Finite Group Databasebeta

← C137×#8885 #46858271

Subgroups — C137×#8885 #46858271

Order 35072.

546 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2354×C137C211yesmaximal, characteristic
2#1948×C137C211yesmaximal, characteristic, complemented
3#1845×C137C211yesmaximal, characteristic, complemented
4#1802×C137C211yesmaximal, characteristic
5C2×D4⋊C8×C137C211yesmaximal, characteristic
6#1296×C137C211yesmaximal, characteristic, complemented
7#1279×C137C211yesmaximal, characteristic, complemented
8C2×C4×D4×C137C2211yescharacteristic
9C2×#117×C137—21no—
10C2×#107×C137—22no—
11C2×#106×C137—21no—
12C2×C4⋊C8×C137C2211yescharacteristic
13C2×C4⋊C8×C137C2211yescharacteristic
14C2×#102×C137—21no—
15C2×C4×C8×C137C2211yescharacteristic
16#390×C137—21no—
17#388×C137—22no—
18#384×C137C2211yescharacteristic
19#384×C137C2211yescharacteristic
20#380×C137—21no—
21C4×C4⋊C4×C137—21no—
22C4×C4⋊C4×C137C2211yescharacteristic
23#340×C137—21no—
24#340×C137—21no—
25D4⋊C8×C137C414yescomplemented
26C22×D4×C137D411yescharacteristic
27C23×C4×C137—21no—
28C22×C8×C137—21no—
29C22×C8×C137—21no—
30C22×C8×C137—21no—
31C4×D4×C137—21no—
32C4×D4×C137—21no—
33C4×D4×C137C2×C412yes—
34C4×D4×C137Q812yes—
35#117×C137—42no—
36#117×C137—42no—
37C2×C4⋊C4×C137—21no—
38C2×C4⋊C4×C137—21no—
39C2×C4⋊C4×C137—21no—
40C2×C4⋊C4×C137—21no—
41C2×C4⋊C4×C137—21no—
42C2×C4⋊C4×C137D411yescharacteristic
43C2×C4⋊C4×C137D411yescharacteristic
44C2×C4⋊C4×C137D411yescharacteristic
45C2×C4⋊C4×C137D412yes—
46C2×C22⋊C4×C137—21no—
47C2×C22⋊C4×C137—22no—
48C2×C22⋊C4×C137—22no—
49C2×C42×C137—22no—
50C2×C42×C137—21no—
51C2×C42×C137C2311yescharacteristic
52#107×C137—44no—
53#106×C137—42no—
54C4⋊C8×C137—21no—
55C4⋊C8×C137—21no—
56C4⋊C8×C137—21no—
57C4⋊C8×C137C2×C412yes—
58#102×C137—42no—
59C4×C8×C137—21no—
60C4×C8×C137C2×C412yes—
61#95×C137—22no—
62#95×C137—21no—
63C24×C137—21no—
64C2×D4×C137—21no—
65C2×D4×C137—21no—
66C2×D4×C137—21no—
67C2×D4×C137—21no—
68C2×D4×C137—21no—
69C2×D4×C137C4⋊C412yes—
70C22×C4×C137—21no—
71C22×C4×C137—21no—
72C22×C4×C137—22no—
73C22×C4×C137—22no—
74C22×C4×C137—21no—
75C22×C4×C137—22no—
76C22×C4×C137—41no—
77C22×C4×C137—41no—
78C22×C4×C137—41no—
79C22×C4×C137—41no—
80C22×C4×C137—41no—
81C22×C4×C137C2×D411yescharacteristic
82C22×C4×C137C2×D411yescharacteristic
83C22×C4×C137C2×D411yescharacteristic
84C2×C8×C137—22no—
85C2×C8×C137—22no—
86C2×C8×C137—22no—
87C2×C8×C137—22no—
88C2×C8×C137—41no—
89C2×C8×C137—41no—
90C2×C8×C137—41no—
91C2×C8×C137—41no—
92C2×C8×C137—41no—
93C4⋊C4×C137—21no—
94C4⋊C4×C137—21no—
95C4⋊C4×C137—21no—
96C4⋊C4×C137—21no—
97C4⋊C4×C137—42no—
98C4⋊C4×C137—42no—
99C4⋊C4×C137—41no—
100C4⋊C4×C137—41no—
101C4⋊C4×C137—41no—
102C4⋊C4×C137—41no—
103C4⋊C4×C137—41no—
104C4⋊C4×C137—41no—
105C4⋊C4×C137—41no—
106C4⋊C4×C137—41no—
107C4⋊C4×C137C4⋊C412yes—
108C4⋊C4×C137D812yes—
109C22⋊C4×C137—22no—
110C22⋊C4×C137—22no—
111C22⋊C4×C137—44no—
112C22⋊C4×C137—82no—
113C42×C137—44no—
114C42×C137—41no—
115C42×C137—41no—
116C42×C137C22×C411yescharacteristic
117C42×C137C2×Q811yescharacteristic
118C42×C137#4111yescharacteristic
119C42×C137#4111yescharacteristic
120C23×C137—22no—
121C23×C137—41no—
122C23×C137—41no—
123C23×C137—41no—
124C23×C137—41no—
125C23×C137—41no—
126C23×C137—41no—
127C23×C137#12011yescharacteristic
128D4×C137—22no—
129D4×C137—22no—
130D4×C137—41no—
131D4×C137—41no—
132C2×C4×C137—21no—
133C2×C4×C137—21no—
134C2×C4×C137—22no—
135C2×C4×C137—22no—
136C2×C4×C137—41no—
137C2×C4×C137—41no—
138C2×C4×C137—41no—
139C2×C4×C137—41no—
140C2×C4×C137—42no—
141C2×C4×C137—42no—
142C2×C4×C137—42no—
143C2×C4×C137—42no—
144C2×C4×C137—42no—
145C2×C4×C137—42no—
146C2×C4×C137—41no—
147C2×C4×C137—41no—
148C2×C4×C137—41no—
149C2×C4×C137—42no—
150C2×C4×C137—81no—
151C2×C4×C137—81no—
152C2×C4×C137—81no—
153C2×C4×C137C2×C4⋊C411yescharacteristic
154C2×C4×C137C4×D411yescharacteristic
155C2×C4×C137C4×D411yescharacteristic
156C2×C4×C137C22⋊Q811yescharacteristic
157C2×C4×C137C22⋊Q811yescharacteristic
158C2×C4×C137#12311yescharacteristic
159C2×C4×C137C2×D811yescharacteristic
160C2×C4×C137#13511yescharacteristic
161C2×C4×C137#13511yescharacteristic
162C2×C4×C137#13511yescharacteristic
163C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C137#13711yescharacteristic
166C2×C4×C137#13711yescharacteristic
167C8×C137—24no—
168C8×C137—42no—
169C8×C137—81no—
170C22×C137—42no—
171C22×C137—42no—
172C22×C137—42no—
173C22×C137—81no—
174C22×C137—81no—
175C22×C137—81no—
176C22×C137—81no—
177C22×C137#38511yescharacteristic
178C22×C137#44711yescharacteristic
179C22×C137#44911yescharacteristic
180C22×C137#45211yescharacteristic
181C22×C137#45211yescharacteristic
182C22×C137#45311yescharacteristic
183C22×C137#45611yescharacteristic
184C4×C137—21no—
185C4×C137—21no—
186C4×C137—42no—
187C4×C137—42no—
188C4×C137—82no—
189C4×C137—81no—
190C4×C137—161no—
191C4×C137#42711yescharacteristic
192C4×C137#42811yescharacteristic
193C4×C137C4×D811yescharacteristic
194C4×C137#44011yescharacteristic
195C4×C137#47411yescharacteristic
196C4×C137#47811yescharacteristic
197C4×C137#48211yescharacteristic
198C4×C137#48511yescharacteristic
199C2×C137—82no—
200C2×C137#162111yescharacteristic
201C2×C137#163411yescharacteristic
202C2×C137#164711yescharacteristic
203C2×C137#165011yescharacteristic
204C2×C137#185411yescharacteristic
205C2×C137#185911yescharacteristic
206C2×C137#186211yescharacteristic
207#8885C13711yesmaximal, characteristic, direct product factor, Sylow
208C137#888511yescharacteristic, direct product factor, Sylow
209#2354C2×C13711yescharacteristic
210#1948C2×C13711yescharacteristic, complemented
211#1845C2×C13711yescharacteristic, complemented
212#1802C2×C13711yescharacteristic
213C2×D4⋊C8C2×C13711yescharacteristic
214#1296C2×C13711yescharacteristic, complemented
215#1279C2×C13711yescharacteristic, complemented
216C2×C4×D4C22×C13711yescharacteristic
217C2×#117—21no—
218C2×#107—22no—
219C2×#106—21no—
220C2×C4⋊C8C22×C13711yescharacteristic
221C2×C4⋊C8C22×C13711yescharacteristic
222C2×#102—21no—
223C2×C4×C8C22×C13711yescharacteristic
224#390—21no—
225#388—22no—
226#384C22×C13711yescharacteristic
227#384C22×C13711yescharacteristic
228#380—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4C22×C13711yescharacteristic
231#340—21no—
232#340—21no—
233D4⋊C8C4×C13714yescomplemented
234C22×D4D4×C13711yescharacteristic
235C23×C4—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4C2×C4×C13712yes—
242C4×D4Q8×C13712yes—
243#117—42no—
244#117—42no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4D4×C13711yescharacteristic
251C2×C4⋊C4D4×C13711yescharacteristic
252C2×C4⋊C4D4×C13711yescharacteristic
253C2×C4⋊C4D4×C13712yes—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C42—22no—
258C2×C42—21no—
259C2×C42C23×C13711yescharacteristic
260#107—44no—
261#106—42no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8C2×C4×C13712yes—
266#102—42no—
267C4×C8—21no—
268C4×C8C2×C4×C13712yes—
269#95—22no—
270#95—21no—
271C24—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C4⋊C4×C13712yes—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4C2×D4×C13711yescharacteristic
290C22×C4C2×D4×C13711yescharacteristic
291C22×C4C2×D4×C13711yescharacteristic
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4C4⋊C4×C13712yes—
316C4⋊C4D8×C13712yes—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—44no—
320C22⋊C4—82no—
321C42—44no—
322C42—41no—
323C42—41no—
324C42C22×C4×C13711yescharacteristic
325C42C2×Q8×C13711yescharacteristic
326C42#41×C13711yescharacteristic
327C42#41×C13711yescharacteristic
328C23—22no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23#120×C13711yescharacteristic
336D4—22no—
337D4—22no—
338D4—41no—
339D4—41no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4C2×C4⋊C4×C13711yescharacteristic
362C2×C4C4×D4×C13711yescharacteristic
363C2×C4C4×D4×C13711yescharacteristic
364C2×C4C22⋊Q8×C13711yescharacteristic
365C2×C4C22⋊Q8×C13711yescharacteristic
366C2×C4#123×C13711yescharacteristic
367C2×C4C2×D8×C13711yescharacteristic
368C2×C4#135×C13711yescharacteristic
369C2×C4#135×C13711yescharacteristic
370C2×C4#135×C13711yescharacteristic
371C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
372C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
373C2×C4#137×C13711yescharacteristic
374C2×C4#137×C13711yescharacteristic
375C8—24no—
376C8—42no—
377C8—81no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22#385×C13711yescharacteristic
386C22#447×C13711yescharacteristic
387C22#449×C13711yescharacteristic
388C22#452×C13711yescharacteristic
389C22#452×C13711yescharacteristic
390C22#453×C13711yescharacteristic
391C22#456×C13711yescharacteristic
392C4—21no—
393C4—21no—
394C4—42no—
395C4—42no—
396C4—82no—
397C4—81no—
398C4—161no—
399C4#427×C13711yescharacteristic
400C4#428×C13711yescharacteristic
401C4C4×D8×C13711yescharacteristic
402C4#440×C13711yescharacteristic
403C4#474×C13711yescharacteristic
404C4#478×C13711yescharacteristic
405C4#482×C13711yescharacteristic
406C4#485×C13711yescharacteristic
407C2—82no—
408C2#1621×C13711yescharacteristic
409C2#1634×C13711yescharacteristic
410C2#1647×C13711yescharacteristic
411C2#1650×C13711yescharacteristic
412C2#1854×C13711yescharacteristic
413C2#1859×C13711yescharacteristic
414C2#1862×C13711yescharacteristic
subgroupG/H
center, socleC23×C137#120
commutatorC42C22×C4×C137
Frattini, cosocleC2×C42C23×C137
prime radicalC22×D4×C137D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1948×C137C2semidirect
3. #1845×C137C2semidirect
6. #1296×C137C2semidirect
7. #1279×C137C2semidirect
25. D4⋊C8×C137C4semidirect
207. #8885C137direct (N × H)
208. C137#8885direct (N × H)
210. #1948C2×C137semidirect
211. #1845C2×C137semidirect
214. #1296C2×C137semidirect
215. #1279C2×C137semidirect
233. D4⋊C8C4×C137semidirect

Maximal subgroups

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

subgroupindex
#2354×C1372
#1948×C1372
#1845×C1372
#1802×C1372
C2×D4⋊C8×C1372
#1296×C1372
#1279×C1372
#8885137