Finite Group Databasebeta

← C37×#19057 #22640310

Subgroups — C37×#19057 #22640310

Order 9472.

908 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3548C211yesmaximal, characteristic
2C37×#3237C211yesmaximal, characteristic, complemented
3C37×#3216C211yesmaximal, characteristic, complemented
4C37×#3135C211yesmaximal, characteristic, complemented
5C37×#1662C214yesmaximal, complemented
6C37×#1661C214yesmaximal, complemented
7C37×#1536C211yesmaximal, characteristic, complemented
8C37×#1531C211yesmaximal, characteristic, complemented
9C37×#1530C211yesmaximal, characteristic, complemented
10C37×#562C2214yes—
11C37×#554—21no—
12C37×#554—21no—
13C37×#550—21no—
14C37×#550—21no—
15C37×#547—21no—
16C37×#547—21no—
17C37×#540—22no—
18C37×#537—22no—
19C37×#537—22no—
20C37×#533C2211yescharacteristic
21C37×#533C2211yescharacteristic
22C37×#532C2211yescharacteristic
23C37×#532C2211yescharacteristic
24C37×#501C2212yes—
25C37×#497C2212yes—
26C37×#491—21no—
27C37×#491C2212yes—
28C37×#490—21no—
29C37×#489C2212yes—
30C37×#489C2212yes—
31C37×#489C2212yes—
32C37×#485—22no—
33C37×#477—21no—
34C37×#475—21no—
35C37×#462—21no—
36C37×#460—21no—
37C37×#452—22no—
38C37×#432C2211yescharacteristic
39C37×#432C2211yescharacteristic
40C37×#416—22no—
41C2×#97×C37C2211yescharacteristic
42C37×#330C2214yes—
43C37×#329C2214yes—
44C37×#329C2214yes—
45C2×#41×C37—22no—
46C2×#41×C37—22no—
47C2×#41×C37D412yes—
48C2×#41×C37D412yes—
49C2×Q16×C37—22no—
50C2×SD16×C37—22no—
51C22×C8×C37—21no—
52C4⋊Q8×C37D411yescharacteristic
53C4⋊Q8×C37D411yescharacteristic
54C4⋊Q8×C37D411yescharacteristic
55C4⋊Q8×C37D411yescharacteristic
56C4⋊Q8×C37C2311yescharacteristic
57C4⋊Q8×C37C2311yescharacteristic
58#127×C37—22no—
59#127×C37D411yescharacteristic
60#127×C37D411yescharacteristic
61#125×C37—22no—
62#125×C37—21no—
63#125×C37C2312yes—
64#124×C37C2312yes—
65#124×C37C2312yes—
66#123×C37—24no—
67#123×C37—24no—
68C22⋊Q8×C37—22no—
69C22⋊Q8×C37—22no—
70C22⋊Q8×C37—24no—
71C22⋊Q8×C37—24no—
72C22⋊Q8×C37—21no—
73C22⋊Q8×C37—21no—
74C22⋊Q8×C37—21no—
75C22⋊Q8×C37—21no—
76#121×C37—24no—
77#121×C37—24no—
78#121×C37—22no—
79#121×C37—22no—
80#121×C37—24no—
81#121×C37—24no—
82#121×C37—21no—
83#121×C37—21no—
84#121×C37—21no—
85#121×C37—21no—
86C4×Q8×C37—21no—
87C4×Q8×C37—21no—
88C4×Q8×C37—21no—
89C4×Q8×C37—21no—
90C4×D4×C37—22no—
91C4×D4×C37—22no—
92C4×D4×C37—21no—
93C4×D4×C37—21no—
94C4×D4×C37—21no—
95C4×D4×C37—21no—
96#117×C37—21no—
97#117×C37D412yes—
98C2×C4⋊C4×C37—22no—
99C2×C4⋊C4×C37—22no—
100C2×C42×C37C2311yescharacteristic
101#107×C37—22no—
102#106×C37—22no—
103C4⋊C8×C37—21no—
104C4⋊C8×C37—21no—
105#103×C37—22no—
106#103×C37—22no—
107#103×C37—22no—
108#103×C37—22no—
109#103×C37—22no—
110#102×C37—22no—
111#102×C37—22no—
112#102×C37—22no—
113C22⋊C8×C37—21no—
114C22⋊C8×C37—21no—
115#97×C37—21no—
116#97×C37C2312yes—
117#97×C37C2312yes—
118#97×C37C2312yes—
119#41×C37—44no—
120#41×C37—82no—
121#41×C37—84no—
122#41×C37—84no—
123C2×Q8×C37—21no—
124C2×Q8×C37—21no—
125C2×Q8×C37—21no—
126C2×Q8×C37—21no—
127C2×Q8×C37C2×D412yes—
128C2×Q8×C37C2×D412yes—
129C2×D4×C37—24no—
130C2×D4×C37—24no—
131C2×D4×C37—22no—
132C2×D4×C37—22no—
133C2×D4×C37—21no—
134C2×D4×C37—21no—
135C2×D4×C37—21no—
136C2×D4×C37—21no—
137C2×D4×C37C2×D412yes—
138C2×D4×C37C2×D412yes—
139C22×C4×C37—24no—
140C22×C4×C37—24no—
141C22×C4×C37—22no—
142C22×C4×C37—22no—
143C22×C4×C37C2×D411yescharacteristic
144C22×C4×C37C2×D411yescharacteristic
145C22×C4×C37C2×D411yescharacteristic
146Q16×C37—82no—
147SD16×C37—82no—
148C2×C8×C37—22no—
149C2×C8×C37—22no—
150C2×C8×C37—22no—
151C2×C8×C37—42no—
152C4⋊C4×C37—24no—
153C4⋊C4×C37—24no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—21no—
157C4⋊C4×C37—21no—
158C4⋊C4×C37—21no—
159C4⋊C4×C37—21no—
160C4⋊C4×C37—22no—
161C4⋊C4×C37—22no—
162C4⋊C4×C37—21no—
163C4⋊C4×C37—21no—
164C4⋊C4×C37—21no—
165C4⋊C4×C37—21no—
166C4⋊C4×C37—41no—
167C4⋊C4×C37—41no—
168C4⋊C4×C37C2×D412yes—
169C4⋊C4×C37C2×D412yes—
170C22⋊C4×C37—24no—
171C22⋊C4×C37—24no—
172C22⋊C4×C37—22no—
173C22⋊C4×C37—22no—
174C22⋊C4×C37—22no—
175C22⋊C4×C37—22no—
176C22⋊C4×C37—22no—
177C22⋊C4×C37—41no—
178C42×C37—22no—
179C42×C37—41no—
180C42×C37C2×D411yescharacteristic
181C42×C37C2×D411yescharacteristic
182C42×C37C2×D411yescharacteristic
183C42×C37C2411yescharacteristic
184C23×C37—22no—
185C23×C37—22no—
186C23×C37#12011yescharacteristic
187Q8×C37—42no—
188Q8×C37—42no—
189Q8×C37—42no—
190Q8×C37—41no—
191Q8×C37—41no—
192Q8×C37—42no—
193Q8×C37—42no—
194D4×C37—42no—
195D4×C37—42no—
196D4×C37—42no—
197D4×C37—42no—
198D4×C37—42no—
199D4×C37—42no—
200D4×C37—82no—
201D4×C37—82no—
202D4×C37—84no—
203D4×C37—84no—
204C2×C4×C37—22no—
205C2×C4×C37—22no—
206C2×C4×C37—22no—
207C2×C4×C37—22no—
208C2×C4×C37—22no—
209C2×C4×C37—41no—
210C2×C4×C37—41no—
211C2×C4×C37—44no—
212C2×C4×C37—44no—
213C2×C4×C37—41no—
214C2×C4×C37—41no—
215C2×C4×C37—84no—
216C2×C4×C37—84no—
217C2×C4×C37#12011yescharacteristic
218C2×C4×C37#12011yescharacteristic
219C2×C4×C37#12011yescharacteristic
220C2×C4×C37C22×D411yescharacteristic
221C2×C4×C37C22×D411yescharacteristic
222C2×C4×C37C22×D411yescharacteristic
223C8×C37—42no—
224C8×C37—42no—
225C8×C37—42no—
226#19057C3711yesmaximal, characteristic, direct product factor, Sylow
227C22×C37—21no—
228C22×C37—21no—
229C22×C37—21no—
230C22×C37—42no—
231C22×C37—42no—
232C22×C37—42no—
233C22×C37—42no—
234C22×C37—42no—
235C22×C37—42no—
236C22×C37C2×#12011yescharacteristic
237C4×C37—21no—
238C4×C37—21no—
239C4×C37—21no—
240C4×C37—21no—
241C4×C37—21no—
242C4×C37—42no—
243C4×C37—42no—
244C4×C37—42no—
245C4×C37—42no—
246C4×C37—81no—
247C4×C37—81no—
248C4×C37#45512yes—
249#3548C2×C3711yescharacteristic
250#3237C2×C3711yescharacteristic, complemented
251#3216C2×C3711yescharacteristic, complemented
252#3135C2×C3711yescharacteristic, complemented
253#1662C2×C3714yescomplemented
254#1661C2×C3714yescomplemented
255#1536C2×C3711yescharacteristic, complemented
256#1531C2×C3711yescharacteristic, complemented
257#1530C2×C3711yescharacteristic, complemented
258C2×C37—41no—
259C2×C37—82no—
260C2×C37—82no—
261C2×C37C2×#45511yescharacteristic
262C2×C37#301911yescharacteristic
263C2×C37#302011yescharacteristic
264#562C22×C3714yes—
265#554—21no—
266#554—21no—
267#550—21no—
268#550—21no—
269#547—21no—
270#547—21no—
271#540—22no—
272#537—22no—
273#537—22no—
274#533C22×C3711yescharacteristic
275#533C22×C3711yescharacteristic
276#532C22×C3711yescharacteristic
277#532C22×C3711yescharacteristic
278#501C22×C3712yes—
279#497C22×C3712yes—
280#491—21no—
281#491C22×C3712yes—
282#490—21no—
283#489C22×C3712yes—
284#489C22×C3712yes—
285#489C22×C3712yes—
286#485—22no—
287#477—21no—
288#475—21no—
289#462—21no—
290#460—21no—
291#452—22no—
292#432C22×C3711yescharacteristic
293#432C22×C3711yescharacteristic
294#416—22no—
295C2×#97C22×C3711yescharacteristic
296#330C22×C3714yes—
297#329C22×C3714yes—
298#329C22×C3714yes—
299C37#1905711yescharacteristic, direct product factor, Sylow
300C2×#41—22no—
301C2×#41—22no—
302C2×#41D4×C3712yes—
303C2×#41D4×C3712yes—
304C2×Q16—22no—
305C2×SD16—22no—
306C22×C8—21no—
307C4⋊Q8D4×C3711yescharacteristic
308C4⋊Q8D4×C3711yescharacteristic
309C4⋊Q8D4×C3711yescharacteristic
310C4⋊Q8D4×C3711yescharacteristic
311C4⋊Q8C23×C3711yescharacteristic
312C4⋊Q8C23×C3711yescharacteristic
313#127—22no—
314#127D4×C3711yescharacteristic
315#127D4×C3711yescharacteristic
316#125—22no—
317#125—21no—
318#125C23×C3712yes—
319#124C23×C3712yes—
320#124C23×C3712yes—
321#123—24no—
322#123—24no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331#121—24no—
332#121—24no—
333#121—22no—
334#121—22no—
335#121—24no—
336#121—24no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351#117—21no—
352#117D4×C3712yes—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C42C23×C3711yescharacteristic
356#107—22no—
357#106—22no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360#103—22no—
361#103—22no—
362#103—22no—
363#103—22no—
364#103—22no—
365#102—22no—
366#102—22no—
367#102—22no—
368C22⋊C8—21no—
369C22⋊C8—21no—
370#97—21no—
371#97C23×C3712yes—
372#97C23×C3712yes—
373#97C23×C3712yes—
374#41—44no—
375#41—82no—
376#41—84no—
377#41—84no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8C2×D4×C3712yes—
383C2×Q8C2×D4×C3712yes—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4C2×D4×C3712yes—
393C2×D4C2×D4×C3712yes—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4C2×D4×C3711yescharacteristic
399C22×C4C2×D4×C3711yescharacteristic
400C22×C4C2×D4×C3711yescharacteristic
401Q16—82no—
402SD16—82no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—42no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4C2×D4×C3712yes—
424C4⋊C4C2×D4×C3712yes—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—41no—
433C42—22no—
434C42—41no—
435C42C2×D4×C3711yescharacteristic
436C42C2×D4×C3711yescharacteristic
437C42C2×D4×C3711yescharacteristic
438C42C24×C3711yescharacteristic
439C23—22no—
440C23—22no—
441C23#120×C3711yescharacteristic
442Q8—42no—
443Q8—42no—
444Q8—42no—
445Q8—41no—
446Q8—41no—
447Q8—42no—
448Q8—42no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—82no—
456D4—82no—
457D4—84no—
458D4—84no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—84no—
471C2×C4—84no—
472C2×C4#120×C3711yescharacteristic
473C2×C4#120×C3711yescharacteristic
474C2×C4#120×C3711yescharacteristic
475C2×C4C22×D4×C3711yescharacteristic
476C2×C4C22×D4×C3711yescharacteristic
477C2×C4C22×D4×C3711yescharacteristic
478C8—42no—
479C8—42no—
480C8—42no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22C2×#120×C3711yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—81no—
501C4—81no—
502C4C37×#45512yes—
503C2—41no—
504C2—82no—
505C2—82no—
506C2C2×C37×#45511yescharacteristic
507C2C37×#301911yescharacteristic
508C2C37×#302011yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3548C2
LCSG ▷ C42 ▷ 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×#3237C2semidirect
3. C37×#3216C2semidirect
4. C37×#3135C2semidirect
5. C37×#1662C2semidirect
6. C37×#1661C2semidirect
7. C37×#1536C2semidirect
8. C37×#1531C2semidirect
9. C37×#1530C2semidirect
226. #19057C37direct (N × H)
250. #3237C2×C37semidirect
251. #3216C2×C37semidirect
252. #3135C2×C37semidirect
253. #1662C2×C37semidirect
254. #1661C2×C37semidirect
255. #1536C2×C37semidirect
256. #1531C2×C37semidirect
257. #1530C2×C37semidirect
299. C37#19057direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35482
C37×#32372
C37×#32162
C37×#31352
C37×#16622
C37×#16612
C37×#15362
C37×#15312
C37×#15302
#1905737