Finite Group Databasebeta

← C137×#19477 #46868863

Subgroups — C137×#19477 #46868863

Order 35072.

598 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3226×C137C211yesmaximal, characteristic
2#3112×C137C211yesmaximal, characteristic
3C2×#477×C137C211yesmaximal, characteristic, complemented
4#2984×C137C211yesmaximal, characteristic, complemented
5#1698×C137C212yesmaximal, complemented
6#1696×C137C212yesmaximal, complemented
7#1678×C137C212yesmaximal, complemented
8#1676×C137C212yesmaximal, complemented
9#1573×C137C211yesmaximal, characteristic, complemented
10#1558×C137C211yesmaximal, characteristic, complemented
11#1551×C137C211yesmaximal, characteristic
12#532×C137C2211yescharacteristic
13C2×C4⋊Q8×C137C2211yescharacteristic
14C2×C4×Q8×C137C2211yescharacteristic
15#500×C137C2212yes—
16#486×C137C2212yes—
17#480×C137—21no—
18#480×C137—21no—
19#480×C137—21no—
20#477×C137—21no—
21#477×C137—21no—
22#477×C137C2212yes—
23#477×C137C2212yes—
24#477×C137C2211yescharacteristic
25#477×C137C2211yescharacteristic
26#474×C137—22no—
27#460×C137C2211yescharacteristic
28#460×C137C2211yescharacteristic
29#448×C137—21no—
30#446×C137—22no—
31#446×C137C2212yes—
32C8×Q8×C137C2212yes—
33#440×C137—21no—
34#440×C137—21no—
35#432×C137—21no—
36#432×C137C2211yescharacteristic
37#432×C137C2211yescharacteristic
38#431×C137—21no—
39#431×C137C2211yescharacteristic
40C2×#107×C137—21no—
41C2×C4⋊C8×C137C2211yescharacteristic
42C2×#103×C137—21no—
43#335×C137C2212yes—
44#334×C137C2212yes—
45#333×C137C2212yes—
46#333×C137C2212yes—
47#333×C137C2212yes—
48#331×C137C2212yes—
49C2×#41×C137—21no—
50C22×Q8×C137—21no—
51C22×Q8×C137D411yescharacteristic
52C2×SD16×C137—21no—
53C2×SD16×C137—21no—
54C22×C8×C137—21no—
55C4⋊Q8×C137—21no—
56C4⋊Q8×C137—21no—
57C4⋊Q8×C137—21no—
58C4⋊Q8×C137C2312yes—
59C4⋊Q8×C137C2311yescharacteristic
60#127×C137C2311yescharacteristic
61#124×C137—21no—
62#121×C137—21no—
63#121×C137—21no—
64C4×Q8×C137—21no—
65C4×Q8×C137—21no—
66C4×Q8×C137D411yescharacteristic
67C4×Q8×C137D411yescharacteristic
68C4×Q8×C137C2311yescharacteristic
69C4×Q8×C137C2311yescharacteristic
70C4×D4×C137—21no—
71C4×D4×C137—21no—
72C2×C4⋊C4×C137—21no—
73C2×C4⋊C4×C137—21no—
74C2×C4⋊C4×C137—21no—
75C2×C4⋊C4×C137D411yescharacteristic
76C2×C42×C137—21no—
77C2×C42×C137C2311yescharacteristic
78#107×C137—22no—
79#107×C137—22no—
80#107×C137—22no—
81#107×C137—22no—
82#107×C137—21no—
83#107×C137—21no—
84C4⋊C8×C137—22no—
85C4⋊C8×C137—22no—
86C4⋊C8×C137—21no—
87C4⋊C8×C137D412yes—
88C4⋊C8×C137C2312yes—
89C4⋊C8×C137C2312yes—
90C4⋊C8×C137C2311yescharacteristic
91C4⋊C8×C137C2311yescharacteristic
92#103×C137—22no—
93#103×C137—22no—
94#103×C137—21no—
95#103×C137—21no—
96#102×C137—22no—
97#102×C137—22no—
98#102×C137—21no—
99#102×C137—21no—
100C22⋊C8×C137—21no—
101C22⋊C8×C137—21no—
102C22⋊C8×C137D411yescharacteristic
103C22⋊C8×C137D411yescharacteristic
104#97×C137—22no—
105#97×C137—21no—
106#97×C137—21no—
107C4×C8×C137—22no—
108C4×C8×C137C2312yes—
109#41×C137—82no—
110C2×Q8×C137—21no—
111C2×Q8×C137—22no—
112C2×Q8×C137—21no—
113C2×Q8×C137—22no—
114C2×Q8×C137—41no—
115C2×Q8×C137—41no—
116C2×Q8×C137—82no—
117C2×Q8×C137C2×D411yescharacteristic
118C2×Q8×C137C2×D411yescharacteristic
119C2×D4×C137—21no—
120C2×D4×C137—21no—
121C2×D4×C137—21no—
122C2×D4×C137—41no—
123C22×C4×C137—21no—
124C22×C4×C137—21no—
125C22×C4×C137—41no—
126C22×C4×C137—41no—
127C22×C4×C137C2×D411yescharacteristic
128C22×C4×C137C2×D411yescharacteristic
129C22×C4×C137#4111yescharacteristic
130SD16×C137—42no—
131SD16×C137—42no—
132C2×C8×C137—22no—
133C2×C8×C137—21no—
134C2×C8×C137—21no—
135C2×C8×C137—22no—
136C2×C8×C137—42no—
137C2×C8×C137C2×D412yes—
138C2×C8×C137C2×D412yes—
139C4⋊C4×C137—21no—
140C4⋊C4×C137—21no—
141C4⋊C4×C137—21no—
142C4⋊C4×C137—21no—
143C4⋊C4×C137—21no—
144C4⋊C4×C137—22no—
145C4⋊C4×C137—22no—
146C4⋊C4×C137—21no—
147C4⋊C4×C137—21no—
148C4⋊C4×C137—41no—
149C4⋊C4×C137—41no—
150C4⋊C4×C137C2×D411yescharacteristic
151C4⋊C4×C137C2×D411yescharacteristic
152C22⋊C4×C137—41no—
153C22⋊C4×C137—41no—
154C42×C137—21no—
155C42×C137—21no—
156C42×C137—21no—
157C42×C137—21no—
158C42×C137C2×D411yescharacteristic
159C42×C137C2×D411yescharacteristic
160C42×C137#4111yescharacteristic
161C42×C137C2411yescharacteristic
162C23×C137—41no—
163C23×C137#12111yescharacteristic
164Q8×C137—21no—
165Q8×C137—21no—
166Q8×C137—21no—
167Q8×C137—42no—
168Q8×C137—82no—
169Q8×C137—81no—
170Q8×C137—82no—
171Q8×C137#13712yes—
172D4×C137—41no—
173D4×C137—41no—
174D4×C137—42no—
175D4×C137—81no—
176D4×C137—82no—
177C2×C4×C137—21no—
178C2×C4×C137—22no—
179C2×C4×C137—21no—
180C2×C4×C137—21no—
181C2×C4×C137—22no—
182C2×C4×C137—21no—
183C2×C4×C137—21no—
184C2×C4×C137—21no—
185C2×C4×C137—42no—
186C2×C4×C137—42no—
187C2×C4×C137—41no—
188C2×C4×C137—42no—
189C2×C4×C137—82no—
190C2×C4×C137—82no—
191C2×C4×C137#12111yescharacteristic
192C2×C4×C137#12111yescharacteristic
193C2×C4×C137#12111yescharacteristic
194C2×C4×C137C22×D411yescharacteristic
195C2×C4×C137C22×D411yescharacteristic
196C2×C4×C137C2×#4111yescharacteristic
197C8×C137—22no—
198C8×C137—22no—
199C8×C137—41no—
200C8×C137—42no—
201C8×C137—41no—
202C8×C137—42no—
203C22×C137—21no—
204C22×C137—21no—
205C22×C137—81no—
206C22×C137—81no—
207C22×C137—81no—
208C22×C137#47212yes—
209C22×C137C2×#12111yescharacteristic
210C4×C137—21no—
211C4×C137—21no—
212C4×C137—22no—
213C4×C137—21no—
214C4×C137—21no—
215C4×C137—41no—
216C4×C137—41no—
217C4×C137—41no—
218C4×C137—81no—
219C4×C137—82no—
220C4×C137C2×#13711yescharacteristic
221C4×C137#57511yescharacteristic
222C4×C137#57812yes—
223C2×C137—22no—
224C2×C137—161no—
225C2×C137#304411yescharacteristic
226C2×C137#305611yescharacteristic
227C2×C137C2×#47211yescharacteristic
228#19477C13711yesmaximal, characteristic, direct product factor, Sylow
229C137#1947711yescharacteristic, direct product factor, Sylow
230#3226C2×C13711yescharacteristic
231#3112C2×C13711yescharacteristic
232C2×#477C2×C13711yescharacteristic, complemented
233#2984C2×C13711yescharacteristic, complemented
234#1698C2×C13712yescomplemented
235#1696C2×C13712yescomplemented
236#1678C2×C13712yescomplemented
237#1676C2×C13712yescomplemented
238#1573C2×C13711yescharacteristic, complemented
239#1558C2×C13711yescharacteristic, complemented
240#1551C2×C13711yescharacteristic
241#532C22×C13711yescharacteristic
242C2×C4⋊Q8C22×C13711yescharacteristic
243C2×C4×Q8C22×C13711yescharacteristic
244#500C22×C13712yes—
245#486C22×C13712yes—
246#480—21no—
247#480—21no—
248#480—21no—
249#477—21no—
250#477—21no—
251#477C22×C13712yes—
252#477C22×C13712yes—
253#477C22×C13711yescharacteristic
254#477C22×C13711yescharacteristic
255#474—22no—
256#460C22×C13711yescharacteristic
257#460C22×C13711yescharacteristic
258#448—21no—
259#446—22no—
260#446C22×C13712yes—
261C8×Q8C22×C13712yes—
262#440—21no—
263#440—21no—
264#432—21no—
265#432C22×C13711yescharacteristic
266#432C22×C13711yescharacteristic
267#431—21no—
268#431C22×C13711yescharacteristic
269C2×#107—21no—
270C2×C4⋊C8C22×C13711yescharacteristic
271C2×#103—21no—
272#335C22×C13712yes—
273#334C22×C13712yes—
274#333C22×C13712yes—
275#333C22×C13712yes—
276#333C22×C13712yes—
277#331C22×C13712yes—
278C2×#41—21no—
279C22×Q8—21no—
280C22×Q8D4×C13711yescharacteristic
281C2×SD16—21no—
282C2×SD16—21no—
283C22×C8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8C23×C13712yes—
288C4⋊Q8C23×C13711yescharacteristic
289#127C23×C13711yescharacteristic
290#124—21no—
291#121—21no—
292#121—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8D4×C13711yescharacteristic
296C4×Q8D4×C13711yescharacteristic
297C4×Q8C23×C13711yescharacteristic
298C4×Q8C23×C13711yescharacteristic
299C4×D4—21no—
300C4×D4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C13711yescharacteristic
305C2×C42—21no—
306C2×C42C23×C13711yescharacteristic
307#107—22no—
308#107—22no—
309#107—22no—
310#107—22no—
311#107—21no—
312#107—21no—
313C4⋊C8—22no—
314C4⋊C8—22no—
315C4⋊C8—21no—
316C4⋊C8D4×C13712yes—
317C4⋊C8C23×C13712yes—
318C4⋊C8C23×C13712yes—
319C4⋊C8C23×C13711yescharacteristic
320C4⋊C8C23×C13711yescharacteristic
321#103—22no—
322#103—22no—
323#103—21no—
324#103—21no—
325#102—22no—
326#102—22no—
327#102—21no—
328#102—21no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C22⋊C8D4×C13711yescharacteristic
332C22⋊C8D4×C13711yescharacteristic
333#97—22no—
334#97—21no—
335#97—21no—
336C4×C8—22no—
337C4×C8C23×C13712yes—
338#41—82no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—82no—
346C2×Q8C2×D4×C13711yescharacteristic
347C2×Q8C2×D4×C13711yescharacteristic
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—41no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4C2×D4×C13711yescharacteristic
357C22×C4C2×D4×C13711yescharacteristic
358C22×C4#41×C13711yescharacteristic
359SD16—42no—
360SD16—42no—
361C2×C8—22no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—22no—
365C2×C8—42no—
366C2×C8C2×D4×C13712yes—
367C2×C8C2×D4×C13712yes—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4C2×D4×C13711yescharacteristic
380C4⋊C4C2×D4×C13711yescharacteristic
381C22⋊C4—41no—
382C22⋊C4—41no—
383C42—21no—
384C42—21no—
385C42—21no—
386C42—21no—
387C42C2×D4×C13711yescharacteristic
388C42C2×D4×C13711yescharacteristic
389C42#41×C13711yescharacteristic
390C42C24×C13711yescharacteristic
391C23—41no—
392C23#121×C13711yescharacteristic
393Q8—21no—
394Q8—21no—
395Q8—21no—
396Q8—42no—
397Q8—82no—
398Q8—81no—
399Q8—82no—
400Q8#137×C13712yes—
401D4—41no—
402D4—41no—
403D4—42no—
404D4—81no—
405D4—82no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4#121×C13711yescharacteristic
421C2×C4#121×C13711yescharacteristic
422C2×C4#121×C13711yescharacteristic
423C2×C4C22×D4×C13711yescharacteristic
424C2×C4C22×D4×C13711yescharacteristic
425C2×C4C2×#41×C13711yescharacteristic
426C8—22no—
427C8—22no—
428C8—41no—
429C8—42no—
430C8—41no—
431C8—42no—
432C22—21no—
433C22—21no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22#472×C13712yes—
438C22C2×#121×C13711yescharacteristic
439C4—21no—
440C4—21no—
441C4—22no—
442C4—21no—
443C4—21no—
444C4—41no—
445C4—41no—
446C4—41no—
447C4—81no—
448C4—82no—
449C4C2×#137×C13711yescharacteristic
450C4#575×C13711yescharacteristic
451C4#578×C13712yes—
452C2—22no—
453C2—161no—
454C2#3044×C13711yescharacteristic
455C2#3056×C13711yescharacteristic
456C2C2×#472×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radical#532×C137C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#477×C137C2semidirect
4. #2984×C137C2semidirect
5. #1698×C137C2semidirect
6. #1696×C137C2semidirect
7. #1678×C137C2semidirect
8. #1676×C137C2semidirect
9. #1573×C137C2semidirect
10. #1558×C137C2semidirect
228. #19477C137direct (N × H)
229. C137#19477direct (N × H)
232. C2×#477C2×C137semidirect
233. #2984C2×C137semidirect
234. #1698C2×C137semidirect
235. #1696C2×C137semidirect
236. #1678C2×C137semidirect
237. #1676C2×C137semidirect
238. #1573C2×C137semidirect
239. #1558C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3226×C1372
#3112×C1372
C2×#477×C1372
#2984×C1372
#1698×C1372
#1696×C1372
#1678×C1372
#1676×C1372
#1573×C1372
#1558×C1372
#1551×C1372
#19477137