Finite Group Databasebeta

← #33013926

Subgroups — #33013926

Order 18688.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988480C211yesmaximal, characteristic
2C2×#17988462C211yesmaximal, characteristic
3C2×#17988462C211yesmaximal, characteristic
4C2×#17988453C211yesmaximal, characteristic, complemented
5#22608196C211yesmaximal, characteristic, complemented
6#22608196C211yesmaximal, characteristic, complemented
7#22608188C211yesmaximal, characteristic, complemented
8#22608184C211yesmaximal, characteristic, complemented
9#22608176C211yesmaximal, characteristic
10#22608176C211yesmaximal, characteristic
11#22608165C211yesmaximal, characteristic, complemented
12#22608161C211yesmaximal, characteristic, complemented
13#22608160C211yesmaximal, characteristic, complemented
14#22608153C211yesmaximal, characteristic
15C2×#388×C73C211yesmaximal, characteristic
16C24×Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21C22×C4⋊Dic73C2211yescharacteristic
22C22×C4⋊Dic73C2211yescharacteristic
23C22×C4⋊Dic73C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×C22⋊Dic73C2211yescharacteristic
26C22×C22⋊Dic73C2211yescharacteristic
27C22×C4×Dic73C2211yescharacteristic
28#17988480—24no—
29#17988462—24no—
30#17988462—24no—
31#17988453—24no—
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2211yescharacteristic
35C2×#14556498C2211yescharacteristic
36C2×#14556498C2211yescharacteristic
37C2×#14556498C2211yescharacteristic
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C22×C4⋊C4×C73C2211yescharacteristic
49C22×C22⋊C4×C73C2211yescharacteristic
50C22×C22⋊C4×C73C2211yescharacteristic
51C22×C22⋊C4×C73C2211yescharacteristic
52C22×C42×C73C2211yescharacteristic
53#388×C73C418yescomplemented
54C2×#95×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C23×Dic73—22no—
57C23×Dic73—22no—
58C23×Dic73—22no—
59C23×Dic73—41no—
60C23×Dic73—41no—
61C23×Dic73—41no—
62C23×Dic73—41no—
63C23×Dic73C2311yescharacteristic
64C23×Dic73C2311yescharacteristic
65C23×Dic73C2311yescharacteristic
66C23×Dic73C2311yescharacteristic
67C23×Dic73C2311yescharacteristic
68C23×Dic73C2311yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C2×C4⋊Dic73—22no—
72C2×C4⋊Dic73—22no—
73C2×C4⋊Dic73—22no—
74C2×C4⋊Dic73—22no—
75C2×C4⋊Dic73—22no—
76C2×C4⋊Dic73—22no—
77C2×C4⋊Dic73—22no—
78C2×C4⋊Dic73—22no—
79C2×C4⋊Dic73—22no—
80C2×C4⋊Dic73—22no—
81C2×C4⋊Dic73—22no—
82C2×C4⋊Dic73—41no—
83C2×C4⋊Dic73—41no—
84C2×C4⋊Dic73—41no—
85C2×C4⋊Dic73—41no—
86C2×C4⋊Dic73—41no—
87C2×C4⋊Dic73—41no—
88C2×C4⋊Dic73—41no—
89C2×C4⋊Dic73—41no—
90C2×C4⋊Dic73—41no—
91C2×C4⋊Dic73—41no—
92C2×C22⋊Dic73—22no—
93C2×C22⋊Dic73—22no—
94C2×C22⋊Dic73—22no—
95C2×C22⋊Dic73—22no—
96C2×C22⋊Dic73—22no—
97C2×C22⋊Dic73—41no—
98C2×C22⋊Dic73—41no—
99C2×C22⋊Dic73—41no—
100C2×C22⋊Dic73—41no—
101C2×C4×Dic73—22no—
102C2×C4×Dic73—22no—
103C2×C4×Dic73—41no—
104#14556498—22no—
105#14556498—22no—
106#14556498—22no—
107#14556498—22no—
108#14556498—22no—
109#14556498—22no—
110#14556498—22no—
111#14556498—22no—
112#14556498—41no—
113#14556498—41no—
114#14556498—41no—
115#14556498—41no—
116#14556498—41no—
117#14556498—41no—
118#14556498—41no—
119#14556498D414yes—
120C25×C73C2311yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C23×C4×C73C2311yescharacteristic
124C23×C4×C73C2311yescharacteristic
125C23×C4×C73C2311yescharacteristic
126C23×C4×C73C2311yescharacteristic
127C2×C4⋊C4×C73—41no—
128C2×C4⋊C4×C73—41no—
129C2×C4⋊C4×C73C2×C414yescomplemented
130C2×C22⋊C4×C73—22no—
131C2×C22⋊C4×C73—22no—
132C2×C22⋊C4×C73—41no—
133C2×C22⋊C4×C73—41no—
134C2×C22⋊C4×C73C2×C414yes—
135C2×C22⋊C4×C73C2×C414yes—
136C2×C22⋊C4×C73C2×C414yes—
137C2×C22⋊C4×C73D414yes—
138C2×C22⋊C4×C73Q814yes—
139C2×C42×C73—22no—
140C2×C42×C73—22no—
141C2×C42×C73C2×C414yescomplemented
142#95×C73C2×C414yescomplemented
143#95×C73C2×C414yescomplemented
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—21no—
148C22×Dic73—21no—
149C22×Dic73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—21no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C22×Dic73—21no—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73—21no—
181C22×Dic73—21no—
182C22×Dic73—21no—
183C22×Dic73—21no—
184C22×Dic73—21no—
185C22×Dic73—21no—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73—44no—
197C22×Dic73—44no—
198C22×Dic73—44no—
199C22×Dic73—44no—
200C22×Dic73—44no—
201C22×Dic73—44no—
202C22×Dic73—44no—
203C22×Dic73C2×D412yes—
204C22×Dic73C2×D412yes—
205C22×Dic73#4112yes—
206C22×Dic73#4112yes—
207C4⋊Dic73—44no—
208C4⋊Dic73—44no—
209C4⋊Dic73—44no—
210C4⋊Dic73—44no—
211C4⋊Dic73—44no—
212C4⋊Dic73—44no—
213C4⋊Dic73—44no—
214C22⋊Dic73—44no—
215C22⋊Dic73—44no—
216C22⋊Dic73—44no—
217C4×Dic73—44no—
218C24×C73—21no—
219C24×C73—21no—
220C24×C73—21no—
221C24×C73—21no—
222C24×C73—21no—
223C24×C73—21no—
224C24×C73—21no—
225C24×C73—21no—
226C24×C73—21no—
227C24×C73—21no—
228C24×C73—21no—
229C24×C73—21no—
230C24×C73C22×C412yes—
231C24×C73C2×D412yes—
232C24×C73C2×Q812yes—
233C24×C73C2411yescharacteristic
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73C22×C412yes—
265C22×C4×C73C22×C412yes—
266C22×C4×C73C22×C412yes—
267C22×C4×C73C22×C412yes—
268C22×C4×C73C22×C412yes—
269C22×C4×C73C22×C412yes—
270C22×C4×C73C2×D412yes—
271C22×C4×C73C2×D412yes—
272C22×C4×C73C2×D412yes—
273C22×C4×C73C2×Q812yes—
274C22×C4×C73C2×Q812yes—
275C22×C4×C73#4112yes—
276C4⋊C4×C73—44no—
277C22⋊C4×C73—28no—
278C22⋊C4×C73—44no—
279C22⋊C4×C73C4⋊C4116yescomplemented
280C42×C73—28no—
281C23×C73—22no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—22no—
287C23×C73—22no—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—22no—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—22no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—41no—
307C23×C73—41no—
308C23×C73—41no—
309C23×C73—41no—
310C23×C73—41no—
311C23×C73—41no—
312C23×C73—41no—
313C23×C73—41no—
314C23×C73—41no—
315C23×C73C2×C4⋊C414yes—
316C23×C73C23×C411yescharacteristic
317C23×C73C22×D411yescharacteristic
318C23×C73C22×D411yescharacteristic
319C23×C73C22×Q811yescharacteristic
320C23×C73C2×#4111yescharacteristic
321C23×C73C2×#4111yescharacteristic
322C23×C73C2×#4111yescharacteristic
323C23×C73H(5,𝔽2)11yescharacteristic
324C23×C73H(5,𝔽2)11yescharacteristic
325C23×C73H(5,𝔽2)11yescharacteristic
326C23×C73H(5,𝔽2)11yescharacteristic
327C23×C73H(5,𝔽2)11yescharacteristic
328C23×C732−1+411yescharacteristic
329C23×C732−1+411yescharacteristic
330C23×C732−1+411yescharacteristic
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—22no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—22no—
346C2×C4×C73—22no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—22no—
354C2×C4×C73—22no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—22no—
358C2×C4×C73—41no—
359C2×C4×C73—41no—
360C2×C4×C73—41no—
361C2×C4×C73—41no—
362C2×C4×C73—41no—
363C2×C4×C73—41no—
364C2×C4×C73—41no—
365C2×C4×C73—41no—
366C2×C4×C73—41no—
367C2×C4×C73—41no—
368C2×C4×C73—41no—
369C2×C4×C73—41no—
370C2×C4×C73C2×C4⋊C414yes—
371C2×C4×C73C2×C4⋊C414yes—
372C2×C4×C73C4×D414yes—
373C2×Dic73—22no—
374C2×Dic73—22no—
375C2×Dic73—22no—
376C2×Dic73—22no—
377C2×Dic73—22no—
378C2×Dic73—22no—
379C2×Dic73—22no—
380C2×Dic73—22no—
381C2×Dic73—22no—
382C2×Dic73—22no—
383C2×Dic73—22no—
384C2×Dic73—22no—
385C2×Dic73—416no—
386C2×Dic73—41no—
387C2×Dic73—41no—
388C2×Dic73—41no—
389C2×Dic73—41no—
390C2×Dic73—41no—
391C2×Dic73—41no—
392C2×Dic73—41no—
393C2×Dic73—41no—
394C2×Dic73—41no—
395C2×Dic73—41no—
396C2×Dic73—41no—
397C2×Dic73—41no—
398C2×Dic73—41no—
399C2×Dic73—41no—
400C2×Dic73—41no—
401C2×Dic73—41no—
402C2×Dic73—41no—
403C2×Dic73—41no—
404C2×Dic73—41no—
405C2×Dic73—41no—
406C2×Dic73—41no—
407C2×Dic73—41no—
408C2×Dic73—41no—
409C2×Dic73—41no—
410C2×Dic73—41no—
411C2×Dic73—41no—
412C2×Dic73—41no—
413C2×Dic73—41no—
414C2×Dic73—41no—
415C2×Dic73—41no—
416C2×Dic73—41no—
417C2×Dic73—41no—
418C2×Dic73—41no—
419C2×Dic73—41no—
420C2×Dic73—41no—
421C2×Dic73—41no—
422C2×Dic73—41no—
423C2×Dic73—41no—
424C2×Dic73—41no—
425C2×Dic73—41no—
426C2×Dic73—41no—
427C2×Dic73—41no—
428C2×Dic73—41no—
429C2×Dic73—41no—
430C22×C73—24no—
431C22×C73—24no—
432C22×C73—24no—
433C22×C73—42no—
434C22×C73—42no—
435C22×C73—42no—
436C22×C73—42no—
437C22×C73—42no—
438C22×C73—42no—
439C22×C73—42no—
440C22×C73—42no—
441C22×C73—42no—
442C22×C73—42no—
443C22×C73—42no—
444C22×C73—42no—
445C22×C73C22×C4⋊C411yescharacteristic
446C22×C73C2×C4×D411yescharacteristic
447C22×C73C4×#4111yescharacteristic
448C22×C73#51811yescharacteristic
449C22×C73#52011yescharacteristic
450C22×C73#52011yescharacteristic
451C22×C73#52011yescharacteristic
452C22×C73#53511yescharacteristic
453C22×C73#53511yescharacteristic
454C22×C73#53611yescharacteristic
455C22×C73#53711yescharacteristic
456C22×C73#53811yescharacteristic
457C22×C73#53911yescharacteristic
458C22×C73#54011yescharacteristic
459C22×C73#54111yescharacteristic
460C22×C73#54211yescharacteristic
461C22×C73#54211yescharacteristic
462C22×C73#54411yescharacteristic
463C22×C73#54411yescharacteristic
464C22×C73D4211yescharacteristic
465C22×C73#54611yescharacteristic
466C22×C73#54611yescharacteristic
467C22×C73#54611yescharacteristic
468C22×C73#54711yescharacteristic
469C22×C73#54711yescharacteristic
470C22×C73D4×Q811yescharacteristic
471C22×C73#55111yescharacteristic
472C22×C73#55211yescharacteristic
473C22×C73#55411yescharacteristic
474C22×C73#55411yescharacteristic
475C22×C73#55411yescharacteristic
476C22×C73H(3,𝔽4)11yescharacteristic
477C22×C73#56211yescharacteristic
478C22×C73#56211yescharacteristic
479C22×C73#56311yescharacteristic
480C4×C73—24no—
481C4×C73—24no—
482C4×C73—24no—
483C4×C73—42no—
484C4×C73—42no—
485C4×C73—42no—
486Dic73—42no—
487Dic73—42no—
488Dic73—42no—
489Dic73—42no—
490Dic73—81no—
491Dic73—81no—
492Dic73—81no—
493Dic73—81no—
494#14403—731nomaximal, Sylow
495C2×C73—44no—
496C2×C73#231711yescharacteristic
497C2×C73#232411yescharacteristic
498C2×C73#233411yescharacteristic
499C2×C73D4×C4⋊C411yescharacteristic
500C2×C73#234911yescharacteristic
501C2×C73#235911yescharacteristic
502C2×C73#237911yescharacteristic
503C2×C73#267011yescharacteristic
504C2×C73#267211yescharacteristic
505C2×C73#269811yescharacteristic
506C2×C73#270411yescharacteristic
507C2×C73#270611yescharacteristic
508C2×C73#272011yescharacteristic
509C2×C73#276311yescharacteristic
510C2×C73#276811yescharacteristic
511C2×#388—731no—
512C2×#388D7311yescharacteristic
513C2×#385—731no—
514C2×#385—731no—
515C2×#382—731no—
516#1444—731no—
517#1444—731no—
518#1442—731no—
519#1441—731no—
520#1439—731no—
521#1439—731no—
522#1436—731no—
523C4⋊#95—731no—
524C4⋊#95—731no—
525C22⋊#95—731no—
526C73#1440311yescharacteristic, complemented, Sylow
527C24×C4—731no—
528C22×C4⋊C4—731no—
529C22×C4⋊C4—731no—
530C22×C4⋊C4—731no—
531C22×C4⋊C4—731no—
532C22×C4⋊C4—731no—
533C22×C4⋊C4—731no—
534C22×C4⋊C4—731no—
535C22×C4⋊C4C2×D7311yescharacteristic
536C22×C22⋊C4—731no—
537C22×C22⋊C4—731no—
538C22×C22⋊C4—731no—
539C22×C22⋊C4C2×D7311yescharacteristic
540C22×C22⋊C4C2×D7311yescharacteristic
541C22×C22⋊C4C2×D7311yescharacteristic
542C22×C42—731no—
543C22×C42C2×D7311yescharacteristic
544#388—1464no—
545#388Dic7318yescomplemented
546#385—1464no—
547#385—1464no—
548#382—1464no—
549C2×#95—731no—
550C2×#95—731no—
551C2×#95—731no—
552C2×#95—731no—
553C2×#95—731no—
554C2×#95—731no—
555C2×#95—731no—
556C2×#95—731no—
557C2×#95—731no—
558C2×#95—731no—
559C2×#95—731no—
560C2×#95—731no—
561C2×#95—731no—
562C2×#95—731no—
563C2×#95—731no—
564C2×#95—731no—
565C2×#95C2×D7311yescharacteristic
566C2×#95C2×D7311yescharacteristic
567C25C22×D7311yescharacteristic
568C23×C4—2921no—
569C23×C4—2921no—
570C23×C4—2921no—
571C23×C4—2921no—
572C23×C4—731no—
573C23×C4—731no—
574C23×C4—731no—
575C23×C4—731no—
576C23×C4—731no—
577C23×C4—731no—
578C23×C4—731no—
579C23×C4—731no—
580C23×C4—1462no—
581C23×C4—1462no—
582C23×C4—1462no—
583C23×C4C22×D7311yescharacteristic
584C23×C4C22×D7311yescharacteristic
585C23×C4C22×D7311yescharacteristic
586C23×C4C22×D7311yescharacteristic
587C23×C4C22×D7311yescharacteristic
588C23×C4C22×D7311yescharacteristic
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—2921no—
592C2×C4⋊C4—2921no—
593C2×C4⋊C4—2921no—
594C2×C4⋊C4—2921no—
595C2×C4⋊C4—2921no—
596C2×C4⋊C4—2921no—
597C2×C4⋊C4—2921no—
598C2×C4⋊C4—2921no—
599C2×C4⋊C4—2921no—
600C2×C4⋊C4—2921no—
601C2×C4⋊C4—1462no—
602C2×C4⋊C4—1462no—
603C2×C4⋊C4—1462no—
604C2×C4⋊C4—1462no—
605C2×C4⋊C4—1462no—
606C2×C4⋊C4—1462no—
607C2×C4⋊C4—1462no—
608C2×C4⋊C4—1462no—
609C2×C4⋊C4—1462no—
610C2×C4⋊C4—1462no—
611C2×C4⋊C4—1462no—
612C2×C4⋊C4C2×Dic7314yescomplemented
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—2921no—
618C2×C22⋊C4—2921no—
619C2×C22⋊C4—2921no—
620C2×C22⋊C4—2921no—
621C2×C22⋊C4—1462no—
622C2×C22⋊C4—1462no—
623C2×C22⋊C4—1462no—
624C2×C22⋊C4—1462no—
625C2×C22⋊C4—1462no—
626C2×C22⋊C4Dic14614yes—
627C2×C22⋊C4D29214yes—
628C2×C22⋊C4C2×Dic7314yes—
629C2×C22⋊C4C2×Dic7314yes—
630C2×C22⋊C4C2×Dic7314yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—2921no—
634C2×C42—1462no—
635C2×C42—1462no—
636C2×C42C2×Dic7314yescomplemented
637#95—2921no—
638#95—2921no—
639#95—2921no—
640#95—2921no—
641#95—2921no—
642#95—2921no—
643#95—2921no—
644#95—734no—
645#95—1462no—
646#95—1462no—
647#95—1462no—
648#95—1462no—
649#95—1462no—
650#95—1462no—
651#95—1462no—
652#95—1462no—
653#95C2×Dic7314yescomplemented
654#95C2×Dic7314yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×Dic7312yes—
668C24C2×D29212yes—
669C24C2×Dic14612yes—
670C24C23×D7311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—2924no—
702C22×C4—2924no—
703C22×C4—2924no—
704C22×C4—2924no—
705C22×C4—2924no—
706C22×C4—2924no—
707C22×C4—2924no—
708C22×C4—732no—
709C22×C4—732no—
710C22×C4—732no—
711C22×C4—732no—
712C22×C4—1461no—
713C22×C4—1461no—
714C22×C4—1461no—
715C22×C4—1461no—
716C22×C4—1461no—
717C22×C4—1461no—
718C22×C4—1461no—
719C22×C4—1461no—
720C22×C4—1461no—
721C22×C4—1461no—
722C22×C4—1461no—
723C22×C4—1461no—
724C22×C4—1461no—
725C22×C4—1461no—
726C22×C4—1461no—
727C22×C4—1461no—
728C22×C4—1461no—
729C22×C4—1461no—
730C22×C4—1461no—
731C22×C4—1461no—
732C22×C4—1461no—
733C22×C4—1461no—
734C22×C4—1461no—
735C22×C4—1461no—
736C22×C4—1461no—
737C22×C4—1461no—
738C22×C4—1461no—
739C22×C4—1461no—
740C22×C4—1461no—
741C22×C4—1461no—
742C22×C4—1461no—
743C22×C4—1461no—
744C22×C4—1461no—
745C22×C4—1461no—
746C22×C4—1461no—
747C22×C4—1461no—
748C22×C4—1461no—
749C22×C4—1461no—
750C22×C4—1461no—
751C22×C4—1461no—
752C22×C4—1461no—
753C22×C4—1461no—
754C22×C4—1461no—
755C22×C4—1461no—
756C22×C4—1461no—
757C22×C4—1461no—
758C22×C4—1461no—
759C22×C4—1461no—
760C22×C4—1461no—
761C22×C4—1461no—
762C22×C4—1461no—
763C22×C4—1461no—
764C22×C4C22×Dic7312yes—
765C22×C4C22×Dic7312yes—
766C22×C4C22×Dic7312yes—
767C22×C4C22×Dic7312yes—
768C22×C4C22×Dic7312yes—
769C22×C4C22×Dic7312yes—
770C22×C4D4×D7312yes—
771C22×C4C2×D29212yes—
772C22×C4C2×D29212yes—
773C22×C4C2×Dic14612yes—
774C22×C4C2×Dic14612yes—
775C22×C4#1192402712yes—
776C4⋊C4—44no—
777C4⋊C4—2924no—
778C4⋊C4—2924no—
779C4⋊C4—2924no—
780C4⋊C4—2924no—
781C4⋊C4—2924no—
782C4⋊C4—2924no—
783C4⋊C4—2924no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—2924no—
787C22⋊C4—2924no—
788C22⋊C4—2924no—
789C22⋊C4C4⋊Dic73116yescomplemented
790C42—28no—
791C42—2924no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊Dic7314yes—
827C23C23×Dic7311yescharacteristic
828C23C2×D4×D7311yescharacteristic
829C23C22×D29211yescharacteristic
830C23C22×Dic14611yescharacteristic
831C23#41×D7311yescharacteristic
832C23#41×D7311yescharacteristic
833C23C2×#1192402711yescharacteristic
834C23#1455663611yescharacteristic
835C23#1455663611yescharacteristic
836C23#1455663711yescharacteristic
837C23#1455663711yescharacteristic
838C23#1455663711yescharacteristic
839C23#1455663811yescharacteristic
840C23#1455663811yescharacteristic
841C23#1455663811yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—29216no—
882C2×C4—2921no—
883C2×C4—2921no—
884C2×C4—2921no—
885C2×C4—2921no—
886C2×C4—2921no—
887C2×C4—2921no—
888C2×C4—2921no—
889C2×C4—2921no—
890C2×C4—2921no—
891C2×C4—2921no—
892C2×C4—2921no—
893C2×C4—2921no—
894C2×C4—2921no—
895C2×C4—2921no—
896C2×C4—2921no—
897C2×C4—2921no—
898C2×C4—2921no—
899C2×C4—2921no—
900C2×C4—2921no—
901C2×C4—2921no—
902C2×C4—2921no—
903C2×C4—2921no—
904C2×C4—2921no—
905C2×C4—2921no—
906C2×C4—2921no—
907C2×C4—2921no—
908C2×C4—2921no—
909C2×C4—2921no—
910C2×C4—2921no—
911C2×C4—2921no—
912C2×C4—2921no—
913C2×C4—2921no—
914C2×C4—2921no—
915C2×C4—2921no—
916C2×C4—2921no—
917C2×C4—2921no—
918C2×C4—2921no—
919C2×C4—2921no—
920C2×C4—2921no—
921C2×C4—2921no—
922C2×C4—2921no—
923C2×C4—2921no—
924C2×C4—2921no—
925C2×C4—2921no—
926C2×C4—1462no—
927C2×C4—1462no—
928C2×C4—1462no—
929C2×C4—1462no—
930C2×C4—1462no—
931C2×C4—1462no—
932C2×C4—1462no—
933C2×C4—1462no—
934C2×C4—1462no—
935C2×C4—1462no—
936C2×C4—1462no—
937C2×C4—1462no—
938C2×C4C2×C4⋊Dic7314yes—
939C2×C4C2×C4⋊Dic7314yes—
940C2×C4D4×Dic7314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊Dic7311yescharacteristic
957C22C2×D4×Dic7311yescharacteristic
958C22#41×Dic7311yescharacteristic
959C22#1798906211yescharacteristic
960C22#1798907011yescharacteristic
961C22#1798907011yescharacteristic
962C22#1798907011yescharacteristic
963C22#1798915311yescharacteristic
964C22#1798915611yescharacteristic
965C22#1798916311yescharacteristic
966C22#1798916611yescharacteristic
967C22#1798917611yescharacteristic
968C22#1798917811yescharacteristic
969C22#1798919011yescharacteristic
970C22#1798919411yescharacteristic
971C22#1798920311yescharacteristic
972C22#1798920411yescharacteristic
973C22#1798921511yescharacteristic
974C22#1798921511yescharacteristic
975C22D4×D29211yescharacteristic
976C22#1798922911yescharacteristic
977C22#1798923211yescharacteristic
978C22#1798923211yescharacteristic
979C22#1798923511yescharacteristic
980C22#1798924111yescharacteristic
981C22D4×Dic14611yescharacteristic
982C22#1798926011yescharacteristic
983C22#1798927411yescharacteristic
984C22#1798929411yescharacteristic
985C22#1798929611yescharacteristic
986C22#1798929611yescharacteristic
987C22#1798932911yescharacteristic
988C22#1798933111yescharacteristic
989C22#1798933111yescharacteristic
990C22#1798933711yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—2922no—
998C4—2922no—
999C4—2922no—
1000C4—2922no—
1001C4—5841no—
1002C4—5841no—
1003C4—5841no—
1004C4—5841no—
1005C2—44no—
1006C2#2261255411yescharacteristic
1007C2#2261262611yescharacteristic
1008C2#2261271011yescharacteristic
1009C2D4×C4⋊Dic7311yescharacteristic
1010C2#2261284111yescharacteristic
1011C2#2261292711yescharacteristic
1012C2#2261310511yescharacteristic
1013C2#2261615511yescharacteristic
1014C2#2261618011yescharacteristic
1015C2#2261650311yescharacteristic
1016C2#2261659011yescharacteristic
1017C2#2261661711yescharacteristic
1018C2#2261681511yescharacteristic
1019C2#2261734711yescharacteristic
1020C2#2261741511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#388×C73C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#388D73
hypocenterC73#14403
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#17988453C2semidirect
5. #22608196C2semidirect
6. #22608196C2semidirect
7. #22608188C2semidirect
8. #22608184C2semidirect
11. #22608165C2semidirect
12. #22608161C2semidirect
13. #22608160C2semidirect
53. #388×C73C4semidirect
129. C2×C4⋊C4×C73C2×C4semidirect
141. C2×C42×C73C2×C4semidirect
142. #95×C73C2×C4semidirect
143. #95×C73C2×C4semidirect
279. C22⋊C4×C73C4⋊C4semidirect
526. C73#14403semidirect
545. #388Dic73semidirect
612. C2×C4⋊C4C2×Dic73semidirect
636. C2×C42C2×Dic73semidirect
653. #95C2×Dic73semidirect
654. #95C2×Dic73semidirect
789. C22⋊C4C4⋊Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179884802
C2×#179884622
C2×#179884532
#226081962
#226081882
#226081842
#226081762
#226081652
#226081612
#226081602
#226081532
C2×#388×C732
#1440373