Finite Group Databasebeta

← #33007929

Subgroups — #33007929

Order 18688.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988478C212yesmaximal
2C2×#17988456C211yesmaximal, characteristic, complemented
3C2×#17988444C211yesmaximal, characteristic
4C2×#17988444C211yesmaximal, characteristic
5C2×C4×#11924005C211yesmaximal, characteristic
6#22608186C212yesmaximal, complemented
7#22608175C212yesmaximal
8#22608164C212yesmaximal, complemented
9#22608161C211yesmaximal, characteristic, complemented
10#22608160C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C73C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic
13C22×C4⋊Dic73C2211yescharacteristic
14C22×C4⋊Dic73C2211yescharacteristic
15C22×#11924007C2212yes—
16C22×#11924007C2212yes—
17C22×#11924005C2212yes—
18C22×#11924005C2212yes—
19C22×#11924005C2211yescharacteristic
20C22×#11924005C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22#17988478—28no—
23#17988456—24no—
24#17988444—24no—
25#17988444—24no—
26C4×#11924005C418yescomplemented
27C2×#14556498C2212yes—
28C2×#14556498C2212yes—
29C2×#14556498C2212yes—
30C2×#14556498C2212yes—
31C2×#14556498C2212yes—
32C2×#14556498C2212yes—
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2211yescharacteristic
35C22×C4⋊C4×C73C2211yescharacteristic
36C22×C4⋊C4×C73C2211yescharacteristic
37C22×C42×C73C2212yes—
38C22×C42×C73C2211yescharacteristic
39C4×C4⋊C4×C73—24no—
40C2×#95×C73C2212yes—
41C24×D73C2311yescharacteristic
42C23×Dic73C2312yes—
43C23×Dic73C2312yes—
44C23×Dic73C2311yescharacteristic
45C23×Dic73C2311yescharacteristic
46C23×Dic73C2311yescharacteristic
47C22×C4×D73—22no—
48C22×C4×D73—22no—
49C22×C4×D73—22no—
50C22×C4×D73—22no—
51C22×C4×D73—22no—
52C22×C4×D73—22no—
53C22×C4×D73C2×C414yes—
54C2×C4⋊Dic73—22no—
55C2×C4⋊Dic73—22no—
56C2×C4⋊Dic73—22no—
57C2×C4⋊Dic73—22no—
58C2×C4⋊Dic73—22no—
59C2×C4⋊Dic73—22no—
60C2×#11924007—24no—
61C2×#11924007—24no—
62C2×#11924007—24no—
63C2×#11924007—24no—
64C2×#11924007—42no—
65C2×#11924007—42no—
66C2×#11924005—22no—
67C2×#11924005—22no—
68C2×#11924005—24no—
69C2×#11924005—24no—
70C2×#11924005—24no—
71C2×#11924005—24no—
72C2×#11924005—42no—
73C2×#11924005—42no—
74C2×#11924005C2×C414yes—
75C2×#11924005C2×C414yes—
76C2×#11924005D414yes—
77C2×#11924005Q814yes—
78C2×C4×Dic73—22no—
79C2×C4×Dic73—22no—
80C2×C4×Dic73C2×C414yes—
81#14556498—24no—
82#14556498—24no—
83#14556498—24no—
84#14556498—24no—
85#14556498—24no—
86#14556498—42no—
87#14556498C2×C414yes—
88#14556498C2×C414yes—
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2312yes—
91C23×C4×C73C2312yes—
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73—22no—
96C2×C4⋊C4×C73—22no—
97C2×C4⋊C4×C73—22no—
98C2×C4⋊C4×C73D414yes—
99C2×C4⋊C4×C73D414yes—
100C2×C42×C73—22no—
101C2×C42×C73—22no—
102C2×C42×C73—24no—
103C2×C42×C73—24no—
104C2×C42×C73—42no—
105C2×C42×C73C2×C414yes—
106#95×C73—24no—
107C23×D73—21no—
108C23×D73—21no—
109C23×D73—21no—
110C23×D73—21no—
111C23×D73—21no—
112C23×D73—21no—
113C23×D73—21no—
114C23×D73—21no—
115C23×D73—21no—
116C23×D73—21no—
117C23×D73—21no—
118C23×D73—21no—
119C23×D73C22×C412yes—
120C23×D73C2×D412yes—
121C23×D73C2×Q812yes—
122C22×Dic73—21no—
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—22no—
137C22×Dic73—22no—
138C22×Dic73—22no—
139C22×Dic73—22no—
140C22×Dic73—22no—
141C22×Dic73—22no—
142C22×Dic73—22no—
143C22×Dic73—22no—
144C22×Dic73—22no—
145C22×Dic73—22no—
146C22×Dic73—22no—
147C22×Dic73—22no—
148C22×Dic73—22no—
149C22×Dic73—22no—
150C22×Dic73C22×C412yes—
151C22×Dic73C22×C412yes—
152C22×Dic73C22×C412yes—
153C22×Dic73C2×D412yes—
154C22×Dic73C2×Q812yes—
155C22×Dic73#4112yes—
156C22×Dic73#4112yes—
157C2×C4×D73—28no—
158C2×C4×D73—28no—
159C2×C4×D73—28no—
160C2×C4×D73—44no—
161C2×C4×D73—44no—
162C2×C4×D73—44no—
163C2×C4×D73—44no—
164C4⋊Dic73—44no—
165C4⋊Dic73—44no—
166#11924007—48no—
167#11924007—48no—
168#11924005—28no—
169#11924005—48no—
170#11924005—48no—
171#11924005C4⋊C4116yescomplemented
172C4×Dic73—28no—
173C24×C73C2411yescharacteristic
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—22no—
180C22×C4×C73—22no—
181C22×C4×C73—22no—
182C22×C4×C73—21no—
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—22no—
186C22×C4×C73—22no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—22no—
190C22×C4×C73—22no—
191C22×C4×C73—22no—
192C22×C4×C73—21no—
193C22×C4×C73—22no—
194C22×C4×C73—21no—
195C22×C4×C73—22no—
196C22×C4×C73C22×C412yes—
197C22×C4×C73C22×C412yes—
198C22×C4×C73C22×C412yes—
199C22×C4×C73C2×D412yes—
200C22×C4×C73C2×D414yes—
201C22×C4×C73C2×D412yes—
202C22×C4×C73C2×D414yes—
203C22×C4×C73C2×D412yes—
204C22×C4×C73C2×Q812yes—
205C22×C4×C73#4112yes—
206C22×C4×C73#4112yes—
207C22×C4×C73#4112yes—
208C22×C4×C73#4112yes—
209C4⋊C4×C73—28no—
210C4⋊C4×C73—28no—
211C42×C73—28no—
212C42×C73—48no—
213C23×C73C23×C411yescharacteristic
214C23×C73C22×D411yescharacteristic
215C23×C73C22×D411yescharacteristic
216C23×C73C22×D411yescharacteristic
217C23×C73C22×Q811yescharacteristic
218C23×C73C2×#4111yescharacteristic
219C23×C73C2×#4111yescharacteristic
220C23×C73C2×#4111yescharacteristic
221C23×C73C2×#4111yescharacteristic
222C23×C73C2×#4111yescharacteristic
223C23×C73C2×#4111yescharacteristic
224C23×C73H(5,𝔽2)11yescharacteristic
225C23×C73H(5,𝔽2)11yescharacteristic
226C23×C732−1+411yescharacteristic
227C23×C732−1+411yescharacteristic
228C22×D73—22no—
229C22×D73—22no—
230C22×D73—22no—
231C22×D73—22no—
232C22×D73—22no—
233C22×D73—22no—
234C22×D73—22no—
235C22×D73—22no—
236C22×D73—22no—
237C22×D73—22no—
238C22×D73—22no—
239C22×D73—22no—
240C22×D73—22no—
241C22×D73—22no—
242C22×D73—22no—
243C22×D73—22no—
244C22×D73—22no—
245C22×D73—22no—
246C22×D73—41no—
247C22×D73—41no—
248C22×D73—41no—
249C22×D73—41no—
250C22×D73—41no—
251C22×D73—41no—
252C22×D73—41no—
253C22×D73—41no—
254C22×D73—41no—
255C22×D73—41no—
256C22×D73—41no—
257C22×D73—41no—
258C22×D73—41no—
259C22×D73—41no—
260C22×D73—41no—
261C22×D73—41no—
262C22×D73C2×C4⋊C414yes—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—24no—
273C2×C4×C73—24no—
274C2×C4×C73—24no—
275C2×C4×C73—24no—
276C2×C4×C73—24no—
277C2×C4×C73—24no—
278C2×C4×C73—42no—
279C2×C4×C73—42no—
280C2×C4×C73—42no—
281C2×C4×C73—42no—
282C2×C4×C73—42no—
283C2×C4×C73—41no—
284C2×C4×C73—42no—
285C2×C4×C73—41no—
286C2×C4×C73—42no—
287C2×C4×C73—42no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73C2×C4⋊C414yes—
291C2×C4×C73#11714yes—
292C2×C4×C73C4×D414yes—
293C2×C4×C73C4×D414yes—
294C2×C4×C73#12114yes—
295C2×C4×C73#12314yes—
296C2×C4×C73#12414yes—
297C2×C4×C73#12614yes—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C2×Dic73—41no—
316C2×Dic73—41no—
317C2×Dic73—42no—
318C2×Dic73—42no—
319C2×Dic73—42no—
320C2×Dic73—42no—
321C2×Dic73—42no—
322C2×Dic73—42no—
323C2×Dic73—42no—
324C2×Dic73—42no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330C2×Dic73—42no—
331C2×Dic73C2×C4⋊C414yes—
332C2×Dic73#11714yes—
333C4×D73—416no—
334C22×C73C22×C4⋊C411yescharacteristic
335C22×C73C2×#11711yescharacteristic
336C22×C73C2×#11711yescharacteristic
337C22×C73C2×C4×D411yescharacteristic
338C22×C73C2×C4×D411yescharacteristic
339C22×C73#52011yescharacteristic
340C22×C73#52011yescharacteristic
341C22×C73C2×#12111yescharacteristic
342C22×C73C2×#12311yescharacteristic
343C22×C73C2×#12411yescharacteristic
344C22×C73C2×#12611yescharacteristic
345C22×C73#53211yescharacteristic
346C22×C73#53211yescharacteristic
347C22×C73#53311yescharacteristic
348C22×C73#53311yescharacteristic
349C22×C73#54011yescharacteristic
350C22×C73#54111yescharacteristic
351C22×C73#54211yescharacteristic
352C22×C73#54211yescharacteristic
353C22×C73D4211yescharacteristic
354C22×C73D4211yescharacteristic
355C22×C73#54611yescharacteristic
356C22×C73#54711yescharacteristic
357C22×C73#54711yescharacteristic
358C22×C73#54711yescharacteristic
359C22×C73#54811yescharacteristic
360C22×C73D4×Q811yescharacteristic
361C22×C73D4×Q811yescharacteristic
362C22×C73#55011yescharacteristic
363C22×C73#55211yescharacteristic
364C22×C73#55311yescharacteristic
365C22×C73#55411yescharacteristic
366C22×C73#55411yescharacteristic
367C22×C73#55511yescharacteristic
368C22×C73#55611yescharacteristic
369C2×D73—24no—
370C2×D73—24no—
371C2×D73—24no—
372C2×D73—42no—
373C2×D73—42no—
374C2×D73—42no—
375C2×D73—42no—
376C2×D73—42no—
377C2×D73—42no—
378C2×D73—42no—
379C2×D73—42no—
380C2×D73—42no—
381C2×D73—42no—
382C2×D73—42no—
383C2×D73—42no—
384C4×C73—24no—
385C4×C73—42no—
386C4×C73—44no—
387C4×C73—44no—
388C4×C73#38818yescomplemented
389Dic73—24no—
390Dic73—24no—
391Dic73—42no—
392Dic73—82no—
393Dic73—82no—
394#13876—731nomaximal, Sylow
395C2×C73#228511yescharacteristic
396C2×C73C2×#38811yescharacteristic
397C2×C73#231411yescharacteristic
398C2×C73D4×C4⋊C411yescharacteristic
399C2×C73D4×C4⋊C411yescharacteristic
400C2×C73#235211yescharacteristic
401C2×C73#235411yescharacteristic
402C2×C73#242211yescharacteristic
403C2×C73#242311yescharacteristic
404C2×C73#242811yescharacteristic
405C2×C73#242911yescharacteristic
406C2×C73#249111yescharacteristic
407C2×C73#249211yescharacteristic
408C2×C73#249611yescharacteristic
409C2×C73#249711yescharacteristic
410D73—44no—
411C2×#388—732no—
412C2×#384—731no—
413C2×#380—731no—
414C2×#380—731no—
415C2×C4×C4⋊C4D7311yescharacteristic, complemented
416C2×C4×C22⋊C4—731no—
417#1442—732no—
418#1439—732no—
419#1436—732no—
420C4⋊#95—731no—
421C4⋊#95—731no—
422C73#1387611yescharacteristic, complemented, Sylow
423C24×C4—731no—
424C22×C4⋊C4—732no—
425C22×C4⋊C4—732no—
426C22×C4⋊C4—731no—
427C22×C4⋊C4—731no—
428C22×C4⋊C4C2×D7311yescharacteristic
429C22×C4⋊C4C2×D7311yescharacteristic
430C22×C22⋊C4—732no—
431C22×C22⋊C4—732no—
432C22×C22⋊C4—731no—
433C22×C22⋊C4—731no—
434C22×C42—731no—
435C22×C42C2×D7312yes—
436C22×C42C2×D7311yescharacteristic
437#388—1468no—
438#384—1464no—
439#380—1464no—
440#380—1464no—
441C4×C4⋊C4—24no—
442C4×C22⋊C4—738no—
443C2×#95—732no—
444C2×#95—731no—
445C2×#95—731no—
446C2×#95—732no—
447C2×#95—732no—
448C2×#95—732no—
449C2×#95—732no—
450C2×#95—732no—
451C2×#95C2×D7312yes—
452C25—731no—
453C23×C4—731no—
454C23×C4—731no—
455C23×C4—731no—
456C23×C4—734no—
457C23×C4—732no—
458C23×C4—732no—
459C23×C4—1462no—
460C23×C4—1462no—
461C23×C4—1462no—
462C23×C4—1462no—
463C23×C4—1462no—
464C23×C4—1462no—
465C23×C4C22×D7311yescharacteristic
466C23×C4C22×D7312yes—
467C23×C4C22×D7312yes—
468C23×C4C22×D7311yescharacteristic
469C23×C4C22×D7311yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—2922no—
475C2×C4⋊C4—2922no—
476C2×C4⋊C4—1464no—
477C2×C4⋊C4—1464no—
478C2×C4⋊C4—1462no—
479C2×C4⋊C4—1462no—
480C2×C4⋊C4—1464no—
481C2×C4⋊C4—1464no—
482C2×C4⋊C4—1462no—
483C2×C4⋊C4—1462no—
484C2×C4⋊C4—1462no—
485C2×C4⋊C4—1462no—
486C2×C4⋊C4D29214yes—
487C2×C4⋊C4C22⋊D7314yes—
488C2×C22⋊C4—2922no—
489C2×C22⋊C4—2922no—
490C2×C22⋊C4—734no—
491C2×C22⋊C4—734no—
492C2×C22⋊C4—734no—
493C2×C22⋊C4—734no—
494C2×C22⋊C4—1464no—
495C2×C22⋊C4—1464no—
496C2×C22⋊C4—1464no—
497C2×C22⋊C4—1464no—
498C2×C22⋊C4—1462no—
499C2×C22⋊C4—1462no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—24no—
503C2×C42—24no—
504C2×C42—42no—
505C2×C42—734no—
506C2×C42—1462no—
507C2×C42—1462no—
508C2×C42C4×D7314yes—
509#95—24no—
510#95—2922no—
511#95—734no—
512#95—734no—
513#95—1464no—
514#95—1464no—
515#95—1464no—
516#95—1464no—
517#95—1464no—
518C24—732no—
519C24—732no—
520C24—732no—
521C24—1461no—
522C24—1461no—
523C24—1461no—
524C24—1461no—
525C24—1461no—
526C24—1461no—
527C24—1461no—
528C24—1461no—
529C24—1461no—
530C24—1461no—
531C24—1461no—
532C24—1461no—
533C24C23×D7311yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—2924no—
557C22×C4—2924no—
558C22×C4—2924no—
559C22×C4—2924no—
560C22×C4—732no—
561C22×C4—732no—
562C22×C4—732no—
563C22×C4—732no—
564C22×C4—732no—
565C22×C4—732no—
566C22×C4—732no—
567C22×C4—1462no—
568C22×C4—1462no—
569C22×C4—1462no—
570C22×C4—1462no—
571C22×C4—1462no—
572C22×C4—1462no—
573C22×C4—1462no—
574C22×C4—1462no—
575C22×C4—1462no—
576C22×C4—1462no—
577C22×C4—1462no—
578C22×C4—1462no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4—1461no—
582C22×C4—1461no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4—1468no—
588C22×C4—1468no—
589C22×C4—1468no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4—1461no—
598C22×C4C2×C4×D7312yes—
599C22×C4C2×C4×D7312yes—
600C22×C4C2×C4×D7312yes—
601C22×C4D4×D7312yes—
602C22×C4C2×C22⋊D7314yes—
603C22×C4C2×C22⋊D7312yes—
604C22×C4C2×D29214yes—
605C22×C4C2×D29212yes—
606C22×C4Q8×D7312yes—
607C22×C4#1192402812yes—
608C22×C4#1192402812yes—
609C22×C4#1192402812yes—
610C22×C4#1192402812yes—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—2928no—
614C4⋊C4—2928no—
615C4⋊C4—2924no—
616C4⋊C4—2924no—
617C22⋊C4—2928no—
618C22⋊C4—2928no—
619C22⋊C4—7316no—
620C22⋊C4—1468no—
621C42—28no—
622C42—48no—
623C42—1468no—
624C23—2921no—
625C23—2921no—
626C23—2921no—
627C23—2921no—
628C23—2921no—
629C23—2921no—
630C23—2921no—
631C23—2921no—
632C23—2921no—
633C23—2921no—
634C23—2921no—
635C23—2921no—
636C23—2921no—
637C23—2921no—
638C23—2921no—
639C23—2921no—
640C23—734no—
641C23—1462no—
642C23—1462no—
643C23—1462no—
644C23—1462no—
645C23—1462no—
646C23—1462no—
647C23—1462no—
648C23—1462no—
649C23—1462no—
650C23—1462no—
651C23—1462no—
652C23—1462no—
653C23—1462no—
654C23—1462no—
655C23—1462no—
656C23—1462no—
657C23—1462no—
658C23—1462no—
659C23C22×C4×D7311yescharacteristic
660C23C2×D4×D7311yescharacteristic
661C23C22×C22⋊D7311yescharacteristic
662C23C22×D29211yescharacteristic
663C23C2×Q8×D7311yescharacteristic
664C23#41×D7311yescharacteristic
665C23#41×D7311yescharacteristic
666C23C2×#1192402811yescharacteristic
667C23C2×#1192402811yescharacteristic
668C23C2×#1192402811yescharacteristic
669C23C2×#1192402811yescharacteristic
670C23#1455663611yescharacteristic
671C23#1455663711yescharacteristic
672C23#1455663811yescharacteristic
673C23#1455663911yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—2921no—
702C2×C4—2921no—
703C2×C4—2921no—
704C2×C4—2921no—
705C2×C4—29216no—
706C2×C4—2922no—
707C2×C4—2922no—
708C2×C4—2922no—
709C2×C4—2922no—
710C2×C4—2922no—
711C2×C4—2922no—
712C2×C4—2922no—
713C2×C4—2922no—
714C2×C4—2922no—
715C2×C4—2922no—
716C2×C4—2922no—
717C2×C4—2922no—
718C2×C4—2922no—
719C2×C4—2922no—
720C2×C4—734no—
721C2×C4—734no—
722C2×C4—1462no—
723C2×C4—1462no—
724C2×C4—1462no—
725C2×C4—1462no—
726C2×C4—1462no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4C4⋊C4×D7314yes—
738C2×C4#1455654814yes—
739C2×C4C4×C22⋊D7314yes—
740C2×C4C4×D29214yes—
741C2×C4#1455656514yes—
742C2×C4#1455657414yes—
743C2×C4#1455657914yes—
744C2×C4#1455658514yes—
745C22—2922no—
746C22—2922no—
747C22—2922no—
748C22—2922no—
749C22—2922no—
750C22—2922no—
751C22—2922no—
752C22—2922no—
753C22—2922no—
754C22—2922no—
755C22—2922no—
756C22—2922no—
757C22—1464no—
758C22—1464no—
759C22—1464no—
760C22C2×C4⋊C4×D7311yescharacteristic
761C22#117×D7311yescharacteristic
762C22C2×#1455654811yescharacteristic
763C22C2×C4×C22⋊D7311yescharacteristic
764C22C2×C4×D29211yescharacteristic
765C22#1798906711yescharacteristic
766C22#1798906811yescharacteristic
767C22C2×#1455656511yescharacteristic
768C22C2×#1455657411yescharacteristic
769C22C2×#1455657911yescharacteristic
770C22C2×#1455658511yescharacteristic
771C22#1798913411yescharacteristic
772C22#1798913411yescharacteristic
773C22#1798914111yescharacteristic
774C22#1798914111yescharacteristic
775C22#1798918811yescharacteristic
776C22#1798919511yescharacteristic
777C22#1798920211yescharacteristic
778C22#1798920911yescharacteristic
779C22D4×C22⋊D7311yescharacteristic
780C22D4×D29211yescharacteristic
781C22#1798923211yescharacteristic
782C22#1798923611yescharacteristic
783C22#1798923811yescharacteristic
784C22#1798924211yescharacteristic
785C22#1798924911yescharacteristic
786C22Q8×C22⋊D7311yescharacteristic
787C22Q8×D29211yescharacteristic
788C22#1798925611yescharacteristic
789C22#1798927811yescharacteristic
790C22#1798928711yescharacteristic
791C22#1798929211yescharacteristic
792C22#1798929711yescharacteristic
793C22#1798930011yescharacteristic
794C22#1798930511yescharacteristic
795C4—24no—
796C4—44no—
797C4—42no—
798C4—44no—
799C4—2922no—
800C4—5842no—
801C4—5842no—
802C4—1464no—
803C4—1464no—
804C4#1798847818yescomplemented
805C2—2924no—
806C2#2261233511yescharacteristic
807C2C2×#1798847811yescharacteristic
808C2#2261253611yescharacteristic
809C2C4⋊C4×C22⋊D7311yescharacteristic
810C2C4⋊C4×D29211yescharacteristic
811C2#2261286311yescharacteristic
812C2#2261288111yescharacteristic
813C2#2261343911yescharacteristic
814C2#2261345011yescharacteristic
815C2#2261351311yescharacteristic
816C2#2261352411yescharacteristic
817C2#2261428811yescharacteristic
818C2#2261429911yescharacteristic
819C2#2261434711yescharacteristic
820C2#2261435811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×C4×C4⋊C4×C73C2
socle, cosocleC24×C73C24
prime radicalC24×D73C23
hypercenterC2×C4×C4⋊C4D73
hypocenterC73#13876
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#17988456C2semidirect
6. #22608186C2semidirect
8. #22608164C2semidirect
9. #22608161C2semidirect
10. #22608160C2semidirect
11. C2×C4×C4⋊C4×C73C2semidirect
26. C4×#11924005C4semidirect
171. #11924005C4⋊C4semidirect
388. C4×C73#388semidirect
415. C2×C4×C4⋊C4D73semidirect
422. C73#13876semidirect
804. C4#17988478semidirect

Maximal subgroups

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

subgroupindex
C2×#179884782
C2×#179884562
C2×#179884442
C2×C4×#119240052
#226081862
#226081752
#226081642
#226081612
#226081602
C2×C4×C4⋊C4×C732
#1387673