Finite Group Databasebeta

← C37×#28298 #22649551

Subgroups — C37×#28298 #22649551

Order 9472.

698 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
1C37×#3078C211yesmaximal, characteristic, complemented
2C37×#3077C211yesmaximal, characteristic
3C37×#2961C211yesmaximal, characteristic, complemented
4C2×C37×#440C211yesmaximal, characteristic
5C37×#2064C212yesmaximal, complemented
6C37×#2063C212yesmaximal
7C37×#1977C212yesmaximal
8C37×#1952C212yesmaximal, complemented
9C37×#1849C211yesmaximal, characteristic, complemented
10C37×#1801C211yesmaximal, characteristic, complemented
11C37×#1800C211yesmaximal, characteristic
12C22×SD16×C37C2211yescharacteristic
13C37×#533C2211yescharacteristic
14C2×C4×Q8×C37C2211yescharacteristic
15C2×C4×D4×C37C2211yescharacteristic
16C37×#479—22no—
17C37×#478—22no—
18C37×#477—21no—
19C37×#476—21no—
20C37×#475—21no—
21C37×#474—21no—
22C37×#446—22no—
23C37×#446—22no—
24C37×#440—22no—
25C37×#440—22no—
26C2×#108×C37C2212yes—
27C2×#108×C37C2212yes—
28C37×#428C2212yes—
29C37×#428C2212yes—
30C2×#107×C37C2211yescharacteristic
31C37×#424C2212yes—
32C37×#423C2211yescharacteristic
33C37×#423C2211yescharacteristic
34C37×#423C2211yescharacteristic
35C37×#419C2212yes—
36C37×#418C2212yes—
37C2×#103×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#101×C37C2212yes—
40C2×#100×C37C2212yes—
41C37×#405C2212yes—
42C2×#97×C37C2211yescharacteristic
43C37×#343C2212yes—
44C37×#343C2212yes—
45C22×Q8×C37C2311yescharacteristic
46C22×D4×C37C2311yescharacteristic
47C23×C4×C37—21no—
48C2×SD16×C37—22no—
49C2×SD16×C37—22no—
50C2×SD16×C37Q814yescomplemented
51C2×M16×C37C2312yes—
52C2×M16×C37C2312yes—
53C2×M16×C37C2312yes—
54C22×C8×C37C2311yescharacteristic
55C22×C8×C37C2311yescharacteristic
56C4⋊Q8×C37D411yescharacteristic
57C4⋊Q8×C37D411yescharacteristic
58#125×C37D412yes—
59C22⋊Q8×C37—21no—
60C22⋊Q8×C37—21no—
61C4×Q8×C37—21no—
62C4×Q8×C37—21no—
63C4×Q8×C37—21no—
64C4×Q8×C37—21no—
65C4×Q8×C37—21no—
66C4×Q8×C37—21no—
67C4×D4×C37—21no—
68C4×D4×C37—21no—
69C4×D4×C37—21no—
70C4×D4×C37—21no—
71#117×C37C2312yes—
72C2×C4⋊C4×C37—21no—
73C2×C4⋊C4×C37C2311yescharacteristic
74C2×C4⋊C4×C37C2311yescharacteristic
75C2×C22⋊C4×C37—21no—
76C2×C42×C37—21no—
77C2×C42×C37C2311yescharacteristic
78#108×C37—24no—
79#108×C37—42no—
80#107×C37—22no—
81#107×C37—22no—
82#107×C37—22no—
83#106×C37—22no—
84#106×C37—22no—
85C4⋊C8×C37—24no—
86C4⋊C8×C37—21no—
87C4⋊C8×C37—21no—
88C4⋊C8×C37—21no—
89C4⋊C8×C37—21no—
90C4⋊C8×C37—21no—
91C4⋊C8×C37—21no—
92#103×C37—22no—
93#103×C37—22no—
94#103×C37—22no—
95#102×C37—22no—
96#102×C37—22no—
97#102×C37—22no—
98#101×C37—42no—
99#100×C37—42no—
100#97×C37—22no—
101#97×C37D412yes—
102#97×C37D412yes—
103C4×C8×C37—22no—
104C24×C37—21no—
105C2×Q8×C37—21no—
106C2×Q8×C37—21no—
107C2×Q8×C37—21no—
108C2×Q8×C37—21no—
109C2×Q8×C37—21no—
110C2×Q8×C37—21no—
111C2×Q8×C37—21no—
112C2×Q8×C37C2×Q812yes—
113C2×D4×C37—21no—
114C2×D4×C37—21no—
115C2×D4×C37—21no—
116C2×D4×C37—21no—
117C2×D4×C37—21no—
118C2×D4×C37C2×Q812yes—
119C22×C4×C37—21no—
120C22×C4×C37—21no—
121C22×C4×C37—21no—
122C22×C4×C37—41no—
123C22×C4×C37—41no—
124C22×C4×C37—82no—
125C22×C4×C37#4111yescharacteristic
126C22×C4×C37#4111yescharacteristic
127C22×C4×C37C2411yescharacteristic
128SD16×C37—28no—
129M16×C37—22no—
130M16×C37—22no—
131M16×C37—22no—
132M16×C37—22no—
133M16×C37—22no—
134M16×C37—22no—
135C2×C8×C37—21no—
136C2×C8×C37—21no—
137C2×C8×C37—22no—
138C2×C8×C37—22no—
139C2×C8×C37—22no—
140C2×C8×C37C2×D412yes—
141C2×C8×C37C2×D412yes—
142C2×C8×C37C2×Q812yes—
143C2×C8×C37#4112yes—
144C4⋊C4×C37—22no—
145C4⋊C4×C37—22no—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—21no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—41no—
153C4⋊C4×C37—41no—
154C4⋊C4×C37C2×D412yes—
155C4⋊C4×C37C2×D412yes—
156C22⋊C4×C37—22no—
157C22⋊C4×C37—41no—
158C22⋊C4×C37—41no—
159C42×C37—22no—
160C42×C37—41no—
161C42×C37—41no—
162C42×C37C2×D411yescharacteristic
163C42×C37C2×D411yescharacteristic
164C42×C37C2×D411yescharacteristic
165C42×C37C2×D411yescharacteristic
166C23×C37—22no—
167C23×C37—41no—
168C23×C37—41no—
169C23×C37—81no—
170C23×C37—81no—
171C23×C37C2×#4111yescharacteristic
172Q8×C37—22no—
173Q8×C37—22no—
174Q8×C37—41no—
175Q8×C37—41no—
176Q8×C37—81no—
177Q8×C37—81no—
178D4×C37—22no—
179D4×C37—22no—
180D4×C37—41no—
181D4×C37—41no—
182C2×C4×C37—22no—
183C2×C4×C37—22no—
184C2×C4×C37—22no—
185C2×C4×C37—41no—
186C2×C4×C37—41no—
187C2×C4×C37—41no—
188C2×C4×C37—41no—
189C2×C4×C37—41no—
190C2×C4×C37—41no—
191C2×C4×C37—82no—
192C2×C4×C37—82no—
193C2×C4×C37—81no—
194C2×C4×C37—81no—
195C2×C4×C37#12111yescharacteristic
196C2×C4×C37#12111yescharacteristic
197C2×C4×C37#12111yescharacteristic
198C2×C4×C37#12111yescharacteristic
199C2×C4×C37C22×D411yescharacteristic
200C2×C4×C37C22×D411yescharacteristic
201C2×C4×C37C22×Q811yescharacteristic
202C2×C4×C37C2×#4111yescharacteristic
203C2×C4×C37H(5,𝔽2)11yescharacteristic
204C2×C4×C372−1+411yescharacteristic
205C8×C37—22no—
206C8×C37—42no—
207C8×C37—42no—
208C8×C37—42no—
209C8×C37C22⋊Q814yes—
210#28298C3711yesmaximal, characteristic, direct product factor, Sylow
211C22×C37—21no—
212C22×C37—21no—
213C22×C37—42no—
214C22×C37—82no—
215C22×C37—82no—
216C22×C37—81no—
217C22×C37—81no—
218C22×C37C2×#12111yescharacteristic
219C22×C37#55411yescharacteristic
220C22×C37#55611yescharacteristic
221C4×C37—21no—
222C4×C37—21no—
223C4×C37—21no—
224C4×C37—21no—
225C4×C37—42no—
226C4×C37—42no—
227C4×C37—42no—
228C4×C37—81no—
229C4×C37—81no—
230C4×C37C2×C22⋊Q811yescharacteristic
231C4×C37#53711yescharacteristic
232C4×C37D4×Q811yescharacteristic
233C4×C37#55011yescharacteristic
234#3078C2×C3711yescharacteristic, complemented
235#3077C2×C3711yescharacteristic
236#2961C2×C3711yescharacteristic, complemented
237C2×#440C2×C3711yescharacteristic
238#2064C2×C3712yescomplemented
239#2063C2×C3712yes—
240#1977C2×C3712yes—
241#1952C2×C3712yescomplemented
242#1849C2×C3711yescharacteristic, complemented
243#1801C2×C3711yescharacteristic, complemented
244#1800C2×C3711yescharacteristic
245C2×C37—21no—
246C2×C37—21no—
247C2×C37—82no—
248C2×C37#253811yescharacteristic
249C2×C37#306811yescharacteristic
250C2×C37#306911yescharacteristic
251C22×SD16C22×C3711yescharacteristic
252#533C22×C3711yescharacteristic
253C2×C4×Q8C22×C3711yescharacteristic
254C2×C4×D4C22×C3711yescharacteristic
255#479—22no—
256#478—22no—
257#477—21no—
258#476—21no—
259#475—21no—
260#474—21no—
261#446—22no—
262#446—22no—
263#440—22no—
264#440—22no—
265C2×#108C22×C3712yes—
266C2×#108C22×C3712yes—
267#428C22×C3712yes—
268#428C22×C3712yes—
269C2×#107C22×C3711yescharacteristic
270#424C22×C3712yes—
271#423C22×C3711yescharacteristic
272#423C22×C3711yescharacteristic
273#423C22×C3711yescharacteristic
274#419C22×C3712yes—
275#418C22×C3712yes—
276C2×#103C22×C3711yescharacteristic
277C2×#102C22×C3711yescharacteristic
278C2×#101C22×C3712yes—
279C2×#100C22×C3712yes—
280#405C22×C3712yes—
281C2×#97C22×C3711yescharacteristic
282#343C22×C3712yes—
283#343C22×C3712yes—
284C37#2829811yescharacteristic, direct product factor, Sylow
285C22×Q8C23×C3711yescharacteristic
286C22×D4C23×C3711yescharacteristic
287C23×C4—21no—
288C2×SD16—22no—
289C2×SD16—22no—
290C2×SD16Q8×C3714yescomplemented
291C2×M16C23×C3712yes—
292C2×M16C23×C3712yes—
293C2×M16C23×C3712yes—
294C22×C8C23×C3711yescharacteristic
295C22×C8C23×C3711yescharacteristic
296C4⋊Q8D4×C3711yescharacteristic
297C4⋊Q8D4×C3711yescharacteristic
298#125D4×C3712yes—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311#117C23×C3712yes—
312C2×C4⋊C4—21no—
313C2×C4⋊C4C23×C3711yescharacteristic
314C2×C4⋊C4C23×C3711yescharacteristic
315C2×C22⋊C4—21no—
316C2×C42—21no—
317C2×C42C23×C3711yescharacteristic
318#108—24no—
319#108—42no—
320#107—22no—
321#107—22no—
322#107—22no—
323#106—22no—
324#106—22no—
325C4⋊C8—24no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8—21no—
329C4⋊C8—21no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332#103—22no—
333#103—22no—
334#103—22no—
335#102—22no—
336#102—22no—
337#102—22no—
338#101—42no—
339#100—42no—
340#97—22no—
341#97D4×C3712yes—
342#97D4×C3712yes—
343C4×C8—22no—
344C24—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8C2×Q8×C3712yes—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4C2×Q8×C3712yes—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—82no—
365C22×C4#41×C3711yescharacteristic
366C22×C4#41×C3711yescharacteristic
367C22×C4C24×C3711yescharacteristic
368SD16—28no—
369M16—22no—
370M16—22no—
371M16—22no—
372M16—22no—
373M16—22no—
374M16—22no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8C2×D4×C3712yes—
381C2×C8C2×D4×C3712yes—
382C2×C8C2×Q8×C3712yes—
383C2×C8#41×C3712yes—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4C2×D4×C3712yes—
395C4⋊C4C2×D4×C3712yes—
396C22⋊C4—22no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C42—22no—
400C42—41no—
401C42—41no—
402C42C2×D4×C3711yescharacteristic
403C42C2×D4×C3711yescharacteristic
404C42C2×D4×C3711yescharacteristic
405C42C2×D4×C3711yescharacteristic
406C23—22no—
407C23—41no—
408C23—41no—
409C23—81no—
410C23—81no—
411C23C2×#41×C3711yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—41no—
415Q8—41no—
416Q8—81no—
417Q8—81no—
418D4—22no—
419D4—22no—
420D4—41no—
421D4—41no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4#121×C3711yescharacteristic
436C2×C4#121×C3711yescharacteristic
437C2×C4#121×C3711yescharacteristic
438C2×C4#121×C3711yescharacteristic
439C2×C4C22×D4×C3711yescharacteristic
440C2×C4C22×D4×C3711yescharacteristic
441C2×C4C22×Q8×C3711yescharacteristic
442C2×C4C2×#41×C3711yescharacteristic
443C2×C4H(5,𝔽2)×C3711yescharacteristic
444C2×C42−1+4×C3711yescharacteristic
445C8—22no—
446C8—42no—
447C8—42no—
448C8—42no—
449C8C22⋊Q8×C3714yes—
450C22—21no—
451C22—21no—
452C22—42no—
453C22—82no—
454C22—82no—
455C22—81no—
456C22—81no—
457C22C2×#121×C3711yescharacteristic
458C22C37×#55411yescharacteristic
459C22C37×#55611yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4C2×C22⋊Q8×C3711yescharacteristic
470C4C37×#53711yescharacteristic
471C4D4×Q8×C3711yescharacteristic
472C4C37×#55011yescharacteristic
473C2—21no—
474C2—21no—
475C2—82no—
476C2C37×#253811yescharacteristic
477C2C37×#306811yescharacteristic
478C2C37×#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×#3078C2semidirect
3. C37×#2961C2semidirect
5. C37×#2064C2semidirect
8. C37×#1952C2semidirect
9. C37×#1849C2semidirect
10. C37×#1801C2semidirect
50. C2×SD16×C37Q8semidirect
210. #28298C37direct (N × H)
234. #3078C2×C37semidirect
236. #2961C2×C37semidirect
238. #2064C2×C37semidirect
241. #1952C2×C37semidirect
242. #1849C2×C37semidirect
243. #1801C2×C37semidirect
284. C37#28298direct (N × H)
290. C2×SD16Q8×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#30782
C37×#30772
C37×#29612
C2×C37×#4402
C37×#20642
C37×#20632
C37×#19772
C37×#19522
C37×#18492
C37×#18012
C37×#18002
#2829837