Finite Group Databasebeta

← C137×#13382 #46862768

Subgroups — C137×#13382 #46862768

Order 35072.

446 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
1C2×#467×C137C211yesmaximal, characteristic
2C2×#367×C137C211yesmaximal, characteristic, complemented
3C2×#358×C137C211yesmaximal, characteristic, complemented
4C2×#358×C137C211yesmaximal, characteristic, complemented
5C2×C22⋊C16×C137C211yesmaximal, characteristic
6#1808×C137C211yesmaximal, characteristic
7#1380×C137C211yesmaximal, characteristic, complemented
8C22×Q16×C137C2211yescharacteristic
9C23×C8×C137C2211yescharacteristic
10C2×C22⋊Q8×C137—21no—
11C22×C16×C137C2211yescharacteristic
12C22×C16×C137C2211yescharacteristic
13#467×C137—22no—
14#467×C137—22no—
15C2×#107×C137C2211yescharacteristic
16C2×#107×C137C2211yescharacteristic
17C2×#107×C137C2211yescharacteristic
18C2×#103×C137—21no—
19#380×C137—21no—
20#367×C137—22no—
21#358×C137—22no—
22#358×C137—22no—
23C22⋊C16×C137—22no—
24#340×C137—21no—
25C22×Q8×C137—21no—
26C23×C4×C137D411yescharacteristic
27C2×Q16×C137—21no—
28C2×Q16×C137—21no—
29C2×Q16×C137—21no—
30C2×Q16×C137—21no—
31C2×Q16×C137—21no—
32C2×Q16×C137D412yes—
33C22×C8×C137—21no—
34C22×C8×C137—21no—
35C22×C8×C137—21no—
36C22×C8×C137—21no—
37C22×C8×C137—21no—
38C22×C8×C137—21no—
39C22×C8×C137D411yescharacteristic
40C22×C8×C137C2311yescharacteristic
41C22⋊Q8×C137—24no—
42C22⋊Q8×C137—42no—
43C2×C4⋊C4×C137—21no—
44C2×C4⋊C4×C137—21no—
45C2×C4⋊C4×C137—21no—
46C2×C4⋊C4×C137—41no—
47C2×C22⋊C4×C137—41no—
48C2×C22⋊C4×C137—41no—
49C2×C16×C137—21no—
50C2×C16×C137—21no—
51C2×C16×C137—21no—
52C2×C16×C137—21no—
53C2×C16×C137—21no—
54C2×C16×C137D412yes—
55#107×C137—21no—
56#107×C137—21no—
57#107×C137—21no—
58#107×C137—21no—
59#107×C137—21no—
60#107×C137D412yes—
61#103×C137—24no—
62#95×C137—41no—
63C24×C137D811yescharacteristic
64C2×Q8×C137—22no—
65C2×Q8×C137—41no—
66C2×Q8×C137—41no—
67C2×Q8×C137—41no—
68C2×Q8×C137—41no—
69C2×Q8×C137—41no—
70C22×C4×C137—21no—
71C22×C4×C137—21no—
72C22×C4×C137—21no—
73C22×C4×C137—21no—
74C22×C4×C137—21no—
75C22×C4×C137—21no—
76C22×C4×C137—41no—
77C22×C4×C137—41no—
78C22×C4×C137—41no—
79C22×C4×C137—41no—
80C22×C4×C137D811yescharacteristic
81C22×C4×C137C2×D411yescharacteristic
82Q16×C137—22no—
83Q16×C137—22no—
84Q16×C137—41no—
85Q16×C137—41no—
86C2×C8×C137—21no—
87C2×C8×C137—21no—
88C2×C8×C137—21no—
89C2×C8×C137—41no—
90C2×C8×C137—41no—
91C2×C8×C137—41no—
92C2×C8×C137—41no—
93C2×C8×C137C2×D411yescharacteristic
94C2×C8×C137C2×D411yescharacteristic
95C2×C8×C137C2×D411yescharacteristic
96C2×C8×C137#4111yescharacteristic
97C2×C8×C137#4111yescharacteristic
98C2×C8×C137#4111yescharacteristic
99C4⋊C4×C137—22no—
100C4⋊C4×C137—44no—
101C4⋊C4×C137—41no—
102C4⋊C4×C137—41no—
103C4⋊C4×C137—41no—
104C4⋊C4×C137—41no—
105C4⋊C4×C137—41no—
106C22⋊C4×C137—44no—
107C22⋊C4×C137—82no—
108C16×C137—22no—
109C16×C137—41no—
110C23×C137—21no—
111C23×C137—21no—
112C23×C137—21no—
113C23×C137—21no—
114C23×C137—21no—
115C23×C137—21no—
116C23×C137SD3212yes—
117C23×C137C2×D811yescharacteristic
118Q8×C137—42no—
119Q8×C137—42no—
120Q8×C137—81no—
121Q8×C137—81no—
122C2×C4×C137—21no—
123C2×C4×C137—21no—
124C2×C4×C137—21no—
125C2×C4×C137—41no—
126C2×C4×C137—41no—
127C2×C4×C137—41no—
128C2×C4×C137—41no—
129C2×C4×C137—42no—
130C2×C4×C137—42no—
131C2×C4×C137—81no—
132C2×C4×C137—81no—
133C2×C4×C137—81no—
134C2×C4×C137—81no—
135C2×C4×C137—81no—
136C2×C4×C137—81no—
137C2×C4×C137—81no—
138C2×C4×C137—81no—
139C2×C4×C137—81no—
140C2×C4×C137—81no—
141C2×C4×C137#12011yescharacteristic
142C2×C4×C137#12111yescharacteristic
143C2×C4×C137#12311yescharacteristic
144C2×C4×C137#13511yescharacteristic
145C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C137#13711yescharacteristic
147C8×C137—41no—
148C8×C137#12111yescharacteristic
149C8×C137#12111yescharacteristic
150C8×C137#12311yescharacteristic
151C8×C137#12411yescharacteristic
152C22×C137—22no—
153C22×C137—22no—
154C22×C137—22no—
155C22×C137—41no—
156C22×C137—41no—
157C22×C137—41no—
158C22×C137—41no—
159C22×C137#44711yescharacteristic
160C22×C137#46611yescharacteristic
161C22×C137#48011yescharacteristic
162C22×C137C2×SD3211yescharacteristic
163C22×C137#50811yescharacteristic
164C22×C137#51011yescharacteristic
165C22×C137#51011yescharacteristic
166C4×C137—41no—
167C4×C137—82no—
168C4×C137—82no—
169C4×C137—161no—
170C4×C137—161no—
171C4×C137#39411yescharacteristic
172C4×C137#45211yescharacteristic
173C4×C137#46811yescharacteristic
174C4×C137#48211yescharacteristic
175C2×C137—42no—
176C2×C137#203311yescharacteristic
177C2×C137#218511yescharacteristic
178C2×C137#218911yescharacteristic
179C2×C137#221711yescharacteristic
180C2×C137#221911yescharacteristic
181C2×C137#223511yescharacteristic
182C2×C137#223711yescharacteristic
183#13382C13711yesmaximal, characteristic, direct product factor, Sylow
184C137#1338211yescharacteristic, direct product factor, Sylow
185C2×#467C2×C13711yescharacteristic
186C2×#367C2×C13711yescharacteristic, complemented
187C2×#358C2×C13711yescharacteristic, complemented
188C2×#358C2×C13711yescharacteristic, complemented
189C2×C22⋊C16C2×C13711yescharacteristic
190#1808C2×C13711yescharacteristic
191#1380C2×C13711yescharacteristic, complemented
192C22×Q16C22×C13711yescharacteristic
193C23×C8C22×C13711yescharacteristic
194C2×C22⋊Q8—21no—
195C22×C16C22×C13711yescharacteristic
196C22×C16C22×C13711yescharacteristic
197#467—22no—
198#467—22no—
199C2×#107C22×C13711yescharacteristic
200C2×#107C22×C13711yescharacteristic
201C2×#107C22×C13711yescharacteristic
202C2×#103—21no—
203#380—21no—
204#367—22no—
205#358—22no—
206#358—22no—
207C22⋊C16—22no—
208#340—21no—
209C22×Q8—21no—
210C23×C4D4×C13711yescharacteristic
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16D4×C13712yes—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8D4×C13711yescharacteristic
224C22×C8C23×C13711yescharacteristic
225C22⋊Q8—24no—
226C22⋊Q8—42no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—41no—
231C2×C22⋊C4—41no—
232C2×C22⋊C4—41no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16D4×C13712yes—
239#107—21no—
240#107—21no—
241#107—21no—
242#107—21no—
243#107—21no—
244#107D4×C13712yes—
245#103—24no—
246#95—41no—
247C24D8×C13711yescharacteristic
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4D8×C13711yescharacteristic
265C22×C4C2×D4×C13711yescharacteristic
266Q16—22no—
267Q16—22no—
268Q16—41no—
269Q16—41no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C2×D4×C13711yescharacteristic
278C2×C8C2×D4×C13711yescharacteristic
279C2×C8C2×D4×C13711yescharacteristic
280C2×C8#41×C13711yescharacteristic
281C2×C8#41×C13711yescharacteristic
282C2×C8#41×C13711yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—44no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C22⋊C4—44no—
291C22⋊C4—82no—
292C16—22no—
293C16—41no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23SD32×C13712yes—
301C23C2×D8×C13711yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4#120×C13711yescharacteristic
326C2×C4#121×C13711yescharacteristic
327C2×C4#123×C13711yescharacteristic
328C2×C4#135×C13711yescharacteristic
329C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
330C2×C4#137×C13711yescharacteristic
331C8—41no—
332C8#121×C13711yescharacteristic
333C8#121×C13711yescharacteristic
334C8#123×C13711yescharacteristic
335C8#124×C13711yescharacteristic
336C22—22no—
337C22—22no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22#447×C13711yescharacteristic
344C22#466×C13711yescharacteristic
345C22#480×C13711yescharacteristic
346C22C2×SD32×C13711yescharacteristic
347C22#508×C13711yescharacteristic
348C22#510×C13711yescharacteristic
349C22#510×C13711yescharacteristic
350C4—41no—
351C4—82no—
352C4—82no—
353C4—161no—
354C4—161no—
355C4#394×C13711yescharacteristic
356C4#452×C13711yescharacteristic
357C4#468×C13711yescharacteristic
358C4#482×C13711yescharacteristic
359C2—42no—
360C2#2033×C13711yescharacteristic
361C2#2185×C13711yescharacteristic
362C2#2189×C13711yescharacteristic
363C2#2217×C13711yescharacteristic
364C2#2219×C13711yescharacteristic
365C2#2235×C13711yescharacteristic
366C2#2237×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C2×D8
commutator, Frattini, cosocleC22×C8C23×C137
prime radicalC24×C137D8
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C23×C4×C137 ◁ C23×C8×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#367×C137C2semidirect
3. C2×#358×C137C2semidirect
4. C2×#358×C137C2semidirect
7. #1380×C137C2semidirect
183. #13382C137direct (N × H)
184. C137#13382direct (N × H)
186. C2×#367C2×C137semidirect
187. C2×#358C2×C137semidirect
188. C2×#358C2×C137semidirect
191. #1380C2×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#467×C1372
C2×#367×C1372
C2×#358×C1372
C2×C22⋊C16×C1372
#1808×C1372
#1380×C1372
#13382137