Finite Group Databasebeta

← C37×#17679 #22638932

Subgroups — C37×#17679 #22638932

Order 9472.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3514C211yesmaximal, characteristic
2C37×#2970C211yesmaximal, characteristic, complemented
3C37×#2923C211yesmaximal, characteristic, complemented
4C37×#1536C211yesmaximal, characteristic, complemented
5C37×#1535C211yesmaximal, characteristic, complemented
6C37×#1535C211yesmaximal, characteristic, complemented
7C37×#1533C211yesmaximal, characteristic, complemented
8C37×#1532C211yesmaximal, characteristic, complemented
9C37×#1532C211yesmaximal, characteristic, complemented
10C37×#1530C211yesmaximal, characteristic, complemented
11C37×#1529C211yesmaximal, characteristic, complemented
12C37×#1527C211yesmaximal, characteristic, complemented
13C37×#1527C211yesmaximal, characteristic, complemented
14C37×#1524C211yesmaximal, characteristic, complemented
15C2×C37×#329C211yesmaximal, characteristic, complemented
16C37×#559C411yescharacteristic
17C37×#556C411yescharacteristic
18C37×#555—21no—
19C37×#551—21no—
20C37×#551—21no—
21D4×Q8×C37C411yescharacteristic
22C37×#548C411yescharacteristic
23C37×#548C411yescharacteristic
24C37×#546—21no—
25C37×#546C411yescharacteristic
26C37×#546C411yescharacteristic
27D42×C37C411yescharacteristic
28C37×#542—21no—
29C37×#538—21no—
30C37×#538—21no—
31C37×#532C2211yescharacteristic
32C37×#529C2211yescharacteristic
33C37×#529C2211yescharacteristic
34C37×#529C2211yescharacteristic
35C2×#124×C37C2211yescharacteristic
36C2×#124×C37C2211yescharacteristic
37C37×#518—21no—
38C4×#41×C37C2211yescharacteristic
39C37×#446—21no—
40C37×#435—21no—
41C37×#435—21no—
42C8×D4×C37—21no—
43C37×#433—21no—
44C37×#433—21no—
45C37×#432C2211yescharacteristic, complemented
46C37×#432C2211yescharacteristic, complemented
47C37×#432C2211yescharacteristic, complemented
48C37×#432C2211yescharacteristic, complemented
49C37×#432C2211yescharacteristic, complemented
50C37×#432C2211yescharacteristic, complemented
51C37×#432C2211yescharacteristic, complemented
52C37×#424—21no—
53C37×#408—21no—
54C4×M16×C37C2211yescharacteristic, complemented
55C4×M16×C37C2211yescharacteristic, complemented
56C2×#97×C37C2211yescharacteristic, complemented
57C2×#97×C37C2211yescharacteristic, complemented
58C2×#97×C37C2211yescharacteristic, complemented
59C37×#330C2211yescharacteristic, complemented
60C37×#330C2211yescharacteristic, complemented
61C37×#330C2211yescharacteristic, complemented
62C37×#330C2211yescharacteristic, complemented
63C37×#329C2211yescharacteristic
64C37×#329C2211yescharacteristic
65C37×#329C2211yescharacteristic
66C37×#329C2211yescharacteristic
67C37×#329C2211yescharacteristic, complemented
68C37×#329C2211yescharacteristic, complemented
69C37×#329C2211yescharacteristic, complemented
70C37×#329C2211yescharacteristic, complemented
71C37×#329C2211yescharacteristic, complemented
72C37×#329C2211yescharacteristic, complemented
73C37×#329C2211yescharacteristic, complemented
74C37×#329C2211yescharacteristic, complemented
75C2×#41×C37C2×C411yescharacteristic
76C2×#41×C37C2×C411yescharacteristic
77C2×#41×C37D411yescharacteristic
78C22×Q8×C37C2×C411yescharacteristic
79C22×Q8×C37C2×C411yescharacteristic
80C22×D4×C37—21no—
81C22×D4×C37C2×C411yescharacteristic
82C22×D4×C37C2×C411yescharacteristic
83C2×M16×C37—21no—
84C2×M16×C37—21no—
85C22×C8×C37—21no—
86C22×C8×C37—21no—
87C22×C8×C37—21no—
88C4⋊Q8×C37—21no—
89C4⋊Q8×C37C2×C411yescharacteristic
90#127×C37C2×C411yescharacteristic
91#126×C37—21no—
92#126×C37—21no—
93#126×C37—21no—
94#126×C37—21no—
95#126×C37—21no—
96#125×C37C2311yescharacteristic
97#124×C37—21no—
98#124×C37—21no—
99#124×C37—21no—
100#124×C37—21no—
101#124×C37—21no—
102#124×C37—21no—
103#124×C37—21no—
104#124×C37C2×C411yescharacteristic
105#124×C37C2×C411yescharacteristic
106#124×C37C2×C411yescharacteristic
107#124×C37C2×C411yescharacteristic
108#124×C37C2311yescharacteristic
109#124×C37C2311yescharacteristic
110#124×C37C2311yescharacteristic
111#123×C37—21no—
112#123×C37—21no—
113#123×C37—21no—
114#123×C37—21no—
115#123×C37—21no—
116#123×C37—21no—
117#123×C37—21no—
118C22⋊Q8×C37—21no—
119C22⋊Q8×C37—21no—
120C22⋊Q8×C37—21no—
121C22⋊Q8×C37—21no—
122C22⋊Q8×C37—21no—
123C22⋊Q8×C37C2×C411yescharacteristic
124C22⋊Q8×C37C2×C411yescharacteristic
125C22⋊Q8×C37C2×C411yescharacteristic
126#121×C37—21no—
127#121×C37—21no—
128#121×C37—21no—
129#121×C37—21no—
130#121×C37—21no—
131#121×C37—21no—
132#121×C37—21no—
133#121×C37C2×C411yescharacteristic
134#121×C37C2×C411yescharacteristic
135#121×C37C2×C411yescharacteristic
136#120×C37—21no—
137#120×C37—21no—
138#120×C37—21no—
139#120×C37—21no—
140C4×Q8×C37C2×C411yescharacteristic
141C4×Q8×C37C2×C411yescharacteristic
142C4×Q8×C37C2×C411yescharacteristic
143C4×Q8×C37C2×C411yescharacteristic
144C4×Q8×C37D411yescharacteristic
145C4×D4×C37—21no—
146C4×D4×C37—21no—
147C4×D4×C37—21no—
148C4×D4×C37—21no—
149C4×D4×C37—21no—
150C4×D4×C37—21no—
151C4×D4×C37—21no—
152C4×D4×C37—21no—
153C4×D4×C37—21no—
154C4×D4×C37C2×C411yescharacteristic
155C4×D4×C37C2×C411yescharacteristic
156C4×D4×C37C2×C411yescharacteristic
157C4×D4×C37C2×C411yescharacteristic
158C4×D4×C37C2×C411yescharacteristic
159C4×D4×C37C2×C411yescharacteristic
160C4×D4×C37D411yescharacteristic
161C4×D4×C37D411yescharacteristic
162C4×D4×C37D411yescharacteristic
163#117×C37—21no—
164#117×C37—21no—
165#117×C37—21no—
166#117×C37—21no—
167#117×C37D411yescharacteristic
168#117×C37D411yescharacteristic
169#117×C37D411yescharacteristic
170C2×C22⋊C4×C37—21no—
171C2×C22⋊C4×C37—21no—
172C2×C22⋊C4×C37—21no—
173C2×C22⋊C4×C37—21no—
174C2×C22⋊C4×C37—21no—
175C2×C22⋊C4×C37—21no—
176C2×C42×C37C2311yescharacteristic
177C2×C42×C37C2311yescharacteristic
178C2×C42×C37C2311yescharacteristic
179C4⋊C8×C37—21no—
180C4⋊C8×C37—21no—
181C4⋊C8×C37—21no—
182C4⋊C8×C37—21no—
183C4⋊C8×C37—21no—
184C4⋊C8×C37—21no—
185C4⋊C8×C37—21no—
186C22⋊C8×C37—21no—
187C22⋊C8×C37—21no—
188C22⋊C8×C37—21no—
189C22⋊C8×C37—21no—
190C22⋊C8×C37—21no—
191C22⋊C8×C37—21no—
192C22⋊C8×C37—21no—
193#97×C37—21no—
194#97×C37—21no—
195#97×C37—21no—
196#97×C37C2311yescharacteristic
197#97×C37C2311yescharacteristic
198#97×C37C2311yescharacteristic
199#97×C37C2311yescharacteristic
200#97×C37C2311yescharacteristic
201#97×C37C2311yescharacteristic
202#97×C37C2311yescharacteristic
203#97×C37C2311yescharacteristic
204C4×C8×C37—21no—
205C4×C8×C37—21no—
206C24×C37—21no—
207C24×C37—21no—
208#41×C37—42no—
209#41×C37—81no—
210#41×C37—81no—
211C2×Q8×C37—21no—
212C2×Q8×C37—21no—
213C2×Q8×C37—81no—
214C2×Q8×C37—81no—
215C2×Q8×C37C22⋊C411yescharacteristic
216C2×Q8×C37C22×C411yescharacteristic
217C2×Q8×C37C22×C411yescharacteristic
218C2×Q8×C37C22×C411yescharacteristic
219C2×D4×C37—21no—
220C2×D4×C37—21no—
221C2×D4×C37—21no—
222C2×D4×C37—21no—
223C2×D4×C37—21no—
224C2×D4×C37—21no—
225C2×D4×C37—21no—
226C2×D4×C37—21no—
227C2×D4×C37—21no—
228C2×D4×C37—44no—
229C2×D4×C37—81no—
230C2×D4×C37—81no—
231C2×D4×C37C22⋊C411yescharacteristic
232C2×D4×C37C22⋊C411yescharacteristic
233C2×D4×C37C22⋊C411yescharacteristic
234C2×D4×C37C22×C411yescharacteristic
235C2×D4×C37C22×C411yescharacteristic
236C2×D4×C37C22×C411yescharacteristic
237C22×C4×C37—21no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37C22×C411yescharacteristic
245C22×C4×C37C22×C411yescharacteristic
246C22×C4×C37C22×C411yescharacteristic
247C22×C4×C37C2×D411yescharacteristic
248C22×C4×C37C2×D411yescharacteristic
249C22×C4×C37C2×D411yescharacteristic
250C22×C4×C37C2×D411yescharacteristic
251C22×C4×C37C2×D411yescharacteristic
252C22×C4×C37C2×D411yescharacteristic
253M16×C37—42no—
254M16×C37—42no—
255C2×C8×C37—21no—
256C2×C8×C37—21no—
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—42no—
264C2×C8×C37—42no—
265C2×C8×C37—42no—
266C4⋊C4×C37—21no—
267C4⋊C4×C37—21no—
268C4⋊C4×C37—21no—
269C4⋊C4×C37—21no—
270C4⋊C4×C37—21no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37C22⋊C411yescharacteristic
277C4⋊C4×C37C22⋊C411yescharacteristic
278C4⋊C4×C37C22⋊C411yescharacteristic
279C4⋊C4×C37C22⋊C411yescharacteristic
280C4⋊C4×C37C22⋊C411yescharacteristic
281C4⋊C4×C37C22⋊C411yescharacteristic
282C4⋊C4×C37C22×C411yescharacteristic
283C4⋊C4×C37C22×C411yescharacteristic
284C22⋊C4×C37—21no—
285C22⋊C4×C37—21no—
286C22⋊C4×C37—21no—
287C22⋊C4×C37—21no—
288C22⋊C4×C37—21no—
289C22⋊C4×C37—21no—
290C22⋊C4×C37—21no—
291C22⋊C4×C37—21no—
292C22⋊C4×C37—21no—
293C22⋊C4×C37—21no—
294C22⋊C4×C37—21no—
295C22⋊C4×C37—21no—
296C22⋊C4×C37—21no—
297C22⋊C4×C37—21no—
298C22⋊C4×C37—21no—
299C22⋊C4×C37—21no—
300C22⋊C4×C37—21no—
301C22⋊C4×C37—21no—
302C22⋊C4×C37—21no—
303C22⋊C4×C37—21no—
304C22⋊C4×C37—21no—
305C22⋊C4×C37—21no—
306C22⋊C4×C37—21no—
307C22⋊C4×C37C22⋊C411yescharacteristic
308C22⋊C4×C37C22⋊C411yescharacteristic
309C22⋊C4×C37C22⋊C411yescharacteristic
310C22⋊C4×C37C22⋊C411yescharacteristic
311C22⋊C4×C37C22⋊C411yescharacteristic
312C22⋊C4×C37C22⋊C411yescharacteristic
313C42×C37—21no—
314C42×C37—21no—
315C42×C37—21no—
316C42×C37C22×C411yescharacteristic
317C42×C37C22×C411yescharacteristic
318C42×C37C22×C411yescharacteristic
319C42×C37C2×D411yescharacteristic
320C42×C37C2×D411yescharacteristic
321C42×C37C2×D411yescharacteristic
322C42×C37C2×D411yescharacteristic
323C42×C37C2×D411yescharacteristic
324C42×C37C2×D411yescharacteristic
325C42×C37C2411yescharacteristic
326C23×C37—21no—
327C23×C37—21no—
328C23×C37—21no—
329C23×C37—42no—
330C23×C37—42no—
331C23×C37—81no—
332C23×C37—81no—
333C23×C37—81no—
334C23×C37—81no—
335C23×C37C2×C22⋊C411yescharacteristic
336C23×C37C2×C22⋊C411yescharacteristic
337C23×C37C2×C22⋊C411yescharacteristic
338Q8×C37—41no—
339Q8×C37—41no—
340Q8×C37—41no—
341Q8×C37—41no—
342Q8×C37—81no—
343Q8×C37—81no—
344D4×C37—22no—
345D4×C37—22no—
346D4×C37—41no—
347D4×C37—41no—
348D4×C37—41no—
349D4×C37—41no—
350D4×C37—42no—
351D4×C37—42no—
352D4×C37—42no—
353D4×C37—81no—
354D4×C37—81no—
355D4×C37—81no—
356D4×C37—81no—
357D4×C37—81no—
358D4×C37—81no—
359C2×C4×C37—22no—
360C2×C4×C37—21no—
361C2×C4×C37—21no—
362C2×C4×C37—21no—
363C2×C4×C37—21no—
364C2×C4×C37—21no—
365C2×C4×C37—41no—
366C2×C4×C37—41no—
367C2×C4×C37—41no—
368C2×C4×C37—41no—
369C2×C4×C37—41no—
370C2×C4×C37—41no—
371C2×C4×C37—41no—
372C2×C4×C37—41no—
373C2×C4×C37—42no—
374C2×C4×C37—81no—
375C2×C4×C37—81no—
376C2×C4×C37—81no—
377C2×C4×C37—81no—
378C2×C4×C37—81no—
379C2×C4×C37—81no—
380C2×C4×C37C2×C22⋊C411yescharacteristic
381C2×C4×C37C2×C22⋊C411yescharacteristic
382C2×C4×C37C2×C22⋊C411yescharacteristic
383C2×C4×C37C2×C22⋊C411yescharacteristic
384C2×C4×C37C2×C22⋊C411yescharacteristic
385C2×C4×C37C2×C22⋊C411yescharacteristic
386C2×C4×C37C2×C22⋊C411yescharacteristic
387C2×C4×C37C2×C22⋊C411yescharacteristic
388C2×C4×C37C2×C22⋊C411yescharacteristic
389C2×C4×C37C23×C411yescharacteristic
390C2×C4×C37C22×D411yescharacteristic
391C2×C4×C37C22×D411yescharacteristic
392C8×C37—22no—
393C8×C37—41no—
394C8×C37—41no—
395C8×C37—41no—
396C8×C37—41no—
397C8×C37—41no—
398C8×C37—41no—
399C8×C37—41no—
400#17679C3711yesmaximal, characteristic, direct product factor, Sylow
401C22×C37—21no—
402C22×C37—21no—
403C22×C37—21no—
404C22×C37—21no—
405C22×C37—21no—
406C22×C37—21no—
407C22×C37—21no—
408C22×C37—21no—
409C22×C37—41no—
410C22×C37—41no—
411C22×C37—41no—
412C22×C37—41no—
413C22×C37—41no—
414C22×C37—41no—
415C22×C37—41no—
416C22×C37—41no—
417C22×C37—41no—
418C22×C37—162no—
419C22×C37—162no—
420C22×C37#42112yes—
421C22×C37C22×C22⋊C411yescharacteristic
422C4×C37—21no—
423C4×C37—21no—
424C4×C37—21no—
425C4×C37—21no—
426C4×C37—21no—
427C4×C37—21no—
428C4×C37—21no—
429C4×C37—21no—
430C4×C37—21no—
431C4×C37—21no—
432C4×C37—21no—
433C4×C37—21no—
434C4×C37—41no—
435C4×C37—41no—
436C4×C37—41no—
437C4×C37—41no—
438C4×C37—41no—
439#3514C2×C3711yescharacteristic
440#2970C2×C3711yescharacteristic, complemented
441#2923C2×C3711yescharacteristic, complemented
442#1536C2×C3711yescharacteristic, complemented
443#1535C2×C3711yescharacteristic, complemented
444#1535C2×C3711yescharacteristic, complemented
445#1533C2×C3711yescharacteristic, complemented
446#1532C2×C3711yescharacteristic, complemented
447#1532C2×C3711yescharacteristic, complemented
448#1530C2×C3711yescharacteristic, complemented
449#1529C2×C3711yescharacteristic, complemented
450#1527C2×C3711yescharacteristic, complemented
451#1527C2×C3711yescharacteristic, complemented
452#1524C2×C3711yescharacteristic, complemented
453C2×#329C2×C3711yescharacteristic, complemented
454C2×C37—22no—
455C2×C37—41no—
456C2×C37—41no—
457C2×C37—81no—
458C2×C37—81no—
459C2×C37—81no—
460C2×C37#288811yescharacteristic
461C2×C37C2×#42111yescharacteristic
462C2×C37#290111yescharacteristic
463#559C4×C3711yescharacteristic
464#556C4×C3711yescharacteristic
465#555—21no—
466#551—21no—
467#551—21no—
468D4×Q8C4×C3711yescharacteristic
469#548C4×C3711yescharacteristic
470#548C4×C3711yescharacteristic
471#546—21no—
472#546C4×C3711yescharacteristic
473#546C4×C3711yescharacteristic
474D42C4×C3711yescharacteristic
475#542—21no—
476#538—21no—
477#538—21no—
478#532C22×C3711yescharacteristic
479#529C22×C3711yescharacteristic
480#529C22×C3711yescharacteristic
481#529C22×C3711yescharacteristic
482C2×#124C22×C3711yescharacteristic
483C2×#124C22×C3711yescharacteristic
484#518—21no—
485C4×#41C22×C3711yescharacteristic
486#446—21no—
487#435—21no—
488#435—21no—
489C8×D4—21no—
490#433—21no—
491#433—21no—
492#432C22×C3711yescharacteristic, complemented
493#432C22×C3711yescharacteristic, complemented
494#432C22×C3711yescharacteristic, complemented
495#432C22×C3711yescharacteristic, complemented
496#432C22×C3711yescharacteristic, complemented
497#432C22×C3711yescharacteristic, complemented
498#432C22×C3711yescharacteristic, complemented
499#424—21no—
500#408—21no—
501C4×M16C22×C3711yescharacteristic, complemented
502C4×M16C22×C3711yescharacteristic, complemented
503C2×#97C22×C3711yescharacteristic, complemented
504C2×#97C22×C3711yescharacteristic, complemented
505C2×#97C22×C3711yescharacteristic, complemented
506#330C22×C3711yescharacteristic, complemented
507#330C22×C3711yescharacteristic, complemented
508#330C22×C3711yescharacteristic, complemented
509#330C22×C3711yescharacteristic, complemented
510#329C22×C3711yescharacteristic
511#329C22×C3711yescharacteristic
512#329C22×C3711yescharacteristic
513#329C22×C3711yescharacteristic
514#329C22×C3711yescharacteristic, complemented
515#329C22×C3711yescharacteristic, complemented
516#329C22×C3711yescharacteristic, complemented
517#329C22×C3711yescharacteristic, complemented
518#329C22×C3711yescharacteristic, complemented
519#329C22×C3711yescharacteristic, complemented
520#329C22×C3711yescharacteristic, complemented
521#329C22×C3711yescharacteristic, complemented
522C37#1767911yescharacteristic, direct product factor, Sylow
523C2×#41C2×C4×C3711yescharacteristic
524C2×#41C2×C4×C3711yescharacteristic
525C2×#41D4×C3711yescharacteristic
526C22×Q8C2×C4×C3711yescharacteristic
527C22×Q8C2×C4×C3711yescharacteristic
528C22×D4—21no—
529C22×D4C2×C4×C3711yescharacteristic
530C22×D4C2×C4×C3711yescharacteristic
531C2×M16—21no—
532C2×M16—21no—
533C22×C8—21no—
534C22×C8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8C2×C4×C3711yescharacteristic
538#127C2×C4×C3711yescharacteristic
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#125C23×C3711yescharacteristic
545#124—21no—
546#124—21no—
547#124—21no—
548#124—21no—
549#124—21no—
550#124—21no—
551#124—21no—
552#124C2×C4×C3711yescharacteristic
553#124C2×C4×C3711yescharacteristic
554#124C2×C4×C3711yescharacteristic
555#124C2×C4×C3711yescharacteristic
556#124C23×C3711yescharacteristic
557#124C23×C3711yescharacteristic
558#124C23×C3711yescharacteristic
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8C2×C4×C3711yescharacteristic
572C22⋊Q8C2×C4×C3711yescharacteristic
573C22⋊Q8C2×C4×C3711yescharacteristic
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121C2×C4×C3711yescharacteristic
582#121C2×C4×C3711yescharacteristic
583#121C2×C4×C3711yescharacteristic
584#120—21no—
585#120—21no—
586#120—21no—
587#120—21no—
588C4×Q8C2×C4×C3711yescharacteristic
589C4×Q8C2×C4×C3711yescharacteristic
590C4×Q8C2×C4×C3711yescharacteristic
591C4×Q8C2×C4×C3711yescharacteristic
592C4×Q8D4×C3711yescharacteristic
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4C2×C4×C3711yescharacteristic
603C4×D4C2×C4×C3711yescharacteristic
604C4×D4C2×C4×C3711yescharacteristic
605C4×D4C2×C4×C3711yescharacteristic
606C4×D4C2×C4×C3711yescharacteristic
607C4×D4C2×C4×C3711yescharacteristic
608C4×D4D4×C3711yescharacteristic
609C4×D4D4×C3711yescharacteristic
610C4×D4D4×C3711yescharacteristic
611#117—21no—
612#117—21no—
613#117—21no—
614#117—21no—
615#117D4×C3711yescharacteristic
616#117D4×C3711yescharacteristic
617#117D4×C3711yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C42C23×C3711yescharacteristic
625C2×C42C23×C3711yescharacteristic
626C2×C42C23×C3711yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—21no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640C22⋊C8—21no—
641#97—21no—
642#97—21no—
643#97—21no—
644#97C23×C3711yescharacteristic
645#97C23×C3711yescharacteristic
646#97C23×C3711yescharacteristic
647#97C23×C3711yescharacteristic
648#97C23×C3711yescharacteristic
649#97C23×C3711yescharacteristic
650#97C23×C3711yescharacteristic
651#97C23×C3711yescharacteristic
652C4×C8—21no—
653C4×C8—21no—
654C24—21no—
655C24—21no—
656#41—42no—
657#41—81no—
658#41—81no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—81no—
662C2×Q8—81no—
663C2×Q8C22⋊C4×C3711yescharacteristic
664C2×Q8C22×C4×C3711yescharacteristic
665C2×Q8C22×C4×C3711yescharacteristic
666C2×Q8C22×C4×C3711yescharacteristic
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—44no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4C22⋊C4×C3711yescharacteristic
680C2×D4C22⋊C4×C3711yescharacteristic
681C2×D4C22⋊C4×C3711yescharacteristic
682C2×D4C22×C4×C3711yescharacteristic
683C2×D4C22×C4×C3711yescharacteristic
684C2×D4C22×C4×C3711yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4C22×C4×C3711yescharacteristic
693C22×C4C22×C4×C3711yescharacteristic
694C22×C4C22×C4×C3711yescharacteristic
695C22×C4C2×D4×C3711yescharacteristic
696C22×C4C2×D4×C3711yescharacteristic
697C22×C4C2×D4×C3711yescharacteristic
698C22×C4C2×D4×C3711yescharacteristic
699C22×C4C2×D4×C3711yescharacteristic
700C22×C4C2×D4×C3711yescharacteristic
701M16—42no—
702M16—42no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—42no—
712C2×C8—42no—
713C2×C8—42no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4C22⋊C4×C3711yescharacteristic
725C4⋊C4C22⋊C4×C3711yescharacteristic
726C4⋊C4C22⋊C4×C3711yescharacteristic
727C4⋊C4C22⋊C4×C3711yescharacteristic
728C4⋊C4C22⋊C4×C3711yescharacteristic
729C4⋊C4C22⋊C4×C3711yescharacteristic
730C4⋊C4C22×C4×C3711yescharacteristic
731C4⋊C4C22×C4×C3711yescharacteristic
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4C22⋊C4×C3711yescharacteristic
756C22⋊C4C22⋊C4×C3711yescharacteristic
757C22⋊C4C22⋊C4×C3711yescharacteristic
758C22⋊C4C22⋊C4×C3711yescharacteristic
759C22⋊C4C22⋊C4×C3711yescharacteristic
760C22⋊C4C22⋊C4×C3711yescharacteristic
761C42—21no—
762C42—21no—
763C42—21no—
764C42C22×C4×C3711yescharacteristic
765C42C22×C4×C3711yescharacteristic
766C42C22×C4×C3711yescharacteristic
767C42C2×D4×C3711yescharacteristic
768C42C2×D4×C3711yescharacteristic
769C42C2×D4×C3711yescharacteristic
770C42C2×D4×C3711yescharacteristic
771C42C2×D4×C3711yescharacteristic
772C42C2×D4×C3711yescharacteristic
773C42C24×C3711yescharacteristic
774C23—21no—
775C23—21no—
776C23—21no—
777C23—42no—
778C23—42no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23C2×C22⋊C4×C3711yescharacteristic
784C23C2×C22⋊C4×C3711yescharacteristic
785C23C2×C22⋊C4×C3711yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4C2×C22⋊C4×C3711yescharacteristic
829C2×C4C2×C22⋊C4×C3711yescharacteristic
830C2×C4C2×C22⋊C4×C3711yescharacteristic
831C2×C4C2×C22⋊C4×C3711yescharacteristic
832C2×C4C2×C22⋊C4×C3711yescharacteristic
833C2×C4C2×C22⋊C4×C3711yescharacteristic
834C2×C4C2×C22⋊C4×C3711yescharacteristic
835C2×C4C2×C22⋊C4×C3711yescharacteristic
836C2×C4C2×C22⋊C4×C3711yescharacteristic
837C2×C4C23×C4×C3711yescharacteristic
838C2×C4C22×D4×C3711yescharacteristic
839C2×C4C22×D4×C3711yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C8—41no—
847C8—41no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—162no—
866C22—162no—
867C22C37×#42112yes—
868C22C22×C22⋊C4×C3711yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—41no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—81no—
890C2—81no—
891C2—81no—
892C2C37×#288811yescharacteristic
893C2C2×C37×#42111yescharacteristic
894C2C37×#290111yescharacteristic
subgroupG/H
center, socleC22×C37C22×C22⋊C4
commutatorC2×C4C23×C4×C37
Frattini, cosocleC42C24×C37
prime radicalC37×#3514C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C4×#41×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2970C2semidirect
3. C37×#2923C2semidirect
4. C37×#1536C2semidirect
5. C37×#1535C2semidirect
6. C37×#1535C2semidirect
7. C37×#1533C2semidirect
8. C37×#1532C2semidirect
9. C37×#1532C2semidirect
10. C37×#1530C2semidirect
11. C37×#1529C2semidirect
12. C37×#1527C2semidirect
13. C37×#1527C2semidirect
14. C37×#1524C2semidirect
15. C2×C37×#329C2semidirect
45. C37×#432C22semidirect
46. C37×#432C22semidirect
47. C37×#432C22semidirect
48. C37×#432C22semidirect
49. C37×#432C22semidirect
50. C37×#432C22semidirect
51. C37×#432C22semidirect
54. C4×M16×C37C22semidirect
55. C4×M16×C37C22semidirect
56. C2×#97×C37C22semidirect
57. C2×#97×C37C22semidirect
58. C2×#97×C37C22semidirect
59. C37×#330C22semidirect
60. C37×#330C22semidirect
61. C37×#330C22semidirect
62. C37×#330C22semidirect
67. C37×#329C22semidirect
68. C37×#329C22semidirect
69. C37×#329C22semidirect
70. C37×#329C22semidirect
71. C37×#329C22semidirect
72. C37×#329C22semidirect
73. C37×#329C22semidirect
74. C37×#329C22semidirect
400. #17679C37direct (N × H)
440. #2970C2×C37semidirect
441. #2923C2×C37semidirect
442. #1536C2×C37semidirect
443. #1535C2×C37semidirect
444. #1535C2×C37semidirect
445. #1533C2×C37semidirect
446. #1532C2×C37semidirect
447. #1532C2×C37semidirect
448. #1530C2×C37semidirect
449. #1529C2×C37semidirect
450. #1527C2×C37semidirect
451. #1527C2×C37semidirect
452. #1524C2×C37semidirect
453. C2×#329C2×C37semidirect
492. #432C22×C37semidirect
493. #432C22×C37semidirect
494. #432C22×C37semidirect
495. #432C22×C37semidirect
496. #432C22×C37semidirect
497. #432C22×C37semidirect
498. #432C22×C37semidirect
501. C4×M16C22×C37semidirect
502. C4×M16C22×C37semidirect
503. C2×#97C22×C37semidirect
504. C2×#97C22×C37semidirect
505. C2×#97C22×C37semidirect
506. #330C22×C37semidirect
507. #330C22×C37semidirect
508. #330C22×C37semidirect
509. #330C22×C37semidirect
514. #329C22×C37semidirect
515. #329C22×C37semidirect
516. #329C22×C37semidirect
517. #329C22×C37semidirect
518. #329C22×C37semidirect
519. #329C22×C37semidirect
520. #329C22×C37semidirect
521. #329C22×C37semidirect
522. C37#17679direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35142
C37×#29702
C37×#29232
C37×#15362
C37×#15352
C37×#15332
C37×#15322
C37×#15302
C37×#15292
C37×#15272
C37×#15242
C2×C37×#3292
#1767937