Finite Group Databasebeta

← C107×#8226 #41034190

Subgroups — C107×#8226 #41034190

Order 27392.

572 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#124×C107C211yesmaximal, characteristic
2C107×#1745C211yesmaximal, characteristic, complemented
3C4×#97×C107C211yesmaximal, characteristic, complemented
4C2×#329×C107C212yesmaximal
5C107×#1295C212yesmaximal, complemented
6C2×#124×C107C2211yescharacteristic
7C2×C4×Q8×C107C411yescharacteristic
8C2×C4×D4×C107C411yescharacteristic
9C2×#97×C107—21no—
10C2×#97×C107C2212yes—
11C2×#97×C107C2212yes—
12C2×C4×C8×C107—21no—
13#391×C107C411yescharacteristic
14#390×C107C411yescharacteristic
15#388×C107—21no—
16#388×C107—21no—
17#382×C107C2211yescharacteristic
18C4×C22⋊C4×C107—21no—
19C4×C22⋊C4×C107—21no—
20C43×C107C2211yescharacteristic
21#336×C107—21no—
22#336×C107—21no—
23#329×C107C418yescomplemented
24C22×Q8×C107C2×C411yescharacteristic
25C22×D4×C107C2×C411yescharacteristic
26C23×C4×C107—21no—
27C22×C8×C107—22no—
28C22×C8×C107—22no—
29#124×C107—22no—
30#124×C107C2×C414yes—
31C4×Q8×C107—42no—
32C4×D4×C107—42no—
33C2×C4⋊C4×C107—21no—
34C2×C4⋊C4×C107C2×C411yescharacteristic
35C2×C4⋊C4×C107C2×C411yescharacteristic
36C2×C22⋊C4×C107—21no—
37C2×C22⋊C4×C107—21no—
38C2×C22⋊C4×C107—21no—
39C2×C22⋊C4×C107—21no—
40C2×C22⋊C4×C107—21no—
41C2×C42×C107—21no—
42C2×C42×C107C2×C411yescharacteristic
43C2×C42×C107C2×C411yescharacteristic
44C2×C42×C107D411yescharacteristic
45C2×C42×C107D411yescharacteristic
46C2×C42×C107D411yescharacteristic
47C2×C42×C107D411yescharacteristic
48C2×C42×C107C2311yescharacteristic
49#97×C107—24no—
50#97×C107—22no—
51#97×C107—22no—
52#97×C107C2×C414yescomplemented
53#97×C107C2×C414yescomplemented
54C4×C8×C107—24no—
55#95×C107—21no—
56#95×C107—21no—
57#95×C107—21no—
58#95×C107—21no—
59C24×C107—21no—
60C2×Q8×C107—21no—
61C2×Q8×C107—41no—
62C2×Q8×C107—41no—
63C2×Q8×C107C4212yes—
64C2×D4×C107—21no—
65C2×D4×C107—41no—
66C2×D4×C107—41no—
67C2×D4×C107C4212yes—
68C22×C4×C107—21no—
69C22×C4×C107—21no—
70C22×C4×C107—21no—
71C22×C4×C107—42no—
72C22×C4×C107—42no—
73C22×C4×C107—42no—
74C22×C4×C107C22⋊C411yescharacteristic
75C22×C4×C107C22⋊C411yescharacteristic
76C22×C4×C107C22⋊C411yescharacteristic
77C22×C4×C107C22⋊C411yescharacteristic
78C22×C4×C107C22×C411yescharacteristic
79C22×C4×C107C2×D411yescharacteristic
80C22×C4×C107C2×D411yescharacteristic
81C2×C8×C107—24no—
82C2×C8×C107—24no—
83C2×C8×C107—24no—
84C2×C8×C107—24no—
85C2×C8×C107—42no—
86C2×C8×C107—42no—
87C4⋊C4×C107—41no—
88C4⋊C4×C107—41no—
89C4⋊C4×C107—42no—
90C22⋊C4×C107—24no—
91C22⋊C4×C107—24no—
92C22⋊C4×C107—42no—
93C22⋊C4×C107—42no—
94C22⋊C4×C107—42no—
95C42×C107—22no—
96C42×C107—22no—
97C42×C107—22no—
98C42×C107—41no—
99C42×C107—41no—
100C42×C107—41no—
101C42×C107—42no—
102C42×C107C22×C412yes—
103C42×C107#4112yes—
104C23×C107—22no—
105C23×C107—41no—
106C23×C107—41no—
107C23×C107—41no—
108C23×C107—41no—
109C23×C107—41no—
110C23×C107—41no—
111C23×C107C2×C22⋊C411yescharacteristic
112Q8×C107—42no—
113Q8×C107—42no—
114D4×C107—42no—
115D4×C107—42no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107—21no—
128C2×C4×C107—22no—
129C2×C4×C107—21no—
130C2×C4×C107—21no—
131C2×C4×C107—21no—
132C2×C4×C107—41no—
133C2×C4×C107—41no—
134C2×C4×C107—41no—
135C2×C4×C107—41no—
136C2×C4×C107—41no—
137C2×C4×C107—41no—
138C2×C4×C107—41no—
139C2×C4×C107—41no—
140C2×C4×C107—84no—
141C2×C4×C107#10012yes—
142C2×C4×C107#10412yes—
143C2×C4×C107#10412yes—
144C2×C4×C107C2×C4211yescharacteristic
145C2×C4×C107#11711yescharacteristic
146C2×C4×C107C4×D412yes—
147C2×C4×C107C4×D412yes—
148C8×C107—28no—
149C8×C107—44no—
150C22×C107—42no—
151C22×C107—42no—
152C22×C107—42no—
153C22×C107—81no—
154C22×C107—81no—
155C22×C107—81no—
156C22×C107—81no—
157C22×C107C4×C22⋊C411yescharacteristic
158C22×C107C2×#10011yescharacteristic
159C22×C107#41311yescharacteristic
160C22×C107C2×#10411yescharacteristic
161C22×C107C2×#10411yescharacteristic
162C22×C107#42111yescharacteristic
163C22×C107#42111yescharacteristic
164C4×C107—21no—
165C4×C107—21no—
166C4×C107—22no—
167C4×C107—22no—
168C4×C107—22no—
169C4×C107—22no—
170C4×C107—22no—
171C4×C107—42no—
172C4×C107—41no—
173C4×C107—81no—
174C4×C107—81no—
175#8226C10711yesmaximal, characteristic, direct product factor, Sylow
176C2×C107—82no—
177C2×C107#152711yescharacteristic
178C2×C107#152911yescharacteristic
179C2×C107#153011yescharacteristic
180C2×C107#153211yescharacteristic
181C2×C107C4×#10011yescharacteristic
182C2×C107C4×#10411yescharacteristic
183C2×C107#175911yescharacteristic
184C4×#124C2×C10711yescharacteristic
185#1745C2×C10711yescharacteristic, complemented
186C4×#97C2×C10711yescharacteristic, complemented
187C2×#329C2×C10712yes—
188#1295C2×C10712yescomplemented
189C107#822611yescharacteristic, direct product factor, Sylow
190C2×#124C22×C10711yescharacteristic
191C2×C4×Q8C4×C10711yescharacteristic
192C2×C4×D4C4×C10711yescharacteristic
193C2×#97—21no—
194C2×#97C22×C10712yes—
195C2×#97C22×C10712yes—
196C2×C4×C8—21no—
197#391C4×C10711yescharacteristic
198#390C4×C10711yescharacteristic
199#388—21no—
200#388—21no—
201#382C22×C10711yescharacteristic
202C4×C22⋊C4—21no—
203C4×C22⋊C4—21no—
204C43C22×C10711yescharacteristic
205#336—21no—
206#336—21no—
207#329C4×C10718yescomplemented
208C22×Q8C2×C4×C10711yescharacteristic
209C22×D4C2×C4×C10711yescharacteristic
210C23×C4—21no—
211C22×C8—22no—
212C22×C8—22no—
213#124—22no—
214#124C2×C4×C10714yes—
215C4×Q8—42no—
216C4×D4—42no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×C4×C10711yescharacteristic
219C2×C4⋊C4C2×C4×C10711yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42—21no—
226C2×C42C2×C4×C10711yescharacteristic
227C2×C42C2×C4×C10711yescharacteristic
228C2×C42D4×C10711yescharacteristic
229C2×C42D4×C10711yescharacteristic
230C2×C42D4×C10711yescharacteristic
231C2×C42D4×C10711yescharacteristic
232C2×C42C23×C10711yescharacteristic
233#97—24no—
234#97—22no—
235#97—22no—
236#97C2×C4×C10714yescomplemented
237#97C2×C4×C10714yescomplemented
238C4×C8—24no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243C24—21no—
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8C42×C10712yes—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4C42×C10712yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4C22⋊C4×C10711yescharacteristic
259C22×C4C22⋊C4×C10711yescharacteristic
260C22×C4C22⋊C4×C10711yescharacteristic
261C22×C4C22⋊C4×C10711yescharacteristic
262C22×C4C22×C4×C10711yescharacteristic
263C22×C4C2×D4×C10711yescharacteristic
264C22×C4C2×D4×C10711yescharacteristic
265C2×C8—24no—
266C2×C8—24no—
267C2×C8—24no—
268C2×C8—24no—
269C2×C8—42no—
270C2×C8—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C22⋊C4—24no—
275C22⋊C4—24no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C42—22no—
280C42—22no—
281C42—22no—
282C42—41no—
283C42—41no—
284C42—41no—
285C42—42no—
286C42C22×C4×C10712yes—
287C42#41×C10712yes—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23C2×C22⋊C4×C10711yescharacteristic
296Q8—42no—
297Q8—42no—
298D4—42no—
299D4—42no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—84no—
325C2×C4#100×C10712yes—
326C2×C4#104×C10712yes—
327C2×C4#104×C10712yes—
328C2×C4C2×C42×C10711yescharacteristic
329C2×C4#117×C10711yescharacteristic
330C2×C4C4×D4×C10712yes—
331C2×C4C4×D4×C10712yes—
332C8—28no—
333C8—44no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22C4×C22⋊C4×C10711yescharacteristic
342C22C2×#100×C10711yescharacteristic
343C22#413×C10711yescharacteristic
344C22C2×#104×C10711yescharacteristic
345C22C2×#104×C10711yescharacteristic
346C22#421×C10711yescharacteristic
347C22#421×C10711yescharacteristic
348C4—21no—
349C4—21no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—42no—
356C4—41no—
357C4—81no—
358C4—81no—
359C2—82no—
360C2C107×#152711yescharacteristic
361C2C107×#152911yescharacteristic
362C2C107×#153011yescharacteristic
363C2C107×#153211yescharacteristic
364C2C4×#100×C10711yescharacteristic
365C2C4×#104×C10711yescharacteristic
366C2C107×#175911yescharacteristic
subgroupG/H
center, socleC23×C107C2×C22⋊C4
commutatorC2×C4C2×C42×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC22×D4×C107C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C43×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#1745C2semidirect
3. C4×#97×C107C2semidirect
5. C107×#1295C2semidirect
23. #329×C107C4semidirect
52. #97×C107C2×C4semidirect
53. #97×C107C2×C4semidirect
175. #8226C107direct (N × H)
185. #1745C2×C107semidirect
186. C4×#97C2×C107semidirect
188. #1295C2×C107semidirect
189. C107#8226direct (N × H)
207. #329C4×C107semidirect
236. #97C2×C4×C107semidirect
237. #97C2×C4×C107semidirect

Maximal subgroups

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

subgroupindex
C4×#124×C1072
C107×#17452
C4×#97×C1072
C2×#329×C1072
C107×#12952
#8226107