Finite Group Databasebeta

← C107×#10376 #41036340

Subgroups — C107×#10376 #41036340

Order 27392.

464 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2569C211yesmaximal, characteristic, complemented
2C107×#1964C211yesmaximal, characteristic
3C107×#1519C211yesmaximal, characteristic
4C2×#327×C107C211yesmaximal, characteristic
5C107×#1294C211yesmaximal, characteristic, complemented
6C107×#1289C211yesmaximal, characteristic, complemented
7C107×#1282C211yesmaximal, characteristic, complemented
8C2×#121×C107C2211yescharacteristic
9C2×#99×C107—21no—
10C2×#99×C107—21no—
11C2×C22⋊C8×C107C2211yescharacteristic
12C2×C22⋊C8×C107C2211yescharacteristic
13#400×C107—21no—
14#398×C107—21no—
15#387×C107—21no—
16#387×C107—21no—
17#385×C107—21no—
18#380×C107—21no—
19#380×C107C2211yescharacteristic
20#380×C107C2211yescharacteristic
21C4×C22⋊C4×C107C2211yescharacteristic
22C2×#95×C107C2211yescharacteristic
23#327×C107—21no—
24#327×C107—21no—
25#327×C107—21no—
26#327×C107—21no—
27C22×D4×C107—21no—
28C22×D4×C107Q811yescharacteristic
29C23×C4×C107—21no—
30C23×C4×C107C2311yescharacteristic
31C22×C8×C107—21no—
32C22×C8×C107—21no—
33#121×C107—21no—
34#121×C107—21no—
35#121×C107—21no—
36#121×C107—21no—
37C2×C4⋊C4×C107—21no—
38C2×C4⋊C4×C107—21no—
39C2×C4⋊C4×C107—21no—
40C2×C4⋊C4×C107—21no—
41C2×C4⋊C4×C107—21no—
42C2×C4⋊C4×C107—21no—
43C2×C4⋊C4×C107Q811yescharacteristic
44C2×C22⋊C4×C107—21no—
45C2×C22⋊C4×C107—21no—
46C2×C22⋊C4×C107—21no—
47C2×C22⋊C4×C107D411yescharacteristic
48C2×C22⋊C4×C107D411yescharacteristic
49C2×C42×C107—21no—
50#99×C107—42no—
51#99×C107—42no—
52C22⋊C8×C107—21no—
53C22⋊C8×C107—21no—
54C22⋊C8×C107—21no—
55C22⋊C8×C107—21no—
56#95×C107—21no—
57#95×C107—21no—
58#95×C107—21no—
59#95×C107—21no—
60#95×C107—21no—
61#95×C107—21no—
62#95×C107—21no—
63#95×C107D411yescharacteristic
64#95×C107D411yescharacteristic
65#95×C107D411yescharacteristic
66#95×C107D411yescharacteristic
67C24×C107—21no—
68C24×C107C2×D411yescharacteristic
69C2×D4×C107—21no—
70C2×D4×C107—21no—
71C2×D4×C107—41no—
72C2×D4×C107—41no—
73C2×D4×C107—41no—
74C2×D4×C107—41no—
75C2×D4×C107—41no—
76C2×D4×C107—41no—
77C2×D4×C107—81no—
78C22×C4×C107—21no—
79C22×C4×C107—21no—
80C22×C4×C107—21no—
81C22×C4×C107—21no—
82C22×C4×C107—21no—
83C22×C4×C107—21no—
84C22×C4×C107—21no—
85C22×C4×C107—42no—
86C22×C4×C107—41no—
87C22×C4×C107—41no—
88C22×C4×C107—41no—
89C22×C4×C107—81no—
90C22×C4×C107—81no—
91C22×C4×C107C2×D411yescharacteristic
92C22×C4×C107C2×D411yescharacteristic
93C22×C4×C107C2×Q811yescharacteristic
94C22×C4×C107#4111yescharacteristic
95C22×C4×C107#4111yescharacteristic
96C22×C4×C107#4111yescharacteristic
97C2×C8×C107—41no—
98C2×C8×C107—41no—
99C2×C8×C107—81no—
100C2×C8×C107—81no—
101C4⋊C4×C107—21no—
102C4⋊C4×C107—21no—
103C4⋊C4×C107—42no—
104C4⋊C4×C107—42no—
105C4⋊C4×C107—81no—
106C4⋊C4×C107—81no—
107C4⋊C4×C107—81no—
108C4⋊C4×C107—81no—
109C22⋊C4×C107—21no—
110C22⋊C4×C107—21no—
111C22⋊C4×C107—21no—
112C22⋊C4×C107—21no—
113C22⋊C4×C107—41no—
114C22⋊C4×C107—41no—
115C22⋊C4×C107—41no—
116C22⋊C4×C107—41no—
117C22⋊C4×C107—41no—
118C22⋊C4×C107—41no—
119C42×C107—81no—
120C23×C107—41no—
121C23×C107—41no—
122C23×C107—41no—
123C23×C107—41no—
124C23×C107—41no—
125C23×C107—81no—
126C23×C107—81no—
127C23×C107#12011yescharacteristic
128C23×C107C22⋊Q811yescharacteristic
129C23×C107#12411yescharacteristic
130C23×C107#13511yescharacteristic
131C23×C107#13511yescharacteristic
132C23×C107AGL(1,ℤ/8)11yescharacteristic
133C23×C107AGL(1,ℤ/8)11yescharacteristic
134D4×C107—81no—
135D4×C107—81no—
136D4×C107—81no—
137D4×C107—81no—
138D4×C107—81no—
139D4×C107—81no—
140C2×C4×C107—22no—
141C2×C4×C107—41no—
142C2×C4×C107—41no—
143C2×C4×C107—41no—
144C2×C4×C107—41no—
145C2×C4×C107—41no—
146C2×C4×C107—41no—
147C2×C4×C107—41no—
148C2×C4×C107—41no—
149C2×C4×C107—41no—
150C2×C4×C107—41no—
151C2×C4×C107—41no—
152C2×C4×C107—41no—
153C2×C4×C107—41no—
154C2×C4×C107—41no—
155C2×C4×C107—41no—
156C2×C4×C107—41no—
157C2×C4×C107—41no—
158C2×C4×C107—41no—
159C2×C4×C107—41no—
160C2×C4×C107—41no—
161C2×C4×C107—41no—
162C2×C4×C107—41no—
163C2×C4×C107—41no—
164C2×C4×C107—41no—
165C2×C4×C107—41no—
166C2×C4×C107—41no—
167C2×C4×C107—82no—
168C2×C4×C107—82no—
169C2×C4×C107—81no—
170C2×C4×C107—81no—
171C2×C4×C107—81no—
172C2×C4×C107C22⋊Q811yescharacteristic
173C2×C4×C107C22⋊Q811yescharacteristic
174C2×C4×C107#12411yescharacteristic
175C2×C4×C107#12411yescharacteristic
176C8×C107—81no—
177C8×C107—81no—
178C22×C107—21no—
179C22×C107—21no—
180C22×C107—21no—
181C22×C107—21no—
182C22×C107—21no—
183C22×C107—21no—
184C22×C107—41no—
185C22×C107—41no—
186C22×C107—41no—
187C22×C107—41no—
188C22×C107—81no—
189C22×C107—81no—
190C22×C107—81no—
191C22×C107—161no—
192C22×C107—161no—
193C22×C107#39311yescharacteristic
194C22×C107#44911yescharacteristic
195C22×C107#44911yescharacteristic
196C22×C107#47811yescharacteristic
197C22×C107#47811yescharacteristic
198C22×C107#48811yescharacteristic
199C22×C107#49011yescharacteristic
200C4×C107—21no—
201C4×C107—21no—
202C4×C107—21no—
203C4×C107—21no—
204C4×C107—42no—
205C4×C107—81no—
206C4×C107—81no—
207C4×C107—81no—
208C4×C107—81no—
209C4×C107—81no—
210C4×C107—81no—
211C4×C107—161no—
212#10376C10711yesmaximal, characteristic, direct product factor, Sylow
213C2×C107—21no—
214C2×C107—21no—
215C2×C107—21no—
216C2×C107—21no—
217C2×C107—21no—
218C2×C107—21no—
219C2×C107—161no—
220C2×C107#202511yescharacteristic
221C2×C107#203111yescharacteristic
222C2×C107#203211yescharacteristic
223#2569C2×C10711yescharacteristic, complemented
224#1964C2×C10711yescharacteristic
225#1519C2×C10711yescharacteristic
226C2×#327C2×C10711yescharacteristic
227#1294C2×C10711yescharacteristic, complemented
228#1289C2×C10711yescharacteristic, complemented
229#1282C2×C10711yescharacteristic, complemented
230C107#1037611yescharacteristic, direct product factor, Sylow
231C2×#121C22×C10711yescharacteristic
232C2×#99—21no—
233C2×#99—21no—
234C2×C22⋊C8C22×C10711yescharacteristic
235C2×C22⋊C8C22×C10711yescharacteristic
236#400—21no—
237#398—21no—
238#387—21no—
239#387—21no—
240#385—21no—
241#380—21no—
242#380C22×C10711yescharacteristic
243#380C22×C10711yescharacteristic
244C4×C22⋊C4C22×C10711yescharacteristic
245C2×#95C22×C10711yescharacteristic
246#327—21no—
247#327—21no—
248#327—21no—
249#327—21no—
250C22×D4—21no—
251C22×D4Q8×C10711yescharacteristic
252C23×C4—21no—
253C23×C4C23×C10711yescharacteristic
254C22×C8—21no—
255C22×C8—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259#121—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4Q8×C10711yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4D4×C10711yescharacteristic
271C2×C22⋊C4D4×C10711yescharacteristic
272C2×C42—21no—
273#99—42no—
274#99—42no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95D4×C10711yescharacteristic
287#95D4×C10711yescharacteristic
288#95D4×C10711yescharacteristic
289#95D4×C10711yescharacteristic
290C24—21no—
291C24C2×D4×C10711yescharacteristic
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—81no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—81no—
313C22×C4—81no—
314C22×C4C2×D4×C10711yescharacteristic
315C22×C4C2×D4×C10711yescharacteristic
316C22×C4C2×Q8×C10711yescharacteristic
317C22×C4#41×C10711yescharacteristic
318C22×C4#41×C10711yescharacteristic
319C22×C4#41×C10711yescharacteristic
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—81no—
323C2×C8—81no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—81no—
329C4⋊C4—81no—
330C4⋊C4—81no—
331C4⋊C4—81no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—81no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—81no—
349C23—81no—
350C23#120×C10711yescharacteristic
351C23C22⋊Q8×C10711yescharacteristic
352C23#124×C10711yescharacteristic
353C23#135×C10711yescharacteristic
354C23#135×C10711yescharacteristic
355C23AGL(1,ℤ/8)×C10711yescharacteristic
356C23AGL(1,ℤ/8)×C10711yescharacteristic
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4C22⋊Q8×C10711yescharacteristic
396C2×C4C22⋊Q8×C10711yescharacteristic
397C2×C4#124×C10711yescharacteristic
398C2×C4#124×C10711yescharacteristic
399C8—81no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—161no—
415C22—161no—
416C22#393×C10711yescharacteristic
417C22#449×C10711yescharacteristic
418C22#449×C10711yescharacteristic
419C22#478×C10711yescharacteristic
420C22#478×C10711yescharacteristic
421C22#488×C10711yescharacteristic
422C22#490×C10711yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—42no—
428C4—81no—
429C4—81no—
430C4—81no—
431C4—81no—
432C4—81no—
433C4—81no—
434C4—161no—
435C2—21no—
436C2—21no—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—161no—
442C2C107×#202511yescharacteristic
443C2C107×#203111yescharacteristic
444C2C107×#203211yescharacteristic
subgroupG/H
center, socleC22×C107#393
commutator, Frattini, cosocleC23×C4C23×C107
prime radicalC2×#121×C107C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2569C2semidirect
5. C107×#1294C2semidirect
6. C107×#1289C2semidirect
7. C107×#1282C2semidirect
212. #10376C107direct (N × H)
223. #2569C2×C107semidirect
227. #1294C2×C107semidirect
228. #1289C2×C107semidirect
229. #1282C2×C107semidirect
230. C107#10376direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#25692
C107×#19642
C107×#15192
C2×#327×C1072
C107×#12942
C107×#12892
C107×#12822
#10376107