Finite Group Databasebeta

← C37×#19570 #22640823

Subgroups — C37×#19570 #22640823

Order 9472.

584 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3254C211yesmaximal, characteristic
2C37×#3227C211yesmaximal, characteristic
3C37×#3209C211yesmaximal, characteristic, complemented
4C37×#2986C211yesmaximal, characteristic, complemented
5C37×#1702C212yesmaximal, complemented
6C37×#1692C212yesmaximal, complemented
7C37×#1682C212yesmaximal, complemented
8C37×#1672C212yesmaximal, complemented
9C37×#1574C211yesmaximal, characteristic, complemented
10C37×#1546C211yesmaximal, characteristic, complemented
11C37×#1543C211yesmaximal, characteristic
12C37×#533C2211yescharacteristic
13C37×#532C2211yescharacteristic
14C2×C4⋊Q8×C37C2211yescharacteristic
15C37×#498C2212yes—
16C37×#494—21no—
17C37×#487—21no—
18C37×#486C2212yes—
19C37×#481—22no—
20C37×#477C2212yes—
21C37×#476—21no—
22C37×#476—21no—
23C37×#474—21no—
24C37×#468—22no—
25C37×#462C2212yes—
26C37×#462C2212yes—
27C37×#461—21no—
28C37×#460C2212yes—
29C37×#451—22no—
30C37×#446—21no—
31C37×#446C2212yes—
32C8×Q8×C37—21no—
33C8×Q8×C37C2212yes—
34C37×#433—22no—
35C37×#431C2211yescharacteristic
36C37×#431C2211yescharacteristic
37C37×#431C2211yescharacteristic
38C37×#423C2211yescharacteristic
39C37×#335C2212yes—
40C37×#334C2212yes—
41C37×#333C2211yescharacteristic
42C37×#333C2211yescharacteristic
43C37×#332C2212yes—
44C37×#332C2212yes—
45C37×#331C2211yescharacteristic
46C37×#331C2211yescharacteristic
47C2×#41×C37—21no—
48C22×Q8×C37—21no—
49C2×Q16×C37—22no—
50C2×Q16×C37—22no—
51C2×SD16×C37—22no—
52C2×M16×C37—21no—
53C4⋊Q8×C37—21no—
54C4⋊Q8×C37—21no—
55C4⋊Q8×C37—21no—
56C4⋊Q8×C37D411yescharacteristic
57C4⋊Q8×C37D411yescharacteristic
58C4⋊Q8×C37C2312yes—
59C4⋊Q8×C37C2311yescharacteristic
60#127×C37C2311yescharacteristic
61#125×C37—21no—
62#124×C37—21no—
63C22⋊Q8×C37—21no—
64C22⋊Q8×C37D412yes—
65#121×C37—21no—
66#121×C37—21no—
67C4×Q8×C37—21no—
68C4×Q8×C37C2312yes—
69C4×D4×C37—21no—
70C4×D4×C37—21no—
71#117×C37—21no—
72C2×C4⋊C4×C37—21no—
73C2×C4⋊C4×C37—21no—
74C2×C42×C37C2311yescharacteristic
75#107×C37—22no—
76#106×C37—22no—
77#106×C37—22no—
78C4⋊C8×C37—22no—
79C4⋊C8×C37—22no—
80C4⋊C8×C37—21no—
81C4⋊C8×C37D411yescharacteristic
82C4⋊C8×C37D411yescharacteristic
83C4⋊C8×C37C2311yescharacteristic
84C4⋊C8×C37C2311yescharacteristic
85C4⋊C8×C37C2311yescharacteristic
86C4⋊C8×C37C2311yescharacteristic
87C4⋊C8×C37C2312yes—
88#103×C37—22no—
89#103×C37—22no—
90#103×C37—22no—
91#102×C37—22no—
92#102×C37—22no—
93#102×C37—22no—
94C22⋊C8×C37—21no—
95C22⋊C8×C37—21no—
96C22⋊C8×C37D412yes—
97#97×C37—22no—
98C4×C8×C37—22no—
99C4×C8×C37—21no—
100C4×C8×C37—21no—
101C4×C8×C37C2312yes—
102#41×C37—82no—
103C2×Q8×C37—21no—
104C2×Q8×C37—22no—
105C2×Q8×C37—21no—
106C2×Q8×C37—41no—
107C2×Q8×C37—81no—
108C2×Q8×C37—81no—
109C2×Q8×C37C2×D412yes—
110C2×D4×C37—21no—
111C2×D4×C37—21no—
112C2×D4×C37—21no—
113C2×D4×C37—41no—
114C22×C4×C37—41no—
115C22×C4×C37—41no—
116C22×C4×C37C2×D411yescharacteristic
117C22×C4×C37C2×D411yescharacteristic
118C22×C4×C37#4111yescharacteristic
119Q16×C37—82no—
120Q16×C37—82no—
121SD16×C37—82no—
122M16×C37—81no—
123C2×C8×C37—21no—
124C2×C8×C37—21no—
125C2×C8×C37—21no—
126C2×C8×C37—21no—
127C2×C8×C37—22no—
128C2×C8×C37C2×D412yes—
129C2×C8×C37C2×D412yes—
130C4⋊C4×C37—21no—
131C4⋊C4×C37—21no—
132C4⋊C4×C37—21no—
133C4⋊C4×C37—22no—
134C4⋊C4×C37—22no—
135C4⋊C4×C37—22no—
136C4⋊C4×C37—21no—
137C4⋊C4×C37—21no—
138C4⋊C4×C37—22no—
139C4⋊C4×C37—41no—
140C4⋊C4×C37—41no—
141C4⋊C4×C37C2×D412yes—
142C22⋊C4×C37—22no—
143C22⋊C4×C37—41no—
144C22⋊C4×C37—41no—
145C42×C37—22no—
146C42×C37C2×D411yescharacteristic
147C42×C37C2×D411yescharacteristic
148C42×C37#4111yescharacteristic
149C42×C37C2411yescharacteristic
150C23×C37—41no—
151C23×C37#12111yescharacteristic
152Q8×C37—22no—
153Q8×C37—22no—
154Q8×C37—42no—
155Q8×C37—42no—
156Q8×C37—42no—
157Q8×C37—81no—
158Q8×C37—82no—
159D4×C37—41no—
160D4×C37—41no—
161D4×C37—41no—
162D4×C37—41no—
163D4×C37—81no—
164D4×C37—82no—
165C2×C4×C37—21no—
166C2×C4×C37—21no—
167C2×C4×C37—21no—
168C2×C4×C37—21no—
169C2×C4×C37—22no—
170C2×C4×C37—22no—
171C2×C4×C37—22no—
172C2×C4×C37—41no—
173C2×C4×C37—42no—
174C2×C4×C37—82no—
175C2×C4×C37—82no—
176C2×C4×C37#12111yescharacteristic
177C2×C4×C37#12111yescharacteristic
178C2×C4×C37#12111yescharacteristic
179C2×C4×C37C22×D411yescharacteristic
180C2×C4×C37C22×D411yescharacteristic
181C2×C4×C37C2×#4111yescharacteristic
182C8×C37—22no—
183C8×C37—22no—
184C8×C37—42no—
185C8×C37—41no—
186C8×C37—41no—
187C8×C37—41no—
188C8×C37—41no—
189#19570C3711yesmaximal, characteristic, direct product factor, Sylow
190C22×C37—21no—
191C22×C37—21no—
192C22×C37—21no—
193C22×C37—81no—
194C22×C37—81no—
195C22×C37—81no—
196C22×C37C2×#12111yescharacteristic
197C4×C37—21no—
198C4×C37—21no—
199C4×C37—21no—
200C4×C37—42no—
201C4×C37—42no—
202C4×C37—82no—
203C4×C37—81no—
204C4×C37#47112yes—
205C4×C37#57611yescharacteristic
206C4×C37#57711yescharacteristic
207C4×C37#57811yescharacteristic
208C4×C37#57811yescharacteristic
209#3254C2×C3711yescharacteristic
210#3227C2×C3711yescharacteristic
211#3209C2×C3711yescharacteristic, complemented
212#2986C2×C3711yescharacteristic, complemented
213#1702C2×C3712yescomplemented
214#1692C2×C3712yescomplemented
215#1682C2×C3712yescomplemented
216#1672C2×C3712yescomplemented
217#1574C2×C3711yescharacteristic, complemented
218#1546C2×C3711yescharacteristic, complemented
219#1543C2×C3711yescharacteristic
220C2×C37—41no—
221C2×C37—161no—
222C2×C37#304411yescharacteristic
223C2×C37#306211yescharacteristic
224C2×C37C2×#47111yescharacteristic
225#533C22×C3711yescharacteristic
226#532C22×C3711yescharacteristic
227C2×C4⋊Q8C22×C3711yescharacteristic
228#498C22×C3712yes—
229#494—21no—
230#487—21no—
231#486C22×C3712yes—
232#481—22no—
233#477C22×C3712yes—
234#476—21no—
235#476—21no—
236#474—21no—
237#468—22no—
238#462C22×C3712yes—
239#462C22×C3712yes—
240#461—21no—
241#460C22×C3712yes—
242#451—22no—
243#446—21no—
244#446C22×C3712yes—
245C8×Q8—21no—
246C8×Q8C22×C3712yes—
247#433—22no—
248#431C22×C3711yescharacteristic
249#431C22×C3711yescharacteristic
250#431C22×C3711yescharacteristic
251#423C22×C3711yescharacteristic
252#335C22×C3712yes—
253#334C22×C3712yes—
254#333C22×C3711yescharacteristic
255#333C22×C3711yescharacteristic
256#332C22×C3712yes—
257#332C22×C3712yes—
258#331C22×C3711yescharacteristic
259#331C22×C3711yescharacteristic
260C37#1957011yescharacteristic, direct product factor, Sylow
261C2×#41—21no—
262C22×Q8—21no—
263C2×Q16—22no—
264C2×Q16—22no—
265C2×SD16—22no—
266C2×M16—21no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8D4×C3711yescharacteristic
271C4⋊Q8D4×C3711yescharacteristic
272C4⋊Q8C23×C3712yes—
273C4⋊Q8C23×C3711yescharacteristic
274#127C23×C3711yescharacteristic
275#125—21no—
276#124—21no—
277C22⋊Q8—21no—
278C22⋊Q8D4×C3712yes—
279#121—21no—
280#121—21no—
281C4×Q8—21no—
282C4×Q8C23×C3712yes—
283C4×D4—21no—
284C4×D4—21no—
285#117—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C42C23×C3711yescharacteristic
289#107—22no—
290#106—22no—
291#106—22no—
292C4⋊C8—22no—
293C4⋊C8—22no—
294C4⋊C8—21no—
295C4⋊C8D4×C3711yescharacteristic
296C4⋊C8D4×C3711yescharacteristic
297C4⋊C8C23×C3711yescharacteristic
298C4⋊C8C23×C3711yescharacteristic
299C4⋊C8C23×C3711yescharacteristic
300C4⋊C8C23×C3711yescharacteristic
301C4⋊C8C23×C3712yes—
302#103—22no—
303#103—22no—
304#103—22no—
305#102—22no—
306#102—22no—
307#102—22no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8D4×C3712yes—
311#97—22no—
312C4×C8—22no—
313C4×C8—21no—
314C4×C8—21no—
315C4×C8C23×C3712yes—
316#41—82no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—21no—
320C2×Q8—41no—
321C2×Q8—81no—
322C2×Q8—81no—
323C2×Q8C2×D4×C3712yes—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4C2×D4×C3711yescharacteristic
331C22×C4C2×D4×C3711yescharacteristic
332C22×C4#41×C3711yescharacteristic
333Q16—82no—
334Q16—82no—
335SD16—82no—
336M16—81no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—22no—
342C2×C8C2×D4×C3712yes—
343C2×C8C2×D4×C3712yes—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—22no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4C2×D4×C3712yes—
356C22⋊C4—22no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C42—22no—
360C42C2×D4×C3711yescharacteristic
361C42C2×D4×C3711yescharacteristic
362C42#41×C3711yescharacteristic
363C42C24×C3711yescharacteristic
364C23—41no—
365C23#121×C3711yescharacteristic
366Q8—22no—
367Q8—22no—
368Q8—42no—
369Q8—42no—
370Q8—42no—
371Q8—81no—
372Q8—82no—
373D4—41no—
374D4—41no—
375D4—41no—
376D4—41no—
377D4—81no—
378D4—82no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4#121×C3711yescharacteristic
391C2×C4#121×C3711yescharacteristic
392C2×C4#121×C3711yescharacteristic
393C2×C4C22×D4×C3711yescharacteristic
394C2×C4C22×D4×C3711yescharacteristic
395C2×C4C2×#41×C3711yescharacteristic
396C8—22no—
397C8—22no—
398C8—42no—
399C8—41no—
400C8—41no—
401C8—41no—
402C8—41no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22C2×#121×C3711yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—42no—
414C4—42no—
415C4—82no—
416C4—81no—
417C4C37×#47112yes—
418C4C37×#57611yescharacteristic
419C4C37×#57711yescharacteristic
420C4C37×#57811yescharacteristic
421C4C37×#57811yescharacteristic
422C2—41no—
423C2—161no—
424C2C37×#304411yescharacteristic
425C2C37×#306211yescharacteristic
426C2C2×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
3. C37×#3209C2semidirect
4. C37×#2986C2semidirect
5. C37×#1702C2semidirect
6. C37×#1692C2semidirect
7. C37×#1682C2semidirect
8. C37×#1672C2semidirect
9. C37×#1574C2semidirect
10. C37×#1546C2semidirect
189. #19570C37direct (N × H)
211. #3209C2×C37semidirect
212. #2986C2×C37semidirect
213. #1702C2×C37semidirect
214. #1692C2×C37semidirect
215. #1682C2×C37semidirect
216. #1672C2×C37semidirect
217. #1574C2×C37semidirect
218. #1546C2×C37semidirect
260. C37#19570direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32542
C37×#32272
C37×#32092
C37×#29862
C37×#17022
C37×#16922
C37×#16822
C37×#16722
C37×#15742
C37×#15462
C37×#15432
#1957037