Finite Group Databasebeta

← C37×#9084 #22630337

Subgroups — C37×#9084 #22630337

Order 9472.

712 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#432C211yesmaximal, characteristic, complemented
2C2×C37×#388C211yesmaximal, characteristic
3C37×#1817C211yesmaximal, characteristic, complemented
4C2×C37×#323C212yesmaximal
5C37×#1280C212yesmaximal, complemented
6C22×C4⋊C4×C37C411yescharacteristic
7C22×C22⋊C4×C37C411yescharacteristic
8C22×C22⋊C4×C37C411yescharacteristic
9C22×C22⋊C4×C37C2211yescharacteristic
10C22×C42×C37C2211yescharacteristic
11C37×#432—24no—
12C2×C4⋊C8×C37—21no—
13C2×C22⋊C8×C37C2212yes—
14C2×C22⋊C8×C37C2212yes—
15C2×#97×C37—21no—
16C37×#388—21no—
17C37×#388—21no—
18C37×#388—21no—
19C37×#388—21no—
20C2×#95×C37C411yescharacteristic
21C2×#95×C37C2211yescharacteristic
22C37×#336—21no—
23C37×#336—21no—
24C37×#323—24no—
25C25×C37C2×C411yescharacteristic
26C23×C4×C37C2×C411yescharacteristic
27C23×C4×C37C2×C411yescharacteristic
28C23×C4×C37C2×C411yescharacteristic
29C23×C4×C37C2×C411yescharacteristic
30C23×C4×C37C2×C411yescharacteristic
31C23×C4×C37C2311yescharacteristic
32C22×C8×C37—22no—
33C22×C8×C37—22no—
34C2×C4⋊C4×C37—21no—
35C2×C4⋊C4×C37—21no—
36C2×C4⋊C4×C37—42no—
37C2×C22⋊C4×C37—22no—
38C2×C22⋊C4×C37—21no—
39C2×C22⋊C4×C37—21no—
40C2×C22⋊C4×C37—22no—
41C2×C22⋊C4×C37—21no—
42C2×C22⋊C4×C37—21no—
43C2×C22⋊C4×C37—22no—
44C2×C22⋊C4×C37—21no—
45C2×C22⋊C4×C37—21no—
46C2×C22⋊C4×C37—22no—
47C2×C22⋊C4×C37—42no—
48C2×C42×C37—22no—
49C2×C42×C37—22no—
50C2×C42×C37D411yescharacteristic
51C2×C42×C37D411yescharacteristic
52C2×C42×C37D411yescharacteristic
53C2×C42×C37D411yescharacteristic
54C4⋊C8×C37—24no—
55C22⋊C8×C37—22no—
56C22⋊C8×C37—22no—
57C22⋊C8×C37—22no—
58C22⋊C8×C37D414yes—
59#97×C37—24no—
60#95×C37—21no—
61#95×C37—21no—
62#95×C37—21no—
63#95×C37—21no—
64C24×C37—21no—
65C24×C37—21no—
66C24×C37—22no—
67C24×C37—22no—
68C24×C37—41no—
69C24×C37—41no—
70C24×C37—41no—
71C24×C37—41no—
72C24×C37M1612yes—
73C24×C37C22×C411yescharacteristic
74C22×C4×C37—21no—
75C22×C4×C37—22no—
76C22×C4×C37—22no—
77C22×C4×C37—21no—
78C22×C4×C37—21no—
79C22×C4×C37—21no—
80C22×C4×C37—22no—
81C22×C4×C37—22no—
82C22×C4×C37—21no—
83C22×C4×C37—21no—
84C22×C4×C37—22no—
85C22×C4×C37—22no—
86C22×C4×C37—41no—
87C22×C4×C37—41no—
88C22×C4×C37—41no—
89C22×C4×C37—41no—
90C22×C4×C37—41no—
91C22×C4×C37—41no—
92C22×C4×C37—41no—
93C22×C4×C37—41no—
94C22×C4×C37—41no—
95C22×C4×C37C22⋊C411yescharacteristic
96C22×C4×C37C22⋊C411yescharacteristic
97C22×C4×C37C22⋊C411yescharacteristic
98C22×C4×C37C22⋊C411yescharacteristic
99C22×C4×C37M1612yes—
100C22×C4×C37C2×D411yescharacteristic
101C22×C4×C37C2×D411yescharacteristic
102C22×C4×C37C2×D412yes—
103C22×C4×C37#4112yes—
104C2×C8×C37—24no—
105C2×C8×C37—42no—
106C2×C8×C37—42no—
107C2×C8×C37—42no—
108C2×C8×C37—42no—
109C2×C8×C37—42no—
110C4⋊C4×C37—42no—
111C4⋊C4×C37—42no—
112C22⋊C4×C37—24no—
113C22⋊C4×C37—24no—
114C22⋊C4×C37—42no—
115C22⋊C4×C37—42no—
116C22⋊C4×C37—41no—
117C22⋊C4×C37—42no—
118C22⋊C4×C37—41no—
119C42×C37—21no—
120C42×C37—21no—
121C42×C37—22no—
122C42×C37—22no—
123C42×C37—21no—
124C42×C37—21no—
125C23×C37—21no—
126C23×C37—21no—
127C23×C37—21no—
128C23×C37—21no—
129C23×C37—22no—
130C23×C37—24no—
131C23×C37—42no—
132C23×C37—42no—
133C23×C37—42no—
134C23×C37—42no—
135C23×C37—41no—
136C23×C37—41no—
137C23×C37—41no—
138C23×C37—41no—
139C23×C37—41no—
140C23×C37—41no—
141C23×C37—42no—
142C23×C37—82no—
143C23×C37—82no—
144C23×C37—82no—
145C23×C37—82no—
146C23×C37C2×C22⋊C411yescharacteristic
147C23×C37C4×D412yes—
148C23×C37C2×M1611yescharacteristic
149C23×C37C2×M1611yescharacteristic
150C23×C37#13112yes—
151C2×C4×C37—21no—
152C2×C4×C37—21no—
153C2×C4×C37—21no—
154C2×C4×C37—21no—
155C2×C4×C37—21no—
156C2×C4×C37—21no—
157C2×C4×C37—21no—
158C2×C4×C37—21no—
159C2×C4×C37—21no—
160C2×C4×C37—21no—
161C2×C4×C37—21no—
162C2×C4×C37—22no—
163C2×C4×C37—21no—
164C2×C4×C37—21no—
165C2×C4×C37—21no—
166C2×C4×C37—21no—
167C2×C4×C37—42no—
168C2×C4×C37—42no—
169C2×C4×C37—44no—
170C2×C4×C37—42no—
171C2×C4×C37—41no—
172C2×C4×C37—41no—
173C2×C4×C37—42no—
174C2×C4×C37—42no—
175C2×C4×C37—42no—
176C2×C4×C37—41no—
177C2×C4×C37—41no—
178C2×C4×C37—41no—
179C2×C4×C37—41no—
180C2×C4×C37—41no—
181C2×C4×C37—41no—
182C2×C4×C37—82no—
183C2×C4×C37—82no—
184C2×C4×C37#10012yes—
185C2×C4×C37#12011yescharacteristic
186C2×C4×C37#12112yes—
187C2×C4×C37#12311yescharacteristic
188C8×C37—44no—
189C8×C37—82no—
190#9084C3711yesmaximal, characteristic, direct product factor, Sylow
191C22×C37—22no—
192C22×C37—22no—
193C22×C37—21no—
194C22×C37—21no—
195C22×C37—21no—
196C22×C37—21no—
197C22×C37—22no—
198C22×C37—22no—
199C22×C37—42no—
200C22×C37—42no—
201C22×C37—42no—
202C22×C37—84no—
203C22×C37—84no—
204C22×C37—81no—
205C22×C37—81no—
206C22×C37—81no—
207C22×C37—81no—
208C22×C37#38611yescharacteristic
209C22×C37#40711yescharacteristic
210C22×C37#40811yescharacteristic
211C22×C37#41011yescharacteristic
212C22×C37#41011yescharacteristic
213C22×C37C2×#10011yescharacteristic
214C22×C37#41311yescharacteristic
215C22×C37#43512yes—
216C22×C37#43612yes—
217C4×C37—21no—
218C4×C37—22no—
219C4×C37—21no—
220C4×C37—22no—
221C4×C37—41no—
222C4×C37—41no—
223C4×C37—41no—
224C4×C37—42no—
225C4×C37—81no—
226C4×C37—81no—
227C2×#432C2×C3711yescharacteristic, complemented
228C2×#388C2×C3711yescharacteristic
229#1817C2×C3711yescharacteristic, complemented
230C2×#323C2×C3712yes—
231#1280C2×C3712yescomplemented
232C2×C37—22no—
233C2×C37—22no—
234C2×C37—82no—
235C2×C37#146411yescharacteristic
236C2×C37#146611yescharacteristic
237C2×C37#146911yescharacteristic
238C2×C37#147311yescharacteristic
239C2×C37#187011yescharacteristic
240C2×C37#189911yescharacteristic
241C2×C37#190011yescharacteristic
242C22×C4⋊C4C4×C3711yescharacteristic
243C22×C22⋊C4C4×C3711yescharacteristic
244C22×C22⋊C4C4×C3711yescharacteristic
245C22×C22⋊C4C22×C3711yescharacteristic
246C22×C42C22×C3711yescharacteristic
247#432—24no—
248C2×C4⋊C8—21no—
249C2×C22⋊C8C22×C3712yes—
250C2×C22⋊C8C22×C3712yes—
251C2×#97—21no—
252#388—21no—
253#388—21no—
254#388—21no—
255#388—21no—
256C2×#95C4×C3711yescharacteristic
257C2×#95C22×C3711yescharacteristic
258#336—21no—
259#336—21no—
260#323—24no—
261C37#908411yescharacteristic, direct product factor, Sylow
262C25C2×C4×C3711yescharacteristic
263C23×C4C2×C4×C3711yescharacteristic
264C23×C4C2×C4×C3711yescharacteristic
265C23×C4C2×C4×C3711yescharacteristic
266C23×C4C2×C4×C3711yescharacteristic
267C23×C4C2×C4×C3711yescharacteristic
268C23×C4C23×C3711yescharacteristic
269C22×C8—22no—
270C22×C8—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—42no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—42no—
285C2×C42—22no—
286C2×C42—22no—
287C2×C42D4×C3711yescharacteristic
288C2×C42D4×C3711yescharacteristic
289C2×C42D4×C3711yescharacteristic
290C2×C42D4×C3711yescharacteristic
291C4⋊C8—24no—
292C22⋊C8—22no—
293C22⋊C8—22no—
294C22⋊C8—22no—
295C22⋊C8D4×C3714yes—
296#97—24no—
297#95—21no—
298#95—21no—
299#95—21no—
300#95—21no—
301C24—21no—
302C24—21no—
303C24—22no—
304C24—22no—
305C24—41no—
306C24—41no—
307C24—41no—
308C24—41no—
309C24M16×C3712yes—
310C24C22×C4×C3711yescharacteristic
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4C22⋊C4×C3711yescharacteristic
333C22×C4C22⋊C4×C3711yescharacteristic
334C22×C4C22⋊C4×C3711yescharacteristic
335C22×C4C22⋊C4×C3711yescharacteristic
336C22×C4M16×C3712yes—
337C22×C4C2×D4×C3711yescharacteristic
338C22×C4C2×D4×C3711yescharacteristic
339C22×C4C2×D4×C3712yes—
340C22×C4#41×C3712yes—
341C2×C8—24no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—42no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—41no—
354C22⋊C4—42no—
355C22⋊C4—41no—
356C42—21no—
357C42—21no—
358C42—22no—
359C42—22no—
360C42—21no—
361C42—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—22no—
367C23—24no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—42no—
379C23—82no—
380C23—82no—
381C23—82no—
382C23—82no—
383C23C2×C22⋊C4×C3711yescharacteristic
384C23C4×D4×C3712yes—
385C23C2×M16×C3711yescharacteristic
386C23C2×M16×C3711yescharacteristic
387C23#131×C3712yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4#100×C3712yes—
422C2×C4#120×C3711yescharacteristic
423C2×C4#121×C3712yes—
424C2×C4#123×C3711yescharacteristic
425C8—44no—
426C8—82no—
427C22—22no—
428C22—22no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—22no—
434C22—22no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—84no—
439C22—84no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22C37×#38611yescharacteristic
445C22C37×#40711yescharacteristic
446C22C37×#40811yescharacteristic
447C22C37×#41011yescharacteristic
448C22C37×#41011yescharacteristic
449C22C2×#100×C3711yescharacteristic
450C22C37×#41311yescharacteristic
451C22C37×#43512yes—
452C22C37×#43612yes—
453C4—21no—
454C4—22no—
455C4—21no—
456C4—22no—
457C4—41no—
458C4—41no—
459C4—41no—
460C4—42no—
461C4—81no—
462C4—81no—
463C2—22no—
464C2—22no—
465C2—82no—
466C2C37×#146411yescharacteristic
467C2C37×#146611yescharacteristic
468C2C37×#146911yescharacteristic
469C2C37×#147311yescharacteristic
470C2C37×#187011yescharacteristic
471C2C37×#189911yescharacteristic
472C2C37×#190011yescharacteristic
subgroupG/H
center, socleC23×C37C2×C22⋊C4
commutatorC24C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC25×C37C2×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#432C2semidirect
3. C37×#1817C2semidirect
5. C37×#1280C2semidirect
190. #9084C37direct (N × H)
227. C2×#432C2×C37semidirect
229. #1817C2×C37semidirect
231. #1280C2×C37semidirect
261. C37#9084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4322
C2×C37×#3882
C37×#18172
C2×C37×#3232
C37×#12802
#908437