21no—
83C2×C4⋊C4×C107—21no—
84C2×C4⋊C4×C107—21no—
85C2×C4⋊C4×C107—21no—
86C2×C4⋊C4×C107D411yescharacteristic
87C2×C4⋊C4×C107D411yescharacteristic
88C2×C4⋊C4×C107D411yescharacteristic
89C2×C4⋊C4×C107C2311yescharacteristic
90C2×C4⋊C4×C107C2311yescharacteristic
91C2×C4⋊C4×C107C2311yescharacteristic
92C2×C4⋊C4×C107C2311yescharacteristic
93C2×C4⋊C4×C107C2311yescharacteristic
94C2×C4⋊C4×C107C2311yescharacteristic
95C2×C22⋊C4×C107—21no—
96C2×C22⋊C4×C107—21no—
97C2×C22⋊C4×C107—21no—
98C2×C22⋊C4×C107—21no—
99C2×C22⋊C4×C107—21no—
100C2×C42×C107—21no—
101C2×C42×C107C2311yescharacteristic
102C2×C42×C107C2311yescharacteristic
103C2×C42×C107C2311yescharacteristic
104#107×C107—22no—
105#107×C107—41no—
106#107×C107—41no—
107#107×C107—41no—
108#106×C107—41no—
109C4⋊C8×C107—41no—
110#103×C107—22no—
111#103×C107—41no—
112#103×C107—41no—
113#102×C107—22no—
114#102×C107—41no—
115#102×C107—41no—
116#97×C107—41no—
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×C107—21no—
125C24×C107—21no—
126C2×Q8×C107—22no—
127C2×Q8×C107—22no—
128C2×Q8×C107—21no—
129C2×Q8×C107—21no—
130C2×Q8×C107—21no—
131C2×Q8×C107—21no—
132C2×Q8×C107—21no—
133C2×Q8×C107—41no—
134C2×Q8×C107C2×Q812yes—
135C2×D4×C107—21no—
136C2×D4×C107—21no—
137C2×D4×C107—21no—
138C2×D4×C107—21no—
139C2×D4×C107—21no—
140C2×D4×C107C2×Q812yes—
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—42no—
150C22×C4×C107—42no—
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
158SD16×C107—44no—
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×C107—21no—
169C2×C8×C107C2×Q812yes—
170C2×C8×C107#4112yes—
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—21no—
182C4⋊C4×C107—21no—
183C4⋊C4×C107—41no—
184C4⋊C4×C107—41no—
185C4⋊C4×C107—41no—
186C4⋊C4×C107—42no—
187C4⋊C4×C107—42no—
188C4⋊C4×C107—42no—
189C4⋊C4×C107—42no—
190C4⋊C4×C107—42no—
191C4⋊C4×C107—81no—
192C4⋊C4×C107—81no—
193C4⋊C4×C107—81no—
194C4⋊C4×C107—81no—
195C22⋊C4×C107—42no—
196C22⋊C4×C107—42no—
197C22⋊C4×C107—42no—
198C22⋊C4×C107—81no—
199C22⋊C4×C107—81no—
200C42×C107—21no—
201C42×C107—21no—
202C42×C107—21no—
203C42×C107—21no—
204C42×C107—21no—
205C42×C107—21no—
206C42×C107—42no—
207C23×C107—22no—
208C23×C107—41no—
209C23×C107—41no—
210C23×C107—41no—
211C23×C107—41no—
212C23×C107—41no—
213C23×C107—41no—
214C23×C107C22×D411yescharacteristic
215Q8×C107—22no—
216Q8×C107—22no—
217Q8×C107—44no—
218Q8×C107—41no—
219Q8×C107—41no—
220D4×C107—22no—
221D4×C107—22no—
222D4×C107—41no—
223D4×C107—41no—
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—22no—
233C2×C4×C107—21no—
234C2×C4×C107—21no—
235C2×C4×C107—21no—
236C2×C4×C107—21no—
237C2×C4×C107—21no—
238C2×C4×C107—21no—
239C2×C4×C107—21no—
240C2×C4×C107—21no—
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—41no—
257C2×C4×C107—41no—
258C2×C4×C107—41no—
259C2×C4×C107—41no—
260C2×C4×C107—41no—
261C2×C4×C107—84no—
262C2×C4×C107AGL(1,ℤ/8)12yes—
263C2×C4×C107#13712yes—
264C2×C4×C107C22×Q811yescharacteristic
265C2×C4×C107C2×#4111yescharacteristic
266C2×C4×C107H(5,𝔽2)11yescharacteristic
267C2×C4×C107H(5,𝔽2)11yescharacteristic
268C2×C4×C107H(5,𝔽2)11yescharacteristic
269C2×C4×C1072−1+411yescharacteristic
270C8×C107—22no—
271C8×C107—22no—
272C8×C107—41no—
273C8×C107—41no—
274C22×C107—42no—
275C22×C107—42no—
276C22×C107—42no—
277C22×C107—81no—
278C22×C107—81no—
279C22×C107—81no—
280C22×C107—81no—
281C22×C107#53411yescharacteristic
282C22×C107D4×Q811yescharacteristic
283C22×C107#55011yescharacteristic
284C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C107C2×#13711yescharacteristic
286C22×C107#57611yescharacteristic
287C22×C107#57811yescharacteristic
288C4×C107—22no—
289C4×C107—22no—
290C4×C107—41no—
291C4×C107—41no—
292C4×C107—41no—
293C4×C107—41no—
294C4×C107—42no—
295C4×C107—81no—
296C4×C107—81no—
297C4×C107—81no—
298C4×C107—81no—
299C4×C107—81no—
300C4×C107—81no—
301C4×C107#53911yescharacteristic
302C4×C107#54311yescharacteristic
303C4×C107#55411yescharacteristic
304C4×C107#56211yescharacteristic
305#32665C10711yesmaximal, characteristic, direct product factor, Sylow
306C2×C107—82no—
307C2×C107#273211yescharacteristic
308C2×C107#319311yescharacteristic
309C2×C107#320311yescharacteristic
310C2×C107#338511yescharacteristic
311C2×C107#338611yescharacteristic
312C2×C107#339811yescharacteristic
313C2×C107#339911yescharacteristic
314#2582C2×C10711yescharacteristic, complemented
315#2538C2×C10711yescharacteristic
316#2095C2×C10711yescharacteristic, complemented
317#2093C2×C10711yescharacteristic
318#2083C2×C10711yescharacteristic, complemented
319#2083C2×C10711yescharacteristic, complemented
320#2068C2×C10711yescharacteristic, complemented
321#2067C2×C10711yescharacteristic
322#1985C2×C10711yescharacteristic, complemented
323#1973C2×C10711yescharacteristic
324#1943C2×C10711yescharacteristic, complemented
325#1880C2×C10711yescharacteristic
326#1877C2×C10711yescharacteristic
327#1865C2×C10711yescharacteristic, complemented
328#1864C2×C10711yescharacteristic
329C107#3266511yescharacteristic, direct product factor, Sylow
330C22×SD16C22×C10711yescharacteristic
331C2×C22⋊Q8—21no—
332C2×C4×Q8C22×C10711yescharacteristic
333C2×C4×Q8C22×C10711yescharacteristic
334C2×C4×D4C22×C10711yescharacteristic
335C2×#107C22×C10711yescharacteristic
336C2×#107C22×C10711yescharacteristic
337C2×#107C22×C10711yescharacteristic
338C2×#107C22×C10711yescharacteristic
339C2×#106C22×C10711yescharacteristic
340C2×C4⋊C8C22×C10711yescharacteristic
341C2×#103C22×C10711yescharacteristic
342C2×#103C22×C10711yescharacteristic
343C2×#103C22×C10711yescharacteristic
344C2×#102C22×C10711yescharacteristic
345C2×#102C22×C10711yescharacteristic
346C2×#102C22×C10711yescharacteristic
347C2×#97C22×C10711yescharacteristic
348#398—21no—
349#398—21no—
350#396—21no—
351#396—21no—
352#391—21no—
353#391C22×C10711yescharacteristic
354#391C22×C10711yescharacteristic
355#390C22×C10711yescharacteristic
356#390C22×C10711yescharacteristic
357#389—21no—
358#389C22×C10711yescharacteristic
359#389C22×C10711yescharacteristic
360#389C22×C10711yescharacteristic
361#389C22×C10711yescharacteristic
362#384C22×C10711yescharacteristic
363#384C22×C10711yescharacteristic
364#380—21no—
365#340C22×C10711yescharacteristic
366#340C22×C10711yescharacteristic
367#340C22×C10711yescharacteristic
368#340C22×C10711yescharacteristic
369#336C22×C10711yescharacteristic
370#336C22×C10711yescharacteristic
371#336C22×C10711yescharacteristic
372#336C22×C10711yescharacteristic
373C22×Q8D4×C10711yescharacteristic
374C22×Q8C23×C10711yescharacteristic
375C22×D4C23×C10711yescharacteristic
376C23×C4—21no—
377C2×SD16—41no—
378C2×SD16—41no—
379C2×SD16Q8×C10714yescomplemented
380C22×C8C23×C10711yescharacteristic
381C22×C8C23×C10711yescharacteristic
382C22×C8C23×C10711yescharacteristic
383C22×C8C23×C10711yescharacteristic
384C22⋊Q8—44no—
385C4×Q8—41no—
386C4×Q8—41no—
387C4×Q8—41no—
388C4×Q8—41no—
389C4×D4—41no—
390C4×D4—41no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4D4×C10711yescharacteristic
401C2×C4⋊C4D4×C10711yescharacteristic
402C2×C4⋊C4D4×C10711yescharacteristic
403C2×C4⋊C4C23×C10711yescharacteristic
404C2×C4⋊C4C23×C10711yescharacteristic
405C2×C4⋊C4C23×C10711yescharacteristic
406C2×C4⋊C4C23×C10711yescharacteristic
407C2×C4⋊C4C23×C10711yescharacteristic
408C2×C4⋊C4C23×C10711yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C42—21no—
415C2×C42C23×C10711yescharacteristic
416C2×C42C23×C10711yescharacteristic
417C2×C42C23×C10711yescharacteristic
418#107—22no—
419#107—41no—
420#107—41no—
421#107—41no—
422#106—41no—
423C4⋊C8—41no—
424#103—22no—
425#103—41no—
426#103—41no—
427#102—22no—
428#102—41no—
429#102—41no—
430#97—41no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439C24—21no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—41no—
448C2×Q8C2×Q8×C10712yes—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4C2×Q8×C10712yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4C2×D4×C10711yescharacteristic
466C22×C4C2×D4×C10711yescharacteristic
467C22×C4C2×D4×C10711yescharacteristic
468C22×C4C2×D4×C10711yescharacteristic
469C22×C4C2×D4×C10711yescharacteristic
470C22×C4C2×D4×C10711yescharacteristic
471C22×C4C24×C10711yescharacteristic
472SD16—44no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8C2×Q8×C10712yes—
484C2×C8#41×C10712yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4—81no—
508C4⋊C4—81no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—42no—
521C23—22no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C22×D4×C10711yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—44no—
532Q8—41no—
533Q8—41no—
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
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—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
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—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4AGL(1,ℤ/8)×C10712yes—
577C2×C4#137×C10712yes—
578C2×C4C22×Q8×C10711yescharacteristic
579C2×C4C2×#41×C10711yescharacteristic
580C2×C4H(5,𝔽2)×C10711yescharacteristic
581C2×C4H(5,𝔽2)×C10711yescharacteristic
582C2×C4H(5,𝔽2)×C10711yescharacteristic
583C2×C42−1+4×C10711yescharacteristic
584C8—22no—
585C8—22no—
586C8—41no—
587C8—41no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22#534×C10711yescharacteristic
596C22D4×Q8×C10711yescharacteristic
597C22#550×C10711yescharacteristic
598C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
599C22C2×#137×C10711yescharacteristic
600C22#576×C10711yescharacteristic
601C22#578×C10711yescharacteristic
602C4—22no—
603C4—22no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—42no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4#539×C10711yescharacteristic
616C4#543×C10711yescharacteristic
617C4#554×C10711yescharacteristic
618C4#562×C10711yescharacteristic
619C2—82no—
620C2C107×#273211yescharacteristic
621C2C107×#319311yescharacteristic
622C2C107×#320311yescharacteristic
623C2C107×#338511yescharacteristic
624C2C107×#338611yescharacteristic
625C2C107×#339811yescharacteristic
626C2C107×#339911yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C4×Q8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2582C2semidirect
3. C107×#2095C2semidirect
5. C107×#2083C2semidirect
6. C107×#2083C2semidirect
7. C107×#2068C2semidirect
9. C107×#1985C2semidirect
11. C107×#1943C2semidirect
14. C107×#1865C2semidirect
65. C2×SD16×C107Q8semidirect
305. #32665C107direct (N × H)
314. #2582C2×C107semidirect
316. #2095C2×C107semidirect
318. #2083C2×C107semidirect
319. #2083C2×C107semidirect
320. #2068C2×C107semidirect
322. #1985C2×C107semidirect
324. #1943C2×C107semidirect
327. #1865C2×C107semidirect
329. C107#32665direct (N × H)
379. C2×SD16Q8×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#25822
C107×#25382
C107×#20952
C107×#20932
C107×#20832
C107×#20682
C107×#20672
C107×#19852
C107×#19732
C107×#19432
C107×#18802
C107×#18772
C107×#18652
C107×#18642
#32665107