Finite Group Databasebeta

← #33104071

Subgroups — #33104071

Order 18688.

964 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988658C211yesmaximal, characteristic
2C2×#17988656C211yesmaximal, characteristic
3C2×#17988612C211yesmaximal, characteristic, complemented
4#22612390C211yesmaximal, characteristic
5#22610651C211yesmaximal, characteristic, complemented
6#22610651C211yesmaximal, characteristic, complemented
7#22610114C211yesmaximal, characteristic, complemented
8#22610112C211yesmaximal, characteristic, complemented
9#22610109C211yesmaximal, characteristic, complemented
10#22610107C211yesmaximal, characteristic, complemented
11#22610082C211yesmaximal, characteristic, complemented
12#22609915C211yesmaximal, characteristic, complemented
13#22609912C211yesmaximal, characteristic, complemented
14#22609786C211yesmaximal, characteristic, complemented
15C2×#424×C73C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×C4×C22⋊D73C2211yescharacteristic
19C2×#14556548C2211yescharacteristic
20#17988658—24no—
21#17988656—24no—
22#17988612—24no—
23C2×C4⋊#10596831C2211yescharacteristic
24C2×C4⋊#10596831C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×#14556520C2211yescharacteristic
27C2×#14556520C2211yescharacteristic
28C2×#14556520C2211yescharacteristic
29C2×#14556520C2211yescharacteristic
30C2×#14556520C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×C22⋊#10596831C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556503C2211yescharacteristic
35C2×#14556501C2211yescharacteristic
36C2×#14556501C2211yescharacteristic
37#17988487C411yescharacteristic
38#17988487C411yescharacteristic
39#17988482C411yescharacteristic
40#17988482C411yescharacteristic
41#17988481C411yescharacteristic
42#17988481C411yescharacteristic
43#17988477C411yescharacteristic
44#17988477C411yescharacteristic
45C4×#11924007C2211yescharacteristic
46C4×#11924005C2211yescharacteristic
47C4×C22⋊Dic73C2211yescharacteristic
48C42×Dic73C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55C22×M16×C73C2211yescharacteristic
56C23×C8×C73C2211yescharacteristic
57C2×#117×C73C2211yescharacteristic
58#424×C73—24no—
59C2×C4⋊C8×C73C2211yescharacteristic
60C2×C4⋊C8×C73C2211yescharacteristic
61C2×C4⋊C8×C73C2211yescharacteristic
62C2×C4⋊C8×C73C2211yescharacteristic
63C22×C22⋊D73C2×C411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C2×#11924011—22no—
66C2×#11924011—22no—
67C2×#11924011—41no—
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C2×C8×D73—22no—
73C2×C8×D73—22no—
74C2×C8×D73—41no—
75C4×C22⋊D73D414yes—
76C4×C22⋊D73Q814yes—
77#14556548—22no—
78#14556548—22no—
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×#11924007C2×C411yescharacteristic
84C2×C22⋊Dic73C2×C411yescharacteristic
85C2×C22⋊Dic73C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×C4×Dic73C2×C411yescharacteristic
93C2×C4×Dic73C2×C411yescharacteristic
94C2×C4×Dic73C2×C411yescharacteristic
95C2×C4×Dic73C2×C411yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99C4⋊#10596831—22no—
100C4⋊#10596831—22no—
101#14556520—22no—
102#14556520—22no—
103#14556520—22no—
104#14556520—22no—
105#14556520—41no—
106#14556520—41no—
107C22⋊#10596831—22no—
108C22⋊#10596831—22no—
109#14556503—22no—
110#14556503—22no—
111#14556501—22no—
112#14556501—22no—
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119C23×C4×C73C2311yescharacteristic
120C2×M16×C73—22no—
121C2×M16×C73—22no—
122C2×M16×C73—41no—
123C22×C8×C73—22no—
124C22×C8×C73—22no—
125C22×C8×C73—41no—
126C22×C8×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130#117×C73—22no—
131#117×C73—22no—
132C2×C4⋊C4×C73C2×C411yescharacteristic
133C2×C4⋊C4×C73C2×C411yescharacteristic
134C2×C22⋊C4×C73C2×C411yescharacteristic
135C2×C22⋊C4×C73C2×C411yescharacteristic
136C2×C42×C73C2311yescharacteristic
137C2×C42×C73C2311yescharacteristic
138C4⋊C8×C73—22no—
139C4⋊C8×C73—22no—
140C4⋊C8×C73—22no—
141C4⋊C8×C73D414yescomplemented
142C23×D73C22×C411yescharacteristic
143C2×C22⋊D73—41no—
144C2×C22⋊D73—41no—
145C2×C22⋊D73C4⋊C414yes—
146C22×Dic73C22×C411yescharacteristic
147C22×Dic73C22×C411yescharacteristic
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
150C22×Dic73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C22×C411yescharacteristic
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73C2×D412yes—
158C2×C4×D73C2×Q812yes—
159#11924011—44no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C8×D73—44no—
173#11924007—22no—
174#11924007—22no—
175#11924007—41no—
176#11924007—41no—
177#11924007C4⋊C414yes—
178C22⋊Dic73—22no—
179C22⋊Dic73—41no—
180C22⋊Dic73C4⋊C414yes—
181#11924005—22no—
182#11924005—22no—
183#11924005—22no—
184#11924005—41no—
185#11924005C4⋊C414yes—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—22no—
191C4×Dic73—41no—
192C4×Dic73—41no—
193C4×Dic73—41no—
194C4×Dic73C2×D412yes—
195C4×Dic73C2×Q812yes—
196C24×C73C22×C411yescharacteristic
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73C22×C411yescharacteristic
202C22×C4×C73C22×C411yescharacteristic
203C22×C4×C73C22×C411yescharacteristic
204C22×C4×C73C22×C411yescharacteristic
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C2×D412yes—
207C22×C4×C73C2×Q812yes—
208C22×C4×C73C2411yescharacteristic
209M16×C73—44no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—44no—
221C2×C8×C73C2×D412yes—
222C2×C8×C73C2×D412yes—
223C4⋊C4×C73—22no—
224C4⋊C4×C73—22no—
225C22⋊C4×C73—22no—
226C22⋊C4×C73—22no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73C2×D412yes—
230C42×C73#4112yes—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73C2×C4⋊C412yes—
238C23×C73C23×C411yescharacteristic
239C22×D73—21no—
240C22×D73—21no—
241C22×D73—21no—
242C22×D73—21no—
243C22×D73—21no—
244C22×D73—21no—
245C22×D73C2×C4⋊C412yes—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73C2×C4⋊C412yes—
263C2×C4×C73C4×D412yes—
264C2×C4×C73C4×D412yes—
265C2×C4×C73C22×D411yescharacteristic
266C2×C4×C73C22×D411yescharacteristic
267C2×C4×C73C22×Q811yescharacteristic
268C2×C4×C73C2×#4111yescharacteristic
269C2×C4×C73H(5,𝔽2)11yescharacteristic
270C2×C4×C732−1+411yescharacteristic
271C22⋊D73—44no—
272C2×Dic73—21no—
273C2×Dic73—21no—
274C2×Dic73—21no—
275C2×Dic73—21no—
276C2×Dic73—21no—
277C2×Dic73—21no—
278C2×Dic73—21no—
279C2×Dic73—21no—
280C2×Dic73—21no—
281C2×Dic73—21no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73C2×C4⋊C412yes—
290C2×Dic73C2×C4⋊C412yes—
291C2×Dic73C2×C4⋊C412yes—
292C2×Dic73#13112yes—
293C4×D73—22no—
294C4×D73—22no—
295C4×D73—22no—
296C4×D73—22no—
297C8×C73—22no—
298C8×C73—22no—
299C8×C73—41no—
300C8×C73—41no—
301#10596831—41no—
302#10596831—41no—
303#10596831—41no—
304#10596831—41no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—41no—
309C22×C73—41no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73C22×C4⋊C411yescharacteristic
313C22×C73C2×C4×D411yescharacteristic
314C22×C73#52011yescharacteristic
315C22×C73C2×#13111yescharacteristic
316C22×C73#56811yescharacteristic
317C22×C73#56811yescharacteristic
318C22×C73#56811yescharacteristic
319C2×D73—22no—
320C2×D73—22no—
321C2×D73—22no—
322C2×D73—41no—
323C2×D73—41no—
324C2×D73—41no—
325C2×D73—41no—
326C4×C73—22no—
327C4×C73—22no—
328C4×C73—22no—
329C4×C73—41no—
330C4×C73—41no—
331C4×C73D4211yescharacteristic
332C4×C73#54711yescharacteristic
333C4×C73D4×Q811yescharacteristic
334C4×C73#55411yescharacteristic
335Dic73—22no—
336Dic73—22no—
337Dic73—22no—
338Dic73—22no—
339Dic73—41no—
340Dic73—41no—
341Dic73—41no—
342#22652—731nomaximal, Sylow
343C2×C73—42no—
344C2×C73D4×C4⋊C411yescharacteristic
345C2×C73#290511yescharacteristic
346C2×C73#290611yescharacteristic
347C2×C73#293211yescharacteristic
348C2×C73#293511yescharacteristic
349C2×C73#299211yescharacteristic
350C2×C73#299511yescharacteristic
351D73—42no—
352C2×#435—731no—
353C2×#435—731no—
354C2×#424—731no—
355C2×#424D7311yescharacteristic, complemented
356#2293—731no—
357#1940—731no—
358#1940—731no—
359#1851—731no—
360#1851—731no—
361#1850—731no—
362#1850—731no—
363#1842—731no—
364#1798—731no—
365#1798—731no—
366#1767—731no—
367C73#2265211yescharacteristic, complemented, Sylow
368C22×M16—731no—
369C22×M16C2×D7311yescharacteristic
370C23×C8—731no—
371C23×C8C2×D7311yescharacteristic
372C2×C4×D4—731no—
373C2×#117—731no—
374C2×#117C2×D7311yescharacteristic
375#435—1464no—
376#435—1464no—
377#424—24no—
378#424—1464no—
379C2×C4⋊C8—731no—
380C2×C4⋊C8—731no—
381C2×C4⋊C8—731no—
382C2×C4⋊C8—731no—
383C2×C4⋊C8—731no—
384C2×C4⋊C8—731no—
385C2×C4⋊C8—731no—
386C2×C4⋊C8—731no—
387C2×C4⋊C8C2×D7311yescharacteristic
388C2×C4⋊C8C2×D7311yescharacteristic
389C2×C4⋊C8C2×D7311yescharacteristic
390C2×C4⋊C8C2×D7311yescharacteristic
391C2×C22⋊C8—731no—
392C2×C22⋊C8—731no—
393C2×C22⋊C8—731no—
394C2×C22⋊C8—731no—
395C2×#97—731no—
396C2×#97—731no—
397#390—731no—
398#390—731no—
399#389—731no—
400#389—731no—
401#388—731no—
402#388—731no—
403#388—731no—
404#388—731no—
405C4×C4⋊C4—731no—
406C4×C22⋊C4—731no—
407C4×C22⋊C4—731no—
408C43—731no—
409#336—731no—
410#336—731no—
411#336—731no—
412#336—731no—
413#336—731no—
414#336—731no—
415C22×D4—731no—
416C23×C4—731no—
417C23×C4C22×D7311yescharacteristic
418C2×M16—22no—
419C2×M16—22no—
420C2×M16—41no—
421C2×M16—2921no—
422C2×M16—1462no—
423C2×M16—1462no—
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—41no—
427C22×C8—2921no—
428C22×C8—731no—
429C22×C8—731no—
430C22×C8—731no—
431C22×C8—731no—
432C22×C8—1462no—
433C22×C8—1462no—
434C22×C8C22×D7311yescharacteristic
435C22×C8C22×D7311yescharacteristic
436C22×C8C22×D7311yescharacteristic
437C22×C8C22×D7311yescharacteristic
438C4×D4—734no—
439C4×D4—734no—
440#117—22no—
441#117—22no—
442#117—1462no—
443#117—1462no—
444C2×C4⋊C4—731no—
445C2×C4⋊C4—731no—
446C2×C4⋊C4—731no—
447C2×C4⋊C4—731no—
448C2×C4⋊C4—731no—
449C2×C4⋊C4C4×D7311yescharacteristic
450C2×C4⋊C4C4×D7311yescharacteristic
451C2×C22⋊C4—731no—
452C2×C22⋊C4—731no—
453C2×C22⋊C4—731no—
454C2×C22⋊C4—731no—
455C2×C22⋊C4—731no—
456C2×C22⋊C4—731no—
457C2×C22⋊C4—731no—
458C2×C22⋊C4—731no—
459C2×C22⋊C4C4×D7311yescharacteristic
460C2×C22⋊C4C4×D7311yescharacteristic
461C2×C42—731no—
462C2×C42—731no—
463C2×C42—731no—
464C2×C42—731no—
465C2×C42—731no—
466C2×C42—731no—
467C2×C42—731no—
468C2×C42C22×D7311yescharacteristic
469C2×C42C22×D7311yescharacteristic
470C4⋊C8—22no—
471C4⋊C8—22no—
472C4⋊C8—22no—
473C4⋊C8—2921no—
474C4⋊C8—2921no—
475C4⋊C8—1462no—
476C4⋊C8—1462no—
477C4⋊C8—1462no—
478C4⋊C8—1462no—
479C4⋊C8—1462no—
480C4⋊C8—1462no—
481C4⋊C8C22⋊D7314yescomplemented
482C22⋊C8—1462no—
483C22⋊C8—1462no—
484C22⋊C8—1462no—
485C22⋊C8—1462no—
486#97—1462no—
487#97—1462no—
488#95—731no—
489#95—731no—
490#95—731no—
491#95—731no—
492#95—731no—
493#95—731no—
494C24—731no—
495C24C2×C4×D7311yescharacteristic
496C2×D4—2921no—
497C2×D4—2921no—
498C2×D4—734no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—731no—
504C22×C4—731no—
505C22×C4—731no—
506C22×C4—731no—
507C22×C4—732no—
508C22×C4—732no—
509C22×C4—731no—
510C22×C4—731no—
511C22×C4—731no—
512C22×C4—1461no—
513C22×C4—1461no—
514C22×C4—1461no—
515C22×C4—1461no—
516C22×C4C2×C4×D7311yescharacteristic
517C22×C4C2×C4×D7311yescharacteristic
518C22×C4C2×C4×D7311yescharacteristic
519C22×C4C2×C4×D7311yescharacteristic
520C22×C4C2×C4×D7311yescharacteristic
521C22×C4D4×D7312yes—
522C22×C4Q8×D7312yes—
523C22×C4C23×D7311yescharacteristic
524M16—44no—
525M16—2924no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—44no—
537C2×C8—2924no—
538C2×C8—1461no—
539C2×C8—1461no—
540C2×C8—1461no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8—1461no—
548C2×C8—1461no—
549C2×C8—1461no—
550C2×C8C2×C22⋊D7312yes—
551C2×C8C2×C22⋊D7312yes—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—2921no—
555C4⋊C4—2921no—
556C4⋊C4—734no—
557C4⋊C4—1462no—
558C4⋊C4—1462no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—2921no—
562C22⋊C4—2921no—
563C22⋊C4—734no—
564C22⋊C4—734no—
565C22⋊C4—1462no—
566C22⋊C4—1462no—
567C22⋊C4—1462no—
568C22⋊C4—1462no—
569C42—21no—
570C42—21no—
571C42—2921no—
572C42—2921no—
573C42—2921no—
574C42—732no—
575C42—732no—
576C42—1462no—
577C42—1461no—
578C42—1461no—
579C42—1461no—
580C42—1461no—
581C42C2×C22⋊D7312yes—
582C42#1192402812yes—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—732no—
590C23—1461no—
591C23—1461no—
592C23—1461no—
593C23—1461no—
594C23—1461no—
595C23—1461no—
596C23C4⋊C4×D7312yes—
597C23C22×C4×D7311yescharacteristic
598D4—2924no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—732no—
616C2×C4—732no—
617C2×C4—732no—
618C2×C4—732no—
619C2×C4—1461no—
620C2×C4—1461no—
621C2×C4—1461no—
622C2×C4—1461no—
623C2×C4—1461no—
624C2×C4—1461no—
625C2×C4—1461no—
626C2×C4—1461no—
627C2×C4—1461no—
628C2×C4—1461no—
629C2×C4—1461no—
630C2×C4—1461no—
631C2×C4—1461no—
632C2×C4—1461no—
633C2×C4—1461no—
634C2×C4—1461no—
635C2×C4—1461no—
636C2×C4—1462no—
637C2×C4—1462no—
638C2×C4—1462no—
639C2×C4—1462no—
640C2×C4C4⋊C4×D7312yes—
641C2×C4C4×C22⋊D7312yes—
642C2×C4C4×C22⋊D7312yes—
643C2×C4C2×D4×D7311yescharacteristic
644C2×C4C22×C22⋊D7311yescharacteristic
645C2×C4C2×Q8×D7311yescharacteristic
646C2×C4C2×#1192402811yescharacteristic
647C2×C4#1455663611yescharacteristic
648C2×C4#1455663911yescharacteristic
649C8—22no—
650C8—22no—
651C8—41no—
652C8—41no—
653C8—2921no—
654C8—2921no—
655C8—2921no—
656C8—2921no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—2921no—
665C22—2921no—
666C22—2921no—
667C22—2921no—
668C22—1462no—
669C22—1462no—
670C22—1462no—
671C22C2×C4⋊C4×D7311yescharacteristic
672C22C2×C4×C22⋊D7311yescharacteristic
673C22#1798906811yescharacteristic
674C22#131×D7311yescharacteristic
675C22#1798935211yescharacteristic
676C22#1798935211yescharacteristic
677C22#1798935211yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—41no—
682C4—41no—
683C4—2921no—
684C4—2921no—
685C4—2921no—
686C4—1462no—
687C4—1462no—
688C4—1462no—
689C4—1462no—
690C4D4×C22⋊D7311yescharacteristic
691C4#1798923811yescharacteristic
692C4Q8×C22⋊D7311yescharacteristic
693C4#1798929211yescharacteristic
694C2—42no—
695C2—2922no—
696C2C4⋊C4×C22⋊D7311yescharacteristic
697C2#2261849211yescharacteristic
698C2#2261849811yescharacteristic
699C2#2261864711yescharacteristic
700C2#2261867311yescharacteristic
701C2#2261906811yescharacteristic
702C2#2261909911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#424×C73C2
prime radicalC22×C22⋊D73C2×C4
cosocleC22×C4×C73C24
hypercenterC2×#424D73
hypocenterC73#22652
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
3. C2×#17988612C2semidirect
5. #22610651C2semidirect
6. #22610651C2semidirect
7. #22610114C2semidirect
8. #22610112C2semidirect
9. #22610109C2semidirect
10. #22610107C2semidirect
11. #22610082C2semidirect
12. #22609915C2semidirect
13. #22609912C2semidirect
14. #22609786C2semidirect
15. C2×#424×C73C2semidirect
141. C4⋊C8×C73D4semidirect
355. C2×#424D73semidirect
367. C73#22652semidirect
481. C4⋊C8C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886582
C2×#179886562
C2×#179886122
#226123902
#226106512
#226101142
#226101122
#226101092
#226101072
#226100822
#226099152
#226099122
#226097862
C2×#424×C732
#2265273