Finite Group Databasebeta

← C37×#19351 #22640604

Subgroups — C37×#19351 #22640604

Order 9472.

590 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
1C37×#3255C211yesmaximal, characteristic, complemented
2C37×#3254C211yesmaximal, characteristic
3C37×#3167C211yesmaximal, characteristic
4C37×#2960C211yesmaximal, characteristic, complemented
5C37×#1692C212yesmaximal, complemented
6C37×#1686C212yesmaximal, complemented
7C37×#1684C212yesmaximal, complemented
8C37×#1682C212yesmaximal, complemented
9C37×#1567C211yesmaximal, characteristic, complemented
10C37×#1561C211yesmaximal, characteristic, complemented
11C37×#1560C211yesmaximal, characteristic
12C37×#533C2211yescharacteristic
13C37×#533C2211yescharacteristic
14C37×#532C2211yescharacteristic
15C37×#498C2211yescharacteristic
16C37×#492C2211yescharacteristic
17C37×#487C2211yescharacteristic
18C37×#486C2211yescharacteristic
19C37×#477C2212yes—
20C37×#475—21no—
21C37×#475C2212yes—
22C37×#474—21no—
23C37×#470—22no—
24C37×#468—22no—
25C37×#465—21no—
26C37×#465—21no—
27C37×#462—21no—
28C37×#462C2212yes—
29C37×#461—21no—
30C37×#460C2212yes—
31C37×#446—21no—
32C37×#446C2212yes—
33C8×Q8×C37—21no—
34C8×Q8×C37C2212yes—
35C4×SD16×C37—21no—
36C4×SD16×C37—21no—
37C37×#424—21no—
38C37×#423C2211yescharacteristic
39C37×#423C2211yescharacteristic
40C37×#423C2211yescharacteristic
41C37×#405—21no—
42C2×C4×C8×C37C2211yescharacteristic
43C37×#335C2212yes—
44C37×#335C2212yes—
45C37×#333C2212yes—
46C37×#332C2212yes—
47C37×#332C2212yes—
48C37×#331C2212yes—
49C2×#41×C37—21no—
50C2×Q16×C37—22no—
51C2×SD16×C37—22no—
52C2×SD16×C37—21no—
53C2×SD16×C37—21no—
54C2×M16×C37—21no—
55C2×M16×C37—21no—
56C2×M16×C37—21no—
57C22×C8×C37D411yescharacteristic
58C22×C8×C37D411yescharacteristic
59C4⋊Q8×C37D411yescharacteristic
60C4⋊Q8×C37D411yescharacteristic
61C4⋊Q8×C37C2311yescharacteristic
62C4⋊Q8×C37C2311yescharacteristic
63C4⋊Q8×C37C2311yescharacteristic
64#127×C37C2311yescharacteristic
65#125×C37—21no—
66#125×C37—21no—
67#124×C37—21no—
68C22⋊Q8×C37—21no—
69C22⋊Q8×C37—21no—
70C22⋊Q8×C37—21no—
71C22⋊Q8×C37D412yes—
72#121×C37—21no—
73#121×C37—21no—
74C4×Q8×C37—21no—
75C4×Q8×C37—21no—
76C4×Q8×C37—21no—
77C4×Q8×C37C2312yes—
78C4×D4×C37—21no—
79C4×D4×C37—21no—
80#117×C37—21no—
81#117×C37—21no—
82C2×C42×C37C2311yescharacteristic
83#107×C37—22no—
84#106×C37—21no—
85#106×C37—21no—
86#106×C37—22no—
87C4⋊C8×C37—22no—
88C4⋊C8×C37—22no—
89C4⋊C8×C37—21no—
90C4⋊C8×C37—21no—
91C4⋊C8×C37—21no—
92C4⋊C8×C37C2312yes—
93C4⋊C8×C37C2312yes—
94C4⋊C8×C37C2312yes—
95#103×C37—22no—
96#103×C37—22no—
97#103×C37—21no—
98#103×C37—21no—
99#103×C37—22no—
100#102×C37—21no—
101#102×C37—21no—
102#102×C37—22no—
103#97×C37—22no—
104C4×C8×C37—22no—
105C4×C8×C37D411yescharacteristic
106C4×C8×C37D411yescharacteristic
107C4×C8×C37C2311yescharacteristic
108C4×C8×C37C2311yescharacteristic
109#41×C37—82no—
110C2×Q8×C37—21no—
111C2×Q8×C37—21no—
112C2×Q8×C37—21no—
113C2×Q8×C37—21no—
114C2×Q8×C37C2×D412yes—
115C2×D4×C37—21no—
116C2×D4×C37—21no—
117C2×D4×C37—21no—
118C2×D4×C37—41no—
119C22×C4×C37—41no—
120C22×C4×C37C2×D411yescharacteristic
121C22×C4×C37C2×D411yescharacteristic
122C22×C4×C37#4111yescharacteristic
123Q16×C37—82no—
124SD16×C37—42no—
125SD16×C37—42no—
126SD16×C37—82no—
127M16×C37—42no—
128M16×C37—81no—
129M16×C37—81no—
130C2×C8×C37—22no—
131C2×C8×C37—22no—
132C2×C8×C37—22no—
133C2×C8×C37—22no—
134C2×C8×C37—41no—
135C2×C8×C37C2×D411yescharacteristic
136C2×C8×C37C2×D411yescharacteristic
137C2×C8×C37C2×D411yescharacteristic
138C2×C8×C37C2×D411yescharacteristic
139C4⋊C4×C37—21no—
140C4⋊C4×C37—21no—
141C4⋊C4×C37—21no—
142C4⋊C4×C37—22no—
143C4⋊C4×C37—22no—
144C4⋊C4×C37—21no—
145C4⋊C4×C37—21no—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—21no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—41no—
151C4⋊C4×C37—41no—
152C4⋊C4×C37C2×D412yes—
153C22⋊C4×C37—22no—
154C22⋊C4×C37—41no—
155C22⋊C4×C37—41no—
156C22⋊C4×C37—41no—
157C42×C37—22no—
158C42×C37—41no—
159C42×C37C2×D411yescharacteristic
160C42×C37C2×D411yescharacteristic
161C42×C37#4111yescharacteristic
162C42×C37C2411yescharacteristic
163C23×C37—41no—
164C23×C37#12111yescharacteristic
165Q8×C37—22no—
166Q8×C37—22no—
167Q8×C37—42no—
168Q8×C37—41no—
169Q8×C37—41no—
170Q8×C37—41no—
171Q8×C37—41no—
172Q8×C37—81no—
173D4×C37—41no—
174D4×C37—41no—
175D4×C37—41no—
176D4×C37—41no—
177D4×C37—81no—
178D4×C37—82no—
179C2×C4×C37—21no—
180C2×C4×C37—21no—
181C2×C4×C37—21no—
182C2×C4×C37—21no—
183C2×C4×C37—22no—
184C2×C4×C37—22no—
185C2×C4×C37—22no—
186C2×C4×C37—41no—
187C2×C4×C37—41no—
188C2×C4×C37—41no—
189C2×C4×C37—82no—
190C2×C4×C37#12111yescharacteristic
191C2×C4×C37#12111yescharacteristic
192C2×C4×C37#12111yescharacteristic
193C2×C4×C37C22×D411yescharacteristic
194C2×C4×C37C22×D411yescharacteristic
195C2×C4×C37C2×#4111yescharacteristic
196C8×C37—21no—
197C8×C37—21no—
198C8×C37—21no—
199C8×C37—42no—
200C8×C37—42no—
201C8×C37—42no—
202C8×C37#13712yes—
203#19351C3711yesmaximal, characteristic, direct product factor, Sylow
204C22×C37—21no—
205C22×C37—21no—
206C22×C37—21no—
207C22×C37—81no—
208C22×C37—81no—
209C22×C37—81no—
210C22×C37C2×#12111yescharacteristic
211C4×C37—21no—
212C4×C37—21no—
213C4×C37—21no—
214C4×C37—42no—
215C4×C37—42no—
216C4×C37—81no—
217C4×C37—81no—
218C4×C37—81no—
219C4×C37#47112yes—
220C4×C37C2×#13711yescharacteristic
221C4×C37#57511yescharacteristic
222C4×C37#57611yescharacteristic
223C4×C37#57811yescharacteristic
224#3255C2×C3711yescharacteristic, complemented
225#3254C2×C3711yescharacteristic
226#3167C2×C3711yescharacteristic
227#2960C2×C3711yescharacteristic, complemented
228#1692C2×C3712yescomplemented
229#1686C2×C3712yescomplemented
230#1684C2×C3712yescomplemented
231#1682C2×C3712yescomplemented
232#1567C2×C3711yescharacteristic, complemented
233#1561C2×C3711yescharacteristic, complemented
234#1560C2×C3711yescharacteristic
235C2×C37—41no—
236C2×C37—161no—
237C2×C37#303711yescharacteristic
238C2×C37#306111yescharacteristic
239C2×C37C2×#47111yescharacteristic
240#533C22×C3711yescharacteristic
241#533C22×C3711yescharacteristic
242#532C22×C3711yescharacteristic
243#498C22×C3711yescharacteristic
244#492C22×C3711yescharacteristic
245#487C22×C3711yescharacteristic
246#486C22×C3711yescharacteristic
247#477C22×C3712yes—
248#475—21no—
249#475C22×C3712yes—
250#474—21no—
251#470—22no—
252#468—22no—
253#465—21no—
254#465—21no—
255#462—21no—
256#462C22×C3712yes—
257#461—21no—
258#460C22×C3712yes—
259#446—21no—
260#446C22×C3712yes—
261C8×Q8—21no—
262C8×Q8C22×C3712yes—
263C4×SD16—21no—
264C4×SD16—21no—
265#424—21no—
266#423C22×C3711yescharacteristic
267#423C22×C3711yescharacteristic
268#423C22×C3711yescharacteristic
269#405—21no—
270C2×C4×C8C22×C3711yescharacteristic
271#335C22×C3712yes—
272#335C22×C3712yes—
273#333C22×C3712yes—
274#332C22×C3712yes—
275#332C22×C3712yes—
276#331C22×C3712yes—
277C37#1935111yescharacteristic, direct product factor, Sylow
278C2×#41—21no—
279C2×Q16—22no—
280C2×SD16—22no—
281C2×SD16—21no—
282C2×SD16—21no—
283C2×M16—21no—
284C2×M16—21no—
285C2×M16—21no—
286C22×C8D4×C3711yescharacteristic
287C22×C8D4×C3711yescharacteristic
288C4⋊Q8D4×C3711yescharacteristic
289C4⋊Q8D4×C3711yescharacteristic
290C4⋊Q8C23×C3711yescharacteristic
291C4⋊Q8C23×C3711yescharacteristic
292C4⋊Q8C23×C3711yescharacteristic
293#127C23×C3711yescharacteristic
294#125—21no—
295#125—21no—
296#124—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8D4×C3712yes—
301#121—21no—
302#121—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8C23×C3712yes—
307C4×D4—21no—
308C4×D4—21no—
309#117—21no—
310#117—21no—
311C2×C42C23×C3711yescharacteristic
312#107—22no—
313#106—21no—
314#106—21no—
315#106—22no—
316C4⋊C8—22no—
317C4⋊C8—22no—
318C4⋊C8—21no—
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8C23×C3712yes—
322C4⋊C8C23×C3712yes—
323C4⋊C8C23×C3712yes—
324#103—22no—
325#103—22no—
326#103—21no—
327#103—21no—
328#103—22no—
329#102—21no—
330#102—21no—
331#102—22no—
332#97—22no—
333C4×C8—22no—
334C4×C8D4×C3711yescharacteristic
335C4×C8D4×C3711yescharacteristic
336C4×C8C23×C3711yescharacteristic
337C4×C8C23×C3711yescharacteristic
338#41—82no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8C2×D4×C3712yes—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—41no—
348C22×C4—41no—
349C22×C4C2×D4×C3711yescharacteristic
350C22×C4C2×D4×C3711yescharacteristic
351C22×C4#41×C3711yescharacteristic
352Q16—82no—
353SD16—42no—
354SD16—42no—
355SD16—82no—
356M16—42no—
357M16—81no—
358M16—81no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8C2×D4×C3711yescharacteristic
365C2×C8C2×D4×C3711yescharacteristic
366C2×C8C2×D4×C3711yescharacteristic
367C2×C8C2×D4×C3711yescharacteristic
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4C2×D4×C3712yes—
382C22⋊C4—22no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C42—22no—
387C42—41no—
388C42C2×D4×C3711yescharacteristic
389C42C2×D4×C3711yescharacteristic
390C42#41×C3711yescharacteristic
391C42C24×C3711yescharacteristic
392C23—41no—
393C23#121×C3711yescharacteristic
394Q8—22no—
395Q8—22no—
396Q8—42no—
397Q8—41no—
398Q8—41no—
399Q8—41no—
400Q8—41no—
401Q8—81no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—81no—
407D4—82no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—82no—
419C2×C4#121×C3711yescharacteristic
420C2×C4#121×C3711yescharacteristic
421C2×C4#121×C3711yescharacteristic
422C2×C4C22×D4×C3711yescharacteristic
423C2×C4C22×D4×C3711yescharacteristic
424C2×C4C2×#41×C3711yescharacteristic
425C8—21no—
426C8—21no—
427C8—21no—
428C8—42no—
429C8—42no—
430C8—42no—
431C8#137×C3712yes—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22C2×#121×C3711yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—42no—
443C4—42no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4C37×#47112yes—
448C4C2×#137×C3711yescharacteristic
449C4C37×#57511yescharacteristic
450C4C37×#57611yescharacteristic
451C4C37×#57811yescharacteristic
452C2—41no—
453C2—161no—
454C2C37×#303711yescharacteristic
455C2C37×#306111yescharacteristic
456C2C2×C37×#47111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3255C2semidirect
4. C37×#2960C2semidirect
5. C37×#1692C2semidirect
6. C37×#1686C2semidirect
7. C37×#1684C2semidirect
8. C37×#1682C2semidirect
9. C37×#1567C2semidirect
10. C37×#1561C2semidirect
203. #19351C37direct (N × H)
224. #3255C2×C37semidirect
227. #2960C2×C37semidirect
228. #1692C2×C37semidirect
229. #1686C2×C37semidirect
230. #1684C2×C37semidirect
231. #1682C2×C37semidirect
232. #1567C2×C37semidirect
233. #1561C2×C37semidirect
277. C37#19351direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32552
C37×#32542
C37×#31672
C37×#29602
C37×#16922
C37×#16862
C37×#16842
C37×#16822
C37×#15672
C37×#15612
C37×#15602
#1935137