Finite Group Databasebeta

← C2×C107×#1321 #41037401

Subgroups — C2×C107×#1321 #41037401

Order 27392.

518 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#408×C107C211yesmaximal, characteristic
2C2×#349×C107C212yesmaximal, complemented
3C107×#1321C214yesmaximal, direct product factor
4C22×#41×C107C411yescharacteristic
5C22×M16×C107C2211yescharacteristic
6C23×C8×C107C411yescharacteristic
7C2×M32×C107—22no—
8#408×C107—22no—
9#408×C107C412yes—
10#408×C107C2212yes—
11C2×C22⋊C8×C107—22no—
12#349×C107—22no—
13#349×C107C2214yescomplemented
14C2×#41×C107—21no—
15C2×#41×C107—21no—
16C2×#41×C107—41no—
17C2×#41×C107—41no—
18C2×#41×C107—41no—
19C2×#41×C107—41no—
20C2×#41×C107C812yes—
21C2×#41×C107C2×C412yes—
22C22×Q8×C107C811yescharacteristic
23C22×D4×C107—21no—
24C22×D4×C107C811yescharacteristic
25C23×C4×C107—21no—
26C23×C4×C107C2×C411yescharacteristic
27C2×M16×C107—41no—
28C2×M16×C107—41no—
29C2×M16×C107C2×C411yescharacteristic
30C2×M16×C107D412yes—
31C2×M16×C107C2311yescharacteristic
32C22×C8×C107—21no—
33C22×C8×C107—21no—
34C22×C8×C107—41no—
35C22×C8×C107—41no—
36C22×C8×C107C2×C412yes—
37C22×C8×C107D412yes—
38M32×C107—24no—
39M32×C107—42no—
40C2×C16×C107—42no—
41C22⋊C8×C107—24no—
42C22⋊C8×C107—24no—
43C24×C107—21no—
44C24×C107M1611yescharacteristic
45#41×C107—42no—
46#41×C107—42no—
47#41×C107—42no—
48#41×C107—42no—
49#41×C107—42no—
50#41×C107—42no—
51#41×C107—42no—
52#41×C107—42no—
53C2×Q8×C107—21no—
54C2×Q8×C107—41no—
55C2×Q8×C107—41no—
56C2×Q8×C107C2×C812yes—
57C2×D4×C107—22no—
58C2×D4×C107—22no—
59C2×D4×C107—21no—
60C2×D4×C107—41no—
61C2×D4×C107—41no—
62C2×D4×C107—42no—
63C2×D4×C107—42no—
64C2×D4×C107C2×C812yes—
65C22×C4×C107—21no—
66C22×C4×C107—21no—
67C22×C4×C107—21no—
68C22×C4×C107—21no—
69C22×C4×C107—21no—
70C22×C4×C107—22no—
71C22×C4×C107—22no—
72C22×C4×C107—41no—
73C22×C4×C107—41no—
74C22×C4×C107—41no—
75C22×C4×C107—41no—
76C22×C4×C107C22⋊C411yescharacteristic
77C22×C4×C107C22⋊C411yescharacteristic
78C22×C4×C107C2×C811yescharacteristic
79C22×C4×C107C2×C811yescharacteristic
80C22×C4×C107M1611yescharacteristic
81C22×C4×C107C22×C411yescharacteristic
82M16×C107—41no—
83M16×C107—42no—
84M16×C107—41no—
85C2×C8×C107—22no—
86C2×C8×C107—22no—
87C2×C8×C107—22no—
88C2×C8×C107—42no—
89C2×C8×C107—41no—
90C2×C8×C107—41no—
91C2×C8×C107—42no—
92C2×C8×C107C22⋊C412yes—
93C2×C8×C107C2×D412yes—
94C16×C107—44no—
95C23×C107—21no—
96C23×C107—21no—
97C23×C107—22no—
98C23×C107—42no—
99C23×C107—44no—
100C23×C107—41no—
101C23×C107—41no—
102C23×C107C22⋊C811yescharacteristic
103C23×C107C22⋊C811yescharacteristic
104C23×C107C2×M1611yescharacteristic
105Q8×C107—42no—
106Q8×C107—42no—
107D4×C107—42no—
108D4×C107—42no—
109D4×C107—44no—
110D4×C107—44no—
111C2×C4×C107—21no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—22no—
122C2×C4×C107—41no—
123C2×C4×C107—41no—
124C2×C4×C107—42no—
125C2×C4×C107—42no—
126C2×C4×C107—42no—
127C2×C4×C107—42no—
128C2×C4×C107C22⋊C811yescharacteristic
129C2×C4×C107C22⋊C811yescharacteristic
130C2×C4×C107#9911yescharacteristic
131C2×C4×C107#9911yescharacteristic
132C2×C4×C107#10011yescharacteristic
133C2×C4×C107#10011yescharacteristic
134C2×C4×C107C2×C22⋊C411yescharacteristic
135C2×C4×C107C22×C811yescharacteristic
136C8×C107—22no—
137C8×C107—22no—
138C8×C107—42no—
139C22×C107—22no—
140C22×C107—21no—
141C22×C107—21no—
142C22×C107—41no—
143C22×C107—41no—
144C22×C107—42no—
145C22×C107—44no—
146C22×C107—42no—
147C22×C107—42no—
148C22×C107—82no—
149C22×C107—82no—
150C22×C107#32311yescharacteristic
151C22×C107#32311yescharacteristic
152C22×C107C2×C22⋊C811yescharacteristic
153C4×C107—21no—
154C4×C107—21no—
155C4×C107—42no—
156C4×C107#32311yescharacteristic
157C4×C107#32311yescharacteristic
158C4×C107C2×#9911yescharacteristic
159C4×C107C2×#10011yescharacteristic
160C2×#1321C10711yesmaximal, characteristic, direct product factor, Sylow
161C2×C107—21no—
162C2×C107—21no—
163C2×C107—41no—
164C2×C107—41no—
165C2×C107—82no—
166C2×C107#132112yesdirect product factor
167C2×C107C2×#32311yescharacteristic
168C2×#408C2×C10711yescharacteristic
169C2×#349C2×C10712yescomplemented
170#1321C2×C10714yesdirect product factor
171C107C2×#132111yescharacteristic, direct product factor, Sylow
172C22×#41C4×C10711yescharacteristic
173C22×M16C22×C10711yescharacteristic
174C23×C8C4×C10711yescharacteristic
175C2×M32—22no—
176#408—22no—
177#408C4×C10712yes—
178#408C22×C10712yes—
179C2×C22⋊C8—22no—
180#349—22no—
181#349C22×C10714yescomplemented
182C2×#41—21no—
183C2×#41—21no—
184C2×#41—41no—
185C2×#41—41no—
186C2×#41—41no—
187C2×#41—41no—
188C2×#41C8×C10712yes—
189C2×#41C2×C4×C10712yes—
190C22×Q8C8×C10711yescharacteristic
191C22×D4—21no—
192C22×D4C8×C10711yescharacteristic
193C23×C4—21no—
194C23×C4C2×C4×C10711yescharacteristic
195C2×M16—41no—
196C2×M16—41no—
197C2×M16C2×C4×C10711yescharacteristic
198C2×M16D4×C10712yes—
199C2×M16C23×C10711yescharacteristic
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—41no—
203C22×C8—41no—
204C22×C8C2×C4×C10712yes—
205C22×C8D4×C10712yes—
206M32—24no—
207M32—42no—
208C2×C16—42no—
209C22⋊C8—24no—
210C22⋊C8—24no—
211C24—21no—
212C24M16×C10711yescharacteristic
213#41—42no—
214#41—42no—
215#41—42no—
216#41—42no—
217#41—42no—
218#41—42no—
219#41—42no—
220#41—42no—
221C2×Q8—21no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8C2×C8×C10712yes—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—21no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—42no—
231C2×D4—42no—
232C2×D4C2×C8×C10712yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4C22⋊C4×C10711yescharacteristic
245C22×C4C22⋊C4×C10711yescharacteristic
246C22×C4C2×C8×C10711yescharacteristic
247C22×C4C2×C8×C10711yescharacteristic
248C22×C4M16×C10711yescharacteristic
249C22×C4C22×C4×C10711yescharacteristic
250M16—41no—
251M16—42no—
252M16—41no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—42no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—42no—
260C2×C8C22⋊C4×C10712yes—
261C2×C8C2×D4×C10712yes—
262C16—44no—
263C23—21no—
264C23—21no—
265C23—22no—
266C23—42no—
267C23—44no—
268C23—41no—
269C23—41no—
270C23C22⋊C8×C10711yescharacteristic
271C23C22⋊C8×C10711yescharacteristic
272C23C2×M16×C10711yescharacteristic
273Q8—42no—
274Q8—42no—
275D4—42no—
276D4—42no—
277D4—44no—
278D4—44no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4C22⋊C8×C10711yescharacteristic
297C2×C4C22⋊C8×C10711yescharacteristic
298C2×C4#99×C10711yescharacteristic
299C2×C4#99×C10711yescharacteristic
300C2×C4#100×C10711yescharacteristic
301C2×C4#100×C10711yescharacteristic
302C2×C4C2×C22⋊C4×C10711yescharacteristic
303C2×C4C22×C8×C10711yescharacteristic
304C8—22no—
305C8—22no—
306C8—42no—
307C22—22no—
308C22—21no—
309C22—21no—
310C22—41no—
311C22—41no—
312C22—42no—
313C22—44no—
314C22—42no—
315C22—42no—
316C22—82no—
317C22—82no—
318C22#323×C10711yescharacteristic
319C22#323×C10711yescharacteristic
320C22C2×C22⋊C8×C10711yescharacteristic
321C4—21no—
322C4—21no—
323C4—42no—
324C4#323×C10711yescharacteristic
325C4#323×C10711yescharacteristic
326C4C2×#99×C10711yescharacteristic
327C4C2×#100×C10711yescharacteristic
328C2—21no—
329C2—21no—
330C2—41no—
331C2—41no—
332C2—82no—
333C2C107×#132112yesdirect product factor
334C2C2×#323×C10711yescharacteristic
subgroupG/H
centerC2×C4×C107#99
commutatorC2×C4C22×C8×C107
Frattini, cosocleC2×M16C23×C107
socleC22×C107#323
prime radicalC22×#41×C107C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C22×C4×C107 ◁ C22×M16×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#349×C107C2semidirect
3. C107×#1321C2direct (N × H)
13. #349×C107C22semidirect
160. C2×#1321C107direct (N × H)
166. C2×C107#1321direct (N × H)
169. C2×#349C2×C107semidirect
170. #1321C2×C107direct (N × H)
171. C107C2×#1321direct (N × H)
181. #349C22×C107semidirect
333. C2C107×#1321direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#408×C1072
C2×#349×C1072
C107×#13212
C2×#1321107