Finite Group Databasebeta

← C107×#32657 #41058621

Subgroups — C107×#32657 #41058621

Order 27392.

712 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2582C211yesmaximal, characteristic, complemented
2C107×#2580C211yesmaximal, characteristic
3C107×#2097C211yesmaximal, characteristic, complemented
4C107×#2093C211yesmaximal, characteristic
5C107×#2085C211yesmaximal, characteristic, complemented
6C107×#2084C211yesmaximal, characteristic, complemented
7C107×#2068C211yesmaximal, characteristic, complemented
8C107×#2065C211yesmaximal, characteristic
9C107×#1984C211yesmaximal, characteristic, complemented
10C107×#1968C211yesmaximal, characteristic
11C107×#1942C211yesmaximal, characteristic, complemented
12C107×#1880C211yesmaximal, characteristic
13C107×#1877C211yesmaximal, characteristic
14C107×#1863C211yesmaximal, characteristic, complemented
15C107×#1862C211yesmaximal, characteristic
16C22×SD16×C107C2211yescharacteristic
17C2×C4×Q8×C107C2211yescharacteristic
18C2×C4×Q8×C107C2211yescharacteristic
19C2×C4×D4×C107C2211yescharacteristic
20C2×#107×C107C2211yescharacteristic
21C2×#107×C107C2211yescharacteristic
22C2×#107×C107C2211yescharacteristic
23C2×#106×C107C2211yescharacteristic
24C2×#106×C107C2211yescharacteristic
25C2×C4⋊C8×C107C2211yescharacteristic
26C2×#103×C107C2211yescharacteristic
27C2×#103×C107C2211yescharacteristic
28C2×#103×C107C2211yescharacteristic
29C2×#102×C107C2211yescharacteristic
30C2×#102×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×C4×C8×C107C2211yescharacteristic
33#399×C107—21no—
34#398×C107—21no—
35#398×C107—21no—
36#393×C107—21no—
37#391×C107—21no—
38#391×C107C2211yescharacteristic
39#391×C107C2211yescharacteristic
40#390×C107C2211yescharacteristic
41#390×C107C2211yescharacteristic
42#389×C107—21no—
43#389×C107C2211yescharacteristic
44#389×C107C2211yescharacteristic
45#389×C107C2211yescharacteristic
46#389×C107C2211yescharacteristic
47#385×C107—21no—
48#385×C107—21no—
49#384×C107C2211yescharacteristic
50#382×C107C2211yescharacteristic
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
70C4×Q8×C107—41no—
71C4×Q8×C107—41no—
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×C107—21no—
83C2×C4⋊C4×C107D411yescharacteristic
84C2×C4⋊C4×C107D411yescharacteristic
85C2×C4⋊C4×C107D411yescharacteristic
86C2×C4⋊C4×C107C2311yescharacteristic
87C2×C4⋊C4×C107C2311yescharacteristic
88C2×C4⋊C4×C107C2311yescharacteristic
89C2×C4⋊C4×C107C2311yescharacteristic
90C2×C4⋊C4×C107C2311yescharacteristic
91C2×C4⋊C4×C107C2311yescharacteristic
92C2×C22⋊C4×C107—21no—
93C2×C22⋊C4×C107—21no—
94C2×C22⋊C4×C107—21no—
95C2×C22⋊C4×C107—21no—
96C2×C22⋊C4×C107—21no—
97C2×C42×C107—21no—
98C2×C42×C107C2311yescharacteristic
99C2×C42×C107C2311yescharacteristic
100C2×C42×C107C2311yescharacteristic
101#107×C107—22no—
102#107×C107—41no—
103#107×C107—41no—
104#106×C107—41no—
105#106×C107—41no—
106C4⋊C8×C107—41no—
107#103×C107—22no—
108#103×C107—41no—
109#103×C107—41no—
110#102×C107—22no—
111#102×C107—41no—
112#102×C107—41no—
113C4×C8×C107—41no—
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—
124C24×C107—21no—
125C2×Q8×C107—22no—
126C2×Q8×C107—22no—
127C2×Q8×C107—21no—
128C2×Q8×C107—21no—
129C2×Q8×C107—21no—
130C2×Q8×C107—21no—
131C2×Q8×C107—21no—
132C2×Q8×C107—41no—
133C2×Q8×C107C2×Q812yes—
134C2×D4×C107—21no—
135C2×D4×C107—21no—
136C2×D4×C107—21no—
137C2×D4×C107—21no—
138C2×D4×C107—21no—
139C2×D4×C107C2×Q812yes—
140C22×C4×C107—21no—
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—42no—
148C22×C4×C107—81no—
149C22×C4×C107—81no—
150C22×C4×C107C2×D411yescharacteristic
151C22×C4×C107C2×D411yescharacteristic
152C22×C4×C107C2×D411yescharacteristic
153C22×C4×C107C2×D411yescharacteristic
154C22×C4×C107C2×D411yescharacteristic
155C22×C4×C107C2×D411yescharacteristic
156C22×C4×C107C2411yescharacteristic
157SD16×C107—44no—
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×C107C2×Q812yes—
169C2×C8×C107#4112yes—
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—21no—
180C4⋊C4×C107—21no—
181C4⋊C4×C107—21no—
182C4⋊C4×C107—41no—
183C4⋊C4×C107—41no—
184C4⋊C4×C107—41no—
185C4⋊C4×C107—42no—
186C4⋊C4×C107—42no—
187C4⋊C4×C107—81no—
188C4⋊C4×C107—81no—
189C4⋊C4×C107—81no—
190C4⋊C4×C107—81no—
191C4⋊C4×C107—81no—
192C22⋊C4×C107—42no—
193C22⋊C4×C107—42no—
194C22⋊C4×C107—42no—
195C22⋊C4×C107—81no—
196C22⋊C4×C107—81no—
197C42×C107—21no—
198C42×C107—21no—
199C42×C107—21no—
200C42×C107—21no—
201C42×C107—21no—
202C42×C107—21no—
203C42×C107—42no—
204C23×C107—22no—
205C23×C107—41no—
206C23×C107—41no—
207C23×C107—41no—
208C23×C107—41no—
209C23×C107—41no—
210C23×C107—41no—
211C23×C107C22×D411yescharacteristic
212Q8×C107—22no—
213Q8×C107—22no—
214Q8×C107—44no—
215Q8×C107—41no—
216Q8×C107—41no—
217D4×C107—22no—
218D4×C107—22no—
219D4×C107—41no—
220D4×C107—41no—
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—21no—
229C2×C4×C107—22no—
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—41no—
257C2×C4×C107—41no—
258C2×C4×C107—84no—
259C2×C4×C107#13512yes—
260C2×C4×C107#13712yes—
261C2×C4×C107C22×Q811yescharacteristic
262C2×C4×C107C2×#4111yescharacteristic
263C2×C4×C107H(5,𝔽2)11yescharacteristic
264C2×C4×C107H(5,𝔽2)11yescharacteristic
265C2×C4×C107H(5,𝔽2)11yescharacteristic
266C2×C4×C1072−1+411yescharacteristic
267C8×C107—22no—
268C8×C107—22no—
269C8×C107—41no—
270C8×C107—41no—
271C22×C107—42no—
272C22×C107—42no—
273C22×C107—42no—
274C22×C107—81no—
275C22×C107—81no—
276C22×C107—81no—
277C22×C107—81no—
278C22×C107#53411yescharacteristic
279C22×C107D4×Q811yescharacteristic
280C22×C107#55011yescharacteristic
281C22×C107C2×#13511yescharacteristic
282C22×C107C2×#13711yescharacteristic
283C22×C107#57611yescharacteristic
284C22×C107#57711yescharacteristic
285C4×C107—22no—
286C4×C107—22no—
287C4×C107—41no—
288C4×C107—41no—
289C4×C107—41no—
290C4×C107—41no—
291C4×C107—42no—
292C4×C107—81no—
293C4×C107—81no—
294C4×C107—81no—
295C4×C107—81no—
296C4×C107—81no—
297C4×C107—81no—
298C4×C107#53911yescharacteristic
299C4×C107#54311yescharacteristic
300C4×C107#55411yescharacteristic
301C4×C107#56211yescharacteristic
302#32657C10711yesmaximal, characteristic, direct product factor, Sylow
303C2×C107—82no—
304C2×C107#273211yescharacteristic
305C2×C107#319011yescharacteristic
306C2×C107#319811yescharacteristic
307C2×C107#338111yescharacteristic
308C2×C107#338511yescharacteristic
309C2×C107#339611yescharacteristic
310C2×C107#340011yescharacteristic
311#2582C2×C10711yescharacteristic, complemented
312#2580C2×C10711yescharacteristic
313#2097C2×C10711yescharacteristic, complemented
314#2093C2×C10711yescharacteristic
315#2085C2×C10711yescharacteristic, complemented
316#2084C2×C10711yescharacteristic, complemented
317#2068C2×C10711yescharacteristic, complemented
318#2065C2×C10711yescharacteristic
319#1984C2×C10711yescharacteristic, complemented
320#1968C2×C10711yescharacteristic
321#1942C2×C10711yescharacteristic, complemented
322#1880C2×C10711yescharacteristic
323#1877C2×C10711yescharacteristic
324#1863C2×C10711yescharacteristic, complemented
325#1862C2×C10711yescharacteristic
326C107#3265711yescharacteristic, direct product factor, Sylow
327C22×SD16C22×C10711yescharacteristic
328C2×C4×Q8C22×C10711yescharacteristic
329C2×C4×Q8C22×C10711yescharacteristic
330C2×C4×D4C22×C10711yescharacteristic
331C2×#107C22×C10711yescharacteristic
332C2×#107C22×C10711yescharacteristic
333C2×#107C22×C10711yescharacteristic
334C2×#106C22×C10711yescharacteristic
335C2×#106C22×C10711yescharacteristic
336C2×C4⋊C8C22×C10711yescharacteristic
337C2×#103C22×C10711yescharacteristic
338C2×#103C22×C10711yescharacteristic
339C2×#103C22×C10711yescharacteristic
340C2×#102C22×C10711yescharacteristic
341C2×#102C22×C10711yescharacteristic
342C2×#102C22×C10711yescharacteristic
343C2×C4×C8C22×C10711yescharacteristic
344#399—21no—
345#398—21no—
346#398—21no—
347#393—21no—
348#391—21no—
349#391C22×C10711yescharacteristic
350#391C22×C10711yescharacteristic
351#390C22×C10711yescharacteristic
352#390C22×C10711yescharacteristic
353#389—21no—
354#389C22×C10711yescharacteristic
355#389C22×C10711yescharacteristic
356#389C22×C10711yescharacteristic
357#389C22×C10711yescharacteristic
358#385—21no—
359#385—21no—
360#384C22×C10711yescharacteristic
361#382C22×C10711yescharacteristic
362#340C22×C10711yescharacteristic
363#340C22×C10711yescharacteristic
364#340C22×C10711yescharacteristic
365#340C22×C10711yescharacteristic
366#336C22×C10711yescharacteristic
367#336C22×C10711yescharacteristic
368#336C22×C10711yescharacteristic
369#336C22×C10711yescharacteristic
370C22×Q8D4×C10711yescharacteristic
371C22×Q8C23×C10711yescharacteristic
372C22×D4C23×C10711yescharacteristic
373C23×C4—21no—
374C2×SD16—41no—
375C2×SD16—41no—
376C2×SD16Q8×C10714yescomplemented
377C22×C8C23×C10711yescharacteristic
378C22×C8C23×C10711yescharacteristic
379C22×C8C23×C10711yescharacteristic
380C22×C8C23×C10711yescharacteristic
381C4×Q8—41no—
382C4×Q8—41no—
383C4×Q8—41no—
384C4×Q8—41no—
385C4×D4—41no—
386C4×D4—41no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4D4×C10711yescharacteristic
395C2×C4⋊C4D4×C10711yescharacteristic
396C2×C4⋊C4D4×C10711yescharacteristic
397C2×C4⋊C4C23×C10711yescharacteristic
398C2×C4⋊C4C23×C10711yescharacteristic
399C2×C4⋊C4C23×C10711yescharacteristic
400C2×C4⋊C4C23×C10711yescharacteristic
401C2×C4⋊C4C23×C10711yescharacteristic
402C2×C4⋊C4C23×C10711yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42C23×C10711yescharacteristic
410C2×C42C23×C10711yescharacteristic
411C2×C42C23×C10711yescharacteristic
412#107—22no—
413#107—41no—
414#107—41no—
415#106—41no—
416#106—41no—
417C4⋊C8—41no—
418#103—22no—
419#103—41no—
420#103—41no—
421#102—22no—
422#102—41no—
423#102—41no—
424C4×C8—41no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435C24—21no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8C2×Q8×C10712yes—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×Q8×C10712yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—42no—
459C22×C4—81no—
460C22×C4—81no—
461C22×C4C2×D4×C10711yescharacteristic
462C22×C4C2×D4×C10711yescharacteristic
463C22×C4C2×D4×C10711yescharacteristic
464C22×C4C2×D4×C10711yescharacteristic
465C22×C4C2×D4×C10711yescharacteristic
466C22×C4C2×D4×C10711yescharacteristic
467C22×C4C24×C10711yescharacteristic
468SD16—44no—
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×C8—21no—
478C2×C8—21no—
479C2×C8C2×Q8×C10712yes—
480C2×C8#41×C10712yes—
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—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4—81no—
502C4⋊C4—81no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—42no—
515C23—22no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23C22×D4×C10711yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—44no—
526Q8—41no—
527Q8—41no—
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
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—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—84no—
570C2×C4#135×C10712yes—
571C2×C4#137×C10712yes—
572C2×C4C22×Q8×C10711yescharacteristic
573C2×C4C2×#41×C10711yescharacteristic
574C2×C4H(5,𝔽2)×C10711yescharacteristic
575C2×C4H(5,𝔽2)×C10711yescharacteristic
576C2×C4H(5,𝔽2)×C10711yescharacteristic
577C2×C42−1+4×C10711yescharacteristic
578C8—22no—
579C8—22no—
580C8—41no—
581C8—41no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22#534×C10711yescharacteristic
590C22D4×Q8×C10711yescharacteristic
591C22#550×C10711yescharacteristic
592C22C2×#135×C10711yescharacteristic
593C22C2×#137×C10711yescharacteristic
594C22#576×C10711yescharacteristic
595C22#577×C10711yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4#539×C10711yescharacteristic
610C4#543×C10711yescharacteristic
611C4#554×C10711yescharacteristic
612C4#562×C10711yescharacteristic
613C2—82no—
614C2C107×#273211yescharacteristic
615C2C107×#319011yescharacteristic
616C2C107×#319811yescharacteristic
617C2C107×#338111yescharacteristic
618C2C107×#338511yescharacteristic
619C2C107×#339611yescharacteristic
620C2C107×#340011yescharacteristic
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×#2097C2semidirect
5. C107×#2085C2semidirect
6. C107×#2084C2semidirect
7. C107×#2068C2semidirect
9. C107×#1984C2semidirect
11. C107×#1942C2semidirect
14. C107×#1863C2semidirect
65. C2×SD16×C107Q8semidirect
302. #32657C107direct (N × H)
311. #2582C2×C107semidirect
313. #2097C2×C107semidirect
315. #2085C2×C107semidirect
316. #2084C2×C107semidirect
317. #2068C2×C107semidirect
319. #1984C2×C107semidirect
321. #1942C2×C107semidirect
324. #1863C2×C107semidirect
326. C107#32657direct (N × H)
376. 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×#25802
C107×#20972
C107×#20932
C107×#20852
C107×#20842
C107×#20682
C107×#20652
C107×#19842
C107×#19682
C107×#19422
C107×#18802
C107×#18772
C107×#18632
C107×#18622
#32657107