Finite Group Databasebeta

← C37×#9525 #22630778

Subgroups — C37×#9525 #22630778

Order 9472.

538 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3094C211yesmaximal, characteristic
2C37×#2333C211yesmaximal, characteristic
3C37×#1826C211yesmaximal, characteristic, complemented
4C37×#1820C211yesmaximal, characteristic, complemented
5C37×#1510C211yesmaximal, characteristic
6C37×#1306C211yesmaximal, characteristic, complemented
7C37×#1284C211yesmaximal, characteristic, complemented
8C2×#121×C37C2211yescharacteristic
9C2×#117×C37C2211yescharacteristic
10C37×#482—22no—
11C37×#481C412yescomplemented
12C37×#480C412yescomplemented
13C37×#428—21no—
14C37×#418—21no—
15C37×#407C2211yescharacteristic
16C37×#407C2211yescharacteristic
17C37×#390—21no—
18C37×#388—21no—
19C37×#387—21no—
20C37×#386—21no—
21C37×#386—21no—
22C37×#381C2211yescharacteristic
23C37×#381C2211yescharacteristic
24C4×C22⋊C4×C37—21no—
25C4×C22⋊C4×C37C2211yescharacteristic
26C37×#342—21no—
27C37×#342—21no—
28C37×#339—21no—
29C37×#339—21no—
30C37×#327—22no—
31C22×D4×C37—21no—
32C22×D4×C37D411yescharacteristic
33C23×C4×C37—21no—
34C23×C4×C37C2311yescharacteristic
35C2×M16×C37—21no—
36C2×M16×C37—21no—
37#121×C37—21no—
38#121×C37—21no—
39#121×C37C2×C412yes—
40#121×C37D412yes—
41#117×C37—21no—
42#117×C37—21no—
43#117×C37—21no—
44#117×C37—21no—
45C2×C4⋊C4×C37—21no—
46C2×C4⋊C4×C37C2×C411yescharacteristic, complemented
47C2×C4⋊C4×C37C2×C411yescharacteristic, complemented
48C2×C4⋊C4×C37D411yescharacteristic
49C2×C22⋊C4×C37—21no—
50C2×C22⋊C4×C37—21no—
51C2×C22⋊C4×C37—21no—
52C2×C22⋊C4×C37—21no—
53C2×C22⋊C4×C37—21no—
54C2×C22⋊C4×C37—21no—
55C2×C22⋊C4×C37—21no—
56C2×C22⋊C4×C37D411yescharacteristic
57C2×C22⋊C4×C37D411yescharacteristic
58C2×C42×C37—21no—
59C2×C42×C37—21no—
60C2×C42×C37D411yescharacteristic
61C2×C42×C37D411yescharacteristic
62#107×C37—22no—
63#106×C37—22no—
64#102×C37—22no—
65#102×C37—22no—
66C22⋊C8×C37—21no—
67C22⋊C8×C37—21no—
68C22⋊C8×C37—21no—
69C22⋊C8×C37C2×C412yescomplemented
70#95×C37—21no—
71#95×C37—21no—
72#95×C37—21no—
73#95×C37—21no—
74#95×C37—21no—
75#95×C37—21no—
76#95×C37—21no—
77C24×C37—21no—
78C24×C37C2×D411yescharacteristic
79C2×D4×C37—22no—
80C2×D4×C37—22no—
81C2×D4×C37—21no—
82C2×D4×C37—41no—
83C2×D4×C37—41no—
84C2×D4×C37—81no—
85C2×D4×C37—81no—
86C2×D4×C37C22⋊C412yes—
87C22×C4×C37—21no—
88C22×C4×C37—21no—
89C22×C4×C37—21no—
90C22×C4×C37—21no—
91C22×C4×C37—21no—
92C22×C4×C37—21no—
93C22×C4×C37—21no—
94C22×C4×C37—41no—
95C22×C4×C37—41no—
96C22×C4×C37—42no—
97C22×C4×C37—41no—
98C22×C4×C37—81no—
99C22×C4×C37—81no—
100C22×C4×C37C22×C411yescharacteristic
101C22×C4×C37C2×D411yescharacteristic
102C22×C4×C37C2×D411yescharacteristic
103C22×C4×C37C2×D411yescharacteristic
104C22×C4×C37#4111yescharacteristic
105C22×C4×C37#4111yescharacteristic
106M16×C37—41no—
107M16×C37—41no—
108M16×C37—41no—
109M16×C37—41no—
110C2×C8×C37—22no—
111C2×C8×C37—41no—
112C4⋊C4×C37—21no—
113C4⋊C4×C37—21no—
114C4⋊C4×C37—21no—
115C4⋊C4×C37—21no—
116C4⋊C4×C37—21no—
117C4⋊C4×C37—81no—
118C4⋊C4×C37C22⋊C412yes—
119C22⋊C4×C37—22no—
120C22⋊C4×C37—22no—
121C22⋊C4×C37—42no—
122C22⋊C4×C37—42no—
123C22⋊C4×C37—41no—
124C22⋊C4×C37—41no—
125C22⋊C4×C37—41no—
126C22⋊C4×C37—41no—
127C22⋊C4×C37—41no—
128C22⋊C4×C37—41no—
129C22⋊C4×C37—81no—
130C22⋊C4×C37—81no—
131C42×C37—41no—
132C42×C37—41no—
133C42×C37—41no—
134C42×C37—41no—
135C42×C37—81no—
136C23×C37—21no—
137C23×C37—21no—
138C23×C37—22no—
139C23×C37—41no—
140C23×C37—41no—
141C23×C37—41no—
142C23×C37—41no—
143C23×C37—41no—
144C23×C37—41no—
145C23×C37—41no—
146C23×C37—41no—
147C23×C37C4×D411yescharacteristic
148C23×C37#12011yescharacteristic
149C23×C37#12111yescharacteristic
150D4×C37—42no—
151D4×C37—81no—
152D4×C37—82no—
153D4×C37—82no—
154C2×C4×C37—21no—
155C2×C4×C37—21no—
156C2×C4×C37—21no—
157C2×C4×C37—21no—
158C2×C4×C37—22no—
159C2×C4×C37—22no—
160C2×C4×C37—41no—
161C2×C4×C37—41no—
162C2×C4×C37—41no—
163C2×C4×C37—41no—
164C2×C4×C37—41no—
165C2×C4×C37—41no—
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—41no—
173C2×C4×C37—41no—
174C2×C4×C37—41no—
175C2×C4×C37—41no—
176C2×C4×C37—41no—
177C2×C4×C37—41no—
178C2×C4×C37—41no—
179C2×C4×C37—84no—
180C2×C4×C37—81no—
181C2×C4×C37—81no—
182C2×C4×C37—81no—
183C2×C4×C37—81no—
184C2×C4×C37—81no—
185C2×C4×C37C2×C22⋊C411yescharacteristic
186C2×C4×C37C4×D411yescharacteristic
187C2×C4×C37#12111yescharacteristic
188C2×C4×C37#12311yescharacteristic
189C8×C37—42no—
190C8×C37—81no—
191#9525C3711yesmaximal, characteristic, direct product factor, Sylow
192C22×C37—21no—
193C22×C37—21no—
194C22×C37—21no—
195C22×C37—21no—
196C22×C37—21no—
197C22×C37—21no—
198C22×C37—21no—
199C22×C37—21no—
200C22×C37—42no—
201C22×C37—42no—
202C22×C37—42no—
203C22×C37—81no—
204C22×C37—81no—
205C22×C37—81no—
206C22×C37—81no—
207C22×C37—81no—
208C22×C37—81no—
209C22×C37#38611yescharacteristic
210C22×C37#45811yescharacteristic
211C22×C37#45811yescharacteristic
212C4×C37—21no—
213C4×C37—21no—
214C4×C37—21no—
215C4×C37—21no—
216C4×C37—42no—
217C4×C37—42no—
218C4×C37—81no—
219C4×C37—81no—
220C4×C37—81no—
221C4×C37—81no—
222C4×C37—81no—
223C4×C37—161no—
224#3094C2×C3711yescharacteristic
225#2333C2×C3711yescharacteristic
226#1826C2×C3711yescharacteristic, complemented
227#1820C2×C3711yescharacteristic, complemented
228#1510C2×C3711yescharacteristic
229#1306C2×C3711yescharacteristic, complemented
230#1284C2×C3711yescharacteristic, complemented
231C2×C37—21no—
232C2×C37—21no—
233C2×C37—41no—
234C2×C37—41no—
235C2×C37—82no—
236C2×C37#189011yescharacteristic
237C2×C37#190411yescharacteristic
238C2×C37#190611yescharacteristic
239C2×#121C22×C3711yescharacteristic
240C2×#117C22×C3711yescharacteristic
241#482—22no—
242#481C4×C3712yescomplemented
243#480C4×C3712yescomplemented
244#428—21no—
245#418—21no—
246#407C22×C3711yescharacteristic
247#407C22×C3711yescharacteristic
248#390—21no—
249#388—21no—
250#387—21no—
251#386—21no—
252#386—21no—
253#381C22×C3711yescharacteristic
254#381C22×C3711yescharacteristic
255C4×C22⋊C4—21no—
256C4×C22⋊C4C22×C3711yescharacteristic
257#342—21no—
258#342—21no—
259#339—21no—
260#339—21no—
261#327—22no—
262C37#952511yescharacteristic, direct product factor, Sylow
263C22×D4—21no—
264C22×D4D4×C3711yescharacteristic
265C23×C4—21no—
266C23×C4C23×C3711yescharacteristic
267C2×M16—21no—
268C2×M16—21no—
269#121—21no—
270#121—21no—
271#121C2×C4×C3712yes—
272#121D4×C3712yes—
273#117—21no—
274#117—21no—
275#117—21no—
276#117—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4C2×C4×C3711yescharacteristic, complemented
279C2×C4⋊C4C2×C4×C3711yescharacteristic, complemented
280C2×C4⋊C4D4×C3711yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4D4×C3711yescharacteristic
289C2×C22⋊C4D4×C3711yescharacteristic
290C2×C42—21no—
291C2×C42—21no—
292C2×C42D4×C3711yescharacteristic
293C2×C42D4×C3711yescharacteristic
294#107—22no—
295#106—22no—
296#102—22no—
297#102—22no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8C2×C4×C3712yescomplemented
302#95—21no—
303#95—21no—
304#95—21no—
305#95—21no—
306#95—21no—
307#95—21no—
308#95—21no—
309C24—21no—
310C24C2×D4×C3711yescharacteristic
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—21no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—81no—
317C2×D4—81no—
318C2×D4C22⋊C4×C3712yes—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—42no—
329C22×C4—41no—
330C22×C4—81no—
331C22×C4—81no—
332C22×C4C22×C4×C3711yescharacteristic
333C22×C4C2×D4×C3711yescharacteristic
334C22×C4C2×D4×C3711yescharacteristic
335C22×C4C2×D4×C3711yescharacteristic
336C22×C4#41×C3711yescharacteristic
337C22×C4#41×C3711yescharacteristic
338M16—41no—
339M16—41no—
340M16—41no—
341M16—41no—
342C2×C8—22no—
343C2×C8—41no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—81no—
350C4⋊C4C22⋊C4×C3712yes—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—42no—
354C22⋊C4—42no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—81no—
362C22⋊C4—81no—
363C42—41no—
364C42—41no—
365C42—41no—
366C42—41no—
367C42—81no—
368C23—21no—
369C23—21no—
370C23—22no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23C4×D4×C3711yescharacteristic
380C23#120×C3711yescharacteristic
381C23#121×C3711yescharacteristic
382D4—42no—
383D4—81no—
384D4—82no—
385D4—82no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—84no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4C2×C22⋊C4×C3711yescharacteristic
418C2×C4C4×D4×C3711yescharacteristic
419C2×C4#121×C3711yescharacteristic
420C2×C4#123×C3711yescharacteristic
421C8—42no—
422C8—81no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—42no—
432C22—42no—
433C22—42no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22C37×#38611yescharacteristic
441C22C37×#45811yescharacteristic
442C22C37×#45811yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—161no—
455C2—21no—
456C2—21no—
457C2—41no—
458C2—41no—
459C2—82no—
460C2C37×#189011yescharacteristic
461C2C37×#190411yescharacteristic
462C2C37×#190611yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC22×C4C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#1826C2semidirect
4. C37×#1820C2semidirect
6. C37×#1306C2semidirect
7. C37×#1284C2semidirect
11. C37×#481C4semidirect
12. C37×#480C4semidirect
46. C2×C4⋊C4×C37C2×C4semidirect
47. C2×C4⋊C4×C37C2×C4semidirect
69. C22⋊C8×C37C2×C4semidirect
191. #9525C37direct (N × H)
226. #1826C2×C37semidirect
227. #1820C2×C37semidirect
229. #1306C2×C37semidirect
230. #1284C2×C37semidirect
242. #481C4×C37semidirect
243. #480C4×C37semidirect
262. C37#9525direct (N × H)
278. C2×C4⋊C4C2×C4×C37semidirect
279. C2×C4⋊C4C2×C4×C37semidirect
301. C22⋊C8C2×C4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#30942
C37×#23332
C37×#18262
C37×#18202
C37×#15102
C37×#13062
C37×#12842
#952537