Finite Group Databasebeta

← C107×#10076 #41036040

Subgroups — C107×#10076 #41036040

Order 27392.

654 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#500×C107C211yesmaximal, characteristic, complemented
2C2×#474×C107C211yesmaximal, characteristic
3C107×#2542C211yesmaximal, characteristic
4C107×#1981C211yesmaximal, characteristic, complemented
5C2×#332×C107C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C107C211yesmaximal, characteristic
7C107×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C107C2211yescharacteristic
9C2×C4⋊Q8×C107C2211yescharacteristic
10C2×C22⋊Q8×C107—22no—
11C2×C4×D4×C107C2211yescharacteristic
12#500×C107—22no—
13#500×C107—22no—
14#474×C107—22no—
15#474×C107—22no—
16C2×#107×C107—22no—
17C2×#107×C107—21no—
18C2×C4⋊C8×C107C2211yescharacteristic
19C2×C4⋊C8×C107C2211yescharacteristic
20C2×#103×C107—22no—
21C2×#102×C107—21no—
22C2×C4×C8×C107C2211yescharacteristic
23#399×C107—22no—
24#390×C107—21no—
25#384×C107—21no—
26C4×C4⋊C4×C107C2211yescharacteristic
27#332×C107—22no—
28D4⋊C8×C107—22no—
29C22×Q8×C107—21no—
30C22×Q8×C107—21no—
31C22×D4×C107D411yescharacteristic
32C23×C4×C107—21no—
33C22×C8×C107—21no—
34C22×C8×C107—21no—
35C22×C8×C107—21no—
36C4⋊Q8×C107—21no—
37C4⋊Q8×C107—21no—
38C4⋊Q8×C107—21no—
39C4⋊Q8×C107—21no—
40C4⋊Q8×C107—21no—
41C4⋊Q8×C107—21no—
42C4⋊Q8×C107—21no—
43C4⋊Q8×C107D412yes—
44C22⋊Q8×C107—44no—
45C22⋊Q8×C107—44no—
46C4×D4×C107—21no—
47C4×D4×C107—21no—
48C4×D4×C107—21no—
49C4×D4×C107—21no—
50C2×C4⋊C4×C107—21no—
51C2×C4⋊C4×C107—21no—
52C2×C4⋊C4×C107—24no—
53C2×C4⋊C4×C107—21no—
54C2×C4⋊C4×C107D411yescharacteristic
55C2×C4⋊C4×C107D412yes—
56C2×C4⋊C4×C107D412yes—
57C2×C22⋊C4×C107—24no—
58C2×C22⋊C4×C107—21no—
59C2×C42×C107—21no—
60C2×C42×C107C2311yescharacteristic
61#107×C107—24no—
62#107×C107—28no—
63C4⋊C8×C107—21no—
64C4⋊C8×C107—21no—
65C4⋊C8×C107—21no—
66C4⋊C8×C107D412yes—
67#103×C107—44no—
68#102×C107—24no—
69C4×C8×C107—21no—
70C4×C8×C107D412yes—
71#95×C107—21no—
72C24×C107—21no—
73C2×Q8×C107—22no—
74C2×Q8×C107—41no—
75C2×Q8×C107—41no—
76C2×Q8×C107—41no—
77C2×Q8×C107—42no—
78C2×Q8×C107—42no—
79C2×Q8×C107—42no—
80C2×Q8×C107—42no—
81C2×D4×C107—21no—
82C2×D4×C107—21no—
83C2×D4×C107—21no—
84C2×D4×C107—21no—
85C2×D4×C107—21no—
86C2×D4×C107Q1612yes—
87C22×C4×C107—22no—
88C22×C4×C107—22no—
89C22×C4×C107—21no—
90C22×C4×C107—41no—
91C22×C4×C107—41no—
92C22×C4×C107—41no—
93C22×C4×C107—42no—
94C22×C4×C107—42no—
95C22×C4×C107C2×D411yescharacteristic
96C22×C4×C107C2×D411yescharacteristic
97C22×C4×C107C2×D411yescharacteristic
98C2×C8×C107—24no—
99C2×C8×C107—22no—
100C2×C8×C107—22no—
101C2×C8×C107—41no—
102C2×C8×C107—41no—
103C2×C8×C107—41no—
104C2×C8×C107—42no—
105C4⋊C4×C107—22no—
106C4⋊C4×C107—22no—
107C4⋊C4×C107—22no—
108C4⋊C4×C107—21no—
109C4⋊C4×C107—22no—
110C4⋊C4×C107—21no—
111C4⋊C4×C107—22no—
112C4⋊C4×C107—48no—
113C4⋊C4×C107—41no—
114C4⋊C4×C107—41no—
115C4⋊C4×C107—41no—
116C4⋊C4×C107—41no—
117C4⋊C4×C107D814yes—
118C22⋊C4×C107—48no—
119C22⋊C4×C107—41no—
120C22⋊C4×C107—41no—
121C42×C107—41no—
122C42×C107—41no—
123C42×C107C2×D411yescharacteristic
124C42×C107C2×D411yescharacteristic
125C42×C107C2×D411yescharacteristic
126C42×C107#4111yescharacteristic
127C23×C107—22no—
128C23×C107—41no—
129C23×C107—42no—
130C23×C107—41no—
131C23×C107—42no—
132C23×C107#12011yescharacteristic
133Q8×C107—44no—
134Q8×C107—82no—
135Q8×C107—81no—
136Q8×C107—81no—
137Q8×C107—81no—
138Q8×C107—81no—
139D4×C107—22no—
140D4×C107—22no—
141D4×C107—41no—
142D4×C107—41no—
143C2×C4×C107—22no—
144C2×C4×C107—24no—
145C2×C4×C107—42no—
146C2×C4×C107—42no—
147C2×C4×C107—41no—
148C2×C4×C107—42no—
149C2×C4×C107—42no—
150C2×C4×C107—44no—
151C2×C4×C107—42no—
152C2×C4×C107—82no—
153C2×C4×C107—82no—
154C2×C4×C107—81no—
155C2×C4×C107—81no—
156C2×C4×C107#12011yescharacteristic
157C2×C4×C107#12011yescharacteristic
158C2×C4×C107#12111yescharacteristic
159C2×C4×C107#12111yescharacteristic
160C2×C4×C107#12111yescharacteristic
161C2×C4×C107#12711yescharacteristic
162C2×C4×C107C2×D812yes—
163C2×C4×C107C2×Q1611yescharacteristic
164C2×C4×C107#13511yescharacteristic
165C2×C4×C107AGL(1,ℤ/8)12yes—
166C2×C4×C107#13711yescharacteristic
167C2×C4×C107#13711yescharacteristic
168C8×C107—24no—
169C8×C107—42no—
170C8×C107—81no—
171C22×C107—44no—
172C22×C107—42no—
173C22×C107—82no—
174C22×C107—81no—
175C22×C107—81no—
176C22×C107#39211yescharacteristic
177C22×C107#44712yes—
178C22×C107#45111yescharacteristic
179C22×C107#45211yescharacteristic
180C22×C107#45612yes—
181C4×C107—21no—
182C4×C107—21no—
183C4×C107—44no—
184C4×C107—81no—
185C4×C107—82no—
186C4×C107—82no—
187C4×C107#45111yescharacteristic
188C4×C107#45211yescharacteristic
189C4×C107#45912yes—
190C4×C107#46711yescharacteristic
191C4×C107#47011yescharacteristic
192C4×C107#49311yescharacteristic
193C4×C107#49611yescharacteristic
194#10076C10711yesmaximal, characteristic, direct product factor, Sylow
195C2×C107—82no—
196C2×C107#164712yes—
197C2×C107#164912yes—
198C2×C107#200111yescharacteristic
199C2×C107#200511yescharacteristic
200C2×C107#201111yescharacteristic
201C2×#500C2×C10711yescharacteristic, complemented
202C2×#474C2×C10711yescharacteristic
203#2542C2×C10711yescharacteristic
204#1981C2×C10711yescharacteristic, complemented
205C2×#332C2×C10711yescharacteristic, complemented
206C2×D4⋊C8C2×C10711yescharacteristic
207#1279C2×C10711yescharacteristic, complemented
208C107#1007611yescharacteristic, direct product factor, Sylow
209C2×C4⋊Q8C22×C10711yescharacteristic
210C2×C4⋊Q8C22×C10711yescharacteristic
211C2×C22⋊Q8—22no—
212C2×C4×D4C22×C10711yescharacteristic
213#500—22no—
214#500—22no—
215#474—22no—
216#474—22no—
217C2×#107—22no—
218C2×#107—21no—
219C2×C4⋊C8C22×C10711yescharacteristic
220C2×C4⋊C8C22×C10711yescharacteristic
221C2×#103—22no—
222C2×#102—21no—
223C2×C4×C8C22×C10711yescharacteristic
224#399—22no—
225#390—21no—
226#384—21no—
227C4×C4⋊C4C22×C10711yescharacteristic
228#332—22no—
229D4⋊C8—22no—
230C22×Q8—21no—
231C22×Q8—21no—
232C22×D4D4×C10711yescharacteristic
233C23×C4—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8D4×C10712yes—
245C22⋊Q8—44no—
246C22⋊Q8—44no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4D4×C10711yescharacteristic
256C2×C4⋊C4D4×C10712yes—
257C2×C4⋊C4D4×C10712yes—
258C2×C22⋊C4—24no—
259C2×C22⋊C4—21no—
260C2×C42—21no—
261C2×C42C23×C10711yescharacteristic
262#107—24no—
263#107—28no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8D4×C10712yes—
268#103—44no—
269#102—24no—
270C4×C8—21no—
271C4×C8D4×C10712yes—
272#95—21no—
273C24—21no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—42no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4Q16×C10712yes—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4C2×D4×C10711yescharacteristic
297C22×C4C2×D4×C10711yescharacteristic
298C22×C4C2×D4×C10711yescharacteristic
299C2×C8—24no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—42no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—48no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4D8×C10714yes—
319C22⋊C4—48no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C42—41no—
323C42—41no—
324C42C2×D4×C10711yescharacteristic
325C42C2×D4×C10711yescharacteristic
326C42C2×D4×C10711yescharacteristic
327C42#41×C10711yescharacteristic
328C23—22no—
329C23—41no—
330C23—42no—
331C23—41no—
332C23—42no—
333C23#120×C10711yescharacteristic
334Q8—44no—
335Q8—82no—
336Q8—81no—
337Q8—81no—
338Q8—81no—
339Q8—81no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344C2×C4—22no—
345C2×C4—24no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4#120×C10711yescharacteristic
358C2×C4#120×C10711yescharacteristic
359C2×C4#121×C10711yescharacteristic
360C2×C4#121×C10711yescharacteristic
361C2×C4#121×C10711yescharacteristic
362C2×C4#127×C10711yescharacteristic
363C2×C4C2×D8×C10712yes—
364C2×C4C2×Q16×C10711yescharacteristic
365C2×C4#135×C10711yescharacteristic
366C2×C4AGL(1,ℤ/8)×C10712yes—
367C2×C4#137×C10711yescharacteristic
368C2×C4#137×C10711yescharacteristic
369C8—24no—
370C8—42no—
371C8—81no—
372C22—44no—
373C22—42no—
374C22—82no—
375C22—81no—
376C22—81no—
377C22#392×C10711yescharacteristic
378C22#447×C10712yes—
379C22#451×C10711yescharacteristic
380C22#452×C10711yescharacteristic
381C22#456×C10712yes—
382C4—21no—
383C4—21no—
384C4—44no—
385C4—81no—
386C4—82no—
387C4—82no—
388C4#451×C10711yescharacteristic
389C4#452×C10711yescharacteristic
390C4#459×C10712yes—
391C4#467×C10711yescharacteristic
392C4#470×C10711yescharacteristic
393C4#493×C10711yescharacteristic
394C4#496×C10711yescharacteristic
395C2—82no—
396C2C107×#164712yes—
397C2C107×#164912yes—
398C2C107×#200111yescharacteristic
399C2C107×#200511yescharacteristic
400C2C107×#201111yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutator, Frattini, cosocleC2×C42C23×C107
prime radicalC22×D4×C107D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#500×C107C2semidirect
4. C107×#1981C2semidirect
5. C2×#332×C107C2semidirect
7. C107×#1279C2semidirect
194. #10076C107direct (N × H)
201. C2×#500C2×C107semidirect
204. #1981C2×C107semidirect
205. C2×#332C2×C107semidirect
207. #1279C2×C107semidirect
208. C107#10076direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#500×C1072
C2×#474×C1072
C107×#25422
C107×#19812
C2×#332×C1072
C2×D4⋊C8×C1072
C107×#12792
#10076107