Finite Group Databasebeta

← C37×#8470 #22629723

Subgroups — C37×#8470 #22629723

Order 9472.

754 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3511C211yesmaximal, characteristic
2C37×#1997C211yesmaximal, characteristic, complemented
3C37×#1966C211yesmaximal, characteristic, complemented
4C37×#1560C211yesmaximal, characteristic, complemented
5C37×#1525C211yesmaximal, characteristic, complemented
6C37×#1489C211yesmaximal, characteristic, complemented
7C37×#1489C211yesmaximal, characteristic, complemented
8C37×#556—21no—
9C37×#555—21no—
10C37×#554—21no—
11C37×#553—22no—
12C37×#548—22no—
13C37×#547—21no—
14C37×#542—22no—
15C37×#537C412yes—
16C37×#533—21no—
17C37×#532—21no—
18C37×#532C2211yescharacteristic
19C2×C4⋊Q8×C37C2211yescharacteristic
20C37×#520C412yes—
21C4×#41×C37C2211yescharacteristic
22C37×#423C2211yescharacteristic
23C37×#423C2211yescharacteristic
24C2×#101×C37—22no—
25C4×M16×C37C2211yescharacteristic
26C4×M16×C37C2211yescharacteristic
27C37×#343—22no—
28C37×#333—21no—
29C37×#331—21no—
30C37×#329—22no—
31C37×Q8⋊C8—21no—
32C37×Q8⋊C8—21no—
33C37×D4⋊C8—21no—
34C37×D4⋊C8—21no—
35C2×#41×C37—22no—
36C2×#41×C37C2×C412yes—
37C2×#41×C37C2×C411yescharacteristic
38C22×Q8×C37D412yes—
39C2×M16×C37—21no—
40C2×M16×C37—21no—
41C2×M16×C37—21no—
42C2×M16×C37—21no—
43C4⋊Q8×C37—21no—
44C4⋊Q8×C37—21no—
45C4⋊Q8×C37—21no—
46C4⋊Q8×C37—21no—
47C4⋊Q8×C37D411yescharacteristic
48#127×C37D411yescharacteristic
49#126×C37—24no—
50#125×C37—22no—
51#124×C37—22no—
52#124×C37—24no—
53#124×C37D412yes—
54#123×C37—24no—
55C22⋊Q8×C37—22no—
56C22⋊Q8×C37—24no—
57C22⋊Q8×C37—22no—
58C22⋊Q8×C37—22no—
59#121×C37—22no—
60#121×C37—22no—
61#121×C37—22no—
62#121×C37—24no—
63#121×C37—21no—
64#121×C37—21no—
65C4×Q8×C37—22no—
66C4×Q8×C37—22no—
67C4×Q8×C37D411yescharacteristic
68C4×Q8×C37D411yescharacteristic
69C4×D4×C37—22no—
70C4×D4×C37—22no—
71C4×D4×C37—24no—
72C4×D4×C37—21no—
73C4×D4×C37—21no—
74C4×D4×C37—21no—
75C4×D4×C37—21no—
76C4×D4×C37D411yescharacteristic
77C4×D4×C37D411yescharacteristic
78#117×C37—22no—
79#117×C37—22no—
80#117×C37—21no—
81#117×C37C2×C411yescharacteristic
82C2×C4⋊C4×C37—22no—
83C2×C4⋊C4×C37C2×C412yes—
84C2×C4⋊C4×C37D412yes—
85C2×C42×C37—21no—
86C2×C42×C37C2311yescharacteristic
87C4⋊C8×C37—21no—
88C4⋊C8×C37—21no—
89C4⋊C8×C37—21no—
90C4⋊C8×C37—21no—
91#101×C37—44no—
92#97×C37—21no—
93#97×C37—21no—
94C4×C8×C37—21no—
95C4×C8×C37—21no—
96#41×C37—42no—
97#41×C37—44no—
98#41×C37—82no—
99#41×C37—82no—
100C2×Q8×C37—22no—
101C2×Q8×C37—22no—
102C2×Q8×C37—42no—
103C2×Q8×C37—42no—
104C2×Q8×C37C22⋊C411yescharacteristic
105C2×Q8×C37C22⋊C412yes—
106C2×D4×C37—22no—
107C2×D4×C37—21no—
108C2×D4×C37—24no—
109C2×D4×C37—21no—
110C2×D4×C37—21no—
111C2×D4×C37C22⋊C411yescharacteristic
112C2×D4×C37C22⋊C412yes—
113C22×C4×C37—24no—
114C22×C4×C37—21no—
115C22×C4×C37—22no—
116C22×C4×C37—21no—
117C22×C4×C37—21no—
118C22×C4×C37C22⋊C414yes—
119C22×C4×C37C22×C411yescharacteristic
120C22×C4×C37C2×D411yescharacteristic
121C22×C4×C37C2×D411yescharacteristic
122M16×C37—22no—
123M16×C37—22no—
124M16×C37—41no—
125M16×C37—41no—
126M16×C37—42no—
127M16×C37—42no—
128C2×C8×C37—41no—
129C2×C8×C37—41no—
130C2×C8×C37—41no—
131C2×C8×C37—41no—
132C4⋊C4×C37—24no—
133C4⋊C4×C37—24no—
134C4⋊C4×C37—22no—
135C4⋊C4×C37—22no—
136C4⋊C4×C37—22no—
137C4⋊C4×C37—22no—
138C4⋊C4×C37—21no—
139C4⋊C4×C37—21no—
140C4⋊C4×C37—21no—
141C4⋊C4×C37—21no—
142C4⋊C4×C37C22⋊C411yescharacteristic
143C4⋊C4×C37C22⋊C411yescharacteristic
144C22⋊C4×C37—24no—
145C22⋊C4×C37—24no—
146C22⋊C4×C37—24no—
147C22⋊C4×C37—21no—
148C22⋊C4×C37—21no—
149C22⋊C4×C37—21no—
150C22⋊C4×C37—22no—
151C22⋊C4×C37—22no—
152C42×C37—24no—
153C42×C37—21no—
154C42×C37—21no—
155C42×C37—21no—
156C42×C37C2×D411yescharacteristic
157C42×C37C2×D411yescharacteristic
158C42×C37C2×D411yescharacteristic
159C42×C37C2×D411yescharacteristic
160C23×C37—21no—
161C23×C37—22no—
162C23×C37C2×C22⋊C411yescharacteristic
163Q8×C37—22no—
164Q8×C37—42no—
165Q8×C37—42no—
166Q8×C37—42no—
167Q8×C37—82no—
168D4×C37—22no—
169D4×C37—42no—
170D4×C37—42no—
171D4×C37—44no—
172D4×C37—41no—
173D4×C37—41no—
174D4×C37—41no—
175D4×C37—41no—
176D4×C37—84no—
177C2×C4×C37—22no—
178C2×C4×C37—21no—
179C2×C4×C37—21no—
180C2×C4×C37—21no—
181C2×C4×C37—21no—
182C2×C4×C37—21no—
183C2×C4×C37—21no—
184C2×C4×C37—22no—
185C2×C4×C37—21no—
186C2×C4×C37—24no—
187C2×C4×C37—42no—
188C2×C4×C37—44no—
189C2×C4×C37—41no—
190C2×C4×C37—41no—
191C2×C4×C37—41no—
192C2×C4×C37—41no—
193C2×C4×C37—44no—
194C2×C4×C37—84no—
195C2×C4×C37C2×C22⋊C411yescharacteristic
196C2×C4×C37C2×C22⋊C411yescharacteristic
197C2×C4×C37#12011yescharacteristic
198C2×C4×C37#12011yescharacteristic
199C2×C4×C37#12011yescharacteristic
200C2×C4×C37#12011yescharacteristic
201C8×C37—42no—
202C8×C37—42no—
203C8×C37—81no—
204C8×C37—81no—
205#8470C3711yesmaximal, characteristic, direct product factor, Sylow
206C22×C37—21no—
207C22×C37—21no—
208C22×C37—21no—
209C22×C37—41no—
210C22×C37—42no—
211C22×C37—41no—
212C22×C37—42no—
213C22×C37—41no—
214C22×C37—42no—
215C22×C37#37911yescharacteristic
216C4×C37—21no—
217C4×C37—21no—
218C4×C37—21no—
219C4×C37—41no—
220C4×C37—44no—
221C4×C37—41no—
222C4×C37—41no—
223C4×C37—42no—
224C4×C37#41312yes—
225C4×C37#45311yescharacteristic
226C4×C37#45411yescharacteristic
227C4×C37#45511yescharacteristic
228C4×C37#45611yescharacteristic
229#3511C2×C3711yescharacteristic
230#1997C2×C3711yescharacteristic, complemented
231#1966C2×C3711yescharacteristic, complemented
232#1560C2×C3711yescharacteristic, complemented
233#1525C2×C3711yescharacteristic, complemented
234#1489C2×C3711yescharacteristic, complemented
235#1489C2×C3711yescharacteristic, complemented
236C2×C37—41no—
237C2×C37—81no—
238C2×C37—82no—
239C2×C37#178511yescharacteristic
240C2×C37#179211yescharacteristic
241C2×C37#179311yescharacteristic
242#556—21no—
243#555—21no—
244#554—21no—
245#553—22no—
246#548—22no—
247#547—21no—
248#542—22no—
249#537C4×C3712yes—
250#533—21no—
251#532—21no—
252#532C22×C3711yescharacteristic
253C2×C4⋊Q8C22×C3711yescharacteristic
254#520C4×C3712yes—
255C4×#41C22×C3711yescharacteristic
256#423C22×C3711yescharacteristic
257#423C22×C3711yescharacteristic
258C2×#101—22no—
259C4×M16C22×C3711yescharacteristic
260C4×M16C22×C3711yescharacteristic
261#343—22no—
262#333—21no—
263#331—21no—
264#329—22no—
265Q8⋊C8—21no—
266Q8⋊C8—21no—
267D4⋊C8—21no—
268D4⋊C8—21no—
269C37#847011yescharacteristic, direct product factor, Sylow
270C2×#41—22no—
271C2×#41C2×C4×C3711yescharacteristic
272C2×#41C2×C4×C3712yes—
273C22×Q8D4×C3712yes—
274C2×M16—21no—
275C2×M16—21no—
276C2×M16—21no—
277C2×M16—21no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8D4×C3711yescharacteristic
283#127D4×C3711yescharacteristic
284#126—24no—
285#125—22no—
286#124—22no—
287#124—24no—
288#124D4×C3712yes—
289#123—24no—
290C22⋊Q8—22no—
291C22⋊Q8—24no—
292C22⋊Q8—22no—
293C22⋊Q8—22no—
294#121—22no—
295#121—22no—
296#121—22no—
297#121—24no—
298#121—21no—
299#121—21no—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×Q8D4×C3711yescharacteristic
303C4×Q8D4×C3711yescharacteristic
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—24no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4D4×C3711yescharacteristic
312C4×D4D4×C3711yescharacteristic
313#117—22no—
314#117—22no—
315#117—21no—
316#117C2×C4×C3711yescharacteristic
317C2×C4⋊C4—22no—
318C2×C4⋊C4C2×C4×C3712yes—
319C2×C4⋊C4D4×C3712yes—
320C2×C42—21no—
321C2×C42C23×C3711yescharacteristic
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8—21no—
325C4⋊C8—21no—
326#101—44no—
327#97—21no—
328#97—21no—
329C4×C8—21no—
330C4×C8—21no—
331#41—42no—
332#41—44no—
333#41—82no—
334#41—82no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—42no—
338C2×Q8—42no—
339C2×Q8C22⋊C4×C3711yescharacteristic
340C2×Q8C22⋊C4×C3712yes—
341C2×D4—22no—
342C2×D4—21no—
343C2×D4—24no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4C22⋊C4×C3711yescharacteristic
347C2×D4C22⋊C4×C3712yes—
348C22×C4—24no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4C22⋊C4×C3714yes—
354C22×C4C22×C4×C3711yescharacteristic
355C22×C4C2×D4×C3711yescharacteristic
356C22×C4C2×D4×C3711yescharacteristic
357M16—22no—
358M16—22no—
359M16—41no—
360M16—41no—
361M16—42no—
362M16—42no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4C22⋊C4×C3711yescharacteristic
378C4⋊C4C22⋊C4×C3711yescharacteristic
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C42—24no—
388C42—21no—
389C42—21no—
390C42—21no—
391C42C2×D4×C3711yescharacteristic
392C42C2×D4×C3711yescharacteristic
393C42C2×D4×C3711yescharacteristic
394C42C2×D4×C3711yescharacteristic
395C23—21no—
396C23—22no—
397C23C2×C22⋊C4×C3711yescharacteristic
398Q8—22no—
399Q8—42no—
400Q8—42no—
401Q8—42no—
402Q8—82no—
403D4—22no—
404D4—42no—
405D4—42no—
406D4—44no—
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—84no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—44no—
429C2×C4—84no—
430C2×C4C2×C22⋊C4×C3711yescharacteristic
431C2×C4C2×C22⋊C4×C3711yescharacteristic
432C2×C4#120×C3711yescharacteristic
433C2×C4#120×C3711yescharacteristic
434C2×C4#120×C3711yescharacteristic
435C2×C4#120×C3711yescharacteristic
436C8—42no—
437C8—42no—
438C8—81no—
439C8—81no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—41no—
444C22—42no—
445C22—41no—
446C22—42no—
447C22—41no—
448C22—42no—
449C22C37×#37911yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—41no—
454C4—42no—
455C4—41no—
456C4—44no—
457C4—41no—
458C4C37×#41312yes—
459C4C37×#45311yescharacteristic
460C4C37×#45411yescharacteristic
461C4C37×#45511yescharacteristic
462C4C37×#45611yescharacteristic
463C2—41no—
464C2—81no—
465C2—82no—
466C2C37×#178511yescharacteristic
467C2C37×#179211yescharacteristic
468C2C37×#179311yescharacteristic
subgroupG/H
center, socleC22×C37#379
commutatorC22×C4C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC37×#3511C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#1997C2semidirect
3. C37×#1966C2semidirect
4. C37×#1560C2semidirect
5. C37×#1525C2semidirect
6. C37×#1489C2semidirect
7. C37×#1489C2semidirect
205. #8470C37direct (N × H)
230. #1997C2×C37semidirect
231. #1966C2×C37semidirect
232. #1560C2×C37semidirect
233. #1525C2×C37semidirect
234. #1489C2×C37semidirect
235. #1489C2×C37semidirect
269. C37#8470direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35112
C37×#19972
C37×#19662
C37×#15602
C37×#15252
C37×#14892
#847037