Finite Group Databasebeta

← C137×#9945 #46859331

Subgroups — C137×#9945 #46859331

Order 35072.

574 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3095×C137C211yesmaximal, characteristic
2#2583×C137C211yesmaximal, characteristic
3#2484×C137C211yesmaximal, characteristic
4#1826×C137C211yesmaximal, characteristic
5#1511×C137C211yesmaximal, characteristic
6#1463×C137C211yesmaximal, characteristic
7#1284×C137C211yesmaximal, characteristic
8C2×C22⋊Q8×C137C2211yescharacteristic
9C2×#117×C137C2211yescharacteristic
10C22×C4⋊C4×C137C2211yescharacteristic
11#485×C137—22no—
12#484×C137—21no—
13#483×C137—21no—
14#428×C137—21no—
15#419×C137—21no—
16#407×C137C2211yescharacteristic
17#407×C137C2211yescharacteristic
18#400×C137—21no—
19#398×C137—21no—
20#398×C137—21no—
21#395×C137—21no—
22#389×C137—22no—
23#387×C137—22no—
24#385×C137—21no—
25#385×C137—21no—
26#385×C137—21no—
27#381×C137—21no—
28#381×C137C2211yescharacteristic
29C4×C22⋊C4×C137C2211yescharacteristic
30#339×C137—22no—
31#328×C137—22no—
32#324×C137—22no—
33C22×Q8×C137D411yescharacteristic
34C23×C4×C137D411yescharacteristic
35C23×C4×C137D411yescharacteristic
36C23×C4×C137C2311yescharacteristic
37C2×M16×C137—21no—
38C2×M16×C137—21no—
39C22⋊Q8×C137—21no—
40C22⋊Q8×C137—21no—
41C22⋊Q8×C137—21no—
42C22⋊Q8×C137—21no—
43#117×C137—21no—
44#117×C137—21no—
45#117×C137—21no—
46#117×C137—21no—
47C2×C4⋊C4×C137—22no—
48C2×C4⋊C4×C137—22no—
49C2×C4⋊C4×C137—21no—
50C2×C4⋊C4×C137—21no—
51C2×C4⋊C4×C137—21no—
52C2×C4⋊C4×C137—21no—
53C2×C4⋊C4×C137—21no—
54C2×C4⋊C4×C137—21no—
55C2×C4⋊C4×C137—21no—
56C2×C4⋊C4×C137—22no—
57C2×C4⋊C4×C137D411yescharacteristic
58C2×C4⋊C4×C137D411yescharacteristic
59C2×C4⋊C4×C137D411yescharacteristic
60C2×C22⋊C4×C137—21no—
61C2×C22⋊C4×C137—21no—
62C2×C22⋊C4×C137—21no—
63C2×C22⋊C4×C137—21no—
64C2×C42×C137—21no—
65C2×C42×C137D412yes—
66#107×C137—22no—
67#106×C137—22no—
68#103×C137—22no—
69#103×C137—22no—
70C22⋊C8×C137—21no—
71C22⋊C8×C137—21no—
72C22⋊C8×C137—21no—
73C22⋊C8×C137D412yes—
74#95×C137—22no—
75#95×C137—22no—
76#95×C137—22no—
77#95×C137—22no—
78#95×C137—22no—
79#95×C137—21no—
80#95×C137—21no—
81#95×C137D412yes—
82C24×C137C2×D411yescharacteristic
83C2×Q8×C137—21no—
84C2×Q8×C137—21no—
85C2×Q8×C137—42no—
86C22×C4×C137—22no—
87C22×C4×C137—21no—
88C22×C4×C137—21no—
89C22×C4×C137—21no—
90C22×C4×C137—22no—
91C22×C4×C137—21no—
92C22×C4×C137—21no—
93C22×C4×C137—21no—
94C22×C4×C137—21no—
95C22×C4×C137—21no—
96C22×C4×C137—21no—
97C22×C4×C137—21no—
98C22×C4×C137—42no—
99C22×C4×C137—42no—
100C22×C4×C137—42no—
101C22×C4×C137C2×D411yescharacteristic
102C22×C4×C137C2×D411yescharacteristic
103C22×C4×C137C2×D411yescharacteristic
104C22×C4×C137C2×D411yescharacteristic
105C22×C4×C137C2×D411yescharacteristic
106C22×C4×C137#4111yescharacteristic
107M16×C137—42no—
108M16×C137—42no—
109C2×C8×C137—22no—
110C2×C8×C137—41no—
111C4⋊C4×C137—21no—
112C4⋊C4×C137—21no—
113C4⋊C4×C137—21no—
114C4⋊C4×C137—21no—
115C4⋊C4×C137—21no—
116C4⋊C4×C137—21no—
117C4⋊C4×C137—44no—
118C4⋊C4×C137—44no—
119C4⋊C4×C137—41no—
120C4⋊C4×C137—41no—
121C4⋊C4×C137—41no—
122C4⋊C4×C137—41no—
123C4⋊C4×C137—41no—
124C4⋊C4×C137—41no—
125C4⋊C4×C137—82no—
126C22⋊C4×C137—24no—
127C22⋊C4×C137—42no—
128C22⋊C4×C137—41no—
129C22⋊C4×C137—41no—
130C22⋊C4×C137—41no—
131C22⋊C4×C137—41no—
132C42×C137—42no—
133C42×C137—41no—
134C42×C137—41no—
135C23×C137—22no—
136C23×C137—22no—
137C23×C137—41no—
138C23×C137#12011yescharacteristic
139C23×C137#12011yescharacteristic
140C23×C137#12111yescharacteristic
141Q8×C137—42no—
142Q8×C137—81no—
143C2×C4×C137—22no—
144C2×C4×C137—22no—
145C2×C4×C137—24no—
146C2×C4×C137—22no—
147C2×C4×C137—22no—
148C2×C4×C137—22no—
149C2×C4×C137—41no—
150C2×C4×C137—41no—
151C2×C4×C137—41no—
152C2×C4×C137—41no—
153C2×C4×C137—42no—
154C2×C4×C137—41no—
155C2×C4×C137—41no—
156C2×C4×C137—41no—
157C2×C4×C137—41no—
158C2×C4×C137—42no—
159C2×C4×C137—42no—
160C2×C4×C137—42no—
161C2×C4×C137—42no—
162C2×C4×C137—42no—
163C2×C4×C137—42no—
164C2×C4×C137—41no—
165C2×C4×C137—41no—
166C2×C4×C137—41no—
167C2×C4×C137—41no—
168C2×C4×C137—41no—
169C2×C4×C137—42no—
170C2×C4×C137—42no—
171C2×C4×C137—42no—
172C2×C4×C137—42no—
173C2×C4×C137—81no—
174C2×C4×C137#12011yescharacteristic
175C2×C4×C137#12111yescharacteristic
176C2×C4×C137#12111yescharacteristic
177C2×C4×C137#12711yescharacteristic
178C8×C137—42no—
179C8×C137—81no—
180C22×C137—21no—
181C22×C137—21no—
182C22×C137—21no—
183C22×C137—21no—
184C22×C137—21no—
185C22×C137—21no—
186C22×C137—21no—
187C22×C137—44no—
188C22×C137#39211yescharacteristic
189C22×C137#45612yes—
190C22×C137#45812yes—
191C4×C137—21no—
192C4×C137—21no—
193C4×C137—21no—
194C4×C137—21no—
195C4×C137—44no—
196C4×C137—42no—
197C4×C137—82no—
198C4×C137—81no—
199C4×C137—81no—
200C4×C137—81no—
201C4×C137—81no—
202C4×C137—81no—
203C2×C137—22no—
204C2×C137—22no—
205C2×C137—41no—
206C2×C137#200511yescharacteristic
207C2×C137#201011yescharacteristic
208C2×C137#202211yescharacteristic
209#9945C13711yesmaximal, characteristic, direct product factor, Sylow
210C137#994511yescharacteristic, direct product factor, Sylow
211#3095C2×C13711yescharacteristic
212#2583C2×C13711yescharacteristic
213#2484C2×C13711yescharacteristic
214#1826C2×C13711yescharacteristic
215#1511C2×C13711yescharacteristic
216#1463C2×C13711yescharacteristic
217#1284C2×C13711yescharacteristic
218C2×C22⋊Q8C22×C13711yescharacteristic
219C2×#117C22×C13711yescharacteristic
220C22×C4⋊C4C22×C13711yescharacteristic
221#485—22no—
222#484—21no—
223#483—21no—
224#428—21no—
225#419—21no—
226#407C22×C13711yescharacteristic
227#407C22×C13711yescharacteristic
228#400—21no—
229#398—21no—
230#398—21no—
231#395—21no—
232#389—22no—
233#387—22no—
234#385—21no—
235#385—21no—
236#385—21no—
237#381—21no—
238#381C22×C13711yescharacteristic
239C4×C22⋊C4C22×C13711yescharacteristic
240#339—22no—
241#328—22no—
242#324—22no—
243C22×Q8D4×C13711yescharacteristic
244C23×C4D4×C13711yescharacteristic
245C23×C4D4×C13711yescharacteristic
246C23×C4C23×C13711yescharacteristic
247C2×M16—21no—
248C2×M16—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253#117—21no—
254#117—21no—
255#117—21no—
256#117—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4D4×C13711yescharacteristic
268C2×C4⋊C4D4×C13711yescharacteristic
269C2×C4⋊C4D4×C13711yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C42—21no—
275C2×C42D4×C13712yes—
276#107—22no—
277#106—22no—
278#103—22no—
279#103—22no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8D4×C13712yes—
284#95—22no—
285#95—22no—
286#95—22no—
287#95—22no—
288#95—22no—
289#95—21no—
290#95—21no—
291#95D4×C13712yes—
292C24C2×D4×C13711yescharacteristic
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—42no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4C2×D4×C13711yescharacteristic
312C22×C4C2×D4×C13711yescharacteristic
313C22×C4C2×D4×C13711yescharacteristic
314C22×C4C2×D4×C13711yescharacteristic
315C22×C4C2×D4×C13711yescharacteristic
316C22×C4#41×C13711yescharacteristic
317M16—42no—
318M16—42no—
319C2×C8—22no—
320C2×C8—41no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—44no—
328C4⋊C4—44no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—82no—
336C22⋊C4—24no—
337C22⋊C4—42no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—42no—
343C42—41no—
344C42—41no—
345C23—22no—
346C23—22no—
347C23—41no—
348C23#120×C13711yescharacteristic
349C23#120×C13711yescharacteristic
350C23#121×C13711yescharacteristic
351Q8—42no—
352Q8—81no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—81no—
384C2×C4#120×C13711yescharacteristic
385C2×C4#121×C13711yescharacteristic
386C2×C4#121×C13711yescharacteristic
387C2×C4#127×C13711yescharacteristic
388C8—42no—
389C8—81no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22#392×C13711yescharacteristic
399C22#456×C13712yes—
400C22#458×C13712yes—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—44no—
406C4—42no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—81no—
413C2—22no—
414C2—22no—
415C2—41no—
416C2#2005×C13711yescharacteristic
417C2#2010×C13711yescharacteristic
418C2#2022×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#392
commutator, Frattini, cosocleC23×C4C23×C137
prime radicalC24×C137C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
209. #9945C137direct (N × H)
210. C137#9945direct (N × H)

Maximal subgroups

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

subgroupindex
#3095×C1372
#2583×C1372
#2484×C1372
#1826×C1372
#1511×C1372
#1463×C1372
#1284×C1372
#9945137