Finite Group Databasebeta

← C107×#8367 #41034331

Subgroups — C107×#8367 #41034331

Order 27392.

1138 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C107C211yesmaximal, characteristic
2C4×#100×C107C211yesmaximal, characteristic, complemented
3C107×#1527C212yesmaximal, complemented
4C107×#1490C212yesmaximal, complemented
5C107×#1466C211yesmaximal, characteristic, complemented
6C22×#41×C107C411yescharacteristic
7C23×D4×C107C411yescharacteristic
8#546×C107—24no—
9#546×C107—24no—
10C2×#124×C107C2211yescharacteristic
11C2×#123×C107—21no—
12C2×C22⋊Q8×C107C411yescharacteristic
13C2×#121×C107—21no—
14C2×#121×C107C411yescharacteristic
15C2×#120×C107—21no—
16C2×C4×D4×C107C2211yescharacteristic
17C2×C4×D4×C107C2211yescharacteristic
18C22×C22⋊C4×C107—21no—
19#432×C107C2212yescomplemented
20C2×#100×C107—21no—
21C4×M16×C107C2212yescomplemented
22#343×C107—21no—
23#329×C107—24no—
24D4⋊C8×C107—24no—
25#323×C107—21no—
26#323×C107—21no—
27C25×C107—21no—
28C2×#41×C107—22no—
29C2×#41×C107—22no—
30C2×#41×C107—44no—
31C22×Q8×C107C2×C411yescharacteristic
32C22×D4×C107—21no—
33C22×D4×C107—21no—
34C22×D4×C107—22no—
35C22×D4×C107—22no—
36C22×D4×C107—21no—
37C22×D4×C107—44no—
38C22×D4×C107C2×C411yescharacteristic
39C22×D4×C107C2×C411yescharacteristic
40C22×D4×C107D411yescharacteristic
41C23×C4×C107—21no—
42C23×C4×C107—21no—
43C23×C4×C107C2×C411yescharacteristic
44C23×C4×C107C2×C411yescharacteristic
45C2×M16×C107—22no—
46#124×C107—22no—
47#124×C107D414yes—
48#123×C107—28no—
49C22⋊Q8×C107—22no—
50C22⋊Q8×C107—22no—
51#121×C107—28no—
52#121×C107—22no—
53#121×C107—22no—
54#120×C107—28no—
55C4×D4×C107—22no—
56C4×D4×C107—22no—
57C4×D4×C107—22no—
58C4×D4×C107D414yes—
59C2×C4⋊C4×C107—21no—
60C2×C4⋊C4×C107C2×C411yescharacteristic
61C2×C4⋊C4×C107D411yescharacteristic
62C2×C22⋊C4×C107—28no—
63C2×C22⋊C4×C107—21no—
64C2×C22⋊C4×C107—21no—
65C2×C22⋊C4×C107—21no—
66C2×C22⋊C4×C107—21no—
67C2×C22⋊C4×C107—21no—
68C2×C22⋊C4×C107D411yescharacteristic
69C2×C22⋊C4×C107D411yescharacteristic
70C2×C42×C107C2311yescharacteristic
71C4⋊C8×C107—22no—
72#100×C107—24no—
73C22⋊C8×C107—22no—
74#97×C107—22no—
75#97×C107—22no—
76C4×C8×C107—22no—
77C24×C107—21no—
78C24×C107—24no—
79C24×C107—21no—
80C24×C107—44no—
81C24×C107—42no—
82C24×C107—42no—
83C24×C107—82no—
84C24×C107C22⋊C411yescharacteristic
85C24×C107C22⋊C411yescharacteristic
86#41×C107—48no—
87#41×C107—44no—
88#41×C107—44no—
89C2×Q8×C107—21no—
90C2×Q8×C107—42no—
91C2×Q8×C107C22⋊C412yes—
92C2×D4×C107—24no—
93C2×D4×C107—24no—
94C2×D4×C107—24no—
95C2×D4×C107—22no—
96C2×D4×C107—24no—
97C2×D4×C107—21no—
98C2×D4×C107—21no—
99C2×D4×C107—22no—
100C2×D4×C107—41no—
101C2×D4×C107—42no—
102C2×D4×C107—48no—
103C2×D4×C107—44no—
104C2×D4×C107—44no—
105C2×D4×C107—44no—
106C2×D4×C107—44no—
107C2×D4×C107—82no—
108C2×D4×C107C22⋊C412yes—
109C2×D4×C107C22⋊C412yes—
110C22×C4×C107—24no—
111C22×C4×C107—21no—
112C22×C4×C107—21no—
113C22×C4×C107—21no—
114C22×C4×C107—21no—
115C22×C4×C107—21no—
116C22×C4×C107—21no—
117C22×C4×C107—24no—
118C22×C4×C107—42no—
119C22×C4×C107—42no—
120C22×C4×C107—44no—
121C22×C4×C107—82no—
122C22×C4×C107C22⋊C411yescharacteristic
123C22×C4×C107C22⋊C411yescharacteristic
124C22×C4×C107C22×C411yescharacteristic
125C22×C4×C107C2×D411yescharacteristic
126C22×C4×C107C2×D411yescharacteristic
127M16×C107—24no—
128M16×C107—42no—
129C2×C8×C107—42no—
130C2×C8×C107—42no—
131C4⋊C4×C107—24no—
132C4⋊C4×C107—21no—
133C4⋊C4×C107—22no—
134C4⋊C4×C107C22⋊C412yes—
135C22⋊C4×C107—24no—
136C22⋊C4×C107—24no—
137C22⋊C4×C107—22no—
138C22⋊C4×C107—24no—
139C22⋊C4×C107—24no—
140C22⋊C4×C107—24no—
141C22⋊C4×C107—22no—
142C42×C107C2×D412yes—
143C42×C107C2×D412yes—
144C23×C107—24no—
145C23×C107—21no—
146C23×C107—22no—
147C23×C107—21no—
148C23×C107—22no—
149C23×C107—21no—
150C23×C107—21no—
151C23×C107—21no—
152C23×C107—41no—
153C23×C107—41no—
154C23×C107—42no—
155C23×C107—42no—
156C23×C107—48no—
157C23×C107—42no—
158C23×C107—48no—
159C23×C107—41no—
160C23×C107—41no—
161C23×C107—41no—
162C23×C107—41no—
163C23×C107—41no—
164C23×C107—41no—
165C23×C107—84no—
166C23×C107—88no—
167C23×C107—88no—
168C23×C107#10412yes—
169C23×C107C2×C22⋊C411yescharacteristic
170Q8×C107—42no—
171Q8×C107—42no—
172D4×C107—24no—
173D4×C107—22no—
174D4×C107—44no—
175D4×C107—42no—
176D4×C107—48no—
177D4×C107—48no—
178D4×C107—42no—
179D4×C107—84no—
180D4×C107#10014yescomplemented
181C2×C4×C107—21no—
182C2×C4×C107—21no—
183C2×C4×C107—22no—
184C2×C4×C107—22no—
185C2×C4×C107—21no—
186C2×C4×C107—22no—
187C2×C4×C107—21no—
188C2×C4×C107—41no—
189C2×C4×C107—42no—
190C2×C4×C107—42no—
191C2×C4×C107—42no—
192C2×C4×C107—48no—
193C2×C4×C107—42no—
194C2×C4×C107—42no—
195C2×C4×C107—42no—
196C2×C4×C107—41no—
197C2×C4×C107—41no—
198C2×C4×C107—84no—
199C2×C4×C107C2×C22⋊C411yescharacteristic
200C2×C4×C107C2×C22⋊C411yescharacteristic
201C2×C4×C107#12012yes—
202C2×C4×C107#12012yes—
203C8×C107—44no—
204C8×C107—82no—
205C22×C107—21no—
206C22×C107—21no—
207C22×C107—24no—
208C22×C107—22no—
209C22×C107—42no—
210C22×C107—44no—
211C22×C107—44no—
212C22×C107—42no—
213C22×C107—42no—
214C22×C107—41no—
215C22×C107—41no—
216C22×C107—42no—
217C22×C107—41no—
218C22×C107—42no—
219C22×C107—41no—
220C22×C107—42no—
221C22×C107—41no—
222C22×C107—42no—
223C22×C107—81no—
224C22×C107—81no—
225C22×C107—82no—
226C22×C107—82no—
227C22×C107—816no—
228C22×C107#37911yescharacteristic
229C22×C107C2×#10411yescharacteristic
230C22×C107#42111yescharacteristic
231C4×C107—22no—
232C4×C107—21no—
233C4×C107—22no—
234C4×C107—42no—
235C4×C107—41no—
236C4×C107—42no—
237C4×C107—41no—
238C4×C107C2×#10012yes—
239#8367C10711yesmaximal, characteristic, direct product factor, Sylow
240C2×C107—21no—
241C2×C107—21no—
242C2×C107—44no—
243C2×C107—42no—
244C2×C107—81no—
245C2×C107—82no—
246C2×C107#178311yescharacteristic
247C2×C107#178911yescharacteristic
248C2×C107#179511yescharacteristic
249C2×#546C2×C10711yescharacteristic
250C4×#100C2×C10711yescharacteristic, complemented
251#1527C2×C10712yescomplemented
252#1490C2×C10712yescomplemented
253#1466C2×C10711yescharacteristic, complemented
254C107#836711yescharacteristic, direct product factor, Sylow
255C22×#41C4×C10711yescharacteristic
256C23×D4C4×C10711yescharacteristic
257#546—24no—
258#546—24no—
259C2×#124C22×C10711yescharacteristic
260C2×#123—21no—
261C2×C22⋊Q8C4×C10711yescharacteristic
262C2×#121—21no—
263C2×#121C4×C10711yescharacteristic
264C2×#120—21no—
265C2×C4×D4C22×C10711yescharacteristic
266C2×C4×D4C22×C10711yescharacteristic
267C22×C22⋊C4—21no—
268#432C22×C10712yescomplemented
269C2×#100—21no—
270C4×M16C22×C10712yescomplemented
271#343—21no—
272#329—24no—
273D4⋊C8—24no—
274#323—21no—
275#323—21no—
276C25—21no—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—44no—
280C22×Q8C2×C4×C10711yescharacteristic
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—21no—
286C22×D4—44no—
287C22×D4C2×C4×C10711yescharacteristic
288C22×D4C2×C4×C10711yescharacteristic
289C22×D4D4×C10711yescharacteristic
290C23×C4—21no—
291C23×C4—21no—
292C23×C4C2×C4×C10711yescharacteristic
293C23×C4C2×C4×C10711yescharacteristic
294C2×M16—22no—
295#124—22no—
296#124D4×C10714yes—
297#123—28no—
298C22⋊Q8—22no—
299C22⋊Q8—22no—
300#121—28no—
301#121—22no—
302#121—22no—
303#120—28no—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—22no—
307C4×D4D4×C10714yes—
308C2×C4⋊C4—21no—
309C2×C4⋊C4C2×C4×C10711yescharacteristic
310C2×C4⋊C4D4×C10711yescharacteristic
311C2×C22⋊C4—28no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4D4×C10711yescharacteristic
318C2×C22⋊C4D4×C10711yescharacteristic
319C2×C42C23×C10711yescharacteristic
320C4⋊C8—22no—
321#100—24no—
322C22⋊C8—22no—
323#97—22no—
324#97—22no—
325C4×C8—22no—
326C24—21no—
327C24—24no—
328C24—21no—
329C24—44no—
330C24—42no—
331C24—42no—
332C24—82no—
333C24C22⋊C4×C10711yescharacteristic
334C24C22⋊C4×C10711yescharacteristic
335#41—48no—
336#41—44no—
337#41—44no—
338C2×Q8—21no—
339C2×Q8—42no—
340C2×Q8C22⋊C4×C10712yes—
341C2×D4—24no—
342C2×D4—24no—
343C2×D4—24no—
344C2×D4—22no—
345C2×D4—24no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—22no—
349C2×D4—41no—
350C2×D4—42no—
351C2×D4—48no—
352C2×D4—44no—
353C2×D4—44no—
354C2×D4—44no—
355C2×D4—44no—
356C2×D4—82no—
357C2×D4C22⋊C4×C10712yes—
358C2×D4C22⋊C4×C10712yes—
359C22×C4—24no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—24no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—44no—
370C22×C4—82no—
371C22×C4C22⋊C4×C10711yescharacteristic
372C22×C4C22⋊C4×C10711yescharacteristic
373C22×C4C22×C4×C10711yescharacteristic
374C22×C4C2×D4×C10711yescharacteristic
375C22×C4C2×D4×C10711yescharacteristic
376M16—24no—
377M16—42no—
378C2×C8—42no—
379C2×C8—42no—
380C4⋊C4—24no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4C22⋊C4×C10712yes—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—22no—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C22⋊C4—24no—
390C22⋊C4—22no—
391C42C2×D4×C10712yes—
392C42C2×D4×C10712yes—
393C23—24no—
394C23—21no—
395C23—22no—
396C23—21no—
397C23—22no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—41no—
402C23—41no—
403C23—42no—
404C23—42no—
405C23—48no—
406C23—42no—
407C23—48no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—84no—
415C23—88no—
416C23—88no—
417C23#104×C10712yes—
418C23C2×C22⋊C4×C10711yescharacteristic
419Q8—42no—
420Q8—42no—
421D4—24no—
422D4—22no—
423D4—44no—
424D4—42no—
425D4—48no—
426D4—48no—
427D4—42no—
428D4—84no—
429D4#100×C10714yescomplemented
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—48no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—84no—
448C2×C4C2×C22⋊C4×C10711yescharacteristic
449C2×C4C2×C22⋊C4×C10711yescharacteristic
450C2×C4#120×C10712yes—
451C2×C4#120×C10712yes—
452C8—44no—
453C8—82no—
454C22—21no—
455C22—21no—
456C22—24no—
457C22—22no—
458C22—42no—
459C22—42no—
460C22—44no—
461C22—44no—
462C22—41no—
463C22—42no—
464C22—42no—
465C22—41no—
466C22—41no—
467C22—42no—
468C22—41no—
469C22—42no—
470C22—41no—
471C22—42no—
472C22—81no—
473C22—81no—
474C22—82no—
475C22—82no—
476C22—816no—
477C22#379×C10711yescharacteristic
478C22C2×#104×C10711yescharacteristic
479C22#421×C10711yescharacteristic
480C4—21no—
481C4—22no—
482C4—22no—
483C4—41no—
484C4—42no—
485C4—41no—
486C4—42no—
487C4C2×#100×C10712yes—
488C2—21no—
489C2—21no—
490C2—44no—
491C2—42no—
492C2—82no—
493C2—81no—
494C2C107×#178311yescharacteristic
495C2C107×#178911yescharacteristic
496C2C107×#179511yescharacteristic
subgroupG/H
center, socleC22×C107#379
commutatorC22×C4C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC2×#546×C107C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#100×C107C2semidirect
3. C107×#1527C2semidirect
4. C107×#1490C2semidirect
5. C107×#1466C2semidirect
19. #432×C107C22semidirect
21. C4×M16×C107C22semidirect
180. D4×C107#100semidirect
239. #8367C107direct (N × H)
250. C4×#100C2×C107semidirect
251. #1527C2×C107semidirect
252. #1490C2×C107semidirect
253. #1466C2×C107semidirect
254. C107#8367direct (N × H)
268. #432C22×C107semidirect
270. C4×M16C22×C107semidirect
429. D4#100×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1072
C4×#100×C1072
C107×#15272
C107×#14902
C107×#14662
#8367107