Finite Group Databasebeta

← C137×#21420 #46870806

Subgroups — C137×#21420 #46870806

Order 35072.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C137C211yesmaximal, characteristic
2#2280×C137C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊C4×C137C211yesmaximal, characteristic, complemented
4#1996×C137C212yesmaximal, complemented
5#1964×C137C212yesmaximal, complemented
6#1898×C137C214yesmaximal, complemented
7C4×#99×C137C214yesmaximal, complemented
8C22×#41×C137C411yescharacteristic, complemented
9C24×C4×C137C2211yescharacteristic
10#525×C137—21no—
11#525×C137—21no—
12#525×C137—21no—
13#525×C137—21no—
14#525×C137—21no—
15#525×C137—21no—
16#525×C137—21no—
17#525×C137—21no—
18C2×#123×C137C412yescomplemented
19C2×C22⋊Q8×C137C411yescharacteristic, complemented
20C2×C22⋊Q8×C137C2211yescharacteristic
21C2×#121×C137C411yescharacteristic, complemented
22C2×#121×C137C2211yescharacteristic
23C2×#120×C137C2212yes—
24C2×C4×D4×C137C412yescomplemented
25C2×C4×D4×C137C2212yes—
26C2×#117×C137—21no—
27C2×#117×C137C411yescharacteristic, complemented
28C22×C22⋊C4×C137C2212yes—
29C22×C42×C137—21no—
30C2×#99×C137C2218yes—
31#381×C137—21no—
32#380×C137—21no—
33#380×C137C2212yes—
34#379×C137C2212yes—
35C4×C22⋊C4×C137—21no—
36C4×C22⋊C4×C137—21no—
37C4×C22⋊C4×C137—21no—
38C4×C22⋊C4×C137C2212yes—
39C4×C22⋊C4×C137C2212yes—
40C4×C22⋊C4×C137C2212yes—
41C2×#95×C137—21no—
42#342×C137C2218yes—
43C25×C137C2311yescharacteristic
44C2×#41×C137—21no—
45C2×#41×C137—21no—
46C2×#41×C137—21no—
47C2×#41×C137—21no—
48C2×#41×C137—44no—
49C22×Q8×C137C2×C411yescharacteristic, complemented
50C22×D4×C137C2×C412yes—
51C22×D4×C137C2×C412yes—
52C22×D4×C137C2×C411yescharacteristic, complemented
53C22×D4×C137C2312yes—
54C23×C4×C137—22no—
55C23×C4×C137—44no—
56C23×C4×C137C2×C411yescharacteristic
57C23×C4×C137C2×C411yescharacteristic
58C23×C4×C137C2×C411yescharacteristic
59C23×C4×C137C2×C411yescharacteristic
60C23×C4×C137C2×C412yescomplemented
61C23×C4×C137D411yescharacteristic
62C23×C4×C137D411yescharacteristic
63C23×C4×C137D411yescharacteristic
64C23×C4×C137D411yescharacteristic
65C23×C4×C137D411yescharacteristic
66C23×C4×C137D411yescharacteristic
67C23×C4×C137D411yescharacteristic
68C23×C4×C137D411yescharacteristic
69C23×C4×C137C2311yescharacteristic
70C23×C4×C137C2311yescharacteristic
71#123×C137—22no—
72#123×C137—22no—
73#123×C137—22no—
74#123×C137—22no—
75C22⋊Q8×C137—21no—
76C22⋊Q8×C137—21no—
77C22⋊Q8×C137—21no—
78C22⋊Q8×C137—21no—
79C22⋊Q8×C137—21no—
80C22⋊Q8×C137—21no—
81C22⋊Q8×C137—21no—
82C22⋊Q8×C137—21no—
83#121×C137—21no—
84#121×C137—21no—
85#121×C137—21no—
86#121×C137—21no—
87#121×C137—21no—
88#121×C137—21no—
89#121×C137—21no—
90#121×C137—21no—
91#120×C137—22no—
92#120×C137—22no—
93#120×C137—22no—
94#120×C137—22no—
95C4×D4×C137—22no—
96C4×D4×C137—22no—
97C4×D4×C137—22no—
98C4×D4×C137—22no—
99C4×D4×C137—22no—
100C4×D4×C137—22no—
101C4×D4×C137—22no—
102C4×D4×C137—22no—
103#117×C137—21no—
104#117×C137—21no—
105#117×C137—21no—
106#117×C137—21no—
107#117×C137—44no—
108C2×C4⋊C4×C137—22no—
109C2×C4⋊C4×C137C2×C411yescharacteristic, complemented
110C2×C4⋊C4×C137C2×C411yescharacteristic, complemented
111C2×C4⋊C4×C137C2×C412yescomplemented
112C2×C4⋊C4×C137C2×C412yescomplemented
113C2×C22⋊C4×C137—22no—
114C2×C22⋊C4×C137—28no—
115C2×C22⋊C4×C137—22no—
116C2×C22⋊C4×C137—22no—
117C2×C22⋊C4×C137C2×C412yes—
118C2×C22⋊C4×C137C2×C412yes—
119C2×C22⋊C4×C137C2×C412yescomplemented
120C2×C22⋊C4×C137C2×C412yescomplemented
121C2×C22⋊C4×C137C2314yes—
122C2×C22⋊C4×C137C2312yes—
123C2×C22⋊C4×C137C2314yes—
124C2×C42×C137—22no—
125C2×C42×C137—22no—
126C2×C42×C137—22no—
127C2×C42×C137—44no—
128C2×C42×C137C2×C412yescomplemented
129#99×C137—216no—
130#95×C137—22no—
131#95×C137—22no—
132#95×C137—22no—
133#95×C137—22no—
134C24×C137—24no—
135C24×C137—42no—
136C24×C137—42no—
137C24×C137C22×C411yescharacteristic
138C24×C137C22×C411yescharacteristic
139C24×C137C22×C412yes—
140C24×C137C2×D411yescharacteristic
141C24×C137C2×D411yescharacteristic
142C24×C137C2×D411yescharacteristic
143C24×C137C2×D411yescharacteristic
144C24×C137C2411yescharacteristic
145#41×C137—44no—
146#41×C137—44no—
147#41×C137—44no—
148#41×C137—44no—
149C2×Q8×C137—21no—
150C2×Q8×C137—21no—
151C2×Q8×C137—42no—
152C2×D4×C137—22no—
153C2×D4×C137—22no—
154C2×D4×C137—22no—
155C2×D4×C137—22no—
156C2×D4×C137—22no—
157C2×D4×C137—22no—
158C2×D4×C137—28no—
159C2×D4×C137—21no—
160C2×D4×C137—21no—
161C2×D4×C137—42no—
162C2×D4×C137—44no—
163C2×D4×C137—44no—
164C22×C4×C137—24no—
165C22×C4×C137—24no—
166C22×C4×C137—24no—
167C22×C4×C137—28no—
168C22×C4×C137—24no—
169C22×C4×C137—22no—
170C22×C4×C137—22no—
171C22×C4×C137—24no—
172C22×C4×C137—42no—
173C22×C4×C137—42no—
174C22×C4×C137—42no—
175C22×C4×C137—42no—
176C22×C4×C137—42no—
177C22×C4×C137—42no—
178C22×C4×C137—42no—
179C22×C4×C137—42no—
180C22×C4×C137—42no—
181C22×C4×C137—42no—
182C22×C4×C137—42no—
183C22×C4×C137—44no—
184C22×C4×C137—44no—
185C22×C4×C137—44no—
186C22×C4×C137C22⋊C411yescharacteristic
187C22×C4×C137C22⋊C411yescharacteristic
188C22×C4×C137C22⋊C411yescharacteristic
189C22×C4×C137C22⋊C411yescharacteristic
190C22×C4×C137C22⋊C411yescharacteristic
191C22×C4×C137C22⋊C411yescharacteristic
192C22×C4×C137C22⋊C411yescharacteristic
193C22×C4×C137C22⋊C411yescharacteristic
194C22×C4×C137C22⋊C411yescharacteristic
195C22×C4×C137C22⋊C411yescharacteristic
196C22×C4×C137C22⋊C411yescharacteristic
197C22×C4×C137C22⋊C411yescharacteristic
198C22×C4×C137C22⋊C411yescharacteristic
199C22×C4×C137C22⋊C411yescharacteristic
200C22×C4×C137C22⋊C411yescharacteristic
201C22×C4×C137C22⋊C411yescharacteristic
202C22×C4×C137C22×C412yes—
203C22×C4×C137C22×C411yescharacteristic
204C22×C4×C137C22×C411yescharacteristic
205C22×C4×C137C22×C412yes—
206C22×C4×C137C22×C412yes—
207C22×C4×C137C22×C411yescharacteristic
208C22×C4×C137C22×C411yescharacteristic
209C22×C4×C137C2×D411yescharacteristic
210C22×C4×C137C2×D411yescharacteristic
211C22×C4×C137C2×D411yescharacteristic
212C22×C4×C137C2×D411yescharacteristic
213C22×C4×C137C2×D411yescharacteristic
214C22×C4×C137C2×D411yescharacteristic
215C22×C4×C137C2×D411yescharacteristic
216C22×C4×C137C2×D411yescharacteristic
217C4⋊C4×C137—21no—
218C4⋊C4×C137—21no—
219C4⋊C4×C137—21no—
220C4⋊C4×C137—21no—
221C4⋊C4×C137—22no—
222C4⋊C4×C137—22no—
223C4⋊C4×C137—22no—
224C4⋊C4×C137—22no—
225C4⋊C4×C137—44no—
226C22⋊C4×C137—28no—
227C22⋊C4×C137—22no—
228C22⋊C4×C137—22no—
229C22⋊C4×C137—22no—
230C22⋊C4×C137—22no—
231C22⋊C4×C137—22no—
232C22⋊C4×C137—22no—
233C22⋊C4×C137—24no—
234C22⋊C4×C137—22no—
235C22⋊C4×C137—22no—
236C22⋊C4×C137—22no—
237C22⋊C4×C137—22no—
238C22⋊C4×C137—28no—
239C22⋊C4×C137—44no—
240C22⋊C4×C137—44no—
241C22⋊C4×C137#4118yescomplemented
242C42×C137—22no—
243C42×C137—22no—
244C42×C137—44no—
245C42×C137—44no—
246C42×C137—44no—
247C23×C137—22no—
248C23×C137—22no—
249C23×C137—22no—
250C23×C137—22no—
251C23×C137—22no—
252C23×C137—22no—
253C23×C137—22no—
254C23×C137—22no—
255C23×C137—22no—
256C23×C137—22no—
257C23×C137—22no—
258C23×C137—22no—
259C23×C137—22no—
260C23×C137—24no—
261C23×C137—41no—
262C23×C137—41no—
263C23×C137—41no—
264C23×C137—41no—
265C23×C137—41no—
266C23×C137—41no—
267C23×C137—41no—
268C23×C137—41no—
269C23×C137—416no—
270C23×C137—42no—
271C23×C137—42no—
272C23×C137C2×C22⋊C411yescharacteristic
273C23×C137C2×C22⋊C411yescharacteristic
274C23×C137C2×C22⋊C411yescharacteristic
275C23×C137C2×C22⋊C411yescharacteristic
276C23×C137C23×C411yescharacteristic
277C23×C137C22×D411yescharacteristic
278C23×C137C22×D411yescharacteristic
279C23×C137C2×#4114yes—
280Q8×C137—42no—
281Q8×C137—42no—
282D4×C137—42no—
283D4×C137—44no—
284D4×C137—44no—
285D4×C137—44no—
286D4×C137—44no—
287D4×C137—44no—
288D4×C137—44no—
289D4×C137—42no—
290C2×C4×C137—22no—
291C2×C4×C137—22no—
292C2×C4×C137—22no—
293C2×C4×C137—22no—
294C2×C4×C137—22no—
295C2×C4×C137—22no—
296C2×C4×C137—22no—
297C2×C4×C137—22no—
298C2×C4×C137—22no—
299C2×C4×C137—22no—
300C2×C4×C137—22no—
301C2×C4×C137—22no—
302C2×C4×C137—22no—
303C2×C4×C137—22no—
304C2×C4×C137—22no—
305C2×C4×C137—22no—
306C2×C4×C137—22no—
307C2×C4×C137—22no—
308C2×C4×C137—24no—
309C2×C4×C137—28no—
310C2×C4×C137—41no—
311C2×C4×C137—41no—
312C2×C4×C137—41no—
313C2×C4×C137—41no—
314C2×C4×C137—41no—
315C2×C4×C137—41no—
316C2×C4×C137—41no—
317C2×C4×C137—41no—
318C2×C4×C137—41no—
319C2×C4×C137—41no—
320C2×C4×C137—41no—
321C2×C4×C137—41no—
322C2×C4×C137—44no—
323C2×C4×C137—44no—
324C2×C4×C137—416no—
325C2×C4×C137—44no—
326C2×C4×C137—44no—
327C2×C4×C137—42no—
328C2×C4×C137—42no—
329C2×C4×C137—44no—
330C2×C4×C137—44no—
331C2×C4×C137—44no—
332C2×C4×C137#9914yescomplemented
333C2×C4×C137C2×C22⋊C411yescharacteristic
334C2×C4×C137C2×C22⋊C411yescharacteristic
335C2×C4×C137C2×C22⋊C411yescharacteristic
336C2×C4×C137C2×C22⋊C411yescharacteristic
337C2×C4×C137C2×C22⋊C411yescharacteristic
338C2×C4×C137C2×C22⋊C411yescharacteristic
339C2×C4×C137C2×C22⋊C411yescharacteristic
340C2×C4×C137C2×C22⋊C411yescharacteristic
341C22×C137—28no—
342C22×C137—21no—
343C22×C137—21no—
344C22×C137—21no—
345C22×C137—21no—
346C22×C137—21no—
347C22×C137—21no—
348C22×C137—21no—
349C22×C137—21no—
350C22×C137—21no—
351C22×C137—21no—
352C22×C137—21no—
353C22×C137—21no—
354C22×C137—21no—
355C22×C137—21no—
356C22×C137—21no—
357C22×C137—21no—
358C22×C137—44no—
359C22×C137—44no—
360C22×C137—44no—
361C22×C137—44no—
362C22×C137—44no—
363C22×C137—44no—
364C22×C137—42no—
365C22×C137—42no—
366C22×C137—42no—
367C22×C137—84no—
368C22×C137C2×#9912yes—
369C22×C137#41012yes—
370C22×C137C22×C22⋊C411yescharacteristic
371C22×C137C4×#4112yes—
372C22×C137#52512yes—
373C22×C137#53212yes—
374C4×C137—21no—
375C4×C137—21no—
376C4×C137—21no—
377C4×C137—21no—
378C4×C137—21no—
379C4×C137—21no—
380C4×C137—48no—
381C4×C137—42no—
382C4×C137—42no—
383C4×C137—42no—
384C4×C137—84no—
385C4×C137C2×#9912yes—
386C4×C137C2×#9912yes—
387C2×C137—22no—
388C2×C137—22no—
389C2×C137—22no—
390C2×C137—22no—
391C2×C137—22no—
392C2×C137—41no—
393C2×C137—41no—
394C2×C137—82no—
395C2×C137#229711yescharacteristic
396C2×C137C22×#9911yescharacteristic
397C2×C137C2×#41011yescharacteristic
398#21420C13711yesmaximal, characteristic, direct product factor, Sylow
399C137#2142011yescharacteristic, direct product factor, Sylow
400C2×#525C2×C13711yescharacteristic
401#2280C2×C13711yescharacteristic, complemented
402C2×C4×C22⋊C4C2×C13711yescharacteristic, complemented
403#1996C2×C13712yescomplemented
404#1964C2×C13712yescomplemented
405#1898C2×C13714yescomplemented
406C4×#99C2×C13714yescomplemented
407C22×#41C4×C13711yescharacteristic, complemented
408C24×C4C22×C13711yescharacteristic
409#525—21no—
410#525—21no—
411#525—21no—
412#525—21no—
413#525—21no—
414#525—21no—
415#525—21no—
416#525—21no—
417C2×#123C4×C13712yescomplemented
418C2×C22⋊Q8C4×C13711yescharacteristic, complemented
419C2×C22⋊Q8C22×C13711yescharacteristic
420C2×#121C4×C13711yescharacteristic, complemented
421C2×#121C22×C13711yescharacteristic
422C2×#120C22×C13712yes—
423C2×C4×D4C4×C13712yescomplemented
424C2×C4×D4C22×C13712yes—
425C2×#117—21no—
426C2×#117C4×C13711yescharacteristic, complemented
427C22×C22⋊C4C22×C13712yes—
428C22×C42—21no—
429C2×#99C22×C13718yes—
430#381—21no—
431#380—21no—
432#380C22×C13712yes—
433#379C22×C13712yes—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4C22×C13712yes—
438C4×C22⋊C4C22×C13712yes—
439C4×C22⋊C4C22×C13712yes—
440C2×#95—21no—
441#342C22×C13718yes—
442C25C23×C13711yescharacteristic
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—44no—
448C22×Q8C2×C4×C13711yescharacteristic, complemented
449C22×D4C2×C4×C13712yes—
450C22×D4C2×C4×C13712yes—
451C22×D4C2×C4×C13711yescharacteristic, complemented
452C22×D4C23×C13712yes—
453C23×C4—22no—
454C23×C4—44no—
455C23×C4C2×C4×C13711yescharacteristic
456C23×C4C2×C4×C13711yescharacteristic
457C23×C4C2×C4×C13711yescharacteristic
458C23×C4C2×C4×C13711yescharacteristic
459C23×C4C2×C4×C13712yescomplemented
460C23×C4D4×C13711yescharacteristic
461C23×C4D4×C13711yescharacteristic
462C23×C4D4×C13711yescharacteristic
463C23×C4D4×C13711yescharacteristic
464C23×C4D4×C13711yescharacteristic
465C23×C4D4×C13711yescharacteristic
466C23×C4D4×C13711yescharacteristic
467C23×C4D4×C13711yescharacteristic
468C23×C4C23×C13711yescharacteristic
469C23×C4C23×C13711yescharacteristic
470#123—22no—
471#123—22no—
472#123—22no—
473#123—22no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482#121—21no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—21no—
488#121—21no—
489#121—21no—
490#120—22no—
491#120—22no—
492#120—22no—
493#120—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506#117—44no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4C2×C4×C13711yescharacteristic, complemented
509C2×C4⋊C4C2×C4×C13711yescharacteristic, complemented
510C2×C4⋊C4C2×C4×C13712yescomplemented
511C2×C4⋊C4C2×C4×C13712yescomplemented
512C2×C22⋊C4—22no—
513C2×C22⋊C4—28no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4C2×C4×C13712yes—
517C2×C22⋊C4C2×C4×C13712yes—
518C2×C22⋊C4C2×C4×C13712yescomplemented
519C2×C22⋊C4C2×C4×C13712yescomplemented
520C2×C22⋊C4C23×C13714yes—
521C2×C22⋊C4C23×C13712yes—
522C2×C22⋊C4C23×C13714yes—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—44no—
527C2×C42C2×C4×C13712yescomplemented
528#99—216no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533C24—24no—
534C24—42no—
535C24—42no—
536C24C22×C4×C13711yescharacteristic
537C24C22×C4×C13711yescharacteristic
538C24C22×C4×C13712yes—
539C24C2×D4×C13711yescharacteristic
540C24C2×D4×C13711yescharacteristic
541C24C2×D4×C13711yescharacteristic
542C24C2×D4×C13711yescharacteristic
543C24C24×C13711yescharacteristic
544#41—44no—
545#41—44no—
546#41—44no—
547#41—44no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—42no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—28no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—44no—
562C2×D4—44no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4C22⋊C4×C13711yescharacteristic
586C22×C4C22⋊C4×C13711yescharacteristic
587C22×C4C22⋊C4×C13711yescharacteristic
588C22×C4C22⋊C4×C13711yescharacteristic
589C22×C4C22⋊C4×C13711yescharacteristic
590C22×C4C22⋊C4×C13711yescharacteristic
591C22×C4C22⋊C4×C13711yescharacteristic
592C22×C4C22⋊C4×C13711yescharacteristic
593C22×C4C22⋊C4×C13711yescharacteristic
594C22×C4C22⋊C4×C13711yescharacteristic
595C22×C4C22⋊C4×C13711yescharacteristic
596C22×C4C22⋊C4×C13711yescharacteristic
597C22×C4C22⋊C4×C13711yescharacteristic
598C22×C4C22⋊C4×C13711yescharacteristic
599C22×C4C22⋊C4×C13711yescharacteristic
600C22×C4C22⋊C4×C13711yescharacteristic
601C22×C4C22×C4×C13712yes—
602C22×C4C22×C4×C13711yescharacteristic
603C22×C4C22×C4×C13711yescharacteristic
604C22×C4C22×C4×C13712yes—
605C22×C4C22×C4×C13712yes—
606C22×C4C22×C4×C13711yescharacteristic
607C22×C4C22×C4×C13711yescharacteristic
608C22×C4C2×D4×C13711yescharacteristic
609C22×C4C2×D4×C13711yescharacteristic
610C22×C4C2×D4×C13711yescharacteristic
611C22×C4C2×D4×C13711yescharacteristic
612C22×C4C2×D4×C13711yescharacteristic
613C22×C4C2×D4×C13711yescharacteristic
614C22×C4C2×D4×C13711yescharacteristic
615C22×C4C2×D4×C13711yescharacteristic
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—44no—
625C22⋊C4—28no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4#41×C13718yescomplemented
641C42—22no—
642C42—22no—
643C42—44no—
644C42—44no—
645C42—44no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—416no—
669C23—42no—
670C23—42no—
671C23C2×C22⋊C4×C13711yescharacteristic
672C23C2×C22⋊C4×C13711yescharacteristic
673C23C2×C22⋊C4×C13711yescharacteristic
674C23C2×C22⋊C4×C13711yescharacteristic
675C23C23×C4×C13711yescharacteristic
676C23C22×D4×C13711yescharacteristic
677C23C22×D4×C13711yescharacteristic
678C23C2×#41×C13714yes—
679Q8—42no—
680Q8—42no—
681D4—42no—
682D4—44no—
683D4—44no—
684D4—44no—
685D4—44no—
686D4—44no—
687D4—44no—
688D4—42no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
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—24no—
708C2×C4—28no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—416no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4#99×C13714yescomplemented
732C2×C4C2×C22⋊C4×C13711yescharacteristic
733C2×C4C2×C22⋊C4×C13711yescharacteristic
734C2×C4C2×C22⋊C4×C13711yescharacteristic
735C2×C4C2×C22⋊C4×C13711yescharacteristic
736C2×C4C2×C22⋊C4×C13711yescharacteristic
737C2×C4C2×C22⋊C4×C13711yescharacteristic
738C2×C4C2×C22⋊C4×C13711yescharacteristic
739C2×C4C2×C22⋊C4×C13711yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22C2×#99×C13712yes—
768C22#410×C13712yes—
769C22C22×C22⋊C4×C13711yescharacteristic
770C22C4×#41×C13712yes—
771C22#525×C13712yes—
772C22#532×C13712yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—48no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—84no—
784C4C2×#99×C13712yes—
785C4C2×#99×C13712yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—82no—
794C2#2297×C13711yescharacteristic
795C2C22×#99×C13711yescharacteristic
796C2C2×#410×C13711yescharacteristic
subgroupG/H
centerC2×C4×C137C2×C22⋊C4
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
socleC22×C137C22×C22⋊C4
prime radicalC2×#525×C137C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C137 ◁ C24×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2280×C137C2semidirect
3. C2×C4×C22⋊C4×C137C2semidirect
4. #1996×C137C2semidirect
5. #1964×C137C2semidirect
6. #1898×C137C2semidirect
7. C4×#99×C137C2semidirect
8. C22×#41×C137C4semidirect
18. C2×#123×C137C4semidirect
19. C2×C22⋊Q8×C137C4semidirect
21. C2×#121×C137C4semidirect
24. C2×C4×D4×C137C4semidirect
27. C2×#117×C137C4semidirect
49. C22×Q8×C137C2×C4semidirect
52. C22×D4×C137C2×C4semidirect
60. C23×C4×C137C2×C4semidirect
109. C2×C4⋊C4×C137C2×C4semidirect
110. C2×C4⋊C4×C137C2×C4semidirect
111. C2×C4⋊C4×C137C2×C4semidirect
112. C2×C4⋊C4×C137C2×C4semidirect
119. C2×C22⋊C4×C137C2×C4semidirect
120. C2×C22⋊C4×C137C2×C4semidirect
128. C2×C42×C137C2×C4semidirect
241. C22⋊C4×C137#41semidirect
332. C2×C4×C137#99semidirect
398. #21420C137direct (N × H)
399. C137#21420direct (N × H)
401. #2280C2×C137semidirect
402. C2×C4×C22⋊C4C2×C137semidirect
403. #1996C2×C137semidirect
404. #1964C2×C137semidirect
405. #1898C2×C137semidirect
406. C4×#99C2×C137semidirect
407. C22×#41C4×C137semidirect
417. C2×#123C4×C137semidirect
418. C2×C22⋊Q8C4×C137semidirect
420. C2×#121C4×C137semidirect
423. C2×C4×D4C4×C137semidirect
426. C2×#117C4×C137semidirect
448. C22×Q8C2×C4×C137semidirect
451. C22×D4C2×C4×C137semidirect
459. C23×C4C2×C4×C137semidirect
508. C2×C4⋊C4C2×C4×C137semidirect
509. C2×C4⋊C4C2×C4×C137semidirect
510. C2×C4⋊C4C2×C4×C137semidirect
511. C2×C4⋊C4C2×C4×C137semidirect
518. C2×C22⋊C4C2×C4×C137semidirect
519. C2×C22⋊C4C2×C4×C137semidirect
527. C2×C42C2×C4×C137semidirect
640. C22⋊C4#41×C137semidirect
731. C2×C4#99×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1372
#2280×C1372
C2×C4×C22⋊C4×C1372
#1996×C1372
#1964×C1372
#1898×C1372
C4×#99×C1372
#21420137