Finite Group Databasebeta

← C4×C37×#562 #22655605

Subgroups — C4×C37×#562 #22655605

Order 9472.

2248 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#562C211yesmaximal, characteristic
2C37×#2382C211yesmaximal, characteristic, complemented
3C37×#2379C212yesmaximal, complemented
4C37×#2378C214yesmaximal, complemented
5C37×#2377C214yesmaximal, complemented
6C37×#2376C214yesmaximal, complemented
7C4×#125×C37C211yesmaximal, characteristic, complemented
8C4×#124×C37C212yesmaximal, complemented
9C4×C22⋊Q8×C37C214yesmaximal, complemented
10C4×#123×C37C214yesmaximal, complemented
11C4×#121×C37C214yesmaximal, complemented
12C37×#562C4116yesdirect product factor
13C2×#125×C37C2211yescharacteristic
14C2×#124×C37C2212yes—
15C2×#123×C37C2214yes—
16C2×C22⋊Q8×C37C2214yes—
17C2×#121×C37C2214yes—
18C2×C4×Q8×C37C2212yes—
19C2×C4×D4×C37C2214yes—
20C2×C4×D4×C37C2212yes—
21C22×C42×C37C2214yes—
22C37×#391C2212yes—
23C37×#391C2214yes—
24C37×#390C2214yes—
25C37×#390C2212yes—
26C37×#389C2212yes—
27C37×#389C2214yes—
28C37×#389C2214yes—
29C37×#388C2214yes—
30C37×#388C2214yes—
31C37×#388C2214yes—
32C37×#388C2214yes—
33C37×#388C2214yes—
34C37×#388C2214yes—
35C37×#387C2214yes—
36C37×#387C2214yes—
37C37×#387C2214yes—
38C37×#387C2214yes—
39C37×#387C2214yes—
40C37×#386C2214yes—
41C37×#386C2214yes—
42C37×#386C2214yes—
43C37×#385C2214yes—
44C37×#385C2214yes—
45C37×#385C2214yes—
46C37×#382C2211yescharacteristic
47C37×#382C2212yes—
48C37×#381C2214yes—
49C37×#380C2214yes—
50C37×#380C2214yes—
51C4×C4⋊C4×C37C2214yes—
52C4×C4⋊C4×C37C2212yes—
53C4×C4⋊C4×C37C2214yes—
54C4×C22⋊C4×C37C2214yes—
55C4×C22⋊C4×C37C2214yes—
56C4×C22⋊C4×C37C2214yes—
57C43×C37C2211yescharacteristic
58C22×Q8×C37C2312yes—
59C22×D4×C37C2314yes—
60C22×D4×C37C2312yes—
61C23×C4×C37C2314yes—
62C23×C4×C37C2314yes—
63C23×C4×C37C2314yes—
64#125×C37C2×C418yescomplemented
65#124×C37C2×C4116yescomplemented
66#123×C37C2×C4132yescomplemented
67C22⋊Q8×C37C2×C4132yescomplemented
68#121×C37C2×C4132yescomplemented
69C4×Q8×C37—44no—
70C4×D4×C37—48no—
71C4×D4×C37—44no—
72C2×C4⋊C4×C37C2314yes—
73C2×C4⋊C4×C37C2314yes—
74C2×C4⋊C4×C37C2312yes—
75C2×C4⋊C4×C37C2314yes—
76C2×C4⋊C4×C37C2314yes—
77C2×C4⋊C4×C37C2312yes—
78C2×C4⋊C4×C37C2312yes—
79C2×C4⋊C4×C37C2314yes—
80C2×C4⋊C4×C37C2314yes—
81C2×C4⋊C4×C37C2312yes—
82C2×C22⋊C4×C37C2314yes—
83C2×C22⋊C4×C37C2314yes—
84C2×C22⋊C4×C37C2314yes—
85C2×C22⋊C4×C37C2314yes—
86C2×C22⋊C4×C37C2314yes—
87C2×C22⋊C4×C37C2314yes—
88C2×C22⋊C4×C37C2314yes—
89C2×C22⋊C4×C37C2314yes—
90C2×C22⋊C4×C37C2314yes—
91C2×C42×C37—48no—
92C2×C42×C37C2311yescharacteristic
93C2×C42×C37C2312yes—
94C2×C42×C37C2314yes—
95C2×C42×C37C2314yes—
96C2×C42×C37C2312yes—
97C2×C42×C37C2311yescharacteristic
98C2×C42×C37C2314yes—
99C2×C42×C37C2314yes—
100C2×C42×C37C2311yescharacteristic
101#95×C37C2314yes—
102#95×C37C2314yes—
103#95×C37C2314yes—
104#95×C37C2314yes—
105#95×C37C2314yes—
106#95×C37C2314yes—
107#95×C37C2314yes—
108#95×C37C2314yes—
109#95×C37C2314yes—
110#95×C37C2314yes—
111#95×C37C2314yes—
112C24×C37C2414yes—
113C2×Q8×C37—42no—
114C2×Q8×C37—42no—
115C2×Q8×C37C22×C418yes—
116C2×D4×C37—44no—
117C2×D4×C37—42no—
118C2×D4×C37—42no—
119C2×D4×C37—44no—
120C2×D4×C37C22×C4116yes—
121C2×D4×C37C22×C418yes—
122C22×C4×C37—28no—
123C22×C4×C37—28no—
124C22×C4×C37—28no—
125C22×C4×C37—44no—
126C22×C4×C37—44no—
127C22×C4×C37—44no—
128C22×C4×C37—44no—
129C22×C4×C37—44no—
130C22×C4×C37C22×C4116yes—
131C22×C4×C37C2411yescharacteristic
132C22×C4×C37C2414yes—
133C22×C4×C37C2414yes—
134C22×C4×C37C2414yes—
135C22×C4×C37C2412yes—
136C22×C4×C37C2411yescharacteristic
137C22×C4×C37C2412yes—
138C22×C4×C37C2414yes—
139C22×C4×C37C2414yes—
140C22×C4×C37C2411yescharacteristic
141C4⋊C4×C37—42no—
142C4⋊C4×C37—44no—
143C4⋊C4×C37—44no—
144C4⋊C4×C37—44no—
145C4⋊C4×C37—42no—
146C4⋊C4×C37—44no—
147C4⋊C4×C37—42no—
148C4⋊C4×C37C22×C4116yes—
149C4⋊C4×C37C22×C4116yes—
150C4⋊C4×C37C22×C418yes—
151C22⋊C4×C37—44no—
152C22⋊C4×C37—44no—
153C22⋊C4×C37—44no—
154C22⋊C4×C37—44no—
155C22⋊C4×C37—44no—
156C22⋊C4×C37—44no—
157C22⋊C4×C37C22×C4116yes—
158C22⋊C4×C37C22×C4116yes—
159C22⋊C4×C37C22×C4116yes—
160C42×C37—28no—
161C42×C37—28no—
162C42×C37—24no—
163C42×C37—22no—
164C42×C37—44no—
165C42×C37—44no—
166C42×C37—41no—
167C42×C37—42no—
168C42×C37C22×C414yes—
169C23×C37—24no—
170C23×C37—24no—
171C23×C37—24no—
172C23×C37—24no—
173C23×C37—24no—
174C23×C37—24no—
175C23×C37C23×C418yes—
176C23×C37C2511yescharacteristic
177Q8×C37—48no—
178D4×C37—416no—
179D4×C37—48no—
180C2×C4×C37—24no—
181C2×C4×C37—24no—
182C2×C4×C37—22no—
183C2×C4×C37—21no—
184C2×C4×C37—21no—
185C2×C4×C37—22no—
186C2×C4×C37—24no—
187C2×C4×C37—24no—
188C2×C4×C37—24no—
189C2×C4×C37—24no—
190C2×C4×C37—22no—
191C2×C4×C37—24no—
192C2×C4×C37—24no—
193C2×C4×C37—21no—
194C2×C4×C37—24no—
195C2×C4×C37—22no—
196C2×C4×C37—22no—
197C2×C4×C37—22no—
198C2×C4×C37—24no—
199C2×C4×C37—24no—
200C2×C4×C37—24no—
201C2×C4×C37—24no—
202C2×C4×C37—416no—
203C2×C4×C37—416no—
204C2×C4×C37—416no—
205C2×C4×C37C23×C412yes—
206C2×C4×C37C23×C414yes—
207C2×C4×C37C23×C418yes—
208C2×C4×C37C23×C418yes—
209C2×C4×C37H(5,𝔽2)14yes—
210C2×C4×C372−1+412yes—
211C4×#562C3711yesmaximal, characteristic, direct product factor, Sylow
212C22×C37—28no—
213C22×C37—28no—
214C22×C37—28no—
215C22×C37—44no—
216C22×C37—44no—
217C22×C37—44no—
218C22×C37—44no—
219C22×C37C24×C411yescharacteristic
220C22×C37C2×H(5,𝔽2)12yes—
221C22×C37C2×2−1+411yescharacteristic
222C22×C37#58512yes—
223C22×C37#58511yescharacteristic
224C4×C37—28no—
225C4×C37—28no—
226C4×C37—24no—
227C4×C37—22no—
228C4×C37—44no—
229C4×C37—42no—
230C4×C37—44no—
231C4×C37—44no—
232C4×C37—41no—
233C4×C37#56214yesdirect product factor
234C2×#562C2×C3711yescharacteristic
235#2382C2×C3711yescharacteristic, complemented
236#2379C2×C3712yescomplemented
237#2378C2×C3714yescomplemented
238#2377C2×C3714yescomplemented
239#2376C2×C3714yescomplemented
240C4×#125C2×C3711yescharacteristic, complemented
241C4×#124C2×C3712yescomplemented
242C4×C22⋊Q8C2×C3714yescomplemented
243C4×#123C2×C3714yescomplemented
244C4×#121C2×C3714yescomplemented
245C2×C37—48no—
246C2×C37C4×H(5,𝔽2)12yes—
247C2×C37C4×2−1+411yescharacteristic
248C2×C37C2×#56211yescharacteristic
249C2×C37#352912yes—
250C2×C37#353111yescharacteristic
251#562C4×C37116yesdirect product factor
252C2×#125C22×C3711yescharacteristic
253C2×#124C22×C3712yes—
254C2×#123C22×C3714yes—
255C2×C22⋊Q8C22×C3714yes—
256C2×#121C22×C3714yes—
257C2×C4×Q8C22×C3712yes—
258C2×C4×D4C22×C3714yes—
259C2×C4×D4C22×C3712yes—
260C22×C42C22×C3714yes—
261#391C22×C3712yes—
262#391C22×C3714yes—
263#390C22×C3714yes—
264#390C22×C3712yes—
265#389C22×C3712yes—
266#389C22×C3714yes—
267#389C22×C3714yes—
268#388C22×C3714yes—
269#388C22×C3714yes—
270#388C22×C3714yes—
271#388C22×C3714yes—
272#388C22×C3714yes—
273#388C22×C3714yes—
274#387C22×C3714yes—
275#387C22×C3714yes—
276#387C22×C3714yes—
277#387C22×C3714yes—
278#387C22×C3714yes—
279#386C22×C3714yes—
280#386C22×C3714yes—
281#386C22×C3714yes—
282#385C22×C3714yes—
283#385C22×C3714yes—
284#385C22×C3714yes—
285#382C22×C3711yescharacteristic
286#382C22×C3712yes—
287#381C22×C3714yes—
288#380C22×C3714yes—
289#380C22×C3714yes—
290C4×C4⋊C4C22×C3714yes—
291C4×C4⋊C4C22×C3712yes—
292C4×C4⋊C4C22×C3714yes—
293C4×C22⋊C4C22×C3714yes—
294C4×C22⋊C4C22×C3714yes—
295C4×C22⋊C4C22×C3714yes—
296C43C22×C3711yescharacteristic
297C37C4×#56211yescharacteristic, direct product factor, Sylow
298C22×Q8C23×C3712yes—
299C22×D4C23×C3714yes—
300C22×D4C23×C3712yes—
301C23×C4C23×C3714yes—
302C23×C4C23×C3714yes—
303C23×C4C23×C3714yes—
304#125C2×C4×C3718yescomplemented
305#124C2×C4×C37116yescomplemented
306#123C2×C4×C37132yescomplemented
307C22⋊Q8C2×C4×C37132yescomplemented
308#121C2×C4×C37132yescomplemented
309C4×Q8—44no—
310C4×D4—48no—
311C4×D4—44no—
312C2×C4⋊C4C23×C3714yes—
313C2×C4⋊C4C23×C3712yes—
314C2×C4⋊C4C23×C3714yes—
315C2×C4⋊C4C23×C3712yes—
316C2×C4⋊C4C23×C3714yes—
317C2×C4⋊C4C23×C3714yes—
318C2×C4⋊C4C23×C3712yes—
319C2×C4⋊C4C23×C3714yes—
320C2×C4⋊C4C23×C3714yes—
321C2×C4⋊C4C23×C3712yes—
322C2×C22⋊C4C23×C3714yes—
323C2×C22⋊C4C23×C3714yes—
324C2×C22⋊C4C23×C3714yes—
325C2×C22⋊C4C23×C3714yes—
326C2×C22⋊C4C23×C3714yes—
327C2×C22⋊C4C23×C3714yes—
328C2×C22⋊C4C23×C3714yes—
329C2×C22⋊C4C23×C3714yes—
330C2×C22⋊C4C23×C3714yes—
331C2×C42—48no—
332C2×C42C23×C3712yes—
333C2×C42C23×C3714yes—
334C2×C42C23×C3714yes—
335C2×C42C23×C3711yescharacteristic
336C2×C42C23×C3712yes—
337C2×C42C23×C3711yescharacteristic
338C2×C42C23×C3714yes—
339C2×C42C23×C3714yes—
340C2×C42C23×C3711yescharacteristic
341#95C23×C3714yes—
342#95C23×C3714yes—
343#95C23×C3714yes—
344#95C23×C3714yes—
345#95C23×C3714yes—
346#95C23×C3714yes—
347#95C23×C3714yes—
348#95C23×C3714yes—
349#95C23×C3714yes—
350#95C23×C3714yes—
351#95C23×C3714yes—
352C24C24×C3714yes—
353C2×Q8—42no—
354C2×Q8—42no—
355C2×Q8C22×C4×C3718yes—
356C2×D4—44no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—44no—
360C2×D4C22×C4×C37116yes—
361C2×D4C22×C4×C3718yes—
362C22×C4—28no—
363C22×C4—28no—
364C22×C4—28no—
365C22×C4—44no—
366C22×C4—44no—
367C22×C4—44no—
368C22×C4—44no—
369C22×C4—44no—
370C22×C4C22×C4×C37116yes—
371C22×C4C24×C3711yescharacteristic
372C22×C4C24×C3714yes—
373C22×C4C24×C3714yes—
374C22×C4C24×C3714yes—
375C22×C4C24×C3712yes—
376C22×C4C24×C3711yescharacteristic
377C22×C4C24×C3712yes—
378C22×C4C24×C3714yes—
379C22×C4C24×C3714yes—
380C22×C4C24×C3711yescharacteristic
381C4⋊C4—42no—
382C4⋊C4—44no—
383C4⋊C4—44no—
384C4⋊C4—44no—
385C4⋊C4—42no—
386C4⋊C4—44no—
387C4⋊C4—42no—
388C4⋊C4C22×C4×C37116yes—
389C4⋊C4C22×C4×C37116yes—
390C4⋊C4C22×C4×C3718yes—
391C22⋊C4—44no—
392C22⋊C4—44no—
393C22⋊C4—44no—
394C22⋊C4—44no—
395C22⋊C4—44no—
396C22⋊C4—44no—
397C22⋊C4C22×C4×C37116yes—
398C22⋊C4C22×C4×C37116yes—
399C22⋊C4C22×C4×C37116yes—
400C42—28no—
401C42—28no—
402C42—24no—
403C42—22no—
404C42—44no—
405C42—44no—
406C42—41no—
407C42—42no—
408C42C22×C4×C3714yes—
409C23—24no—
410C23—24no—
411C23—24no—
412C23—24no—
413C23—24no—
414C23—24no—
415C23C23×C4×C3718yes—
416C23C25×C3711yescharacteristic
417Q8—48no—
418D4—416no—
419D4—48no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—21no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—416no—
443C2×C4—416no—
444C2×C4—416no—
445C2×C4C23×C4×C3712yes—
446C2×C4C23×C4×C3714yes—
447C2×C4C23×C4×C3718yes—
448C2×C4C23×C4×C3718yes—
449C2×C4H(5,𝔽2)×C3714yes—
450C2×C42−1+4×C3712yes—
451C22—28no—
452C22—28no—
453C22—28no—
454C22—44no—
455C22—44no—
456C22—44no—
457C22—44no—
458C22C24×C4×C3711yescharacteristic
459C22C2×H(5,𝔽2)×C3712yes—
460C22C2×2−1+4×C3711yescharacteristic
461C22C37×#58512yes—
462C22C37×#58511yescharacteristic
463C4—28no—
464C4—28no—
465C4—24no—
466C4—22no—
467C4—44no—
468C4—44no—
469C4—44no—
470C4—42no—
471C4—41no—
472C4C37×#56214yesdirect product factor
473C2—48no—
474C2C4×H(5,𝔽2)×C3712yes—
475C2C4×2−1+4×C3711yescharacteristic
476C2C2×C37×#56211yescharacteristic
477C2C37×#352912yes—
478C2C37×#353111yescharacteristic
subgroupG/H
centerC22×C4×C37C24
commutatorC22C24×C4×C37
Frattini, cosocleC23C25×C37
socleC23×C37C25
prime radicalC2×C37×#562C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2382C2semidirect
3. C37×#2379C2semidirect
4. C37×#2378C2semidirect
5. C37×#2377C2semidirect
6. C37×#2376C2semidirect
7. C4×#125×C37C2semidirect
8. C4×#124×C37C2semidirect
9. C4×C22⋊Q8×C37C2semidirect
10. C4×#123×C37C2semidirect
11. C4×#121×C37C2semidirect
12. C37×#562C4direct (N × H)
64. #125×C37C2×C4semidirect
65. #124×C37C2×C4semidirect
66. #123×C37C2×C4semidirect
67. C22⋊Q8×C37C2×C4semidirect
68. #121×C37C2×C4semidirect
211. C4×#562C37direct (N × H)
233. C4×C37#562direct (N × H)
235. #2382C2×C37semidirect
236. #2379C2×C37semidirect
237. #2378C2×C37semidirect
238. #2377C2×C37semidirect
239. #2376C2×C37semidirect
240. C4×#125C2×C37semidirect
241. C4×#124C2×C37semidirect
242. C4×C22⋊Q8C2×C37semidirect
243. C4×#123C2×C37semidirect
244. C4×#121C2×C37semidirect
251. #562C4×C37direct (N × H)
297. C37C4×#562direct (N × H)
304. #125C2×C4×C37semidirect
305. #124C2×C4×C37semidirect
306. #123C2×C4×C37semidirect
307. C22⋊Q8C2×C4×C37semidirect
308. #121C2×C4×C37semidirect
472. C4C37×#562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5622
C37×#23822
C37×#23792
C37×#23782
C37×#23772
C37×#23762
C4×#125×C372
C4×#124×C372
C4×C22⋊Q8×C372
C4×#123×C372
C4×#121×C372
C4×#56237