Finite Group Databasebeta

← #33112201

Subgroups — #33112201

Order 18688.

888 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556563C211yesmaximal, characteristic
2#22610723C211yesmaximal, characteristic, complemented
3#22610540C211yesmaximal, characteristic, complemented
4#22610537C211yesmaximal, characteristic, complemented
5#22610488C211yesmaximal, characteristic, complemented
6#22610485C211yesmaximal, characteristic, complemented
7#22610224C211yesmaximal, characteristic, complemented
8#22610221C211yesmaximal, characteristic, complemented
9#22610220C211yesmaximal, characteristic, complemented
10#22610220C211yesmaximal, characteristic, complemented
11#22610108C211yesmaximal, characteristic, complemented
12#22610107C211yesmaximal, characteristic, complemented
13#22609997C211yesmaximal, characteristic, complemented
14#22609909C211yesmaximal, characteristic, complemented
15C73×#1954C211yesmaximal, characteristic, complemented
16C23×#10596831C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×#14556563C411yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×C8×Dic73C2211yescharacteristic
32#17988487C411yescharacteristic
33#17988482C411yescharacteristic
34#17988481C411yescharacteristic
35#17988477C411yescharacteristic
36#17988467C411yescharacteristic
37#17988464C411yescharacteristic
38#17988445C411yescharacteristic
39C4×#11924007C2211yescharacteristic
40C4×#11924005C2211yescharacteristic
41C4×C22⋊Dic73C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C4×C8×C73C2211yescharacteristic
59C22×C22⋊D73C2×C411yescharacteristic
60C22×C22⋊D73C2×C411yescharacteristic
61C23×Dic73C2×C411yescharacteristic
62C23×Dic73C2×C411yescharacteristic
63C22×C4×D73C2311yescharacteristic
64C22×#10596831—41no—
65C22×#10596831—41no—
66C22×#10596831—41no—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C2×C8×D73—41no—
72C2×C8×D73—41no—
73C2×C8×D73—41no—
74#14556563C818yescomplemented
75C4×C22⋊D73—41no—
76C4×C22⋊D73—41no—
77C4×C22⋊D73—41no—
78C4×C22⋊D73—41no—
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×C22⋊Dic73C2×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×C4×Dic73—41no—
92C2×C4×Dic73—41no—
93C2×C4×Dic73C2×C411yescharacteristic
94C2×C4×Dic73C2×C411yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98#14556520—41no—
99#14556520—41no—
100#14556520—41no—
101C22⋊#10596831—41no—
102C22⋊#10596831—41no—
103C22⋊#10596831—41no—
104#14556503—41no—
105#14556503—41no—
106#14556503—41no—
107C8×Dic73—41no—
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114C22×D4×C73C2×C411yescharacteristic
115C23×C4×C73C2311yescharacteristic
116C23×C4×C73C2311yescharacteristic
117C22×C8×C73C2311yescharacteristic
118C22×C8×C73C2311yescharacteristic
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C4×D4×C73—41no—
122C4×D4×C73—41no—
123C2×C4⋊C4×C73C2×C411yescharacteristic
124C2×C22⋊C4×C73C2×C411yescharacteristic
125C2×C22⋊C4×C73C2×C411yescharacteristic
126C2×C42×C73C2311yescharacteristic
127C4⋊C8×C73—41no—
128C22⋊C8×C73—41no—
129C22⋊C8×C73—41no—
130C22⋊C8×C73—41no—
131C22⋊C8×C73—41no—
132C4×C8×C73—41no—
133C23×D73C22×C411yescharacteristic
134C2×C22⋊D73—41no—
135C2×C22⋊D73—41no—
136C2×C22⋊D73—41no—
137C2×C22⋊D73—41no—
138C2×C22⋊D73C2×C814yes—
139C2×C22⋊D73C2×C814yescomplemented
140C22×Dic73—41no—
141C22×Dic73—41no—
142C22×Dic73—41no—
143C22×Dic73—41no—
144C22×Dic73—41no—
145C22×Dic73C2×C814yescomplemented
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×D73—21no—
158C2×C4×D73—21no—
159C2×#10596831—21no—
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—44no—
172C8×D73—44no—
173#11924007—41no—
174#11924007—41no—
175#11924007—41no—
176#11924007C2×C814yescomplemented
177C22⋊Dic73—41no—
178C22⋊Dic73—41no—
179C22⋊Dic73—41no—
180C22⋊Dic73C2×C814yescomplemented
181#11924005—41no—
182#11924005—41no—
183#11924005—41no—
184#11924005C2×C814yescomplemented
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—41no—
192C4×Dic73—41no—
193C24×C73C22×C411yescharacteristic
194C24×C73C22×C411yescharacteristic
195C2×D4×C73—41no—
196C2×D4×C73—41no—
197C2×D4×C73C2×C814yescomplemented
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73C22×C411yescharacteristic
211C22×C4×C73C22×C411yescharacteristic
212C22×C4×C73C22×C411yescharacteristic
213C22×C4×C73C22×C411yescharacteristic
214C22×C4×C73C2411yescharacteristic
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C4⋊C4×C73—41no—
228C22⋊C4×C73—41no—
229C22⋊C4×C73—41no—
230C42×C73—21no—
231C42×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73C22×C812yes—
245C23×C73C22×C812yes—
246C23×C73C23×C411yescharacteristic
247C22×D73—21no—
248C22×D73—21no—
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73—21no—
253C22×D73C22×C812yes—
254D4×C73—44no—
255C2×C4×C73—21no—
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×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73C22×C812yes—
275C2×C4×C73H(5,𝔽2)11yescharacteristic
276C2×C4×C73H(5,𝔽2)11yescharacteristic
277C2×C4×C73H(5,𝔽2)11yescharacteristic
278C2×C4×C73H(5,𝔽2)11yescharacteristic
279C2×C4×C73H(5,𝔽2)11yescharacteristic
280C2×C4×C732−1+411yescharacteristic
281C22⋊D73—44no—
282C22⋊D73—44no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—21no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73—21no—
301C2×Dic73—44no—
302C2×Dic73—44no—
303C2×Dic73C22×C812yes—
304C2×Dic73C22×C812yes—
305C2×Dic73C22×C812yes—
306C4×D73—41no—
307C4×D73—41no—
308C4×D73—41no—
309C4×D73—41no—
310C8×C73—41no—
311C8×C73—41no—
312C8×C73—41no—
313C8×C73—41no—
314#10596831—41no—
315#10596831—41no—
316#10596831—41no—
317#10596831—41no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—22no—
322C22×C73—22no—
323C22×C73—22no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73#51811yescharacteristic
333C22×C73#51811yescharacteristic
334C22×C73#52011yescharacteristic
335C22×C73C23×C811yescharacteristic
336C22×C73#56811yescharacteristic
337C22×C73#56811yescharacteristic
338C22×C73#56811yescharacteristic
339C2×D73—22no—
340C2×D73—22no—
341C2×D73—22no—
342C2×D73—41no—
343C2×D73—41no—
344C2×D73—41no—
345C2×D73—41no—
346C4×C73—22no—
347C4×C73—41no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73#56011yescharacteristic
351C4×C73#56011yescharacteristic
352C4×C73#56211yescharacteristic
353C4×C73#56211yescharacteristic
354Dic73—22no—
355Dic73—22no—
356Dic73—22no—
357Dic73—41no—
358Dic73—41no—
359Dic73—41no—
360Dic73—41no—
361#23326—731nomaximal, Sylow
362C2×C73—42no—
363C2×C73—42no—
364C2×C73#237711yescharacteristic
365C2×C73#297211yescharacteristic
366C2×C73#297211yescharacteristic
367C2×C73#297811yescharacteristic
368C2×C73#298011yescharacteristic
369C2×C73#298811yescharacteristic
370C2×C73#299511yescharacteristic
371D73—42no—
372C4×#121—731no—
373#1954—731no—
374#1954D7311yescharacteristic, complemented
375#1923—731no—
376#1923—731no—
377#1916—731no—
378#1916—731no—
379#1869—731no—
380#1869—731no—
381#1869—731no—
382#1869—731no—
383#1850—731no—
384#1850—731no—
385#1817—731no—
386#1797—731no—
387C73#2332611yescharacteristic, complemented, Sylow
388C23×C8—731no—
389C23×C8—731no—
390C2×#121—731no—
391C2×C4×D4—731no—
392C2×C4×D4—731no—
393C2×C4×D4C2×D7311yescharacteristic
394C22×C42—731no—
395C2×C4⋊C8—731no—
396C2×C4⋊C8—731no—
397C2×C4⋊C8—731no—
398C2×C4⋊C8C2×D7311yescharacteristic
399C2×C22⋊C8—731no—
400C2×C22⋊C8—731no—
401C2×C22⋊C8—731no—
402C2×C22⋊C8—731no—
403C2×C22⋊C8—731no—
404C2×C22⋊C8—731no—
405C2×C22⋊C8C2×D7311yescharacteristic
406C2×C22⋊C8C2×D7311yescharacteristic
407C2×C22⋊C8C2×D7311yescharacteristic
408C2×C22⋊C8C2×D7311yescharacteristic
409C2×C4×C8—731no—
410C2×C4×C8C2×D7311yescharacteristic
411#390—731no—
412#389—731no—
413#388—731no—
414#388—731no—
415#386—731no—
416#386—731no—
417#380—731no—
418C4×C4⋊C4—731no—
419C4×C22⋊C4—731no—
420C4×C22⋊C4—731no—
421#336—731no—
422#336—731no—
423#336—731no—
424#336—731no—
425#336—731no—
426#336—731no—
427#336—731no—
428#336—731no—
429#336—731no—
430#336—731no—
431C22×D4—731no—
432C22×D4—731no—
433C22×D4C4×D7311yescharacteristic
434C23×C4—731no—
435C23×C4—731no—
436C23×C4—731no—
437C23×C4C22×D7311yescharacteristic
438C23×C4C22×D7311yescharacteristic
439C22×C8—2921no—
440C22×C8—2921no—
441C22×C8—2921no—
442C22×C8—2921no—
443C22×C8—2921no—
444C22×C8—2921no—
445C22×C8—731no—
446C22×C8—731no—
447C22×C8—731no—
448C22×C8—731no—
449C22×C8C22×D7311yescharacteristic
450C22×C8C22×D7311yescharacteristic
451C22×C8C22×D7311yescharacteristic
452C22×C8C22×D7311yescharacteristic
453#121—738no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—2921no—
457C4×D4—2921no—
458C4×D4—2921no—
459C4×D4—2921no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—731no—
463C2×C4⋊C4—731no—
464C2×C4⋊C4C4×D7311yescharacteristic
465C2×C22⋊C4—731no—
466C2×C22⋊C4—731no—
467C2×C22⋊C4—731no—
468C2×C22⋊C4—731no—
469C2×C22⋊C4—731no—
470C2×C22⋊C4—731no—
471C2×C22⋊C4—731no—
472C2×C22⋊C4—731no—
473C2×C22⋊C4C4×D7311yescharacteristic
474C2×C22⋊C4C4×D7311yescharacteristic
475C2×C42—2921no—
476C2×C42—2921no—
477C2×C42—731no—
478C2×C42—731no—
479C2×C42—731no—
480C2×C42—731no—
481C2×C42—731no—
482C2×C42C22×D7311yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—2921no—
485C4⋊C8—2921no—
486C4⋊C8—2921no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—2921no—
492C22⋊C8—2921no—
493C22⋊C8—2921no—
494C22⋊C8—2921no—
495C22⋊C8—2921no—
496C22⋊C8—2921no—
497C4×C8—41no—
498C4×C8—2921no—
499#95—731no—
500#95—731no—
501#95—731no—
502#95—731no—
503#95—731no—
504#95—731no—
505C24—731no—
506C24C2×C4×D7311yescharacteristic
507C24C2×C4×D7311yescharacteristic
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—2921no—
511C2×D4—2921no—
512C2×D4—2921no—
513C2×D4—2921no—
514C2×D4—734no—
515C2×D4—734no—
516C2×D4C8×D7314yescomplemented
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—2921no—
530C22×C4—2921no—
531C22×C4—2921no—
532C22×C4—2921no—
533C22×C4—2921no—
534C22×C4—734no—
535C22×C4—731no—
536C22×C4—731no—
537C22×C4—731no—
538C22×C4—731no—
539C22×C4—731no—
540C22×C4—731no—
541C22×C4—731no—
542C22×C4—1461no—
543C22×C4—1461no—
544C22×C4—1461no—
545C22×C4—1461no—
546C22×C4—1461no—
547C22×C4—1461no—
548C22×C4C2×C4×D7311yescharacteristic
549C22×C4C2×C4×D7311yescharacteristic
550C22×C4C2×C4×D7311yescharacteristic
551C22×C4C2×C4×D7311yescharacteristic
552C22×C4C23×D7311yescharacteristic
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—2924no—
566C2×C8—2924no—
567C2×C8—1461no—
568C2×C8—1461no—
569C2×C8—1461no—
570C2×C8—1461no—
571C2×C8—1461no—
572C2×C8—1461no—
573C2×C8—1461no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C4⋊C4—41no—
580C4⋊C4—2921no—
581C4⋊C4—2921no—
582C4⋊C4—2921no—
583C4⋊C4—734no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—2921no—
587C22⋊C4—2921no—
588C22⋊C4—2921no—
589C22⋊C4—2921no—
590C22⋊C4—2921no—
591C22⋊C4—2921no—
592C22⋊C4—734no—
593C22⋊C4—734no—
594C42—21no—
595C42—21no—
596C42—2921no—
597C42—2921no—
598C42—1461no—
599C42—1461no—
600C42—1461no—
601C42—1461no—
602C42—1461no—
603C42—1461no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—732no—
617C23—1461no—
618C23—1461no—
619C23—1461no—
620C23—1461no—
621C23—1461no—
622C23—1461no—
623C23C2×C8×D7312yes—
624C23C2×C8×D7312yes—
625C23C22×C4×D7311yescharacteristic
626D4—44no—
627D4—2924no—
628D4—2924no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—2924no—
649C2×C4—2921no—
650C2×C4—2921no—
651C2×C4—2921no—
652C2×C4—2921no—
653C2×C4—2924no—
654C2×C4—732no—
655C2×C4—732no—
656C2×C4—732no—
657C2×C4—1461no—
658C2×C4—1461no—
659C2×C4—1461no—
660C2×C4—1461no—
661C2×C4—1461no—
662C2×C4—1461no—
663C2×C4—1461no—
664C2×C4—1461no—
665C2×C4—1461no—
666C2×C4—1461no—
667C2×C4—1461no—
668C2×C4—1461no—
669C2×C4—1461no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1461no—
675C2×C4C2×C8×D7312yes—
676C2×C4#1455663611yescharacteristic
677C2×C4#1455663611yescharacteristic
678C2×C4#1455663611yescharacteristic
679C2×C4#1455663611yescharacteristic
680C2×C4#1455663711yescharacteristic
681C2×C4#1455663811yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—2921no—
687C8—2921no—
688C8—2921no—
689C8—2921no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—2921no—
705C22—2921no—
706C22—2921no—
707C22—2921no—
708C22—1462no—
709C22—1462no—
710C22—1462no—
711C22#1798905911yescharacteristic
712C22#1798906011yescharacteristic
713C22#1798906611yescharacteristic
714C22C22×C8×D7311yescharacteristic
715C22#1798935211yescharacteristic
716C22#1798935211yescharacteristic
717C22#1798935311yescharacteristic
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—2921no—
723C4—2921no—
724C4—2921no—
725C4—2921no—
726C4—1462no—
727C4—1462no—
728C4—1462no—
729C4#1798932411yescharacteristic
730C4#1798932511yescharacteristic
731C4#1798933111yescharacteristic
732C4#1798933211yescharacteristic
733C2—42no—
734C2—42no—
735C2—2922no—
736C2#2261308211yescharacteristic
737C2#2261895211yescharacteristic
738C2#2261895311yescharacteristic
739C2#2261898811yescharacteristic
740C2#2261900011yescharacteristic
741C2#2261903811yescharacteristic
742C2#2261909511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutatorC22×C73C23×C8
FittingC73×#1954C2
socleC23×C73C23×C4
prime radicalC2×#14556563C4
cosocleC22×C4×C73C24
hypercenter#1954D73
hypocenterC73#23326
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. #22610723C2semidirect
3. #22610540C2semidirect
4. #22610537C2semidirect
5. #22610488C2semidirect
6. #22610485C2semidirect
7. #22610224C2semidirect
8. #22610221C2semidirect
9. #22610220C2semidirect
10. #22610220C2semidirect
11. #22610108C2semidirect
12. #22610107C2semidirect
13. #22609997C2semidirect
14. #22609909C2semidirect
15. C73×#1954C2semidirect
74. #14556563C8semidirect
139. C2×C22⋊D73C2×C8semidirect
145. C22×Dic73C2×C8semidirect
176. #11924007C2×C8semidirect
180. C22⋊Dic73C2×C8semidirect
184. #11924005C2×C8semidirect
197. C2×D4×C73C2×C8semidirect
374. #1954D73semidirect
387. C73#23326semidirect
516. C2×D4C8×D73semidirect

Maximal subgroups

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

subgroupindex
C4×#145565632
#226107232
#226105402
#226105372
#226104882
#226104852
#226102242
#226102212
#226102202
#226101082
#226101072
#226099972
#226099092
C73×#19542
#2332673