Finite Group Databasebeta

← C107×#13038 #41039002

Subgroups — C107×#13038 #41039002

Order 27392.

474 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C107C211yesmaximal, characteristic
2C2×#441×C107C211yesmaximal, characteristic, complemented
3C2×#362×C107C211yesmaximal, characteristic, complemented
4C2×#360×C107C211yesmaximal, characteristic
5C107×#1975C211yesmaximal, characteristic
6C107×#1383C211yesmaximal, characteristic, complemented
7C107×#1375C211yesmaximal, characteristic, complemented
8C2×#135×C107C2211yescharacteristic
9C22×Q16×C107C2211yescharacteristic
10C2×C4×Q8×C107—21no—
11#510×C107—22no—
12#510×C107—22no—
13C2×Q32×C107C412yescomplemented
14C2×SD32×C107C412yescomplemented
15C2×M32×C107C2211yescharacteristic
16C2×M32×C107C2211yescharacteristic
17#441×C107—22no—
18#441×C107—22no—
19C2×#108×C107C2211yescharacteristic
20C2×#106×C107C2211yescharacteristic
21C2×#104×C107—21no—
22C2×#103×C107—21no—
23#408×C107—21no—
24C2×#97×C107C2211yescharacteristic
25#362×C107—22no—
26#360×C107—22no—
27C2×#41×C107—21no—
28C22×Q8×C107—21no—
29#135×C107—21no—
30#135×C107—21no—
31#135×C107—21no—
32#135×C107—21no—
33C2×Q16×C107—21no—
34C2×Q16×C107—21no—
35C2×Q16×C107—21no—
36C2×Q16×C107C2×C411yescharacteristic
37C2×Q16×C107C2×C412yes—
38C2×Q16×C107D412yes—
39C2×Q16×C107D412yes—
40C2×SD16×C107—21no—
41C2×D8×C107C2×C411yescharacteristic
42C2×M16×C107—21no—
43C22×C8×C107D411yescharacteristic
44C22×C8×C107C2311yescharacteristic
45C4×Q8×C107—24no—
46C4×Q8×C107—42no—
47C2×C4⋊C4×C107—21no—
48C2×C4⋊C4×C107—41no—
49C2×C42×C107—41no—
50C2×C42×C107D411yescharacteristic
51Q32×C107—24no—
52SD32×C107—24no—
53M32×C107—21no—
54M32×C107—21no—
55M32×C107—21no—
56M32×C107—21no—
57C2×C16×C107—21no—
58C2×C16×C107C2×C412yes—
59#108×C107—21no—
60#108×C107—21no—
61#106×C107—21no—
62#106×C107D412yes—
63#104×C107—42no—
64#103×C107—24no—
65C22⋊C8×C107—42no—
66#97×C107—21no—
67#97×C107—21no—
68#41×C107—41no—
69#41×C107—41no—
70#41×C107—41no—
71#41×C107—41no—
72C2×Q8×C107—22no—
73C2×Q8×C107—21no—
74C2×Q8×C107—22no—
75C2×Q8×C107—22no—
76C2×Q8×C107—41no—
77C2×Q8×C107—41no—
78C2×Q8×C107—41no—
79C2×D4×C107—21no—
80C2×D4×C107—41no—
81C22×C4×C107—21no—
82C22×C4×C107—41no—
83C22×C4×C107—41no—
84C22×C4×C107—41no—
85C22×C4×C107C2×D411yescharacteristic
86Q16×C107—21no—
87Q16×C107—22no—
88Q16×C107—21no—
89Q16×C107—22no—
90Q16×C107—22no—
91Q16×C107C22⋊C414yes—
92SD16×C107—41no—
93SD16×C107—41no—
94D8×C107—21no—
95D8×C107—21no—
96M16×C107—41no—
97M16×C107—41no—
98C2×C8×C107—21no—
99C2×C8×C107—21no—
100C2×C8×C107—21no—
101C2×C8×C107—41no—
102C2×C8×C107C22×C411yescharacteristic
103C2×C8×C107C2×D411yescharacteristic
104C2×C8×C107C2×D411yescharacteristic
105C2×C8×C107C2×D411yescharacteristic
106C2×C8×C107#4111yescharacteristic
107C2×C8×C107#4111yescharacteristic
108C4⋊C4×C107—22no—
109C4⋊C4×C107—44no—
110C4⋊C4×C107—41no—
111C42×C107—21no—
112C42×C107—44no—
113C42×C107D812yes—
114C16×C107—22no—
115C16×C107—41no—
116C23×C107—41no—
117C23×C107AGL(1,ℤ/8)11yescharacteristic
118Q8×C107—24no—
119Q8×C107—42no—
120Q8×C107—42no—
121Q8×C107—42no—
122Q8×C107—41no—
123Q8×C107—41no—
124D4×C107—41no—
125D4×C107—41no—
126D4×C107—81no—
127D4×C107—81no—
128C2×C4×C107—22no—
129C2×C4×C107—42no—
130C2×C4×C107—42no—
131C2×C4×C107—42no—
132C2×C4×C107—42no—
133C2×C4×C107—41no—
134C2×C4×C107—42no—
135C2×C4×C107—82no—
136C2×C4×C107—81no—
137C2×C4×C107—81no—
138C2×C4×C107C4×D411yescharacteristic
139C2×C4×C107#12011yescharacteristic
140C2×C4×C107#12111yescharacteristic
141C2×C4×C107C2×D811yescharacteristic
142C2×C4×C107#13511yescharacteristic
143C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
144C8×C107—41no—
145C8×C107—81no—
146C8×C107C2×C22⋊C411yescharacteristic
147C8×C107C4×D411yescharacteristic
148C8×C107#12111yescharacteristic
149C8×C107#12311yescharacteristic
150C22×C107—22no—
151C22×C107—81no—
152C22×C107—82no—
153C22×C107#44211yescharacteristic
154C22×C107#44711yescharacteristic
155C22×C107#46311yescharacteristic
156C4×C107—42no—
157C4×C107—44no—
158C4×C107—82no—
159C4×C107—81no—
160C4×C107#38611yescharacteristic
161C4×C107C4×D811yescharacteristic
162C4×C107#44911yescharacteristic
163C4×C107#45911yescharacteristic
164#13038C10711yesmaximal, characteristic, direct product factor, Sylow
165C2×C107—21no—
166C2×C107—21no—
167C2×C107—161no—
168C2×C107#187911yescharacteristic
169C2×C107#218012yes—
170C2×#510C2×C10711yescharacteristic
171C2×#441C2×C10711yescharacteristic, complemented
172C2×#362C2×C10711yescharacteristic, complemented
173C2×#360C2×C10711yescharacteristic
174#1975C2×C10711yescharacteristic
175#1383C2×C10711yescharacteristic, complemented
176#1375C2×C10711yescharacteristic, complemented
177C107#1303811yescharacteristic, direct product factor, Sylow
178C2×#135C22×C10711yescharacteristic
179C22×Q16C22×C10711yescharacteristic
180C2×C4×Q8—21no—
181#510—22no—
182#510—22no—
183C2×Q32C4×C10712yescomplemented
184C2×SD32C4×C10712yescomplemented
185C2×M32C22×C10711yescharacteristic
186C2×M32C22×C10711yescharacteristic
187#441—22no—
188#441—22no—
189C2×#108C22×C10711yescharacteristic
190C2×#106C22×C10711yescharacteristic
191C2×#104—21no—
192C2×#103—21no—
193#408—21no—
194C2×#97C22×C10711yescharacteristic
195#362—22no—
196#360—22no—
197C2×#41—21no—
198C22×Q8—21no—
199#135—21no—
200#135—21no—
201#135—21no—
202#135—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16C2×C4×C10711yescharacteristic
207C2×Q16C2×C4×C10712yes—
208C2×Q16D4×C10712yes—
209C2×Q16D4×C10712yes—
210C2×SD16—21no—
211C2×D8C2×C4×C10711yescharacteristic
212C2×M16—21no—
213C22×C8D4×C10711yescharacteristic
214C22×C8C23×C10711yescharacteristic
215C4×Q8—24no—
216C4×Q8—42no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—41no—
219C2×C42—41no—
220C2×C42D4×C10711yescharacteristic
221Q32—24no—
222SD32—24no—
223M32—21no—
224M32—21no—
225M32—21no—
226M32—21no—
227C2×C16—21no—
228C2×C16C2×C4×C10712yes—
229#108—21no—
230#108—21no—
231#106—21no—
232#106D4×C10712yes—
233#104—42no—
234#103—24no—
235C22⋊C8—42no—
236#97—21no—
237#97—21no—
238#41—41no—
239#41—41no—
240#41—41no—
241#41—41no—
242C2×Q8—22no—
243C2×Q8—21no—
244C2×Q8—22no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×D4—21no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4C2×D4×C10711yescharacteristic
256Q16—21no—
257Q16—22no—
258Q16—21no—
259Q16—22no—
260Q16—22no—
261Q16C22⋊C4×C10714yes—
262SD16—41no—
263SD16—41no—
264D8—21no—
265D8—21no—
266M16—41no—
267M16—41no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—41no—
272C2×C8C22×C4×C10711yescharacteristic
273C2×C8C2×D4×C10711yescharacteristic
274C2×C8C2×D4×C10711yescharacteristic
275C2×C8C2×D4×C10711yescharacteristic
276C2×C8#41×C10711yescharacteristic
277C2×C8#41×C10711yescharacteristic
278C4⋊C4—22no—
279C4⋊C4—44no—
280C4⋊C4—41no—
281C42—21no—
282C42—44no—
283C42D8×C10712yes—
284C16—22no—
285C16—41no—
286C23—41no—
287C23AGL(1,ℤ/8)×C10711yescharacteristic
288Q8—24no—
289Q8—42no—
290Q8—42no—
291Q8—42no—
292Q8—41no—
293Q8—41no—
294D4—41no—
295D4—41no—
296D4—81no—
297D4—81no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—82no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4C4×D4×C10711yescharacteristic
309C2×C4#120×C10711yescharacteristic
310C2×C4#121×C10711yescharacteristic
311C2×C4C2×D8×C10711yescharacteristic
312C2×C4#135×C10711yescharacteristic
313C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
314C8—41no—
315C8—81no—
316C8C2×C22⋊C4×C10711yescharacteristic
317C8C4×D4×C10711yescharacteristic
318C8#121×C10711yescharacteristic
319C8#123×C10711yescharacteristic
320C22—22no—
321C22—81no—
322C22—82no—
323C22#442×C10711yescharacteristic
324C22#447×C10711yescharacteristic
325C22#463×C10711yescharacteristic
326C4—42no—
327C4—44no—
328C4—82no—
329C4—81no—
330C4#386×C10711yescharacteristic
331C4C4×D8×C10711yescharacteristic
332C4#449×C10711yescharacteristic
333C4#459×C10711yescharacteristic
334C2—21no—
335C2—21no—
336C2—161no—
337C2C107×#187911yescharacteristic
338C2C107×#218012yes—
subgroupG/H
center, socleC22×C107#442
commutatorC2×C8C22×C4×C107
Frattini, cosocleC22×C8C23×C107
prime radicalC2×#135×C107C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C22×C4×C107 ◁ C2×#97×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#441×C107C2semidirect
3. C2×#362×C107C2semidirect
6. C107×#1383C2semidirect
7. C107×#1375C2semidirect
13. C2×Q32×C107C4semidirect
14. C2×SD32×C107C4semidirect
164. #13038C107direct (N × H)
171. C2×#441C2×C107semidirect
172. C2×#362C2×C107semidirect
175. #1383C2×C107semidirect
176. #1375C2×C107semidirect
177. C107#13038direct (N × H)
183. C2×Q32C4×C107semidirect
184. C2×SD32C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#510×C1072
C2×#441×C1072
C2×#362×C1072
C2×#360×C1072
C107×#19752
C107×#13832
C107×#13752
#13038107