Finite Group Databasebeta

← C37×#8996 #22630249

Subgroups — C37×#8996 #22630249

Order 9472.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3035C211yesmaximal, characteristic
2C37×#2925C211yesmaximal, characteristic, complemented
3C37×#1492C211yesmaximal, characteristic, complemented
4C37×#1480C211yesmaximal, characteristic, complemented
5C37×#1476C211yesmaximal, characteristic, complemented
6C37×#1301C211yesmaximal, characteristic, complemented
7C37×#1277C211yesmaximal, characteristic, complemented
8C2×#135×C37—21no—
9C37×#532C2211yescharacteristic
10C4×#41×C37C2211yescharacteristic
11C37×#464—21no—
12C37×#463—21no—
13C37×#462C411yescharacteristic
14C37×#461C411yescharacteristic
15C37×#460C411yescharacteristic
16C37×#459C411yescharacteristic
17C37×#433—22no—
18C37×#432—21no—
19C37×#431—21no—
20C37×#431C2211yescharacteristic
21C37×#423C2211yescharacteristic
22C2×C4⋊C8×C37C2211yescharacteristic
23C2×C4⋊C8×C37C2211yescharacteristic
24C37×#416—21no—
25C37×#408—21no—
26C37×#405—21no—
27C2×C4×C8×C37C2211yescharacteristic
28C37×Q8⋊C8—21no—
29C37×D4⋊C8—21no—
30C37×D4⋊C8—21no—
31C37×D4⋊C8—21no—
32C37×D4⋊C8—22no—
33C2×#41×C37—21no—
34C2×#41×C37D411yescharacteristic
35#135×C37—42no—
36#135×C37—42no—
37C2×Q16×C37—21no—
38C2×SD16×C37—21no—
39C2×SD16×C37—21no—
40C2×D8×C37—21no—
41C2×M16×C37—21no—
42C22×C8×C37—21no—
43C22×C8×C37—21no—
44C22×C8×C37—21no—
45C4⋊Q8×C37C2×C411yescharacteristic
46#127×C37C2×C411yescharacteristic
47#124×C37—21no—
48#121×C37—21no—
49#121×C37—21no—
50C4×Q8×C37C2×C411yescharacteristic
51C4×Q8×C37D411yescharacteristic
52C4×D4×C37—21no—
53C4×D4×C37—21no—
54C4×D4×C37—21no—
55C4×D4×C37—21no—
56C4×D4×C37C2×C411yescharacteristic
57C4×D4×C37D411yescharacteristic
58#117×C37—21no—
59#117×C37D411yescharacteristic
60C2×C42×C37—21no—
61C2×C42×C37C2311yescharacteristic
62C4⋊C8×C37—21no—
63C4⋊C8×C37—21no—
64C4⋊C8×C37—21no—
65C4⋊C8×C37—21no—
66C4⋊C8×C37C2×C411yescharacteristic
67C4⋊C8×C37C2×C411yescharacteristic
68C4⋊C8×C37D411yescharacteristic
69C4⋊C8×C37D411yescharacteristic
70C4⋊C8×C37D412yes—
71#103×C37—21no—
72#103×C37—21no—
73#102×C37—21no—
74#102×C37—21no—
75C22⋊C8×C37—22no—
76C22⋊C8×C37—22no—
77C22⋊C8×C37—21no—
78#97×C37—22no—
79C4×C8×C37—22no—
80C4×C8×C37—21no—
81C4×C8×C37—21no—
82C4×C8×C37—21no—
83#41×C37—21no—
84#41×C37—21no—
85#41×C37—21no—
86#41×C37—21no—
87#41×C37—41no—
88#41×C37—41no—
89#41×C37—41no—
90#41×C37—41no—
91C2×Q8×C37—21no—
92C2×Q8×C37C22⋊C411yescharacteristic
93C2×D4×C37—21no—
94C2×D4×C37—21no—
95C2×D4×C37—21no—
96C2×D4×C37—21no—
97C2×D4×C37—41no—
98C2×D4×C37C22⋊C411yescharacteristic
99C22×C4×C37—21no—
100C22×C4×C37—21no—
101C22×C4×C37—21no—
102C22×C4×C37—41no—
103C22×C4×C37C2×D411yescharacteristic
104C22×C4×C37#4111yescharacteristic
105C22×C4×C37#4111yescharacteristic
106Q16×C37—42no—
107SD16×C37—42no—
108SD16×C37—42no—
109D8×C37—42no—
110M16×C37—41no—
111M16×C37—41no—
112C2×C8×C37—22no—
113C2×C8×C37—21no—
114C2×C8×C37—21no—
115C2×C8×C37—21no—
116C2×C8×C37—22no—
117C2×C8×C37—21no—
118C2×C8×C37—41no—
119C2×C8×C37—41no—
120C2×C8×C37—41no—
121C2×C8×C37—41no—
122C2×C8×C37—41no—
123C2×C8×C37—41no—
124C2×C8×C37—41no—
125C4⋊C4×C37—21no—
126C4⋊C4×C37—21no—
127C4⋊C4×C37—21no—
128C4⋊C4×C37—21no—
129C4⋊C4×C37C22⋊C411yescharacteristic
130C4⋊C4×C37C22⋊C411yescharacteristic
131C22⋊C4×C37—21no—
132C22⋊C4×C37—21no—
133C22⋊C4×C37—21no—
134C22⋊C4×C37—41no—
135C22⋊C4×C37—41no—
136C42×C37—21no—
137C42×C37—21no—
138C42×C37—21no—
139C42×C37C22×C411yescharacteristic
140C42×C37C2×D411yescharacteristic
141C42×C37C2×D411yescharacteristic
142C42×C37C2×D411yescharacteristic
143C23×C37—21no—
144C23×C37—41no—
145C23×C37#12311yescharacteristic
146Q8×C37—21no—
147Q8×C37—21no—
148Q8×C37—41no—
149Q8×C37—41no—
150D4×C37—21no—
151D4×C37—21no—
152D4×C37—42no—
153D4×C37—41no—
154D4×C37—41no—
155D4×C37—41no—
156D4×C37—41no—
157D4×C37—41no—
158D4×C37—41no—
159D4×C37—81no—
160D4×C37—81no—
161C2×C4×C37—21no—
162C2×C4×C37—21no—
163C2×C4×C37—21no—
164C2×C4×C37—21no—
165C2×C4×C37—21no—
166C2×C4×C37—41no—
167C2×C4×C37—41no—
168C2×C4×C37—41no—
169C2×C4×C37—41no—
170C2×C4×C37—41no—
171C2×C4×C37—41no—
172C2×C4×C37—81no—
173C2×C4×C37—81no—
174C2×C4×C37—81no—
175C2×C4×C37C2×C22⋊C411yescharacteristic
176C2×C4×C37C4×D411yescharacteristic
177C2×C4×C37C4×D411yescharacteristic
178C2×C4×C37#12011yescharacteristic
179C2×C4×C37#12111yescharacteristic
180C2×C4×C37#12111yescharacteristic
181C2×C4×C37#13511yescharacteristic
182C2×C4×C37#13511yescharacteristic
183C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
185C8×C37—42no—
186C8×C37—41no—
187C8×C37—41no—
188C8×C37—41no—
189C8×C37—41no—
190C8×C37—42no—
191C8×C37—81no—
192#8996C3711yesmaximal, characteristic, direct product factor, Sylow
193C22×C37—21no—
194C22×C37—21no—
195C22×C37—41no—
196C22×C37—41no—
197C22×C37—41no—
198C22×C37—81no—
199C22×C37—81no—
200C22×C37—81no—
201C22×C37#38611yescharacteristic
202C22×C37#48211yescharacteristic
203C22×C37#48211yescharacteristic
204C4×C37—21no—
205C4×C37—21no—
206C4×C37—21no—
207C4×C37—41no—
208C4×C37—41no—
209C4×C37—41no—
210C4×C37—81no—
211C4×C37#41611yescharacteristic
212C4×C37#41811yescharacteristic
213C4×C37#44311yescharacteristic
214C4×C37#44411yescharacteristic
215C4×C37#44911yescharacteristic
216C4×C37#44911yescharacteristic
217#3035C2×C3711yescharacteristic
218#2925C2×C3711yescharacteristic, complemented
219#1492C2×C3711yescharacteristic, complemented
220#1480C2×C3711yescharacteristic, complemented
221#1476C2×C3711yescharacteristic, complemented
222#1301C2×C3711yescharacteristic, complemented
223#1277C2×C3711yescharacteristic, complemented
224C2×C37—21no—
225C2×C37—21no—
226C2×C37—81no—
227C2×C37—161no—
228C2×C37#187511yescharacteristic
229C2×C37#187611yescharacteristic
230C2×C37#188111yescharacteristic
231C2×#135—21no—
232#532C22×C3711yescharacteristic
233C4×#41C22×C3711yescharacteristic
234#464—21no—
235#463—21no—
236#462C4×C3711yescharacteristic
237#461C4×C3711yescharacteristic
238#460C4×C3711yescharacteristic
239#459C4×C3711yescharacteristic
240#433—22no—
241#432—21no—
242#431—21no—
243#431C22×C3711yescharacteristic
244#423C22×C3711yescharacteristic
245C2×C4⋊C8C22×C3711yescharacteristic
246C2×C4⋊C8C22×C3711yescharacteristic
247#416—21no—
248#408—21no—
249#405—21no—
250C2×C4×C8C22×C3711yescharacteristic
251Q8⋊C8—21no—
252D4⋊C8—21no—
253D4⋊C8—21no—
254D4⋊C8—21no—
255D4⋊C8—22no—
256C37#899611yescharacteristic, direct product factor, Sylow
257C2×#41—21no—
258C2×#41D4×C3711yescharacteristic
259#135—42no—
260#135—42no—
261C2×Q16—21no—
262C2×SD16—21no—
263C2×SD16—21no—
264C2×D8—21no—
265C2×M16—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C4⋊Q8C2×C4×C3711yescharacteristic
270#127C2×C4×C3711yescharacteristic
271#124—21no—
272#121—21no—
273#121—21no—
274C4×Q8C2×C4×C3711yescharacteristic
275C4×Q8D4×C3711yescharacteristic
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4C2×C4×C3711yescharacteristic
281C4×D4D4×C3711yescharacteristic
282#117—21no—
283#117D4×C3711yescharacteristic
284C2×C42—21no—
285C2×C42C23×C3711yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8C2×C4×C3711yescharacteristic
291C4⋊C8C2×C4×C3711yescharacteristic
292C4⋊C8D4×C3711yescharacteristic
293C4⋊C8D4×C3711yescharacteristic
294C4⋊C8D4×C3712yes—
295#103—21no—
296#103—21no—
297#102—21no—
298#102—21no—
299C22⋊C8—22no—
300C22⋊C8—22no—
301C22⋊C8—21no—
302#97—22no—
303C4×C8—22no—
304C4×C8—21no—
305C4×C8—21no—
306C4×C8—21no—
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—41no—
312#41—41no—
313#41—41no—
314#41—41no—
315C2×Q8—21no—
316C2×Q8C22⋊C4×C3711yescharacteristic
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4C22⋊C4×C3711yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4C2×D4×C3711yescharacteristic
328C22×C4#41×C3711yescharacteristic
329C22×C4#41×C3711yescharacteristic
330Q16—42no—
331SD16—42no—
332SD16—42no—
333D8—42no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—22no—
341C2×C8—21no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4C22⋊C4×C3711yescharacteristic
354C4⋊C4C22⋊C4×C3711yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C42—21no—
361C42—21no—
362C42—21no—
363C42C22×C4×C3711yescharacteristic
364C42C2×D4×C3711yescharacteristic
365C42C2×D4×C3711yescharacteristic
366C42C2×D4×C3711yescharacteristic
367C23—21no—
368C23—41no—
369C23#123×C3711yescharacteristic
370Q8—21no—
371Q8—21no—
372Q8—41no—
373Q8—41no—
374D4—21no—
375D4—21no—
376D4—42no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—41no—
381D4—41no—
382D4—41no—
383D4—81no—
384D4—81no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4C2×C22⋊C4×C3711yescharacteristic
400C2×C4C4×D4×C3711yescharacteristic
401C2×C4C4×D4×C3711yescharacteristic
402C2×C4#120×C3711yescharacteristic
403C2×C4#121×C3711yescharacteristic
404C2×C4#121×C3711yescharacteristic
405C2×C4#135×C3711yescharacteristic
406C2×C4#135×C3711yescharacteristic
407C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
408C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
409C8—42no—
410C8—41no—
411C8—41no—
412C8—41no—
413C8—41no—
414C8—42no—
415C8—81no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22C37×#38611yescharacteristic
425C22C37×#48211yescharacteristic
426C22C37×#48211yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4C37×#41611yescharacteristic
435C4C37×#41811yescharacteristic
436C4C37×#44311yescharacteristic
437C4C37×#44411yescharacteristic
438C4C37×#44911yescharacteristic
439C4C37×#44911yescharacteristic
440C2—21no—
441C2—21no—
442C2—81no—
443C2—161no—
444C2C37×#187511yescharacteristic
445C2C37×#187611yescharacteristic
446C2C37×#188111yescharacteristic
subgroupG/H
centerC2×C4×C37#120
commutatorC42C22×C4×C37
Frattini, cosocleC2×C42C23×C37
socleC22×C37#386
prime radicalC37×#3035C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2925C2semidirect
3. C37×#1492C2semidirect
4. C37×#1480C2semidirect
5. C37×#1476C2semidirect
6. C37×#1301C2semidirect
7. C37×#1277C2semidirect
192. #8996C37direct (N × H)
218. #2925C2×C37semidirect
219. #1492C2×C37semidirect
220. #1480C2×C37semidirect
221. #1476C2×C37semidirect
222. #1301C2×C37semidirect
223. #1277C2×C37semidirect
256. C37#8996direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#30352
C37×#29252
C37×#14922
C37×#14802
C37×#14762
C37×#13012
C37×#12772
#899637