Finite Group Databasebeta

← #33014001

Subgroups — #33014001

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×#17988486C211yesmaximal, characteristic, complemented
2C2×#17988480C211yesmaximal, characteristic
3C2×#17988480C211yesmaximal, characteristic
4C2×#17988447C211yesmaximal, characteristic
5#22608196C211yesmaximal, characteristic, complemented
6#22608188C211yesmaximal, characteristic, complemented
7#22608184C211yesmaximal, characteristic, complemented
8#22608184C211yesmaximal, characteristic, complemented
9#22608176C211yesmaximal, characteristic
10#22608176C211yesmaximal, characteristic
11#22608165C211yesmaximal, characteristic, complemented
12#22608165C211yesmaximal, characteristic, complemented
13#22608160C211yesmaximal, characteristic, complemented
14#22608154C211yesmaximal, characteristic
15C2×#385×C73C211yesmaximal, characteristic
16C22×C4⋊Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20C22×C4⋊Dic73C2211yescharacteristic
21C22×C4⋊Dic73C2211yescharacteristic
22C22×C22⋊Dic73C2211yescharacteristic
23C22×C22⋊Dic73C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×C22⋊Dic73C2211yescharacteristic
26C22×C4×Dic73C2211yescharacteristic
27C22×C4×Dic73C2211yescharacteristic
28#17988486—24no—
29#17988480—24no—
30#17988480—24no—
31#17988447—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
48C24×C4×C73C2211yescharacteristic
49C22×C4⋊C4×C73C2211yescharacteristic
50C22×C4⋊C4×C73C2211yescharacteristic
51C22×C22⋊C4×C73C2211yescharacteristic
52C22×C22⋊C4×C73C2211yescharacteristic
53#385×C73C418yescomplemented
54C2×#95×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C23×Dic73C2311yescharacteristic
57C23×Dic73C2311yescharacteristic
58C23×Dic73C2311yescharacteristic
59C23×Dic73C2311yescharacteristic
60C23×Dic73C2311yescharacteristic
61C23×Dic73C2311yescharacteristic
62C23×Dic73C2311yescharacteristic
63C23×Dic73C2311yescharacteristic
64C2×C4⋊Dic73—22no—
65C2×C4⋊Dic73—22no—
66C2×C4⋊Dic73—22no—
67C2×C4⋊Dic73—22no—
68C2×C4⋊Dic73—22no—
69C2×C4⋊Dic73—22no—
70C2×C4⋊Dic73—22no—
71C2×C4⋊Dic73—41no—
72C2×C4⋊Dic73—41no—
73C2×C4⋊Dic73—41no—
74C2×C4⋊Dic73—41no—
75C2×C4⋊Dic73—41no—
76C2×C4⋊Dic73—41no—
77C2×C4⋊Dic73—41no—
78C2×C4⋊Dic73—41no—
79C2×C4⋊Dic73—41no—
80C2×C4⋊Dic73—41no—
81C2×C4⋊Dic73D414yes—
82C2×C22⋊Dic73—22no—
83C2×C22⋊Dic73—22no—
84C2×C22⋊Dic73—22no—
85C2×C22⋊Dic73—22no—
86C2×C22⋊Dic73—22no—
87C2×C22⋊Dic73—22no—
88C2×C22⋊Dic73—22no—
89C2×C22⋊Dic73—22no—
90C2×C22⋊Dic73—41no—
91C2×C22⋊Dic73—41no—
92C2×C22⋊Dic73—41no—
93C2×C22⋊Dic73—41no—
94C2×C4×Dic73—22no—
95C2×C4×Dic73—22no—
96C2×C4×Dic73—22no—
97C2×C4×Dic73—22no—
98C2×C4×Dic73—41no—
99C2×C4×Dic73—41no—
100#14556498—22no—
101#14556498—22no—
102#14556498—22no—
103#14556498—22no—
104#14556498—22no—
105#14556498—22no—
106#14556498—22no—
107#14556498—22no—
108#14556498—22no—
109#14556498—22no—
110#14556498—41no—
111#14556498—41no—
112#14556498—41no—
113#14556498—41no—
114#14556498—41no—
115#14556498—41no—
116C25×C73C2311yescharacteristic
117C23×C4×C73—22no—
118C23×C4×C73—22no—
119C23×C4×C73—41no—
120C23×C4×C73—41no—
121C23×C4×C73—41no—
122C23×C4×C73—41no—
123C23×C4×C73C2×C414yes—
124C23×C4×C73C2311yescharacteristic
125C23×C4×C73C2311yescharacteristic
126C23×C4×C73C2311yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C2×C4⋊C4×C73—22no—
131C2×C4⋊C4×C73—22no—
132C2×C4⋊C4×C73—41no—
133C2×C4⋊C4×C73—41no—
134C2×C4⋊C4×C73C2×C414yes—
135C2×C4⋊C4×C73C2×C414yes—
136C2×C22⋊C4×C73—41no—
137C2×C22⋊C4×C73—41no—
138C2×C22⋊C4×C73C2×C414yes—
139C2×C22⋊C4×C73C2×C414yes—
140C2×C22⋊C4×C73D414yes—
141C2×C22⋊C4×C73Q814yes—
142#95×C73C2×C414yes—
143#95×C73C2×C414yes—
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×Dic73C2×D412yes—
197C22×Dic73C2×D412yes—
198C22×Dic73#4112yes—
199C22×Dic73#4112yes—
200C4⋊Dic73—44no—
201C4⋊Dic73—44no—
202C4⋊Dic73—44no—
203C4⋊Dic73—44no—
204C4⋊Dic73—44no—
205C4⋊Dic73—44no—
206C22⋊Dic73—44no—
207C22⋊Dic73—44no—
208C22⋊Dic73—44no—
209C22⋊Dic73—44no—
210C4×Dic73—44no—
211C4×Dic73—44no—
212C24×C73—21no—
213C24×C73—21no—
214C24×C73—21no—
215C24×C73—21no—
216C24×C73—21no—
217C24×C73—21no—
218C24×C73—21no—
219C24×C73—21no—
220C24×C73—21no—
221C24×C73—21no—
222C24×C73—21no—
223C24×C73—21no—
224C24×C73C22×C412yes—
225C24×C73C2×D412yes—
226C24×C73C2×Q812yes—
227C24×C73C2411yescharacteristic
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
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—28no—
259C22×C4×C73—44no—
260C22×C4×C73—44no—
261C22×C4×C73—44no—
262C22×C4×C73—44no—
263C22×C4×C73—44no—
264C22×C4×C73—44no—
265C22×C4×C73C22×C412yes—
266C22×C4×C73C22×C412yes—
267C22×C4×C73C22×C412yes—
268C22×C4×C73C22×C412yes—
269C22×C4×C73C22×C412yes—
270C22×C4×C73C22×C412yes—
271C22×C4×C73C2×D412yes—
272C22×C4×C73C2×D412yes—
273C22×C4×C73C2×D412yes—
274C22×C4×C73C2×Q812yes—
275C22×C4×C73C2×Q812yes—
276C22×C4×C73#4112yes—
277C4⋊C4×C73—28no—
278C4⋊C4×C73—44no—
279C22⋊C4×C73—44no—
280C22⋊C4×C73C4⋊C4116yescomplemented
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—416no—
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×C73—41no—
371C2×C4×C73C2×C4⋊C414yes—
372C2×C4×C73C2×C4⋊C414yes—
373C2×C4×C73C4×D414yes—
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—22no—
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#51811yescharacteristic
450C22×C73#51911yescharacteristic
451C22×C73#52011yescharacteristic
452C22×C73#53411yescharacteristic
453C22×C73#53511yescharacteristic
454C22×C73#53711yescharacteristic
455C22×C73#53711yescharacteristic
456C22×C73#53811yescharacteristic
457C22×C73#53811yescharacteristic
458C22×C73#53811yescharacteristic
459C22×C73#53911yescharacteristic
460C22×C73#54011yescharacteristic
461C22×C73#54211yescharacteristic
462C22×C73#54411yescharacteristic
463C22×C73#54411yescharacteristic
464C22×C73D4211yescharacteristic
465C22×C73#54611yescharacteristic
466C22×C73#54611yescharacteristic
467C22×C73#54711yescharacteristic
468C22×C73#54711yescharacteristic
469C22×C73#54811yescharacteristic
470C22×C73D4×Q811yescharacteristic
471C22×C73#55211yescharacteristic
472C22×C73#55411yescharacteristic
473C22×C73#55411yescharacteristic
474C22×C73#55411yescharacteristic
475C22×C73#55611yescharacteristic
476C22×C73#56211yescharacteristic
477C22×C73#56211yescharacteristic
478C22×C73#56311yescharacteristic
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#14408—731nomaximal, Sylow
495C2×C73—44no—
496C2×C73#231611yescharacteristic
497C2×C73#232111yescharacteristic
498C2×C73#233511yescharacteristic
499C2×C73D4×C4⋊C411yescharacteristic
500C2×C73#234911yescharacteristic
501C2×C73#236211yescharacteristic
502C2×C73#237811yescharacteristic
503C2×C73#267111yescharacteristic
504C2×C73#267611yescharacteristic
505C2×C73#269511yescharacteristic
506C2×C73#271511yescharacteristic
507C2×C73#272011yescharacteristic
508C2×C73#272911yescharacteristic
509C2×C73#276811yescharacteristic
510C2×C73#278811yescharacteristic
511C2×#389—731no—
512C2×#388—731no—
513C2×#388—731no—
514C2×#385D7311yescharacteristic
515C2×#380—731no—
516#1444—731no—
517#1442—731no—
518#1441—731no—
519#1441—731no—
520#1439—731no—
521#1439—731no—
522#1436—731no—
523#1436—731no—
524C4⋊#95—731no—
525C22⋊#95—731no—
526C73#1440811yescharacteristic, complemented, Sylow
527C24×C4C2×D7311yescharacteristic
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⋊C4C2×D7311yescharacteristic
535C22×C4⋊C4C2×D7311yescharacteristic
536C22×C22⋊C4—731no—
537C22×C22⋊C4—731no—
538C22×C22⋊C4—731no—
539C22×C22⋊C4—731no—
540C22×C22⋊C4C2×D7311yescharacteristic
541C22×C22⋊C4C2×D7311yescharacteristic
542C22×C42—731no—
543C22×C42—731no—
544#389—1464no—
545#388—1464no—
546#388—1464no—
547#385Dic7318yescomplemented
548#380—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—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—731no—
575C23×C4—731no—
576C23×C4—731no—
577C23×C4—731no—
578C23×C4—731no—
579C23×C4—731no—
580C23×C4—731no—
581C23×C4—731no—
582C23×C4C2×Dic7314yes—
583C23×C4C22×D7311yescharacteristic
584C23×C4C22×D7311yescharacteristic
585C23×C4C22×D7311yescharacteristic
586C23×C4C22×D7311yescharacteristic
587C23×C4C22×D7311yescharacteristic
588C23×C4C22×D7311yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
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—2921no—
602C2×C4⋊C4—2921no—
603C2×C4⋊C4—734no—
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⋊C4C2×Dic7314yes—
612C2×C4⋊C4C2×Dic7314yes—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—2921no—
616C2×C22⋊C4—2921no—
617C2×C22⋊C4—2921no—
618C2×C22⋊C4—2921no—
619C2×C22⋊C4—1462no—
620C2×C22⋊C4—1462no—
621C2×C22⋊C4—1462no—
622C2×C22⋊C4—1462no—
623C2×C22⋊C4—1462no—
624C2×C22⋊C4—1462no—
625C2×C22⋊C4—1462no—
626C2×C22⋊C4—1462no—
627C2×C22⋊C4Dic14614yes—
628C2×C22⋊C4D29214yes—
629C2×C22⋊C4C2×Dic7314yes—
630C2×C22⋊C4C2×Dic7314yes—
631C2×C42—2921no—
632C2×C42—2921no—
633C2×C42—1462no—
634C2×C42—1462no—
635C2×C42—1462no—
636C2×C42—1462no—
637#95—2921no—
638#95—2921no—
639#95—2921no—
640#95—2921no—
641#95—2921no—
642#95—2921no—
643#95—1462no—
644#95—1462no—
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×Dic7314yes—
654#95C2×Dic7314yes—
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—28no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
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—28no—
777C4⋊C4—44no—
778C4⋊C4—2924no—
779C4⋊C4—2924no—
780C4⋊C4—2924no—
781C4⋊C4—2924no—
782C4⋊C4—2924no—
783C4⋊C4—2924no—
784C22⋊C4—44no—
785C22⋊C4—2924no—
786C22⋊C4—2924no—
787C22⋊C4—2924no—
788C22⋊C4—2924no—
789C22⋊C4C4⋊Dic73116yescomplemented
790C42—2924no—
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#1455663611yescharacteristic
837C23#1455663611yescharacteristic
838C23#1455663711yescharacteristic
839C23#1455663811yescharacteristic
840C23#1455663911yescharacteristic
841C23#1455663911yescharacteristic
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—416no—
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—41no—
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#1798906211yescharacteristic
961C22#1798906511yescharacteristic
962C22#1798907011yescharacteristic
963C22#1798914711yescharacteristic
964C22#1798915211yescharacteristic
965C22#1798916811yescharacteristic
966C22#1798916811yescharacteristic
967C22#1798917211yescharacteristic
968C22#1798917211yescharacteristic
969C22#1798917311yescharacteristic
970C22#1798918011yescharacteristic
971C22#1798918911yescharacteristic
972C22#1798920511yescharacteristic
973C22#1798921811yescharacteristic
974C22#1798921811yescharacteristic
975C22D4×D29211yescharacteristic
976C22#1798923211yescharacteristic
977C22#1798923211yescharacteristic
978C22#1798923911yescharacteristic
979C22#1798924111yescharacteristic
980C22#1798924711yescharacteristic
981C22D4×Dic14611yescharacteristic
982C22#1798927111yescharacteristic
983C22#1798929411yescharacteristic
984C22#1798929611yescharacteristic
985C22#1798929611yescharacteristic
986C22#1798930811yescharacteristic
987C22#1798933311yescharacteristic
988C22#1798933311yescharacteristic
989C22#1798933811yescharacteristic
990C22#1798933811yescharacteristic
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#2261254911yescharacteristic
1007C2#2261259211yescharacteristic
1008C2#2261272511yescharacteristic
1009C2D4×C4⋊Dic7311yescharacteristic
1010C2#2261284111yescharacteristic
1011C2#2261296211yescharacteristic
1012C2#2261309711yescharacteristic
1013C2#2261617011yescharacteristic
1014C2#2261623511yescharacteristic
1015C2#2261646411yescharacteristic
1016C2#2261674011yescharacteristic
1017C2#2261681211yescharacteristic
1018C2#2261691711yescharacteristic
1019C2#2261740811yescharacteristic
1020C2#2261768111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#385×C73C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#385D73
hypocenterC73#14408
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#17988486C2semidirect
5. #22608196C2semidirect
6. #22608188C2semidirect
7. #22608184C2semidirect
8. #22608184C2semidirect
11. #22608165C2semidirect
12. #22608165C2semidirect
13. #22608160C2semidirect
53. #385×C73C4semidirect
280. C22⋊C4×C73C4⋊C4semidirect
526. C73#14408semidirect
547. #385Dic73semidirect
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×#179884862
C2×#179884802
C2×#179884472
#226081962
#226081882
#226081842
#226081762
#226081652
#226081602
#226081542
C2×#385×C732
#1440873