Finite Group Databasebeta

← C37×#28672 #22649925

Subgroups — C37×#28672 #22649925

Order 9472.

648 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3165C211yesmaximal, characteristic, complemented
2C37×#3140C211yesmaximal, characteristic
3C2×C37×#489C211yesmaximal, characteristic
4C37×#2961C211yesmaximal, characteristic, complemented
5C37×#2064C212yesmaximal, complemented
6C37×#2063C212yesmaximal
7C37×#1997C211yesmaximal, characteristic, complemented
8C37×#1967C211yesmaximal, characteristic
9C37×#1931C212yesmaximal
10C37×#1930C212yesmaximal, complemented
11C37×#1778C211yesmaximal, characteristic, complemented
12C37×#533C2211yescharacteristic
13C2×C4⋊Q8×C37C2211yescharacteristic
14C2×#124×C37C2211yescharacteristic
15C37×#501—22no—
16C37×#500—21no—
17C37×#498—21no—
18C37×#489—21no—
19C37×#489—21no—
20C37×#489—22no—
21C37×#489—22no—
22C37×#488—22no—
23C37×#446—22no—
24C37×#446—22no—
25C2×#108×C37C2212yes—
26C37×#428C2212yes—
27C37×#428C2212yes—
28C37×#424C2212yes—
29C37×#423C2211yescharacteristic
30C37×#419C2212yes—
31C37×#418C2212yes—
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#101×C37C2212yes—
37C2×#100×C37C2212yes—
38C37×#405C2212yes—
39C4×M16×C37C2211yescharacteristic
40C4×M16×C37C2211yescharacteristic
41C2×#97×C37C2211yescharacteristic
42C37×#343C2212yes—
43C37×#343C2212yes—
44C37×#341C2212yes—
45C22×Q8×C37—21no—
46C22×Q8×C37C2311yescharacteristic
47C22×D4×C37C2311yescharacteristic
48C2×M16×C37C2312yes—
49C2×M16×C37C2312yes—
50C2×M16×C37C2312yes—
51C22×C8×C37C2311yescharacteristic
52C22×C8×C37C2311yescharacteristic
53C4⋊Q8×C37—21no—
54C4⋊Q8×C37—21no—
55C4⋊Q8×C37—21no—
56C4⋊Q8×C37—21no—
57C4⋊Q8×C37D411yescharacteristic
58C4⋊Q8×C37D411yescharacteristic
59#125×C37D412yes—
60#124×C37—21no—
61#124×C37—21no—
62#124×C37—21no—
63#124×C37—21no—
64C22⋊Q8×C37—21no—
65C22⋊Q8×C37—21no—
66C4×Q8×C37—21no—
67C4×Q8×C37—21no—
68#117×C37C2312yes—
69C2×C4⋊C4×C37—21no—
70C2×C4⋊C4×C37C2311yescharacteristic
71C2×C4⋊C4×C37C2311yescharacteristic
72C2×C22⋊C4×C37—21no—
73C2×C22⋊C4×C37—21no—
74C2×C42×C37C2311yescharacteristic
75#108×C37—24no—
76#107×C37—22no—
77#107×C37—22no—
78#106×C37—22no—
79#106×C37—22no—
80C4⋊C8×C37—24no—
81C4⋊C8×C37—21no—
82C4⋊C8×C37—21no—
83#103×C37—22no—
84#103×C37—22no—
85#103×C37—22no—
86#103×C37—22no—
87#102×C37—22no—
88#102×C37—22no—
89#102×C37—22no—
90#102×C37—22no—
91#101×C37—24no—
92#100×C37—24no—
93#97×C37—22no—
94#97×C37—21no—
95#97×C37—21no—
96#97×C37D412yes—
97#97×C37D412yes—
98C4×C8×C37—22no—
99C4×C8×C37—21no—
100C4×C8×C37—21no—
101C24×C37—21no—
102C2×Q8×C37—21no—
103C2×Q8×C37—21no—
104C2×Q8×C37—21no—
105C2×Q8×C37—21no—
106C2×Q8×C37—22no—
107C2×Q8×C37—22no—
108C2×Q8×C37—41no—
109C2×Q8×C37—41no—
110C2×Q8×C37—82no—
111C2×D4×C37—21no—
112C2×D4×C37—21no—
113C2×D4×C37—22no—
114C2×D4×C37—22no—
115C22×C4×C37—21no—
116C22×C4×C37—21no—
117C22×C4×C37—21no—
118C22×C4×C37#4111yescharacteristic
119C22×C4×C37#4111yescharacteristic
120C22×C4×C37C2411yescharacteristic
121M16×C37—22no—
122M16×C37—22no—
123M16×C37—22no—
124M16×C37—22no—
125M16×C37—22no—
126M16×C37#4114yes—
127C2×C8×C37—22no—
128C2×C8×C37—22no—
129C2×C8×C37—22no—
130C2×C8×C37—22no—
131C2×C8×C37—22no—
132C2×C8×C37C2×D412yes—
133C2×C8×C37C2×D412yes—
134C4⋊C4×C37—22no—
135C4⋊C4×C37—22no—
136C4⋊C4×C37—21no—
137C4⋊C4×C37—21no—
138C4⋊C4×C37—21no—
139C4⋊C4×C37—21no—
140C4⋊C4×C37—21no—
141C4⋊C4×C37—21no—
142C4⋊C4×C37—41no—
143C4⋊C4×C37—41no—
144C4⋊C4×C37C2×D412yes—
145C4⋊C4×C37C2×D412yes—
146C22⋊C4×C37—22no—
147C22⋊C4×C37—41no—
148C22⋊C4×C37—41no—
149C22⋊C4×C37—41no—
150C22⋊C4×C37—41no—
151C42×C37—22no—
152C42×C37C2×D411yescharacteristic
153C42×C37C2×D411yescharacteristic
154C42×C37C2×D411yescharacteristic
155C42×C37C2×D411yescharacteristic
156C23×C37—41no—
157C23×C37—42no—
158C23×C37—81no—
159C23×C37—81no—
160C23×C37C2×#4111yescharacteristic
161Q8×C37—41no—
162Q8×C37—41no—
163Q8×C37—42no—
164Q8×C37—81no—
165Q8×C37—81no—
166Q8×C37—82no—
167Q8×C37—82no—
168D4×C37—41no—
169D4×C37—41no—
170D4×C37—42no—
171C2×C4×C37—22no—
172C2×C4×C37—22no—
173C2×C4×C37—41no—
174C2×C4×C37—41no—
175C2×C4×C37—41no—
176C2×C4×C37—41no—
177C2×C4×C37—41no—
178C2×C4×C37—42no—
179C2×C4×C37—81no—
180C2×C4×C37—81no—
181C2×C4×C37#12111yescharacteristic
182C2×C4×C37#12111yescharacteristic
183C2×C4×C37#12111yescharacteristic
184C2×C4×C37#12111yescharacteristic
185C2×C4×C37C22×D411yescharacteristic
186C2×C4×C37C22×D411yescharacteristic
187C2×C4×C37C2×#4112yes—
188C2×C4×C372−1+412yes—
189C8×C37—22no—
190C8×C37—22no—
191C8×C37—24no—
192C8×C37—42no—
193C8×C37—42no—
194#28672C3711yesmaximal, characteristic, direct product factor, Sylow
195C22×C37—21no—
196C22×C37—21no—
197C22×C37—81no—
198C22×C37—81no—
199C22×C37—81no—
200C22×C37—162no—
201C22×C37C2×#12111yescharacteristic
202C22×C37#55612yes—
203C4×C37—21no—
204C4×C37—21no—
205C4×C37—21no—
206C4×C37—21no—
207C4×C37—42no—
208C4×C37—42no—
209C4×C37—81no—
210C4×C37—81no—
211C4×C37—81no—
212C4×C37#53211yescharacteristic
213C4×C37#53611yescharacteristic
214C4×C37#54812yes—
215#3165C2×C3711yescharacteristic, complemented
216#3140C2×C3711yescharacteristic
217C2×#489C2×C3711yescharacteristic
218#2961C2×C3711yescharacteristic, complemented
219#2064C2×C3712yescomplemented
220#2063C2×C3712yes—
221#1997C2×C3711yescharacteristic, complemented
222#1967C2×C3711yescharacteristic
223#1931C2×C3712yes—
224#1930C2×C3712yescomplemented
225#1778C2×C3711yescharacteristic, complemented
226C2×C37—22no—
227C2×C37—161no—
228C2×C37#254511yescharacteristic
229C2×C37#306811yescharacteristic
230C2×C37#306911yescharacteristic
231#533C22×C3711yescharacteristic
232C2×C4⋊Q8C22×C3711yescharacteristic
233C2×#124C22×C3711yescharacteristic
234#501—22no—
235#500—21no—
236#498—21no—
237#489—21no—
238#489—21no—
239#489—22no—
240#489—22no—
241#488—22no—
242#446—22no—
243#446—22no—
244C2×#108C22×C3712yes—
245#428C22×C3712yes—
246#428C22×C3712yes—
247#424C22×C3712yes—
248#423C22×C3711yescharacteristic
249#419C22×C3712yes—
250#418C22×C3712yes—
251C2×#103C22×C3711yescharacteristic
252C2×#103C22×C3711yescharacteristic
253C2×#102C22×C3711yescharacteristic
254C2×#102C22×C3711yescharacteristic
255C2×#101C22×C3712yes—
256C2×#100C22×C3712yes—
257#405C22×C3712yes—
258C4×M16C22×C3711yescharacteristic
259C4×M16C22×C3711yescharacteristic
260C2×#97C22×C3711yescharacteristic
261#343C22×C3712yes—
262#343C22×C3712yes—
263#341C22×C3712yes—
264C37#2867211yescharacteristic, direct product factor, Sylow
265C22×Q8—21no—
266C22×Q8C23×C3711yescharacteristic
267C22×D4C23×C3711yescharacteristic
268C2×M16C23×C3712yes—
269C2×M16C23×C3712yes—
270C2×M16C23×C3712yes—
271C22×C8C23×C3711yescharacteristic
272C22×C8C23×C3711yescharacteristic
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8D4×C3711yescharacteristic
278C4⋊Q8D4×C3711yescharacteristic
279#125D4×C3712yes—
280#124—21no—
281#124—21no—
282#124—21no—
283#124—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C4×Q8—21no—
287C4×Q8—21no—
288#117C23×C3712yes—
289C2×C4⋊C4—21no—
290C2×C4⋊C4C23×C3711yescharacteristic
291C2×C4⋊C4C23×C3711yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C42C23×C3711yescharacteristic
295#108—24no—
296#107—22no—
297#107—22no—
298#106—22no—
299#106—22no—
300C4⋊C8—24no—
301C4⋊C8—21no—
302C4⋊C8—21no—
303#103—22no—
304#103—22no—
305#103—22no—
306#103—22no—
307#102—22no—
308#102—22no—
309#102—22no—
310#102—22no—
311#101—24no—
312#100—24no—
313#97—22no—
314#97—21no—
315#97—21no—
316#97D4×C3712yes—
317#97D4×C3712yes—
318C4×C8—22no—
319C4×C8—21no—
320C4×C8—21no—
321C24—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—41no—
329C2×Q8—41no—
330C2×Q8—82no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4#41×C3711yescharacteristic
339C22×C4#41×C3711yescharacteristic
340C22×C4C24×C3711yescharacteristic
341M16—22no—
342M16—22no—
343M16—22no—
344M16—22no—
345M16—22no—
346M16#41×C3714yes—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8C2×D4×C3712yes—
353C2×C8C2×D4×C3712yes—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4C2×D4×C3712yes—
365C4⋊C4C2×D4×C3712yes—
366C22⋊C4—22no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C42—22no—
372C42C2×D4×C3711yescharacteristic
373C42C2×D4×C3711yescharacteristic
374C42C2×D4×C3711yescharacteristic
375C42C2×D4×C3711yescharacteristic
376C23—41no—
377C23—42no—
378C23—81no—
379C23—81no—
380C23C2×#41×C3711yescharacteristic
381Q8—41no—
382Q8—41no—
383Q8—42no—
384Q8—81no—
385Q8—81no—
386Q8—82no—
387Q8—82no—
388D4—41no—
389D4—41no—
390D4—42no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4#121×C3711yescharacteristic
402C2×C4#121×C3711yescharacteristic
403C2×C4#121×C3711yescharacteristic
404C2×C4#121×C3711yescharacteristic
405C2×C4C22×D4×C3711yescharacteristic
406C2×C4C22×D4×C3711yescharacteristic
407C2×C4C2×#41×C3712yes—
408C2×C42−1+4×C3712yes—
409C8—22no—
410C8—22no—
411C8—24no—
412C8—42no—
413C8—42no—
414C22—21no—
415C22—21no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—162no—
420C22C2×#121×C3711yescharacteristic
421C22C37×#55612yes—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—81no—
429C4—81no—
430C4—81no—
431C4C37×#53211yescharacteristic
432C4C37×#53611yescharacteristic
433C4C37×#54812yes—
434C2—22no—
435C2—161no—
436C2C37×#254511yescharacteristic
437C2C37×#306811yescharacteristic
438C2C37×#306911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC22×D4×C37C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3165C2semidirect
4. C37×#2961C2semidirect
5. C37×#2064C2semidirect
7. C37×#1997C2semidirect
10. C37×#1930C2semidirect
11. C37×#1778C2semidirect
194. #28672C37direct (N × H)
215. #3165C2×C37semidirect
218. #2961C2×C37semidirect
219. #2064C2×C37semidirect
221. #1997C2×C37semidirect
224. #1930C2×C37semidirect
225. #1778C2×C37semidirect
264. C37#28672direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#31652
C37×#31402
C2×C37×#4892
C37×#29612
C37×#20642
C37×#20632
C37×#19972
C37×#19672
C37×#19312
C37×#19302
C37×#17782
#2867237