Finite Group Databasebeta

← C2×C37×#3345 #22682490

Subgroups — C2×C37×#3345 #22682490

Order 9472.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#553C211yesmaximal, characteristic, complemented
2C2×C37×#547C211yesmaximal, characteristic, complemented
3C37×#3345C2116yesmaximal, direct product factor
4C2×C37×#501C211yesmaximal, characteristic, complemented
5C2×C37×#481C211yesmaximal, characteristic, complemented
6C2×C37×#481C211yesmaximal, characteristic, complemented
7C2×C37×#482C211yesmaximal, characteristic, complemented
8C2×C37×#480C211yesmaximal, characteristic, complemented
9C2×C37×#478C211yesmaximal, characteristic, complemented
10C2×C37×#476C211yesmaximal, characteristic, complemented
11C2×C37×#469C211yesmaximal, characteristic, complemented
12C2×C37×#466C211yesmaximal, characteristic, complemented
13C2×C37×#442C211yesmaximal, characteristic, complemented
14C2×C37×#435C211yesmaximal, characteristic, complemented
15C2×C37×#428C211yesmaximal, characteristic, complemented
16C22×#106×C37C211yesmaximal, characteristic, complemented
17C22×#41×C37—21no—
18C22×D8×C37C2211yescharacteristic
19C22×M16×C37C2211yescharacteristic
20C23×C8×C37C2211yescharacteristic
21C37×#553—24no—
22C37×#553C2218yescomplemented
23C37×#547—24no—
24C37×#547C2218yescomplemented
25C2×C4⋊Q8×C37C2211yescharacteristic
26C2×#126×C37—21no—
27C2×#125×C37C2211yescharacteristic
28C2×#123×C37—21no—
29C2×#123×C37—21no—
30C2×#123×C37—21no—
31C2×C22⋊Q8×C37—21no—
32C2×#121×C37—21no—
33C2×#121×C37C2211yescharacteristic
34C2×#121×C37C2211yescharacteristic
35C2×#121×C37C2211yescharacteristic
36C2×#121×C37C2211yescharacteristic
37C2×C4×D4×C37—21no—
38C2×C4×D4×C37C2211yescharacteristic
39C2×C4×D4×C37C2211yescharacteristic
40C2×C4×D4×C37C2211yescharacteristic
41C2×#117×C37C2211yescharacteristic
42C22×C4⋊C4×C37C2211yescharacteristic
43C22×C4⋊C4×C37C2211yescharacteristic
44C22×C4⋊C4×C37C2211yescharacteristic
45C37×#501C2218yescomplemented
46C37×#482C2218yescomplemented
47C37×#481C2218yescomplemented
48C37×#481C2218yescomplemented
49C37×#480C2218yescomplemented
50C37×#478C2218yescomplemented
51C37×#476C2218yescomplemented
52C37×#469C2218yescomplemented
53C37×#466C2218yescomplemented
54C37×#442C2218yescomplemented
55C37×#435C2218yescomplemented
56C37×#428C2218yescomplemented
57C2×#107×C37C2211yescharacteristic
58C2×#107×C37C2211yescharacteristic
59C2×#107×C37C2211yescharacteristic
60C2×#106×C37C2211yescharacteristic
61C2×#106×C37C2211yescharacteristic
62C2×#106×C37C2211yescharacteristic
63C2×#106×C37C2211yescharacteristic
64C2×#106×C37C2211yescharacteristic
65C2×#106×C37C2211yescharacteristic
66C2×#106×C37C2218yescomplemented
67C2×C4⋊C8×C37C2211yescharacteristic
68C2×#102×C37C2211yescharacteristic
69C2×#102×C37C2211yescharacteristic
70C2×#102×C37C2211yescharacteristic
71C2×#102×C37C2211yescharacteristic
72C2×#102×C37C2211yescharacteristic
73C2×#102×C37C2211yescharacteristic
74C2×C22⋊C8×C37C2211yescharacteristic
75C2×C22⋊C8×C37C2211yescharacteristic
76C2×#97×C37C2211yescharacteristic
77C2×#41×C37—28no—
78C2×#41×C37—48no—
79C22×Q8×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37—21no—
82C22×D4×C37—21no—
83C22×D4×C37—21no—
84C22×D4×C37D411yescharacteristic
85C22×D4×C37C2311yescharacteristic
86C22×D4×C37C2311yescharacteristic
87C23×C4×C37—21no—
88C23×C4×C37—21no—
89C23×C4×C37—21no—
90C23×C4×C37—21no—
91C23×C4×C37—21no—
92C23×C4×C37C2311yescharacteristic
93C23×C4×C37C2311yescharacteristic
94C2×D8×C37—24no—
95C2×D8×C37C2314yes—
96C2×M16×C37—24no—
97C2×M16×C37C2314yes—
98C22×C8×C37—24no—
99C22×C8×C37C2311yescharacteristic
100C22×C8×C37C2314yes—
101C22×C8×C37C2311yescharacteristic
102C22×C8×C37C2311yescharacteristic
103C22×C8×C37C2311yescharacteristic
104C4⋊Q8×C37—22no—
105C4⋊Q8×C37C2314yes—
106#126×C37—28no—
107#125×C37—22no—
108#125×C37C2314yes—
109#123×C37—28no—
110#123×C37—28no—
111#123×C37—28no—
112C22⋊Q8×C37—28no—
113#121×C37—28no—
114#121×C37—22no—
115#121×C37—22no—
116#121×C37—22no—
117#121×C37—22no—
118#121×C37C2314yes—
119#121×C37C2314yes—
120#121×C37C2314yes—
121#121×C37C2314yes—
122C4×D4×C37—28no—
123C4×D4×C37—22no—
124C4×D4×C37—22no—
125C4×D4×C37D414yes—
126C4×D4×C37C2314yes—
127C4×D4×C37C2314yes—
128C4×D4×C37C2314yes—
129#117×C37—22no—
130#117×C37C2314yes—
131C2×C4⋊C4×C37—21no—
132C2×C4⋊C4×C37—21no—
133C2×C4⋊C4×C37—21no—
134C2×C4⋊C4×C37—21no—
135C2×C4⋊C4×C37—21no—
136C2×C4⋊C4×C37—21no—
137C2×C4⋊C4×C37—22no—
138C2×C4⋊C4×C37—22no—
139C2×C4⋊C4×C37—22no—
140C2×C4⋊C4×C37D411yescharacteristic
141C2×C4⋊C4×C37C2311yescharacteristic
142C2×C4⋊C4×C37C2311yescharacteristic
143C2×C4⋊C4×C37C2311yescharacteristic
144C2×C4⋊C4×C37C2311yescharacteristic
145C2×C4⋊C4×C37C2314yes—
146C2×C4⋊C4×C37C2314yes—
147C2×C4⋊C4×C37C2314yes—
148C2×C4⋊C4×C37C2311yescharacteristic
149C2×C4⋊C4×C37C2311yescharacteristic
150C2×C22⋊C4×C37—21no—
151C2×C22⋊C4×C37—21no—
152C2×C22⋊C4×C37—21no—
153C2×C22⋊C4×C37—21no—
154C2×C22⋊C4×C37—21no—
155C2×C22⋊C4×C37—21no—
156C2×C22⋊C4×C37—21no—
157C2×C22⋊C4×C37D411yescharacteristic
158C2×C22⋊C4×C37D411yescharacteristic
159C2×C42×C37—21no—
160C2×C42×C37C2311yescharacteristic
161#107×C37C2314yes—
162#107×C37C2314yes—
163#107×C37C2314yes—
164#106×C37C2314yes—
165#106×C37C2314yes—
166#106×C37C2314yes—
167#106×C37C2314yes—
168#106×C37C2314yes—
169#106×C37C2314yes—
170C4⋊C8×C37C2314yes—
171#102×C37C2314yes—
172#102×C37C2314yes—
173#102×C37C2314yes—
174#102×C37C2314yes—
175#102×C37C2314yes—
176#102×C37C2314yes—
177C22⋊C8×C37C2314yes—
178C22⋊C8×C37C2314yes—
179#97×C37C2314yes—
180C24×C37—21no—
181C24×C37—21no—
182C24×C37C2×D411yescharacteristic
183C24×C37C2×D411yescharacteristic
184#41×C37—432no—
185C2×Q8×C37—24no—
186C2×Q8×C37—44no—
187C2×D4×C37—24no—
188C2×D4×C37—24no—
189C2×D4×C37—24no—
190C2×D4×C37—24no—
191C2×D4×C37—24no—
192C2×D4×C37—21no—
193C2×D4×C37—21no—
194C2×D4×C37—22no—
195C2×D4×C37—22no—
196C2×D4×C37—22no—
197C2×D4×C37—22no—
198C2×D4×C37—44no—
199C2×D4×C37—44no—
200C2×D4×C37—44no—
201C2×D4×C37—82no—
202C2×D4×C37C2×D414yes—
203C2×D4×C37C2412yes—
204C2×D4×C37C2412yes—
205C22×C4×C37—22no—
206C22×C4×C37—22no—
207C22×C4×C37—22no—
208C22×C4×C37—22no—
209C22×C4×C37—24no—
210C22×C4×C37—24no—
211C22×C4×C37—21no—
212C22×C4×C37—21no—
213C22×C4×C37—21no—
214C22×C4×C37—21no—
215C22×C4×C37—21no—
216C22×C4×C37—21no—
217C22×C4×C37—24no—
218C22×C4×C37—24no—
219C22×C4×C37—24no—
220C22×C4×C37—44no—
221C22×C4×C37—44no—
222C22×C4×C37—44no—
223C22×C4×C37—82no—
224C22×C4×C37—82no—
225C22×C4×C37C2×D412yes—
226C22×C4×C37C2×D412yes—
227C22×C4×C37C2×D411yescharacteristic
228C22×C4×C37C2×D411yescharacteristic
229C22×C4×C37C2×D411yescharacteristic
230C22×C4×C37C2×D411yescharacteristic
231C22×C4×C37C2412yes—
232C22×C4×C37C2412yes—
233C22×C4×C37C2411yescharacteristic
234D8×C37—28no—
235M16×C37—28no—
236C2×C8×C37—22no—
237C2×C8×C37—22no—
238C2×C8×C37—22no—
239C2×C8×C37—28no—
240C2×C8×C37#4114yescomplemented
241C2×C8×C37C2412yes—
242C2×C8×C37C2412yes—
243C2×C8×C37C2412yes—
244C2×C8×C37C2412yes—
245C4⋊C4×C37—21no—
246C4⋊C4×C37—21no—
247C4⋊C4×C37—21no—
248C4⋊C4×C37—21no—
249C4⋊C4×C37—21no—
250C4⋊C4×C37—24no—
251C4⋊C4×C37—24no—
252C4⋊C4×C37—24no—
253C4⋊C4×C37—24no—
254C4⋊C4×C37—24no—
255C4⋊C4×C37—24no—
256C4⋊C4×C37—21no—
257C4⋊C4×C37C2×D414yes—
258C4⋊C4×C37C2412yes—
259C4⋊C4×C37C2412yes—
260C4⋊C4×C37C2412yes—
261C4⋊C4×C37C2412yes—
262C4⋊C4×C37C2412yes—
263C4⋊C4×C37C2412yes—
264C22⋊C4×C37—24no—
265C22⋊C4×C37—24no—
266C22⋊C4×C37—24no—
267C22⋊C4×C37—24no—
268C22⋊C4×C37—24no—
269C22⋊C4×C37—24no—
270C22⋊C4×C37—24no—
271C22⋊C4×C37C2×D414yes—
272C22⋊C4×C37C2×D414yes—
273C42×C37—24no—
274C42×C37C2×D412yes—
275C42×C37C2412yes—
276C23×C37—22no—
277C23×C37—22no—
278C23×C37—22no—
279C23×C37—22no—
280C23×C37—22no—
281C23×C37—22no—
282C23×C37—22no—
283C23×C37—42no—
284C23×C37—42no—
285C23×C37—42no—
286C23×C37—42no—
287C23×C37—42no—
288C23×C37—42no—
289C23×C37AGL(1,ℤ/8)14yes—
290C23×C37C22×D412yes—
291C23×C37C22×D412yes—
292C23×C37C22×D411yescharacteristic
293Q8×C37—48no—
294D4×C37—28no—
295D4×C37—22no—
296D4×C37—22no—
297D4×C37—22no—
298D4×C37—22no—
299D4×C37—48no—
300D4×C37—48no—
301D4×C37—48no—
302D4×C37—42no—
303D4×C37—42no—
304D4×C37—84no—
305C2×C4×C37—22no—
306C2×C4×C37—22no—
307C2×C4×C37—22no—
308C2×C4×C37—22no—
309C2×C4×C37—24no—
310C2×C4×C37—24no—
311C2×C4×C37—22no—
312C2×C4×C37—22no—
313C2×C4×C37—22no—
314C2×C4×C37—22no—
315C2×C4×C37—22no—
316C2×C4×C37—22no—
317C2×C4×C37—22no—
318C2×C4×C37—22no—
319C2×C4×C37—22no—
320C2×C4×C37—22no—
321C2×C4×C37—48no—
322C2×C4×C37—48no—
323C2×C4×C37—42no—
324C2×C4×C37—42no—
325C2×C4×C37—42no—
326C2×C4×C37—48no—
327C2×C4×C37—42no—
328C2×C4×C37—42no—
329C2×C4×C37—42no—
330C2×C4×C37—84no—
331C2×C4×C37—84no—
332C2×C4×C37C22×D412yes—
333C2×C4×C37C22×D412yes—
334C2×C4×C37C22×D412yes—
335C2×C4×C37C22×D412yes—
336C2×C4×C37C22×D411yescharacteristic
337C2×C4×C37C2×#4112yes—
338C2×C4×C372−1+412yes—
339C2×C4×C37C2511yescharacteristic
340C8×C37—22no—
341C8×C37—22no—
342C8×C37—22no—
343C8×C37C2×#4114yescomplemented
344C2×#3345C3711yesmaximal, characteristic, direct product factor, Sylow
345C22×C37—28no—
346C22×C37—22no—
347C22×C37—22no—
348C22×C37—22no—
349C22×C37—22no—
350C22×C37—22no—
351C22×C37—44no—
352C22×C37—42no—
353C22×C37—42no—
354C22×C37—42no—
355C22×C37—42no—
356C22×C37—42no—
357C22×C37—42no—
358C22×C37—84no—
359C22×C37—84no—
360C22×C37#54712yes—
361C22×C37C2×AGL(1,ℤ/8)14yes—
362C22×C37C2×AGL(1,ℤ/8)12yes—
363C22×C37#57712yes—
364C22×C37C23×D411yescharacteristic
365C4×C37—22no—
366C4×C37—22no—
367C4×C37—22no—
368C4×C37—22no—
369C4×C37—42no—
370C4×C37—42no—
371C4×C37—42no—
372C4×C37—42no—
373C4×C37—42no—
374C4×C37—42no—
375C4×C37#54712yes—
376C4×C37C22×#4111yescharacteristic
377C4×C37C2×2−1+411yescharacteristic
378C2×#553C2×C3711yescharacteristic, complemented
379C2×#547C2×C3711yescharacteristic, complemented
380#3345C2×C37116yesdirect product factor
381C2×#501C2×C3711yescharacteristic, complemented
382C2×#481C2×C3711yescharacteristic, complemented
383C2×#481C2×C3711yescharacteristic, complemented
384C2×#482C2×C3711yescharacteristic, complemented
385C2×#480C2×C3711yescharacteristic, complemented
386C2×#478C2×C3711yescharacteristic, complemented
387C2×#476C2×C3711yescharacteristic, complemented
388C2×#469C2×C3711yescharacteristic, complemented
389C2×#466C2×C3711yescharacteristic, complemented
390C2×#442C2×C3711yescharacteristic, complemented
391C2×#435C2×C3711yescharacteristic, complemented
392C2×#428C2×C3711yescharacteristic, complemented
393C22×#106C2×C3711yescharacteristic, complemented
394C2×C37—24no—
395C2×C37—42no—
396C2×C37—82no—
397C2×C37—82no—
398C2×C37#334514yesdirect product factor
399C2×C37C2×#54711yescharacteristic
400C2×C37C22×AGL(1,ℤ/8)11yescharacteristic
401C2×C37C2×#57711yescharacteristic
402C22×#41—21no—
403C22×D8C22×C3711yescharacteristic
404C22×M16C22×C3711yescharacteristic
405C23×C8C22×C3711yescharacteristic
406#553—24no—
407#553C22×C3718yescomplemented
408#547—24no—
409#547C22×C3718yescomplemented
410C2×C4⋊Q8C22×C3711yescharacteristic
411C2×#126—21no—
412C2×#125C22×C3711yescharacteristic
413C2×#123—21no—
414C2×#123—21no—
415C2×#123—21no—
416C2×C22⋊Q8—21no—
417C2×#121—21no—
418C2×#121C22×C3711yescharacteristic
419C2×#121C22×C3711yescharacteristic
420C2×#121C22×C3711yescharacteristic
421C2×#121C22×C3711yescharacteristic
422C2×C4×D4—21no—
423C2×C4×D4C22×C3711yescharacteristic
424C2×C4×D4C22×C3711yescharacteristic
425C2×C4×D4C22×C3711yescharacteristic
426C2×#117C22×C3711yescharacteristic
427C22×C4⋊C4C22×C3711yescharacteristic
428C22×C4⋊C4C22×C3711yescharacteristic
429C22×C4⋊C4C22×C3711yescharacteristic
430#501C22×C3718yescomplemented
431#482C22×C3718yescomplemented
432#481C22×C3718yescomplemented
433#481C22×C3718yescomplemented
434#480C22×C3718yescomplemented
435#478C22×C3718yescomplemented
436#476C22×C3718yescomplemented
437#469C22×C3718yescomplemented
438#466C22×C3718yescomplemented
439#442C22×C3718yescomplemented
440#435C22×C3718yescomplemented
441#428C22×C3718yescomplemented
442C2×#107C22×C3711yescharacteristic
443C2×#107C22×C3711yescharacteristic
444C2×#107C22×C3711yescharacteristic
445C2×#106C22×C3711yescharacteristic
446C2×#106C22×C3711yescharacteristic
447C2×#106C22×C3711yescharacteristic
448C2×#106C22×C3711yescharacteristic
449C2×#106C22×C3711yescharacteristic
450C2×#106C22×C3711yescharacteristic
451C2×#106C22×C3718yescomplemented
452C2×C4⋊C8C22×C3711yescharacteristic
453C2×#102C22×C3711yescharacteristic
454C2×#102C22×C3711yescharacteristic
455C2×#102C22×C3711yescharacteristic
456C2×#102C22×C3711yescharacteristic
457C2×#102C22×C3711yescharacteristic
458C2×#102C22×C3711yescharacteristic
459C2×C22⋊C8C22×C3711yescharacteristic
460C2×C22⋊C8C22×C3711yescharacteristic
461C2×#97C22×C3711yescharacteristic
462C37C2×#334511yescharacteristic, direct product factor, Sylow
463C2×#41—28no—
464C2×#41—48no—
465C22×Q8—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4D4×C3711yescharacteristic
471C22×D4C23×C3711yescharacteristic
472C22×D4C23×C3711yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—21no—
477C23×C4—21no—
478C23×C4C23×C3711yescharacteristic
479C23×C4C23×C3711yescharacteristic
480C2×D8—24no—
481C2×D8C23×C3714yes—
482C2×M16—24no—
483C2×M16C23×C3714yes—
484C22×C8—24no—
485C22×C8C23×C3711yescharacteristic
486C22×C8C23×C3714yes—
487C22×C8C23×C3711yescharacteristic
488C22×C8C23×C3711yescharacteristic
489C22×C8C23×C3711yescharacteristic
490C4⋊Q8—22no—
491C4⋊Q8C23×C3714yes—
492#126—28no—
493#125—22no—
494#125C23×C3714yes—
495#123—28no—
496#123—28no—
497#123—28no—
498C22⋊Q8—28no—
499#121—28no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121C23×C3714yes—
505#121C23×C3714yes—
506#121C23×C3714yes—
507#121C23×C3714yes—
508C4×D4—28no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4D4×C3714yes—
512C4×D4C23×C3714yes—
513C4×D4C23×C3714yes—
514C4×D4C23×C3714yes—
515#117—22no—
516#117C23×C3714yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4D4×C3711yescharacteristic
527C2×C4⋊C4C23×C3711yescharacteristic
528C2×C4⋊C4C23×C3711yescharacteristic
529C2×C4⋊C4C23×C3711yescharacteristic
530C2×C4⋊C4C23×C3711yescharacteristic
531C2×C4⋊C4C23×C3711yescharacteristic
532C2×C4⋊C4C23×C3714yes—
533C2×C4⋊C4C23×C3714yes—
534C2×C4⋊C4C23×C3714yes—
535C2×C4⋊C4C23×C3711yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4D4×C3711yescharacteristic
544C2×C22⋊C4D4×C3711yescharacteristic
545C2×C42—21no—
546C2×C42C23×C3711yescharacteristic
547#107C23×C3714yes—
548#107C23×C3714yes—
549#107C23×C3714yes—
550#106C23×C3714yes—
551#106C23×C3714yes—
552#106C23×C3714yes—
553#106C23×C3714yes—
554#106C23×C3714yes—
555#106C23×C3714yes—
556C4⋊C8C23×C3714yes—
557#102C23×C3714yes—
558#102C23×C3714yes—
559#102C23×C3714yes—
560#102C23×C3714yes—
561#102C23×C3714yes—
562#102C23×C3714yes—
563C22⋊C8C23×C3714yes—
564C22⋊C8C23×C3714yes—
565#97C23×C3714yes—
566C24—21no—
567C24—21no—
568C24C2×D4×C3711yescharacteristic
569C24C2×D4×C3711yescharacteristic
570#41—432no—
571C2×Q8—24no—
572C2×Q8—44no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—82no—
588C2×D4C2×D4×C3714yes—
589C2×D4C24×C3712yes—
590C2×D4C24×C3712yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4C2×D4×C3711yescharacteristic
612C22×C4C2×D4×C3711yescharacteristic
613C22×C4C2×D4×C3711yescharacteristic
614C22×C4C2×D4×C3711yescharacteristic
615C22×C4C2×D4×C3712yes—
616C22×C4C2×D4×C3712yes—
617C22×C4C24×C3712yes—
618C22×C4C24×C3712yes—
619C22×C4C24×C3711yescharacteristic
620D8—28no—
621M16—28no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—28no—
626C2×C8#41×C3714yescomplemented
627C2×C8C24×C3712yes—
628C2×C8C24×C3712yes—
629C2×C8C24×C3712yes—
630C2×C8C24×C3712yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4C2×D4×C3714yes—
644C4⋊C4C24×C3712yes—
645C4⋊C4C24×C3712yes—
646C4⋊C4C24×C3712yes—
647C4⋊C4C24×C3712yes—
648C4⋊C4C24×C3712yes—
649C4⋊C4C24×C3712yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4C2×D4×C3714yes—
658C22⋊C4C2×D4×C3714yes—
659C42—24no—
660C42C2×D4×C3712yes—
661C42C24×C3712yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23AGL(1,ℤ/8)×C3714yes—
676C23C22×D4×C3712yes—
677C23C22×D4×C3712yes—
678C23C22×D4×C3711yescharacteristic
679Q8—48no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—48no—
686D4—48no—
687D4—48no—
688D4—42no—
689D4—42no—
690D4—84no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—48no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4C22×D4×C3712yes—
719C2×C4C22×D4×C3712yes—
720C2×C4C22×D4×C3712yes—
721C2×C4C22×D4×C3712yes—
722C2×C4C22×D4×C3711yescharacteristic
723C2×C4C2×#41×C3712yes—
724C2×C42−1+4×C3712yes—
725C2×C4C25×C3711yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8C2×#41×C3714yescomplemented
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—84no—
745C22C37×#54712yes—
746C22C2×AGL(1,ℤ/8)×C3714yes—
747C22C2×AGL(1,ℤ/8)×C3712yes—
748C22C37×#57712yes—
749C22C23×D4×C3711yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4C37×#54712yes—
761C4C22×#41×C3711yescharacteristic
762C4C2×2−1+4×C3711yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—82no—
767C2C37×#334514yesdirect product factor
768C2C2×C37×#54711yescharacteristic
769C2C22×AGL(1,ℤ/8)×C3711yescharacteristic
770C2C2×C37×#57711yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC2×C4C25×C37
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#553C2semidirect
2. C2×C37×#547C2semidirect
3. C37×#3345C2direct (N × H)
4. C2×C37×#501C2semidirect
5. C2×C37×#481C2semidirect
6. C2×C37×#481C2semidirect
7. C2×C37×#482C2semidirect
8. C2×C37×#480C2semidirect
9. C2×C37×#478C2semidirect
10. C2×C37×#476C2semidirect
11. C2×C37×#469C2semidirect
12. C2×C37×#466C2semidirect
13. C2×C37×#442C2semidirect
14. C2×C37×#435C2semidirect
15. C2×C37×#428C2semidirect
16. C22×#106×C37C2semidirect
22. C37×#553C22semidirect
24. C37×#547C22semidirect
45. C37×#501C22semidirect
46. C37×#482C22semidirect
47. C37×#481C22semidirect
48. C37×#481C22semidirect
49. C37×#480C22semidirect
50. C37×#478C22semidirect
51. C37×#476C22semidirect
52. C37×#469C22semidirect
53. C37×#466C22semidirect
54. C37×#442C22semidirect
55. C37×#435C22semidirect
56. C37×#428C22semidirect
66. C2×#106×C37C22semidirect
240. C2×C8×C37#41semidirect
343. C8×C37C2×#41semidirect
344. C2×#3345C37direct (N × H)
378. C2×#553C2×C37semidirect
379. C2×#547C2×C37semidirect
380. #3345C2×C37direct (N × H)
381. C2×#501C2×C37semidirect
382. C2×#481C2×C37semidirect
383. C2×#481C2×C37semidirect
384. C2×#482C2×C37semidirect
385. C2×#480C2×C37semidirect
386. C2×#478C2×C37semidirect
387. C2×#476C2×C37semidirect
388. C2×#469C2×C37semidirect
389. C2×#466C2×C37semidirect
390. C2×#442C2×C37semidirect
391. C2×#435C2×C37semidirect
392. C2×#428C2×C37semidirect
393. C22×#106C2×C37semidirect
398. C2×C37#3345direct (N × H)
407. #553C22×C37semidirect
409. #547C22×C37semidirect
430. #501C22×C37semidirect
431. #482C22×C37semidirect
432. #481C22×C37semidirect
433. #481C22×C37semidirect
434. #480C22×C37semidirect
435. #478C22×C37semidirect
436. #476C22×C37semidirect
437. #469C22×C37semidirect
438. #466C22×C37semidirect
439. #442C22×C37semidirect
440. #435C22×C37semidirect
441. #428C22×C37semidirect
451. C2×#106C22×C37semidirect
462. C37C2×#3345direct (N × H)
626. C2×C8#41×C37semidirect
729. C8C2×#41×C37semidirect
767. C2C37×#3345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5532
C2×C37×#5472
C37×#33452
C2×C37×#5012
C2×C37×#4812
C2×C37×#4822
C2×C37×#4802
C2×C37×#4782
C2×C37×#4762
C2×C37×#4692
C2×C37×#4662
C2×C37×#4422
C2×C37×#4352
C2×C37×#4282
C22×#106×C372
C2×#334537