Finite Group Databasebeta

← C37×#19527 #22640780

Subgroups — C37×#19527 #22640780

Order 9472.

574 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
1C37×#3255C211yesmaximal, characteristic, complemented
2C37×#3246C211yesmaximal, characteristic
3C37×#3210C211yesmaximal, characteristic
4C37×#2985C211yesmaximal, characteristic, complemented
5C37×#1700C212yesmaximal, complemented
6C37×#1686C212yesmaximal, complemented
7C37×#1682C212yesmaximal, complemented
8C37×#1670C212yesmaximal, complemented
9C37×#1571C211yesmaximal, characteristic, complemented
10C37×#1557C211yesmaximal, characteristic
11C37×#1552C211yesmaximal, characteristic, complemented
12C37×#533C2211yescharacteristic
13C37×#533C2211yescharacteristic
14C37×#532C2211yescharacteristic
15C37×#494C2211yescharacteristic
16C37×#492C2211yescharacteristic
17C37×#487C2211yescharacteristic
18C37×#486C2211yescharacteristic
19C37×#476—21no—
20C37×#475—21no—
21C37×#475C2212yes—
22C37×#475C2212yes—
23C37×#470—22no—
24C37×#465—22no—
25C37×#464—22no—
26C37×#462—21no—
27C37×#462C2212yes—
28C37×#461—21no—
29C37×#460C2212yes—
30C37×#452—22no—
31C37×#446—22no—
32C37×#446C2212yes—
33C8×Q8×C37C2212yes—
34C37×#433—22no—
35C37×#432C2211yescharacteristic
36C37×#431C2211yescharacteristic
37C37×#423C2211yescharacteristic
38C2×C4⋊C8×C37C2211yescharacteristic
39C37×#335C2212yes—
40C37×#335C2212yes—
41C37×#332C2212yes—
42C37×#332C2212yes—
43C37×#332C2212yes—
44C37×#331C2212yes—
45C2×#41×C37—21no—
46C2×Q16×C37—22no—
47C2×Q16×C37—22no—
48C2×SD16×C37—22no—
49C2×SD16×C37—22no—
50C2×M16×C37—21no—
51C22×C8×C37—21no—
52C4⋊Q8×C37D411yescharacteristic
53C4⋊Q8×C37D411yescharacteristic
54C4⋊Q8×C37C2311yescharacteristic
55C4⋊Q8×C37C2311yescharacteristic
56C4⋊Q8×C37C2311yescharacteristic
57#127×C37C2311yescharacteristic
58#125×C37—21no—
59#125×C37—21no—
60#124×C37—21no—
61C22⋊Q8×C37—21no—
62C22⋊Q8×C37—21no—
63C22⋊Q8×C37—21no—
64C22⋊Q8×C37D412yes—
65#121×C37—21no—
66#121×C37—21no—
67C4×Q8×C37—21no—
68C4×Q8×C37—21no—
69C4×Q8×C37—21no—
70C4×Q8×C37C2312yes—
71C4×D4×C37—21no—
72C4×D4×C37—21no—
73#117×C37—21no—
74#117×C37—21no—
75C2×C42×C37C2311yescharacteristic
76#106×C37—22no—
77#106×C37—22no—
78C4⋊C8×C37—22no—
79C4⋊C8×C37—22no—
80C4⋊C8×C37—21no—
81C4⋊C8×C37—21no—
82C4⋊C8×C37D412yes—
83C4⋊C8×C37C2312yes—
84C4⋊C8×C37C2312yes—
85C4⋊C8×C37C2312yes—
86#103×C37—22no—
87#103×C37—22no—
88#103×C37—22no—
89#103×C37—22no—
90#102×C37—22no—
91#102×C37—22no—
92C22⋊C8×C37—21no—
93C22⋊C8×C37D412yes—
94#97×C37—22no—
95#97×C37—21no—
96C4×C8×C37—22no—
97C4×C8×C37C2311yescharacteristic
98C4×C8×C37C2311yescharacteristic
99#41×C37—82no—
100C2×Q8×C37—21no—
101C2×Q8×C37—21no—
102C2×Q8×C37—21no—
103C2×Q8×C37—21no—
104C2×Q8×C37C2×D412yes—
105C2×D4×C37—21no—
106C2×D4×C37—21no—
107C2×D4×C37—21no—
108C2×D4×C37—41no—
109C22×C4×C37—41no—
110C22×C4×C37C2×D411yescharacteristic
111C22×C4×C37C2×D411yescharacteristic
112C22×C4×C37#4111yescharacteristic
113Q16×C37—82no—
114Q16×C37—82no—
115SD16×C37—82no—
116SD16×C37—82no—
117M16×C37—81no—
118C2×C8×C37—22no—
119C2×C8×C37—22no—
120C2×C8×C37—22no—
121C2×C8×C37—81no—
122C2×C8×C37C2×D412yes—
123C2×C8×C37C2×D412yes—
124C4⋊C4×C37—21no—
125C4⋊C4×C37—21no—
126C4⋊C4×C37—21no—
127C4⋊C4×C37—22no—
128C4⋊C4×C37—22no—
129C4⋊C4×C37—21no—
130C4⋊C4×C37—21no—
131C4⋊C4×C37—21no—
132C4⋊C4×C37—21no—
133C4⋊C4×C37—21no—
134C4⋊C4×C37—21no—
135C4⋊C4×C37—41no—
136C4⋊C4×C37—41no—
137C4⋊C4×C37C2×D412yes—
138C22⋊C4×C37—22no—
139C22⋊C4×C37—41no—
140C22⋊C4×C37—41no—
141C22⋊C4×C37—41no—
142C42×C37—22no—
143C42×C37—41no—
144C42×C37C2×D411yescharacteristic
145C42×C37C2×D411yescharacteristic
146C42×C37#4111yescharacteristic
147C42×C37C2411yescharacteristic
148C23×C37—41no—
149C23×C37#12111yescharacteristic
150Q8×C37—22no—
151Q8×C37—22no—
152Q8×C37—41no—
153Q8×C37—42no—
154Q8×C37—42no—
155Q8×C37—41no—
156Q8×C37—81no—
157D4×C37—41no—
158D4×C37—42no—
159D4×C37—41no—
160D4×C37—81no—
161D4×C37—82no—
162C2×C4×C37—21no—
163C2×C4×C37—22no—
164C2×C4×C37—21no—
165C2×C4×C37—22no—
166C2×C4×C37—22no—
167C2×C4×C37—41no—
168C2×C4×C37—41no—
169C2×C4×C37—41no—
170C2×C4×C37—41no—
171C2×C4×C37—82no—
172C2×C4×C37#12111yescharacteristic
173C2×C4×C37#12111yescharacteristic
174C2×C4×C37#12111yescharacteristic
175C2×C4×C37C22×D411yescharacteristic
176C2×C4×C37C22×D411yescharacteristic
177C2×C4×C37C2×#4111yescharacteristic
178C8×C37—22no—
179C8×C37—22no—
180C8×C37—42no—
181C8×C37—42no—
182C8×C37—42no—
183#19527C3711yesmaximal, characteristic, direct product factor, Sylow
184C22×C37—21no—
185C22×C37—21no—
186C22×C37—21no—
187C22×C37—81no—
188C22×C37—81no—
189C22×C37—81no—
190C22×C37C2×#12111yescharacteristic
191C4×C37—21no—
192C4×C37—21no—
193C4×C37—21no—
194C4×C37—21no—
195C4×C37—42no—
196C4×C37—42no—
197C4×C37—81no—
198C4×C37—81no—
199C4×C37—81no—
200C4×C37#57611yescharacteristic
201C4×C37#57712yes—
202C4×C37#57811yescharacteristic
203#3255C2×C3711yescharacteristic, complemented
204#3246C2×C3711yescharacteristic
205#3210C2×C3711yescharacteristic
206#2985C2×C3711yescharacteristic, complemented
207#1700C2×C3712yescomplemented
208#1686C2×C3712yescomplemented
209#1682C2×C3712yescomplemented
210#1670C2×C3712yescomplemented
211#1571C2×C3711yescharacteristic, complemented
212#1557C2×C3711yescharacteristic
213#1552C2×C3711yescharacteristic, complemented
214C2×C37—41no—
215C2×C37—161no—
216C2×C37#304311yescharacteristic
217C2×C37#306111yescharacteristic
218C2×C37#306911yescharacteristic
219#533C22×C3711yescharacteristic
220#533C22×C3711yescharacteristic
221#532C22×C3711yescharacteristic
222#494C22×C3711yescharacteristic
223#492C22×C3711yescharacteristic
224#487C22×C3711yescharacteristic
225#486C22×C3711yescharacteristic
226#476—21no—
227#475—21no—
228#475C22×C3712yes—
229#475C22×C3712yes—
230#470—22no—
231#465—22no—
232#464—22no—
233#462—21no—
234#462C22×C3712yes—
235#461—21no—
236#460C22×C3712yes—
237#452—22no—
238#446—22no—
239#446C22×C3712yes—
240C8×Q8C22×C3712yes—
241#433—22no—
242#432C22×C3711yescharacteristic
243#431C22×C3711yescharacteristic
244#423C22×C3711yescharacteristic
245C2×C4⋊C8C22×C3711yescharacteristic
246#335C22×C3712yes—
247#335C22×C3712yes—
248#332C22×C3712yes—
249#332C22×C3712yes—
250#332C22×C3712yes—
251#331C22×C3712yes—
252C37#1952711yescharacteristic, direct product factor, Sylow
253C2×#41—21no—
254C2×Q16—22no—
255C2×Q16—22no—
256C2×SD16—22no—
257C2×SD16—22no—
258C2×M16—21no—
259C22×C8—21no—
260C4⋊Q8D4×C3711yescharacteristic
261C4⋊Q8D4×C3711yescharacteristic
262C4⋊Q8C23×C3711yescharacteristic
263C4⋊Q8C23×C3711yescharacteristic
264C4⋊Q8C23×C3711yescharacteristic
265#127C23×C3711yescharacteristic
266#125—21no—
267#125—21no—
268#124—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8D4×C3712yes—
273#121—21no—
274#121—21no—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×Q8—21no—
278C4×Q8C23×C3712yes—
279C4×D4—21no—
280C4×D4—21no—
281#117—21no—
282#117—21no—
283C2×C42C23×C3711yescharacteristic
284#106—22no—
285#106—22no—
286C4⋊C8—22no—
287C4⋊C8—22no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8D4×C3712yes—
291C4⋊C8C23×C3712yes—
292C4⋊C8C23×C3712yes—
293C4⋊C8C23×C3712yes—
294#103—22no—
295#103—22no—
296#103—22no—
297#103—22no—
298#102—22no—
299#102—22no—
300C22⋊C8—21no—
301C22⋊C8D4×C3712yes—
302#97—22no—
303#97—21no—
304C4×C8—22no—
305C4×C8C23×C3711yescharacteristic
306C4×C8C23×C3711yescharacteristic
307#41—82no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8C2×D4×C3712yes—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C22×C4—41no—
318C22×C4C2×D4×C3711yescharacteristic
319C22×C4C2×D4×C3711yescharacteristic
320C22×C4#41×C3711yescharacteristic
321Q16—82no—
322Q16—82no—
323SD16—82no—
324SD16—82no—
325M16—81no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—81no—
330C2×C8C2×D4×C3712yes—
331C2×C8C2×D4×C3712yes—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4C2×D4×C3712yes—
346C22⋊C4—22no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C42—22no—
351C42—41no—
352C42C2×D4×C3711yescharacteristic
353C42C2×D4×C3711yescharacteristic
354C42#41×C3711yescharacteristic
355C42C24×C3711yescharacteristic
356C23—41no—
357C23#121×C3711yescharacteristic
358Q8—22no—
359Q8—22no—
360Q8—41no—
361Q8—42no—
362Q8—42no—
363Q8—41no—
364Q8—81no—
365D4—41no—
366D4—42no—
367D4—41no—
368D4—81no—
369D4—82no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—82no—
380C2×C4#121×C3711yescharacteristic
381C2×C4#121×C3711yescharacteristic
382C2×C4#121×C3711yescharacteristic
383C2×C4C22×D4×C3711yescharacteristic
384C2×C4C22×D4×C3711yescharacteristic
385C2×C4C2×#41×C3711yescharacteristic
386C8—22no—
387C8—22no—
388C8—42no—
389C8—42no—
390C8—42no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22C2×#121×C3711yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4C37×#57611yescharacteristic
408C4C37×#57712yes—
409C4C37×#57811yescharacteristic
410C2—41no—
411C2—161no—
412C2C37×#304311yescharacteristic
413C2C37×#306111yescharacteristic
414C2C37×#306911yescharacteristic
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×#2985C2semidirect
5. C37×#1700C2semidirect
6. C37×#1686C2semidirect
7. C37×#1682C2semidirect
8. C37×#1670C2semidirect
9. C37×#1571C2semidirect
11. C37×#1552C2semidirect
183. #19527C37direct (N × H)
203. #3255C2×C37semidirect
206. #2985C2×C37semidirect
207. #1700C2×C37semidirect
208. #1686C2×C37semidirect
209. #1682C2×C37semidirect
210. #1670C2×C37semidirect
211. #1571C2×C37semidirect
213. #1552C2×C37semidirect
252. C37#19527direct (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×#32462
C37×#32102
C37×#29852
C37×#17002
C37×#16862
C37×#16822
C37×#16702
C37×#15712
C37×#15572
C37×#15522
#1952737