Finite Group Databasebeta

← C107×#9913 #41035877

Subgroups — C107×#9913 #41035877

Order 27392.

548 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2851C211yesmaximal, characteristic
2C107×#1797C211yesmaximal, characteristic
3C107×#1434C211yesmaximal, characteristic
4C107×#1294C212yesmaximal
5C107×#1294C212yesmaximal
6C2×#125×C107C411yescharacteristic, complemented
7C22×C42×C107C2211yescharacteristic
8C2×C4⋊C8×C107—21no—
9C2×C22⋊C8×C107C2212yes—
10#389×C107C411yescharacteristic, complemented
11#389×C107C411yescharacteristic, complemented
12#387×C107—21no—
13#387×C107—21no—
14#385×C107—21no—
15#385×C107—21no—
16#382×C107C411yescharacteristic, complemented
17#380×C107C2211yescharacteristic
18#380×C107C2211yescharacteristic
19C2×#95×C107—21no—
20C2×#95×C107—21no—
21C2×#95×C107C2212yes—
22#336×C107—21no—
23C23×C4×C107—22no—
24C23×C4×C107D411yescharacteristic
25C23×C4×C107D411yescharacteristic
26C23×C4×C107C2311yescharacteristic
27C22×C8×C107—22no—
28#125×C107—42no—
29C2×C4⋊C4×C107—21no—
30C2×C4⋊C4×C107—21no—
31C2×C4⋊C4×C107—21no—
32C2×C4⋊C4×C107—21no—
33C2×C4⋊C4×C107C2×C411yescharacteristic
34C2×C4⋊C4×C107C2×C411yescharacteristic
35C2×C4⋊C4×C107C2×C411yescharacteristic
36C2×C4⋊C4×C107C2×C411yescharacteristic
37C2×C22⋊C4×C107—21no—
38C2×C22⋊C4×C107—21no—
39C2×C42×C107—42no—
40C2×C42×C107C2×C411yescharacteristic
41C2×C42×C107C2×C411yescharacteristic
42C2×C42×C107D411yescharacteristic
43C2×C42×C107D411yescharacteristic
44C4⋊C8×C107—42no—
45C22⋊C8×C107—24no—
46#95×C107—21no—
47#95×C107—21no—
48#95×C107—21no—
49#95×C107—21no—
50#95×C107—21no—
51#95×C107—21no—
52#95×C107—22no—
53#95×C107—42no—
54#95×C107—42no—
55#95×C107Q814yes—
56C24×C107C2×D411yescharacteristic
57C22×C4×C107—22no—
58C22×C4×C107—21no—
59C22×C4×C107—21no—
60C22×C4×C107—22no—
61C22×C4×C107—21no—
62C22×C4×C107—21no—
63C22×C4×C107—21no—
64C22×C4×C107—21no—
65C22×C4×C107—24no—
66C22×C4×C107—41no—
67C22×C4×C107—41no—
68C22×C4×C107—41no—
69C22×C4×C107—41no—
70C22×C4×C107—41no—
71C22×C4×C107—42no—
72C22×C4×C107—42no—
73C22×C4×C107—42no—
74C22×C4×C107—42no—
75C22×C4×C107—42no—
76C22×C4×C107—42no—
77C22×C4×C107C22⋊C411yescharacteristic
78C22×C4×C107C22⋊C411yescharacteristic
79C22×C4×C107C22⋊C411yescharacteristic
80C22×C4×C107C22⋊C411yescharacteristic
81C22×C4×C107C22×C411yescharacteristic
82C22×C4×C107C2×D411yescharacteristic
83C22×C4×C107C2×Q812yes—
84C22×C4×C107#4112yes—
85C2×C8×C107—42no—
86C2×C8×C107—42no—
87C2×C8×C107—42no—
88C4⋊C4×C107—41no—
89C4⋊C4×C107—41no—
90C4⋊C4×C107—41no—
91C4⋊C4×C107—41no—
92C4⋊C4×C107—42no—
93C4⋊C4×C107—42no—
94C4⋊C4×C107—42no—
95C4⋊C4×C107—42no—
96C22⋊C4×C107—42no—
97C22⋊C4×C107—41no—
98C22⋊C4×C107—41no—
99C42×C107—22no—
100C42×C107—22no—
101C42×C107—41no—
102C42×C107—41no—
103C23×C107—21no—
104C23×C107—21no—
105C23×C107—21no—
106C23×C107—21no—
107C23×C107C2×C22⋊C411yescharacteristic
108C23×C107C22⋊Q812yes—
109C23×C107#13512yes—
110C23×C107AGL(1,ℤ/8)11yescharacteristic
111C23×C107#13711yescharacteristic
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—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107—42no—
128C2×C4×C107—42no—
129C2×C4×C107—44no—
130C2×C4×C107—42no—
131C2×C4×C107—42no—
132C2×C4×C107—44no—
133C2×C4×C107—44no—
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—41no—
141C2×C4×C107—41no—
142C2×C4×C107—41no—
143C2×C4×C107—41no—
144C2×C4×C107—41no—
145C2×C4×C107—41no—
146C2×C4×C107—44no—
147C2×C4×C107—82no—
148C2×C4×C107—82no—
149C2×C4×C107—82no—
150C2×C4×C107—82no—
151C2×C4×C107#9912yes—
152C2×C4×C107C4×Q812yes—
153C2×C4×C107#12411yescharacteristic
154C2×C4×C107C4⋊Q811yescharacteristic
155C8×C107—82no—
156C22×C107—22no—
157C22×C107—22no—
158C22×C107—21no—
159C22×C107—21no—
160C22×C107—21no—
161C22×C107—21no—
162C22×C107—22no—
163C22×C107—22no—
164C22×C107#39111yescharacteristic
165C22×C107C2×#9911yescharacteristic
166C22×C107#41011yescharacteristic
167C22×C107#41611yescharacteristic
168C22×C107#41711yescharacteristic
169C22×C107#42111yescharacteristic
170C22×C107#42111yescharacteristic
171C22×C107#47812yes—
172C22×C107#47912yes—
173C4×C107—21no—
174C4×C107—22no—
175C4×C107—21no—
176C4×C107—22no—
177C4×C107—41no—
178C4×C107—41no—
179C4×C107—41no—
180C4×C107—84no—
181C4×C107—81no—
182C4×C107—81no—
183C4×C107—81no—
184C4×C107—81no—
185#9913C10711yesmaximal, characteristic, direct product factor, Sylow
186C2×C107—22no—
187C2×C107—22no—
188C2×C107#151211yescharacteristic
189C2×C107#151311yescharacteristic
190C2×C107#151611yescharacteristic
191C2×C107#152111yescharacteristic
192C2×C107#198911yescharacteristic
193C2×C107#199511yescharacteristic
194C2×C107#199611yescharacteristic
195#2851C2×C10711yescharacteristic
196#1797C2×C10711yescharacteristic
197#1434C2×C10711yescharacteristic
198#1294C2×C10712yes—
199#1294C2×C10712yes—
200C107#991311yescharacteristic, direct product factor, Sylow
201C2×#125C4×C10711yescharacteristic, complemented
202C22×C42C22×C10711yescharacteristic
203C2×C4⋊C8—21no—
204C2×C22⋊C8C22×C10712yes—
205#389C4×C10711yescharacteristic, complemented
206#389C4×C10711yescharacteristic, complemented
207#387—21no—
208#387—21no—
209#385—21no—
210#385—21no—
211#382C4×C10711yescharacteristic, complemented
212#380C22×C10711yescharacteristic
213#380C22×C10711yescharacteristic
214C2×#95—21no—
215C2×#95—21no—
216C2×#95C22×C10712yes—
217#336—21no—
218C23×C4—22no—
219C23×C4D4×C10711yescharacteristic
220C23×C4D4×C10711yescharacteristic
221C23×C4C23×C10711yescharacteristic
222C22×C8—22no—
223#125—42no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C2×C4×C10711yescharacteristic
229C2×C4⋊C4C2×C4×C10711yescharacteristic
230C2×C4⋊C4C2×C4×C10711yescharacteristic
231C2×C4⋊C4C2×C4×C10711yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C42—42no—
235C2×C42C2×C4×C10711yescharacteristic
236C2×C42C2×C4×C10711yescharacteristic
237C2×C42D4×C10711yescharacteristic
238C2×C42D4×C10711yescharacteristic
239C4⋊C8—42no—
240C22⋊C8—24no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—22no—
248#95—42no—
249#95—42no—
250#95Q8×C10714yes—
251C24C2×D4×C10711yescharacteristic
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—24no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4C22⋊C4×C10711yescharacteristic
273C22×C4C22⋊C4×C10711yescharacteristic
274C22×C4C22⋊C4×C10711yescharacteristic
275C22×C4C22⋊C4×C10711yescharacteristic
276C22×C4C22×C4×C10711yescharacteristic
277C22×C4C2×D4×C10711yescharacteristic
278C22×C4C2×Q8×C10712yes—
279C22×C4#41×C10712yes—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C42—22no—
295C42—22no—
296C42—41no—
297C42—41no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23C2×C22⋊C4×C10711yescharacteristic
303C23C22⋊Q8×C10712yes—
304C23#135×C10712yes—
305C23AGL(1,ℤ/8)×C10711yescharacteristic
306C23#137×C10711yescharacteristic
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—44no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—44no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4#99×C10712yes—
347C2×C4C4×Q8×C10712yes—
348C2×C4#124×C10711yescharacteristic
349C2×C4C4⋊Q8×C10711yescharacteristic
350C8—82no—
351C22—22no—
352C22—22no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—22no—
359C22#391×C10711yescharacteristic
360C22C2×#99×C10711yescharacteristic
361C22#410×C10711yescharacteristic
362C22#416×C10711yescharacteristic
363C22#417×C10711yescharacteristic
364C22#421×C10711yescharacteristic
365C22#421×C10711yescharacteristic
366C22#478×C10712yes—
367C22#479×C10712yes—
368C4—21no—
369C4—22no—
370C4—21no—
371C4—22no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—84no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—81no—
380C2—22no—
381C2—22no—
382C2C107×#151211yescharacteristic
383C2C107×#151311yescharacteristic
384C2C107×#151611yescharacteristic
385C2C107×#152111yescharacteristic
386C2C107×#198911yescharacteristic
387C2C107×#199511yescharacteristic
388C2C107×#199611yescharacteristic
subgroupG/H
center, socleC23×C107C2×C22⋊C4
commutatorC22×C4C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC24×C107C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C22×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×#125×C107C4semidirect
10. #389×C107C4semidirect
11. #389×C107C4semidirect
16. #382×C107C4semidirect
185. #9913C107direct (N × H)
200. C107#9913direct (N × H)
201. C2×#125C4×C107semidirect
205. #389C4×C107semidirect
206. #389C4×C107semidirect
211. #382C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#28512
C107×#17972
C107×#14342
C107×#12942
#9913107