Finite Group Databasebeta

← C37×#9261 #22630514

Subgroups — C37×#9261 #22630514

Order 9472.

566 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
1C2×C37×#481C211yesmaximal, characteristic
2C37×#2345C211yesmaximal, characteristic, complemented
3C37×#1964C211yesmaximal, characteristic
4C37×#1824C211yesmaximal, characteristic, complemented
5C37×#1519C211yesmaximal, characteristic
6C37×#1289C211yesmaximal, characteristic, complemented
7C37×#1282C211yesmaximal, characteristic, complemented
8C2×#121×C37C2211yescharacteristic
9C22×C4⋊C4×C37C2211yescharacteristic
10C37×#481—22no—
11C37×#481—21no—
12C37×#481—21no—
13C2×#106×C37C412yescomplemented
14C2×#102×C37C412yescomplemented
15C2×#99×C37—21no—
16C2×#99×C37—21no—
17C2×C22⋊C8×C37C2211yescharacteristic
18C2×C22⋊C8×C37C2211yescharacteristic
19C37×#389—21no—
20C37×#387—22no—
21C37×#380—21no—
22C37×#380C2211yescharacteristic
23C37×#380C2211yescharacteristic
24C4×C4⋊C4×C37—21no—
25C4×C22⋊C4×C37—21no—
26C4×C22⋊C4×C37C2211yescharacteristic
27C37×#340—22no—
28C37×#327—22no—
29C22×D4×C37—21no—
30C22×D4×C37C2×C411yescharacteristic
31C23×C4×C37—21no—
32C23×C4×C37C2311yescharacteristic
33C22×C8×C37—21no—
34C22×C8×C37C2×C412yes—
35#121×C37—21no—
36#121×C37—21no—
37#121×C37—21no—
38#121×C37—21no—
39C2×C4⋊C4×C37—21no—
40C2×C4⋊C4×C37—21no—
41C2×C4⋊C4×C37—21no—
42C2×C4⋊C4×C37—21no—
43C2×C4⋊C4×C37—21no—
44C2×C4⋊C4×C37—22no—
45C2×C4⋊C4×C37C2×C411yescharacteristic
46C2×C4⋊C4×C37C2×C412yes—
47C2×C4⋊C4×C37D412yes—
48C2×C4⋊C4×C37D411yescharacteristic
49C2×C4⋊C4×C37D411yescharacteristic
50C2×C22⋊C4×C37—21no—
51C2×C22⋊C4×C37—21no—
52C2×C22⋊C4×C37—21no—
53C2×C22⋊C4×C37D411yescharacteristic
54C2×C22⋊C4×C37D411yescharacteristic
55C2×C42×C37—21no—
56C2×C42×C37—22no—
57#106×C37—22no—
58#106×C37—22no—
59#102×C37—22no—
60#102×C37—22no—
61#99×C37—42no—
62#99×C37—42no—
63C22⋊C8×C37—21no—
64C22⋊C8×C37—21no—
65C22⋊C8×C37—21no—
66C22⋊C8×C37—21no—
67#95×C37—22no—
68#95×C37—22no—
69#95×C37—21no—
70#95×C37—21no—
71#95×C37D412yes—
72C24×C37—21no—
73C24×C37C2×D411yescharacteristic
74C2×D4×C37—21no—
75C2×D4×C37—21no—
76C2×D4×C37—42no—
77C2×D4×C37—41no—
78C2×D4×C37—41no—
79C2×D4×C37—41no—
80C2×D4×C37—41no—
81C2×D4×C37—41no—
82C2×D4×C37—41no—
83C22×C4×C37—21no—
84C22×C4×C37—21no—
85C22×C4×C37—21no—
86C22×C4×C37—22no—
87C22×C4×C37—22no—
88C22×C4×C37—21no—
89C22×C4×C37—21no—
90C22×C4×C37—22no—
91C22×C4×C37—42no—
92C22×C4×C37—41no—
93C22×C4×C37—82no—
94C22×C4×C37C22×C411yescharacteristic
95C22×C4×C37C2×D411yescharacteristic
96C22×C4×C37C2×D411yescharacteristic
97C22×C4×C37C2×D411yescharacteristic
98C22×C4×C37#4111yescharacteristic
99C22×C4×C37#4111yescharacteristic
100C2×C8×C37—22no—
101C2×C8×C37—42no—
102C2×C8×C37—42no—
103C2×C8×C37—41no—
104C4⋊C4×C37—22no—
105C4⋊C4×C37—22no—
106C4⋊C4×C37—21no—
107C4⋊C4×C37—21no—
108C4⋊C4×C37—21no—
109C4⋊C4×C37—21no—
110C4⋊C4×C37—42no—
111C4⋊C4×C37—42no—
112C4⋊C4×C37—82no—
113C4⋊C4×C37C22⋊C412yes—
114C4⋊C4×C37C22⋊C412yes—
115C22⋊C4×C37—21no—
116C22⋊C4×C37—21no—
117C22⋊C4×C37—21no—
118C22⋊C4×C37—41no—
119C22⋊C4×C37—41no—
120C22⋊C4×C37—41no—
121C22⋊C4×C37—41no—
122C22⋊C4×C37—41no—
123C22⋊C4×C37—41no—
124C22⋊C4×C37SD1612yes—
125C42×C37—42no—
126C42×C37—82no—
127C23×C37—41no—
128C23×C37—41no—
129C23×C37—41no—
130C23×C37—41no—
131C23×C37—41no—
132C23×C37—81no—
133C23×C37—81no—
134C23×C37C4×D411yescharacteristic
135C23×C37#12011yescharacteristic
136C23×C37#12111yescharacteristic
137C23×C37C2×SD1611yescharacteristic
138C23×C37#13511yescharacteristic
139C23×C37AGL(1,ℤ/8)11yescharacteristic
140C23×C37#13711yescharacteristic
141D4×C37—42no—
142D4×C37—81no—
143D4×C37—81no—
144D4×C37—81no—
145D4×C37—81no—
146D4×C37—81no—
147C2×C4×C37—22no—
148C2×C4×C37—22no—
149C2×C4×C37—22no—
150C2×C4×C37—22no—
151C2×C4×C37—22no—
152C2×C4×C37—22no—
153C2×C4×C37—41no—
154C2×C4×C37—41no—
155C2×C4×C37—41no—
156C2×C4×C37—41no—
157C2×C4×C37—41no—
158C2×C4×C37—42no—
159C2×C4×C37—42no—
160C2×C4×C37—41no—
161C2×C4×C37—42no—
162C2×C4×C37—42no—
163C2×C4×C37—41no—
164C2×C4×C37—41no—
165C2×C4×C37—41no—
166C2×C4×C37—41no—
167C2×C4×C37—41no—
168C2×C4×C37—42no—
169C2×C4×C37—82no—
170C2×C4×C37—82no—
171C2×C4×C37—81no—
172C2×C4×C37—81no—
173C2×C4×C37—81no—
174C2×C4×C37C2×C22⋊C411yescharacteristic
175C2×C4×C37C4×D411yescharacteristic
176C2×C4×C37#12111yescharacteristic
177C2×C4×C37#12311yescharacteristic
178C8×C37—42no—
179C8×C37—81no—
180#9261C3711yesmaximal, characteristic, direct product factor, Sylow
181C22×C37—21no—
182C22×C37—21no—
183C22×C37—21no—
184C22×C37—21no—
185C22×C37—21no—
186C22×C37—21no—
187C22×C37—41no—
188C22×C37—41no—
189C22×C37—41no—
190C22×C37—41no—
191C22×C37—81no—
192C22×C37—81no—
193C22×C37—81no—
194C22×C37—161no—
195C22×C37—161no—
196C22×C37#38611yescharacteristic
197C22×C37C4×SD1611yescharacteristic
198C22×C37#44011yescharacteristic
199C22×C37#44811yescharacteristic
200C22×C37#44911yescharacteristic
201C22×C37#46011yescharacteristic
202C22×C37#46411yescharacteristic
203C4×C37—21no—
204C4×C37—21no—
205C4×C37—21no—
206C4×C37—42no—
207C4×C37—42no—
208C4×C37—42no—
209C4×C37—81no—
210C4×C37—82no—
211C4×C37—81no—
212C4×C37—161no—
213C4×C37#41012yes—
214C2×#481C2×C3711yescharacteristic
215#2345C2×C3711yescharacteristic, complemented
216#1964C2×C3711yescharacteristic
217#1824C2×C3711yescharacteristic, complemented
218#1519C2×C3711yescharacteristic
219#1289C2×C3711yescharacteristic, complemented
220#1282C2×C3711yescharacteristic, complemented
221C2×C37—21no—
222C2×C37—21no—
223C2×C37—21no—
224C2×C37—21no—
225C2×C37—21no—
226C2×C37—21no—
227C2×C37—161no—
228C2×C37#188011yescharacteristic
229C2×C37#189911yescharacteristic
230C2×C37#190411yescharacteristic
231C2×#121C22×C3711yescharacteristic
232C22×C4⋊C4C22×C3711yescharacteristic
233#481—22no—
234#481—21no—
235#481—21no—
236C2×#106C4×C3712yescomplemented
237C2×#102C4×C3712yescomplemented
238C2×#99—21no—
239C2×#99—21no—
240C2×C22⋊C8C22×C3711yescharacteristic
241C2×C22⋊C8C22×C3711yescharacteristic
242#389—21no—
243#387—22no—
244#380—21no—
245#380C22×C3711yescharacteristic
246#380C22×C3711yescharacteristic
247C4×C4⋊C4—21no—
248C4×C22⋊C4—21no—
249C4×C22⋊C4C22×C3711yescharacteristic
250#340—22no—
251#327—22no—
252C37#926111yescharacteristic, direct product factor, Sylow
253C22×D4—21no—
254C22×D4C2×C4×C3711yescharacteristic
255C23×C4—21no—
256C23×C4C23×C3711yescharacteristic
257C22×C8—21no—
258C22×C8C2×C4×C3712yes—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4C2×C4×C3711yescharacteristic
270C2×C4⋊C4C2×C4×C3712yes—
271C2×C4⋊C4D4×C3712yes—
272C2×C4⋊C4D4×C3711yescharacteristic
273C2×C4⋊C4D4×C3711yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4D4×C3711yescharacteristic
278C2×C22⋊C4D4×C3711yescharacteristic
279C2×C42—21no—
280C2×C42—22no—
281#106—22no—
282#106—22no—
283#102—22no—
284#102—22no—
285#99—42no—
286#99—42no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291#95—22no—
292#95—22no—
293#95—21no—
294#95—21no—
295#95D4×C3712yes—
296C24—21no—
297C24C2×D4×C3711yescharacteristic
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—42no—
316C22×C4—41no—
317C22×C4—82no—
318C22×C4C22×C4×C3711yescharacteristic
319C22×C4C2×D4×C3711yescharacteristic
320C22×C4C2×D4×C3711yescharacteristic
321C22×C4C2×D4×C3711yescharacteristic
322C22×C4#41×C3711yescharacteristic
323C22×C4#41×C3711yescharacteristic
324C2×C8—22no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—41no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4—82no—
337C4⋊C4C22⋊C4×C3712yes—
338C4⋊C4C22⋊C4×C3712yes—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4SD16×C3712yes—
349C42—42no—
350C42—82no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—81no—
357C23—81no—
358C23C4×D4×C3711yescharacteristic
359C23#120×C3711yescharacteristic
360C23#121×C3711yescharacteristic
361C23C2×SD16×C3711yescharacteristic
362C23#135×C3711yescharacteristic
363C23AGL(1,ℤ/8)×C3711yescharacteristic
364C23#137×C3711yescharacteristic
365D4—42no—
366D4—81no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—81no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4C2×C22⋊C4×C3711yescharacteristic
399C2×C4C4×D4×C3711yescharacteristic
400C2×C4#121×C3711yescharacteristic
401C2×C4#123×C3711yescharacteristic
402C8—42no—
403C8—81no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—161no—
418C22—161no—
419C22C37×#38611yescharacteristic
420C22C4×SD16×C3711yescharacteristic
421C22C37×#44011yescharacteristic
422C22C37×#44811yescharacteristic
423C22C37×#44911yescharacteristic
424C22C37×#46011yescharacteristic
425C22C37×#46411yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—42no—
431C4—42no—
432C4—81no—
433C4—82no—
434C4—81no—
435C4—161no—
436C4C37×#41012yes—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—161no—
444C2C37×#188011yescharacteristic
445C2C37×#189911yescharacteristic
446C2C37×#190411yescharacteristic
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
2. C37×#2345C2semidirect
4. C37×#1824C2semidirect
6. C37×#1289C2semidirect
7. C37×#1282C2semidirect
13. C2×#106×C37C4semidirect
14. C2×#102×C37C4semidirect
180. #9261C37direct (N × H)
215. #2345C2×C37semidirect
217. #1824C2×C37semidirect
219. #1289C2×C37semidirect
220. #1282C2×C37semidirect
236. C2×#106C4×C37semidirect
237. C2×#102C4×C37semidirect
252. C37#9261direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4812
C37×#23452
C37×#19642
C37×#18242
C37×#15192
C37×#12892
C37×#12822
#926137