Finite Group Databasebeta

← C37×#22889 #22644142

Subgroups — C37×#22889 #22644142

Order 9472.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3002C211yesmaximal, characteristic
2C2×C37×#443C211yesmaximal, characteristic, complemented
3C37×#2933C211yesmaximal, characteristic, complemented
4C2×C37×#421C211yesmaximal, characteristic, complemented
5C37×#2880C211yesmaximal, characteristic, complemented
6C37×#1975C211yesmaximal, characteristic, complemented
7C37×#1937C211yesmaximal, characteristic, complemented
8C37×#1929C211yesmaximal, characteristic, complemented
9C37×#1897C211yesmaximal, characteristic, complemented
10C37×#1876C211yesmaximal, characteristic, complemented
11C37×#1876C211yesmaximal, characteristic, complemented
12C37×#1866C211yesmaximal, characteristic, complemented
13C37×#1855C211yesmaximal, characteristic, complemented
14C37×#1765C211yesmaximal, characteristic, complemented
15C37×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C2×#135×C37C2211yescharacteristic
18C2×#135×C37C2211yescharacteristic
19C2×#131×C37C2211yescharacteristic
20C2×#131×C37C2211yescharacteristic
21C2×#131×C37C2211yescharacteristic, complemented
22C22×M16×C37C2211yescharacteristic
23C37×#525C2211yescharacteristic
24C2×#117×C37C2211yescharacteristic
25C37×#452C411yescharacteristic, complemented
26C37×#452C411yescharacteristic, complemented
27C37×#451C411yescharacteristic, complemented
28C37×#450C411yescharacteristic, complemented
29C37×#449C411yescharacteristic, complemented
30C37×#449C411yescharacteristic, complemented
31C37×#448C411yescharacteristic, complemented
32C37×#447C411yescharacteristic, complemented
33C37×#443—24no—
34C37×#436—21no—
35C37×#435—21no—
36C37×#435—21no—
37C8×D4×C37—21no—
38C2×#108×C37C2211yescharacteristic, complemented
39C2×#108×C37C2211yescharacteristic, complemented
40C37×#424C2211yescharacteristic, complemented
41C37×#421—24no—
42C2×#104×C37C2211yescharacteristic
43C2×#104×C37C2211yescharacteristic
44C2×#104×C37C2211yescharacteristic
45C2×#104×C37C2211yescharacteristic
46C2×#104×C37C2211yescharacteristic, complemented
47C2×#104×C37C2211yescharacteristic, complemented
48C37×#416C2211yescharacteristic
49C37×#416C2211yescharacteristic
50C37×#408—21no—
51C37×#408—21no—
52C37×#408C2211yescharacteristic
53C37×#408C2211yescharacteristic
54C37×#408C2211yescharacteristic, complemented
55C37×#407—21no—
56C37×#407C2211yescharacteristic
57C2×C22⋊C8×C37—21no—
58C2×C22⋊C8×C37C2211yescharacteristic
59C2×C22⋊C8×C37C2211yescharacteristic
60C37×#405C2211yescharacteristic, complemented
61C2×#97×C37C2211yescharacteristic, complemented
62C2×C4×C8×C37C2211yescharacteristic, complemented
63C37×#341C2211yescharacteristic, complemented
64C37×#341C2211yescharacteristic, complemented
65C37×#339C2211yescharacteristic, complemented
66C37×#339C2211yescharacteristic, complemented
67C37×#336C2211yescharacteristic, complemented
68C37×#336C2211yescharacteristic, complemented
69C2×#41×C37—21no—
70C2×#41×C37—21no—
71C2×#41×C37—22no—
72C2×#41×C37—22no—
73C2×#41×C37—41no—
74C2×#41×C37—41no—
75C2×#41×C37C2×C411yescharacteristic
76C2×#41×C37C2×C411yescharacteristic
77C2×#41×C37C2311yescharacteristic
78C2×#41×C37C2311yescharacteristic
79C2×#41×C37C2311yescharacteristic
80C22×Q8×C37C2×C411yescharacteristic
81C22×D4×C37—21no—
82C22×D4×C37C2×C411yescharacteristic
83C23×C4×C37—21no—
84C23×C4×C37C2311yescharacteristic
85#135×C37—22no—
86#135×C37—22no—
87#135×C37—41no—
88#135×C37—41no—
89C2×Q16×C37C2×C411yescharacteristic
90C2×Q16×C37C2×C411yescharacteristic
91C2×SD16×C37C2×C411yescharacteristic
92C2×SD16×C37C2×C411yescharacteristic
93C2×SD16×C37C2×C411yescharacteristic
94C2×SD16×C37C2×C411yescharacteristic
95C2×D8×C37C2×C411yescharacteristic
96C2×D8×C37C2×C411yescharacteristic
97#131×C37—22no—
98#131×C37—22no—
99#131×C37—22no—
100#131×C37—41no—
101#131×C37—41no—
102#131×C37—41no—
103C2×M16×C37—21no—
104C2×M16×C37—21no—
105C2×M16×C37—21no—
106C2×M16×C37—21no—
107C2×M16×C37—22no—
108C2×M16×C37—41no—
109C2×M16×C37C2311yescharacteristic
110C2×M16×C37C2311yescharacteristic
111C2×M16×C37C2311yescharacteristic
112C2×M16×C37C2311yescharacteristic
113C22×C8×C37—21no—
114C22×C8×C37—21no—
115C22×C8×C37—21no—
116C22×C8×C37—21no—
117C22×C8×C37C2311yescharacteristic
118C22×C8×C37C2311yescharacteristic
119C22×C8×C37C2311yescharacteristic
120C22×C8×C37C2311yescharacteristic
121#123×C37—21no—
122C22⋊Q8×C37C2×C411yescharacteristic
123C22⋊Q8×C37C2×C411yescharacteristic
124#121×C37C2×C411yescharacteristic
125#121×C37C2×C411yescharacteristic
126#120×C37—21no—
127C4×D4×C37—21no—
128C4×D4×C37—21no—
129#117×C37—22no—
130#117×C37—41no—
131#117×C37C2311yescharacteristic
132C2×C4⋊C4×C37—21no—
133C2×C22⋊C4×C37—21no—
134C2×C42×C37C2311yescharacteristic
135C2×C42×C37C2311yescharacteristic
136#108×C37—22no—
137#108×C37—41no—
138C4⋊C8×C37—21no—
139C4⋊C8×C37—21no—
140#104×C37—22no—
141#104×C37—22no—
142#104×C37—22no—
143#104×C37—22no—
144#104×C37—41no—
145#104×C37D414yescomplemented
146#103×C37C2×C411yescharacteristic
147#103×C37C2×C411yescharacteristic
148#103×C37C2×C411yescharacteristic
149#103×C37C2×C411yescharacteristic
150#102×C37C2×C411yescharacteristic
151#102×C37C2×C411yescharacteristic
152#102×C37C2×C411yescharacteristic
153#102×C37C2×C411yescharacteristic
154C22⋊C8×C37—21no—
155C22⋊C8×C37—21no—
156C22⋊C8×C37—21no—
157C22⋊C8×C37—21no—
158C22⋊C8×C37—21no—
159C22⋊C8×C37—21no—
160C22⋊C8×C37—21no—
161C22⋊C8×C37—21no—
162C22⋊C8×C37C2×C411yescharacteristic
163C22⋊C8×C37C2×C411yescharacteristic
164C22⋊C8×C37C2×C411yescharacteristic
165C22⋊C8×C37C2×C411yescharacteristic
166C22⋊C8×C37D411yescharacteristic
167C22⋊C8×C37D411yescharacteristic
168C22⋊C8×C37D411yescharacteristic
169C22⋊C8×C37D411yescharacteristic
170#97×C37—21no—
171#97×C37—41no—
172C4×C8×C37—21no—
173C4×C8×C37—22no—
174C24×C37—21no—
175C24×C37#4111yescharacteristic
176#41×C37—21no—
177#41×C37—21no—
178#41×C37—22no—
179#41×C37—22no—
180#41×C37—21no—
181#41×C37—21no—
182#41×C37—21no—
183#41×C37—21no—
184#41×C37—21no—
185#41×C37—21no—
186#41×C37—21no—
187#41×C37—21no—
188#41×C37—42no—
189#41×C37—42no—
190#41×C37—41no—
191#41×C37—41no—
192#41×C37—42no—
193#41×C37—42no—
194#41×C37C2×D412yes—
195#41×C37#4112yes—
196C2×Q8×C37—21no—
197C2×Q8×C37—22no—
198C2×Q8×C37—41no—
199C2×Q8×C37C22×C411yescharacteristic
200C2×Q8×C37C22×C411yescharacteristic
201C2×Q8×C37C22×C411yescharacteristic
202C2×D4×C37—21no—
203C2×D4×C37—22no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—21no—
207C2×D4×C37—21no—
208C2×D4×C37—21no—
209C2×D4×C37—21no—
210C2×D4×C37—21no—
211C2×D4×C37—41no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37C22×C411yescharacteristic
215C2×D4×C37C22×C411yescharacteristic
216C2×D4×C37C22×C411yescharacteristic
217C22×C4×C37—21no—
218C22×C4×C37—21no—
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—21no—
222C22×C4×C37—21no—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—21no—
227C22×C4×C37—21no—
228C22×C4×C37—21no—
229C22×C4×C37—42no—
230C22×C4×C37—42no—
231C22×C4×C37C22×C411yescharacteristic
232C22×C4×C37C22×C411yescharacteristic
233C22×C4×C37C2×D411yescharacteristic
234C22×C4×C37C2×D411yescharacteristic
235C22×C4×C37#4111yescharacteristic
236C22×C4×C37C2411yescharacteristic
237Q16×C37—22no—
238Q16×C37—41no—
239SD16×C37—22no—
240SD16×C37—22no—
241SD16×C37—41no—
242SD16×C37—41no—
243D8×C37—22no—
244D8×C37—41no—
245M16×C37—21no—
246M16×C37—21no—
247M16×C37—21no—
248M16×C37—21no—
249M16×C37—21no—
250M16×C37—21no—
251M16×C37—21no—
252M16×C37—42no—
253M16×C37—42no—
254M16×C37—42no—
255M16×C37—42no—
256M16×C37C2×D412yes—
257C2×C8×C37—21no—
258C2×C8×C37—21no—
259C2×C8×C37—21no—
260C2×C8×C37—21no—
261C2×C8×C37—21no—
262C2×C8×C37—21no—
263C2×C8×C37—21no—
264C2×C8×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—21no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—42no—
270C2×C8×C37—42no—
271C2×C8×C37—42no—
272C2×C8×C37—42no—
273C2×C8×C37C22×C411yescharacteristic
274C2×C8×C37C22×C411yescharacteristic
275C2×C8×C37C22×C411yescharacteristic
276C2×C8×C37C22×C411yescharacteristic
277C2×C8×C37C2×D411yescharacteristic
278C2×C8×C37C2×D411yescharacteristic
279C2×C8×C37C2×D411yescharacteristic
280C2×C8×C37C2×D411yescharacteristic
281C4⋊C4×C37—21no—
282C4⋊C4×C37—21no—
283C4⋊C4×C37—42no—
284C4⋊C4×C37C22×C411yescharacteristic
285C4⋊C4×C37C22×C411yescharacteristic
286C22⋊C4×C37—21no—
287C22⋊C4×C37—21no—
288C22⋊C4×C37—21no—
289C22⋊C4×C37—21no—
290C22⋊C4×C37—21no—
291C22⋊C4×C37—42no—
292C42×C37—21no—
293C42×C37—21no—
294C42×C37—21no—
295C42×C37—21no—
296C42×C37C2×D412yes—
297C23×C37—21no—
298C23×C37—21no—
299C23×C37—21no—
300C23×C37—21no—
301C23×C37—21no—
302C23×C37—41no—
303C23×C37—41no—
304C23×C37—42no—
305C23×C37—42no—
306C23×C37—81no—
307C23×C37C4×D411yescharacteristic
308C23×C37C4×D411yescharacteristic
309C23×C37C2×#4111yescharacteristic
310Q8×C37—21no—
311Q8×C37—21no—
312Q8×C37—21no—
313Q8×C37—21no—
314Q8×C37—21no—
315Q8×C37—42no—
316Q8×C37C4×D412yes—
317D4×C37—22no—
318D4×C37—22no—
319D4×C37—21no—
320D4×C37—21no—
321D4×C37—21no—
322D4×C37—21no—
323D4×C37—21no—
324D4×C37—42no—
325D4×C37—42no—
326D4×C37—42no—
327D4×C37—42no—
328D4×C37—41no—
329D4×C37—41no—
330D4×C37—41no—
331D4×C37—41no—
332D4×C37—81no—
333D4×C37C4×D412yes—
334C2×C4×C37—21no—
335C2×C4×C37—21no—
336C2×C4×C37—21no—
337C2×C4×C37—21no—
338C2×C4×C37—21no—
339C2×C4×C37—21no—
340C2×C4×C37—21no—
341C2×C4×C37—21no—
342C2×C4×C37—22no—
343C2×C4×C37—21no—
344C2×C4×C37—22no—
345C2×C4×C37—21no—
346C2×C4×C37—21no—
347C2×C4×C37—21no—
348C2×C4×C37—21no—
349C2×C4×C37—21no—
350C2×C4×C37—21no—
351C2×C4×C37—22no—
352C2×C4×C37—42no—
353C2×C4×C37—42no—
354C2×C4×C37—42no—
355C2×C4×C37—41no—
356C2×C4×C37—41no—
357C2×C4×C37—41no—
358C2×C4×C37—41no—
359C2×C4×C37—41no—
360C2×C4×C37—41no—
361C2×C4×C37—41no—
362C2×C4×C37—41no—
363C2×C4×C37—41no—
364C2×C4×C37C4×D411yescharacteristic
365C2×C4×C37C4×D411yescharacteristic
366C2×C4×C37C23×C411yescharacteristic
367C2×C4×C37C22×D411yescharacteristic
368C2×C4×C37C22×D411yescharacteristic
369C2×C4×C37C2×#4111yescharacteristic
370C2×C4×C37H(5,𝔽2)11yescharacteristic
371C2×C4×C37H(5,𝔽2)11yescharacteristic
372C8×C37—21no—
373C8×C37—21no—
374C8×C37—21no—
375C8×C37—21no—
376C8×C37—21no—
377C8×C37—21no—
378C8×C37—22no—
379C8×C37—21no—
380C8×C37—21no—
381C8×C37—41no—
382C8×C37—41no—
383C8×C37—41no—
384#22889C3711yesmaximal, characteristic, direct product factor, Sylow
385C22×C37—21no—
386C22×C37—21no—
387C22×C37—21no—
388C22×C37—21no—
389C22×C37—22no—
390C22×C37—21no—
391C22×C37—21no—
392C22×C37—21no—
393C22×C37—21no—
394C22×C37—41no—
395C22×C37—41no—
396C22×C37—41no—
397C22×C37—41no—
398C22×C37—41no—
399C22×C37—41no—
400C22×C37—41no—
401C22×C37—41no—
402C22×C37—81no—
403C22×C37—81no—
404C22×C37—84no—
405C22×C37C2×C4×D411yescharacteristic
406C22×C37#54611yescharacteristic
407C22×C37#55111yescharacteristic
408C4×C37—21no—
409C4×C37—21no—
410C4×C37—22no—
411C4×C37—42no—
412C4×C37—41no—
413C4×C37—41no—
414C4×C37—41no—
415C4×C37—41no—
416C4×C37—81no—
417C4×C37C2×C4×D411yescharacteristic
418C4×C37#51811yescharacteristic
419C4×C37D4211yescharacteristic
420C4×C37#54611yescharacteristic
421#3002C2×C3711yescharacteristic
422C2×#443C2×C3711yescharacteristic, complemented
423#2933C2×C3711yescharacteristic, complemented
424C2×#421C2×C3711yescharacteristic, complemented
425#2880C2×C3711yescharacteristic, complemented
426#1975C2×C3711yescharacteristic, complemented
427#1937C2×C3711yescharacteristic, complemented
428#1929C2×C3711yescharacteristic, complemented
429#1897C2×C3711yescharacteristic, complemented
430#1876C2×C3711yescharacteristic, complemented
431#1876C2×C3711yescharacteristic, complemented
432#1866C2×C3711yescharacteristic, complemented
433#1855C2×C3711yescharacteristic, complemented
434#1765C2×C3711yescharacteristic, complemented
435#1750C2×C3711yescharacteristic, complemented
436C2×C37—21no—
437C2×C37—21no—
438C2×C37—41no—
439C2×C37—41no—
440C2×C37—42no—
441C2×C37—81no—
442C2×C37—81no—
443C2×C37#235811yescharacteristic
444C2×C37#295511yescharacteristic
445C2×C37#295711yescharacteristic
446C22×#41C22×C3711yescharacteristic
447C2×#135C22×C3711yescharacteristic
448C2×#135C22×C3711yescharacteristic
449C2×#131C22×C3711yescharacteristic
450C2×#131C22×C3711yescharacteristic
451C2×#131C22×C3711yescharacteristic, complemented
452C22×M16C22×C3711yescharacteristic
453#525C22×C3711yescharacteristic
454C2×#117C22×C3711yescharacteristic
455#452C4×C3711yescharacteristic, complemented
456#452C4×C3711yescharacteristic, complemented
457#451C4×C3711yescharacteristic, complemented
458#450C4×C3711yescharacteristic, complemented
459#449C4×C3711yescharacteristic, complemented
460#449C4×C3711yescharacteristic, complemented
461#448C4×C3711yescharacteristic, complemented
462#447C4×C3711yescharacteristic, complemented
463#443—24no—
464#436—21no—
465#435—21no—
466#435—21no—
467C8×D4—21no—
468C2×#108C22×C3711yescharacteristic, complemented
469C2×#108C22×C3711yescharacteristic, complemented
470#424C22×C3711yescharacteristic, complemented
471#421—24no—
472C2×#104C22×C3711yescharacteristic
473C2×#104C22×C3711yescharacteristic
474C2×#104C22×C3711yescharacteristic
475C2×#104C22×C3711yescharacteristic
476C2×#104C22×C3711yescharacteristic, complemented
477C2×#104C22×C3711yescharacteristic, complemented
478#416C22×C3711yescharacteristic
479#416C22×C3711yescharacteristic
480#408—21no—
481#408—21no—
482#408C22×C3711yescharacteristic
483#408C22×C3711yescharacteristic
484#408C22×C3711yescharacteristic, complemented
485#407—21no—
486#407C22×C3711yescharacteristic
487C2×C22⋊C8—21no—
488C2×C22⋊C8C22×C3711yescharacteristic
489C2×C22⋊C8C22×C3711yescharacteristic
490#405C22×C3711yescharacteristic, complemented
491C2×#97C22×C3711yescharacteristic, complemented
492C2×C4×C8C22×C3711yescharacteristic, complemented
493#341C22×C3711yescharacteristic, complemented
494#341C22×C3711yescharacteristic, complemented
495#339C22×C3711yescharacteristic, complemented
496#339C22×C3711yescharacteristic, complemented
497#336C22×C3711yescharacteristic, complemented
498#336C22×C3711yescharacteristic, complemented
499C37#2288911yescharacteristic, direct product factor, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C3711yescharacteristic
507C2×#41C2×C4×C3711yescharacteristic
508C2×#41C23×C3711yescharacteristic
509C2×#41C23×C3711yescharacteristic
510C2×#41C23×C3711yescharacteristic
511C22×Q8C2×C4×C3711yescharacteristic
512C22×D4—21no—
513C22×D4C2×C4×C3711yescharacteristic
514C23×C4—21no—
515C23×C4C23×C3711yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×C4×C3711yescharacteristic
521C2×Q16C2×C4×C3711yescharacteristic
522C2×SD16C2×C4×C3711yescharacteristic
523C2×SD16C2×C4×C3711yescharacteristic
524C2×SD16C2×C4×C3711yescharacteristic
525C2×SD16C2×C4×C3711yescharacteristic
526C2×D8C2×C4×C3711yescharacteristic
527C2×D8C2×C4×C3711yescharacteristic
528#131—22no—
529#131—22no—
530#131—22no—
531#131—41no—
532#131—41no—
533#131—41no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16C23×C3711yescharacteristic
541C2×M16C23×C3711yescharacteristic
542C2×M16C23×C3711yescharacteristic
543C2×M16C23×C3711yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8—21no—
548C22×C8C23×C3711yescharacteristic
549C22×C8C23×C3711yescharacteristic
550C22×C8C23×C3711yescharacteristic
551C22×C8C23×C3711yescharacteristic
552#123—21no—
553C22⋊Q8C2×C4×C3711yescharacteristic
554C22⋊Q8C2×C4×C3711yescharacteristic
555#121C2×C4×C3711yescharacteristic
556#121C2×C4×C3711yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C23×C3711yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C23×C3711yescharacteristic
566C2×C42C23×C3711yescharacteristic
567#108—22no—
568#108—41no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—22no—
575#104—41no—
576#104D4×C3714yescomplemented
577#103C2×C4×C3711yescharacteristic
578#103C2×C4×C3711yescharacteristic
579#103C2×C4×C3711yescharacteristic
580#103C2×C4×C3711yescharacteristic
581#102C2×C4×C3711yescharacteristic
582#102C2×C4×C3711yescharacteristic
583#102C2×C4×C3711yescharacteristic
584#102C2×C4×C3711yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8C2×C4×C3711yescharacteristic
594C22⋊C8C2×C4×C3711yescharacteristic
595C22⋊C8C2×C4×C3711yescharacteristic
596C22⋊C8C2×C4×C3711yescharacteristic
597C22⋊C8D4×C3711yescharacteristic
598C22⋊C8D4×C3711yescharacteristic
599C22⋊C8D4×C3711yescharacteristic
600C22⋊C8D4×C3711yescharacteristic
601#97—21no—
602#97—41no—
603C4×C8—21no—
604C4×C8—22no—
605C24—21no—
606C24#41×C3711yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C3712yes—
626#41#41×C3712yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C3711yescharacteristic
631C2×Q8C22×C4×C3711yescharacteristic
632C2×Q8C22×C4×C3711yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C3711yescharacteristic
646C2×D4C22×C4×C3711yescharacteristic
647C2×D4C22×C4×C3711yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4C22×C4×C3711yescharacteristic
663C22×C4C22×C4×C3711yescharacteristic
664C22×C4C2×D4×C3711yescharacteristic
665C22×C4C2×D4×C3711yescharacteristic
666C22×C4#41×C3711yescharacteristic
667C22×C4C24×C3711yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C3712yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C3711yescharacteristic
705C2×C8C22×C4×C3711yescharacteristic
706C2×C8C22×C4×C3711yescharacteristic
707C2×C8C22×C4×C3711yescharacteristic
708C2×C8C2×D4×C3711yescharacteristic
709C2×C8C2×D4×C3711yescharacteristic
710C2×C8C2×D4×C3711yescharacteristic
711C2×C8C2×D4×C3711yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C3711yescharacteristic
716C4⋊C4C22×C4×C3711yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C3712yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C3711yescharacteristic
739C23C4×D4×C3711yescharacteristic
740C23C2×#41×C3711yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C3712yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C3712yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C3711yescharacteristic
796C2×C4C4×D4×C3711yescharacteristic
797C2×C4C23×C4×C3711yescharacteristic
798C2×C4C22×D4×C3711yescharacteristic
799C2×C4C22×D4×C3711yescharacteristic
800C2×C4C2×#41×C3711yescharacteristic
801C2×C4H(5,𝔽2)×C3711yescharacteristic
802C2×C4H(5,𝔽2)×C3711yescharacteristic
803C8—21no—
804C8—21no—
805C8—22no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—21no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C3711yescharacteristic
836C22C37×#54611yescharacteristic
837C22C37×#55111yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C3711yescharacteristic
848C4C37×#51811yescharacteristic
849C4D42×C3711yescharacteristic
850C4C37×#54611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2C37×#235811yescharacteristic
859C2C37×#295511yescharacteristic
860C2C37×#295711yescharacteristic
subgroupG/H
centerC2×C4×C37C22×D4
commutatorC2×C4C23×C4×C37
Frattini, cosocleC22×C4C24×C37
socleC22×C37C2×C4×D4
prime radicalC37×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C37 ◁ C2×C22⋊C8×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#443C2semidirect
3. C37×#2933C2semidirect
4. C2×C37×#421C2semidirect
5. C37×#2880C2semidirect
6. C37×#1975C2semidirect
7. C37×#1937C2semidirect
8. C37×#1929C2semidirect
9. C37×#1897C2semidirect
10. C37×#1876C2semidirect
11. C37×#1876C2semidirect
12. C37×#1866C2semidirect
13. C37×#1855C2semidirect
14. C37×#1765C2semidirect
15. C37×#1750C2semidirect
21. C2×#131×C37C22semidirect
25. C37×#452C4semidirect
26. C37×#452C4semidirect
27. C37×#451C4semidirect
28. C37×#450C4semidirect
29. C37×#449C4semidirect
30. C37×#449C4semidirect
31. C37×#448C4semidirect
32. C37×#447C4semidirect
38. C2×#108×C37C22semidirect
39. C2×#108×C37C22semidirect
40. C37×#424C22semidirect
46. C2×#104×C37C22semidirect
47. C2×#104×C37C22semidirect
54. C37×#408C22semidirect
60. C37×#405C22semidirect
61. C2×#97×C37C22semidirect
62. C2×C4×C8×C37C22semidirect
63. C37×#341C22semidirect
64. C37×#341C22semidirect
65. C37×#339C22semidirect
66. C37×#339C22semidirect
67. C37×#336C22semidirect
68. C37×#336C22semidirect
145. #104×C37D4semidirect
384. #22889C37direct (N × H)
422. C2×#443C2×C37semidirect
423. #2933C2×C37semidirect
424. C2×#421C2×C37semidirect
425. #2880C2×C37semidirect
426. #1975C2×C37semidirect
427. #1937C2×C37semidirect
428. #1929C2×C37semidirect
429. #1897C2×C37semidirect
430. #1876C2×C37semidirect
431. #1876C2×C37semidirect
432. #1866C2×C37semidirect
433. #1855C2×C37semidirect
434. #1765C2×C37semidirect
435. #1750C2×C37semidirect
451. C2×#131C22×C37semidirect
455. #452C4×C37semidirect
456. #452C4×C37semidirect
457. #451C4×C37semidirect
458. #450C4×C37semidirect
459. #449C4×C37semidirect
460. #449C4×C37semidirect
461. #448C4×C37semidirect
462. #447C4×C37semidirect
468. C2×#108C22×C37semidirect
469. C2×#108C22×C37semidirect
470. #424C22×C37semidirect
476. C2×#104C22×C37semidirect
477. C2×#104C22×C37semidirect
484. #408C22×C37semidirect
490. #405C22×C37semidirect
491. C2×#97C22×C37semidirect
492. C2×C4×C8C22×C37semidirect
493. #341C22×C37semidirect
494. #341C22×C37semidirect
495. #339C22×C37semidirect
496. #339C22×C37semidirect
497. #336C22×C37semidirect
498. #336C22×C37semidirect
499. C37#22889direct (N × H)
576. #104D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#30022
C2×C37×#4432
C37×#29332
C2×C37×#4212
C37×#28802
C37×#19752
C37×#19372
C37×#19292
C37×#18972
C37×#18762
C37×#18662
C37×#18552
C37×#17652
C37×#17502
#2288937