Finite Group Databasebeta

← C107×#8882 #41034846

Subgroups — C107×#8882 #41034846

Order 27392.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊C4×C107C211yesmaximal, characteristic
2C107×#1947C211yesmaximal, characteristic, complemented
3C107×#1845C211yesmaximal, characteristic, complemented
4C107×#1802C211yesmaximal, characteristic
5C2×D4⋊C8×C107C211yesmaximal, characteristic
6C107×#1296C211yesmaximal, characteristic, complemented
7C107×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D4×C107—21no—
9C2×C4×D4×C107C2211yescharacteristic
10C22×C4⋊C4×C107—21no—
11C2×#107×C107—21no—
12C2×#107×C107—22no—
13C2×C4⋊C8×C107C2211yescharacteristic
14C2×C4⋊C8×C107C2211yescharacteristic
15C2×#102×C107—21no—
16C2×C4×C8×C107C2211yescharacteristic
17#389×C107—21no—
18#385×C107—22no—
19#384×C107C2211yescharacteristic
20#384×C107C2211yescharacteristic
21#380×C107—21no—
22C4×C4⋊C4×C107C2211yescharacteristic
23#340×C107—21no—
24#340×C107—21no—
25D4⋊C8×C107C414yescomplemented
26C22×D4×C107D411yescharacteristic
27C23×C4×C107—21no—
28C23×C4×C107—22no—
29C22×C8×C107—21no—
30C22×C8×C107—21no—
31C22×C8×C107—21no—
32C4×D4×C107—21no—
33C4×D4×C107—21no—
34C4×D4×C107—42no—
35C4×D4×C107—42no—
36C4×D4×C107C2×C412yes—
37C4×D4×C107Q812yes—
38C2×C4⋊C4×C107—22no—
39C2×C4⋊C4×C107—21no—
40C2×C4⋊C4×C107—21no—
41C2×C4⋊C4×C107—21no—
42C2×C4⋊C4×C107—21no—
43C2×C4⋊C4×C107—21no—
44C2×C4⋊C4×C107—42no—
45C2×C4⋊C4×C107—42no—
46C2×C4⋊C4×C107D411yescharacteristic
47C2×C4⋊C4×C107D411yescharacteristic
48C2×C4⋊C4×C107D411yescharacteristic
49C2×C4⋊C4×C107D412yes—
50C2×C22⋊C4×C107—21no—
51C2×C22⋊C4×C107—22no—
52C2×C42×C107—21no—
53C2×C42×C107C2311yescharacteristic
54#107×C107—44no—
55#107×C107—42no—
56C4⋊C8×C107—21no—
57C4⋊C8×C107—21no—
58C4⋊C8×C107—21no—
59C4⋊C8×C107C2×C412yescomplemented
60#102×C107—42no—
61C4×C8×C107—21no—
62C4×C8×C107C2×C412yescomplemented
63#95×C107—22no—
64#95×C107—21no—
65C24×C107—21no—
66C2×D4×C107—21no—
67C2×D4×C107—21no—
68C2×D4×C107—21no—
69C2×D4×C107C4⋊C412yes—
70C2×D4×C107D812yes—
71C2×D4×C107Q1612yes—
72C22×C4×C107—21no—
73C22×C4×C107—21no—
74C22×C4×C107—22no—
75C22×C4×C107—22no—
76C22×C4×C107—21no—
77C22×C4×C107—22no—
78C22×C4×C107—44no—
79C22×C4×C107—41no—
80C22×C4×C107—41no—
81C22×C4×C107—41no—
82C22×C4×C107—41no—
83C22×C4×C107—44no—
84C22×C4×C107—41no—
85C22×C4×C107—82no—
86C22×C4×C107C2×D411yescharacteristic
87C22×C4×C107C2×D411yescharacteristic
88C22×C4×C107C2×D411yescharacteristic
89C2×C8×C107—22no—
90C2×C8×C107—22no—
91C2×C8×C107—22no—
92C2×C8×C107—22no—
93C2×C8×C107—41no—
94C2×C8×C107—41no—
95C2×C8×C107—41no—
96C2×C8×C107—41no—
97C2×C8×C107—41no—
98C4⋊C4×C107—21no—
99C4⋊C4×C107—21no—
100C4⋊C4×C107—21no—
101C4⋊C4×C107—21no—
102C4⋊C4×C107—42no—
103C4⋊C4×C107—44no—
104C4⋊C4×C107—42no—
105C4⋊C4×C107—41no—
106C4⋊C4×C107—41no—
107C4⋊C4×C107—41no—
108C4⋊C4×C107—41no—
109C4⋊C4×C107—41no—
110C4⋊C4×C107—41no—
111C4⋊C4×C107—41no—
112C4⋊C4×C107—41no—
113C4⋊C4×C107C4⋊C412yes—
114C4⋊C4×C107D812yes—
115C22⋊C4×C107—22no—
116C22⋊C4×C107—22no—
117C22⋊C4×C107—44no—
118C42×C107—41no—
119C42×C107—41no—
120C42×C107C22×C411yescharacteristic
121C42×C107C2×Q811yescharacteristic
122C42×C107#4111yescharacteristic
123C42×C107#4111yescharacteristic
124C23×C107—22no—
125C23×C107—22no—
126C23×C107—22no—
127C23×C107—41no—
128C23×C107—41no—
129C23×C107—41no—
130C23×C107—41no—
131C23×C107#12011yescharacteristic
132D4×C107—22no—
133D4×C107—22no—
134D4×C107—22no—
135D4×C107#10714yescomplemented
136C2×C4×C107—21no—
137C2×C4×C107—21no—
138C2×C4×C107—22no—
139C2×C4×C107—22no—
140C2×C4×C107—41no—
141C2×C4×C107—41no—
142C2×C4×C107—41no—
143C2×C4×C107—41no—
144C2×C4×C107—42no—
145C2×C4×C107—42no—
146C2×C4×C107—42no—
147C2×C4×C107—42no—
148C2×C4×C107—41no—
149C2×C4×C107—42no—
150C2×C4×C107—42no—
151C2×C4×C107—41no—
152C2×C4×C107—42no—
153C2×C4×C107—41no—
154C2×C4×C107—88no—
155C2×C4×C107—81no—
156C2×C4×C107—81no—
157C2×C4×C107—81no—
158C2×C4×C107C2×C4⋊C411yescharacteristic
159C2×C4×C107C4×D411yescharacteristic
160C2×C4×C107C4×D411yescharacteristic
161C2×C4×C107C22⋊Q811yescharacteristic
162C2×C4×C107C22⋊Q811yescharacteristic
163C2×C4×C107#12311yescharacteristic
164C2×C4×C107C2×D811yescharacteristic
165C2×C4×C107C2×D811yescharacteristic
166C2×C4×C107C2×Q1611yescharacteristic
167C2×C4×C107#13511yescharacteristic
168C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C107#13711yescharacteristic
171C2×C4×C107#13711yescharacteristic
172C8×C107—24no—
173C8×C107—42no—
174C8×C107—81no—
175C22×C107—24no—
176C22×C107—42no—
177C22×C107—42no—
178C22×C107—42no—
179C22×C107—42no—
180C22×C107—42no—
181C22×C107—42no—
182C22×C107#38511yescharacteristic
183C22×C107#44711yescharacteristic
184C22×C107#44711yescharacteristic
185C22×C107#45111yescharacteristic
186C22×C107#45211yescharacteristic
187C22×C107#45311yescharacteristic
188C22×C107#45611yescharacteristic
189C4×C107—21no—
190C4×C107—21no—
191C4×C107—42no—
192C4×C107—42no—
193C4×C107—82no—
194C4×C107—81no—
195C4×C107—161no—
196C4×C107C2×#10711yescharacteristic
197C4×C107#42811yescharacteristic
198C4×C107C4×D811yescharacteristic
199C4×C107#44011yescharacteristic
200C4×C107#47411yescharacteristic
201C4×C107#47811yescharacteristic
202C4×C107#48011yescharacteristic
203C4×C107#48411yescharacteristic
204#8882C10711yesmaximal, characteristic, direct product factor, Sylow
205C2×C107—44no—
206C2×C107#161911yescharacteristic
207C2×C107#163211yescharacteristic
208C2×C107#164711yescharacteristic
209C2×C107#164911yescharacteristic
210C2×C107#185211yescharacteristic
211C2×C107#185911yescharacteristic
212C2×C107#186211yescharacteristic
213D4×C4⋊C4C2×C10711yescharacteristic
214#1947C2×C10711yescharacteristic, complemented
215#1845C2×C10711yescharacteristic, complemented
216#1802C2×C10711yescharacteristic
217C2×D4⋊C8C2×C10711yescharacteristic
218#1296C2×C10711yescharacteristic, complemented
219#1279C2×C10711yescharacteristic, complemented
220C107#888211yescharacteristic, direct product factor, Sylow
221C2×C4×D4—21no—
222C2×C4×D4C22×C10711yescharacteristic
223C22×C4⋊C4—21no—
224C2×#107—22no—
225C2×#107—21no—
226C2×C4⋊C8C22×C10711yescharacteristic
227C2×C4⋊C8C22×C10711yescharacteristic
228C2×#102—21no—
229C2×C4×C8C22×C10711yescharacteristic
230#389—21no—
231#385—22no—
232#384C22×C10711yescharacteristic
233#384C22×C10711yescharacteristic
234#380—21no—
235C4×C4⋊C4C22×C10711yescharacteristic
236#340—21no—
237#340—21no—
238D4⋊C8C4×C10714yescomplemented
239C22×D4D4×C10711yescharacteristic
240C23×C4—21no—
241C23×C4—22no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—42no—
248C4×D4—42no—
249C4×D4C2×C4×C10712yes—
250C4×D4Q8×C10712yes—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4D4×C10711yescharacteristic
260C2×C4⋊C4D4×C10711yescharacteristic
261C2×C4⋊C4D4×C10711yescharacteristic
262C2×C4⋊C4D4×C10712yes—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—22no—
265C2×C42—21no—
266C2×C42C23×C10711yescharacteristic
267#107—44no—
268#107—42no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8C2×C4×C10712yescomplemented
273#102—42no—
274C4×C8—21no—
275C4×C8C2×C4×C10712yescomplemented
276#95—22no—
277#95—21no—
278C24—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4C4⋊C4×C10712yes—
283C2×D4D8×C10712yes—
284C2×D4Q16×C10712yes—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—44no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—44no—
297C22×C4—41no—
298C22×C4—82no—
299C22×C4C2×D4×C10711yescharacteristic
300C22×C4C2×D4×C10711yescharacteristic
301C22×C4C2×D4×C10711yescharacteristic
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—42no—
316C4⋊C4—44no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4C4⋊C4×C10712yes—
327C4⋊C4D8×C10712yes—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—44no—
331C42—41no—
332C42—41no—
333C42C22×C4×C10711yescharacteristic
334C42C2×Q8×C10711yescharacteristic
335C42#41×C10711yescharacteristic
336C42#41×C10711yescharacteristic
337C23—22no—
338C23—22no—
339C23—22no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23#120×C10711yescharacteristic
345D4—22no—
346D4—22no—
347D4—22no—
348D4#107×C10714yescomplemented
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—88no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4C2×C4⋊C4×C10711yescharacteristic
372C2×C4C4×D4×C10711yescharacteristic
373C2×C4C4×D4×C10711yescharacteristic
374C2×C4C22⋊Q8×C10711yescharacteristic
375C2×C4C22⋊Q8×C10711yescharacteristic
376C2×C4#123×C10711yescharacteristic
377C2×C4C2×D8×C10711yescharacteristic
378C2×C4C2×D8×C10711yescharacteristic
379C2×C4C2×Q16×C10711yescharacteristic
380C2×C4#135×C10711yescharacteristic
381C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
382C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
383C2×C4#137×C10711yescharacteristic
384C2×C4#137×C10711yescharacteristic
385C8—24no—
386C8—42no—
387C8—81no—
388C22—24no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22#385×C10711yescharacteristic
396C22#447×C10711yescharacteristic
397C22#447×C10711yescharacteristic
398C22#451×C10711yescharacteristic
399C22#452×C10711yescharacteristic
400C22#453×C10711yescharacteristic
401C22#456×C10711yescharacteristic
402C4—21no—
403C4—21no—
404C4—42no—
405C4—42no—
406C4—82no—
407C4—81no—
408C4—161no—
409C4C2×#107×C10711yescharacteristic
410C4#428×C10711yescharacteristic
411C4C4×D8×C10711yescharacteristic
412C4#440×C10711yescharacteristic
413C4#474×C10711yescharacteristic
414C4#478×C10711yescharacteristic
415C4#480×C10711yescharacteristic
416C4#484×C10711yescharacteristic
417C2—44no—
418C2C107×#161911yescharacteristic
419C2C107×#163211yescharacteristic
420C2C107×#164711yescharacteristic
421C2C107×#164911yescharacteristic
422C2C107×#185211yescharacteristic
423C2C107×#185911yescharacteristic
424C2C107×#186211yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC22×D4×C107D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#1947C2semidirect
3. C107×#1845C2semidirect
6. C107×#1296C2semidirect
7. C107×#1279C2semidirect
25. D4⋊C8×C107C4semidirect
59. C4⋊C8×C107C2×C4semidirect
62. C4×C8×C107C2×C4semidirect
135. D4×C107#107semidirect
204. #8882C107direct (N × H)
214. #1947C2×C107semidirect
215. #1845C2×C107semidirect
218. #1296C2×C107semidirect
219. #1279C2×C107semidirect
220. C107#8882direct (N × H)
238. D4⋊C8C4×C107semidirect
272. C4⋊C8C2×C4×C107semidirect
275. C4×C8C2×C4×C107semidirect
348. D4#107×C107semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊C4×C1072
C107×#19472
C107×#18452
C107×#18022
C2×D4⋊C8×C1072
C107×#12962
C107×#12792
#8882107