Finite Group Databasebeta

← #33096040

Subgroups — #33096040

Order 18688.

950 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612312C211yesmaximal, characteristic
2#22610547C211yesmaximal, characteristic, complemented
3#22610546C211yesmaximal, characteristic, complemented
4#22610545C211yesmaximal, characteristic, complemented
5#22610542C211yesmaximal, characteristic, complemented
6#22610537C211yesmaximal, characteristic, complemented
7#22610536C211yesmaximal, characteristic, complemented
8#22610534C211yesmaximal, characteristic, complemented
9#22609914C211yesmaximal, characteristic, complemented
10#22609912C211yesmaximal, characteristic, complemented
11#22609840C211yesmaximal, characteristic
12#22609840C211yesmaximal, characteristic
13#22609698C211yesmaximal, characteristic, complemented
14#22609696C211yesmaximal, characteristic, complemented
15C73×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C2×#14556548C2211yescharacteristic
18C2×#14556548C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic, complemented
20C2×#14556520C2211yescharacteristic, complemented
21C2×#14556520C2211yescharacteristic, complemented
22C2×C22⋊#10596831C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×#14556503C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556502C2211yescharacteristic, complemented
33C2×#14556501C2211yescharacteristic, complemented
34C2×C8×Dic73C2211yescharacteristic, complemented
35#17988449C411yescharacteristic
36#17988449C411yescharacteristic
37#17988446C411yescharacteristic
38#17988446C411yescharacteristic
39#17988445C411yescharacteristic
40#17988445C411yescharacteristic
41#17988442C411yescharacteristic
42#17988442C411yescharacteristic
43C4×#11924005C2211yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46#17988342C2211yescharacteristic, complemented
47#17988342C2211yescharacteristic, complemented
48#17988341C2211yescharacteristic, complemented
49#17988341C2211yescharacteristic, complemented
50#17988341C2211yescharacteristic, complemented
51#17988341C2211yescharacteristic, complemented
52C2×C4⋊C8×C73C2211yescharacteristic, complemented
53C2×C22⋊C8×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C4×C8×C73C2211yescharacteristic, complemented
56C4×C22⋊C4×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic, complemented
58#336×C73C2211yescharacteristic, complemented
59C24×D73C2×C411yescharacteristic
60C23×Dic73C2×C411yescharacteristic
61C22×C4×D73—22no—
62C22×C4×D73—22no—
63C22×C4×D73—41no—
64C22×C4×D73—41no—
65C22×C4×D73—41no—
66C22×C4×D73—41no—
67C22×C4×D73C2×C411yescharacteristic
68C22×C4×D73C2×C411yescharacteristic
69C22×C4×D73C2311yescharacteristic
70C22×C4×D73C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75#14556548—41no—
76#14556548—41no—
77#14556548—41no—
78#14556548—41no—
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×C22⋊Dic73C2×C411yescharacteristic
84C2×C22⋊Dic73C2×C411yescharacteristic
85C2×#11924005C2×C411yescharacteristic
86C2×#11924005C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C4⋊#10596831—41no—
96#14556520—41no—
97#14556520—41no—
98C22⋊#10596831—41no—
99C22⋊#10596831—41no—
100#14556503—22no—
101#14556503—22no—
102#14556503—22no—
103#14556503—22no—
104#14556503—41no—
105#14556503—41no—
106#14556503—41no—
107#14556503—41no—
108#14556502—41no—
109#14556501—41no—
110C8×Dic73—41no—
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117C23×C4×C73C2311yescharacteristic
118C22×C8×C73C2311yescharacteristic
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C2×C22⋊C4×C73C2×C411yescharacteristic
123C2×C22⋊C4×C73C2×C411yescharacteristic
124C2×C42×C73C2311yescharacteristic
125C2×C42×C73C2311yescharacteristic
126C4⋊C8×C73—41no—
127C22⋊C8×C73—41no—
128C22⋊C8×C73—41no—
129C4×C8×C73—41no—
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132C23×D73—22no—
133C23×D73—22no—
134C23×D73—22no—
135C23×D73—41no—
136C23×D73—41no—
137C23×D73—41no—
138C23×D73—41no—
139C23×D73C22×C411yescharacteristic
140C23×D73C22×C411yescharacteristic
141C22×Dic73—22no—
142C22×Dic73—41no—
143C22×Dic73—41no—
144C22×Dic73C22×C411yescharacteristic
145C22×Dic73C22×C411yescharacteristic
146C22×Dic73C22×C411yescharacteristic
147C22×Dic73C22×C411yescharacteristic
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—22no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—22no—
162C2×C4×D73—44no—
163C2×C4×D73—44no—
164C2×C4×D73—44no—
165C2×C4×D73—44no—
166C2×C4×D73—41no—
167C2×C4×D73—41no—
168C2×C4×D73—41no—
169C2×C4×D73—41no—
170C2×C4×D73#4112yes—
171C2×C4×D73#4112yes—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C2×#10596831—21no—
181C2×#10596831—21no—
182C2×#10596831—21no—
183C2×#10596831—21no—
184#11924007—41no—
185#11924007—41no—
186#11924007—41no—
187#11924007—41no—
188C22⋊Dic73—22no—
189C22⋊Dic73—41no—
190#11924005—22no—
191#11924005—22no—
192#11924005—41no—
193#11924005—41no—
194#11924005—41no—
195#11924005—41no—
196#11924005—41no—
197#11924005—41no—
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C4×Dic73—21no—
202C24×C73C22×C411yescharacteristic
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×C73C22×C411yescharacteristic
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—
227C22⋊C4×C73—22no—
228C22⋊C4×C73—41no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73#13112yes—
240C23×C73C23×C411yescharacteristic
241C22×D73—21no—
242C22×D73—21no—
243C22×D73—21no—
244C22×D73—21no—
245C22×D73—21no—
246C22×D73—21no—
247C22×D73—21no—
248C22×D73—21no—
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73—21no—
253C22×D73—44no—
254C22×D73—44no—
255C22×D73—44no—
256C22×D73—44no—
257C22×D73—44no—
258C22×D73—44no—
259C22×D73—44no—
260C22×D73#11712yes—
261C22×D73#13112yes—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73C2×#4111yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73H(5,𝔽2)11yescharacteristic
284C2×C4×C73H(5,𝔽2)11yescharacteristic
285C2×C4×C73H(5,𝔽2)11yescharacteristic
286C2×C4×C73H(5,𝔽2)11yescharacteristic
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—21no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73—44no—
305C2×Dic73#11712yes—
306C4×D73—22no—
307C4×D73—22no—
308C4×D73—22no—
309C4×D73—22no—
310C4×D73—44no—
311C4×D73—44no—
312C4×D73—41no—
313C4×D73—41no—
314C4×D73—41no—
315C4×D73—41no—
316C8×C73—41no—
317C8×C73—41no—
318C8×C73—41no—
319C8×C73—41no—
320#10596831—41no—
321#10596831—41no—
322#10596831—41no—
323#10596831—41no—
324C22×C73—22no—
325C22×C73—22no—
326C22×C73—22no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73C2×#11711yescharacteristic
332C22×C73#51811yescharacteristic
333C22×C73#51811yescharacteristic
334C22×C73C2×#13111yescharacteristic
335C22×C73C2×#13111yescharacteristic
336C22×C73#56811yescharacteristic
337C22×C73#56811yescharacteristic
338C2×D73—22no—
339C2×D73—22no—
340C2×D73—22no—
341C2×D73—22no—
342C2×D73—22no—
343C2×D73—22no—
344C2×D73—416no—
345C2×D73—41no—
346C2×D73—41no—
347C2×D73—41no—
348C2×D73—41no—
349C2×D73—41no—
350C2×D73—41no—
351C2×D73—41no—
352C2×D73—41no—
353C4×C73—41no—
354C4×C73—41no—
355C4×C73—41no—
356C4×C73—41no—
357C4×C73—41no—
358C4×C73#53811yescharacteristic
359C4×C73#53811yescharacteristic
360C4×C73#53811yescharacteristic
361C4×C73#53811yescharacteristic
362Dic73—22no—
363Dic73—41no—
364Dic73—41no—
365Dic73—41no—
366Dic73—41no—
367Dic73—41no—
368#21908—731nomaximal, Sylow
369C2×C73—42no—
370C2×C73#231211yescharacteristic
371C2×C73#292411yescharacteristic
372C2×C73#292411yescharacteristic
373C2×C73#297611yescharacteristic
374C2×C73#297611yescharacteristic
375C2×C73#297711yescharacteristic
376C2×C73#297811yescharacteristic
377D73—42no—
378D73—42no—
379#2280—731no—
380#1924—731no—
381#1924—731no—
382#1924—731no—
383#1924—731no—
384#1923—731no—
385#1923—731no—
386#1923—731no—
387#1923D7311yescharacteristic, complemented
388#1798—731no—
389#1798—731no—
390#1779—731no—
391#1779—731no—
392#1750—731no—
393#1750—731no—
394C73#2190811yescharacteristic, complemented, Sylow
395C24×C4—731no—
396C2×#117—731no—
397C2×#117—731no—
398C2×C4⋊C8—731no—
399C2×C4⋊C8—731no—
400C2×C4⋊C8—731no—
401C2×C4⋊C8C2×D7311yescharacteristic, complemented
402C2×C22⋊C8—731no—
403C2×C22⋊C8—731no—
404C2×C22⋊C8—731no—
405C2×C22⋊C8—731no—
406C2×C22⋊C8—731no—
407C2×C22⋊C8—731no—
408C2×C22⋊C8—731no—
409C2×C22⋊C8—731no—
410C2×C22⋊C8—731no—
411C2×C22⋊C8—731no—
412C2×C22⋊C8C2×D7311yescharacteristic
413C2×C22⋊C8C2×D7311yescharacteristic
414C2×#97—731no—
415C2×#97—731no—
416C2×C4×C8—731no—
417C2×C4×C8C2×D7311yescharacteristic, complemented
418#381—731no—
419#381—731no—
420#380—731no—
421#380—731no—
422#380—731no—
423#380—731no—
424#379—731no—
425#379—731no—
426C4×C22⋊C4—731no—
427C4×C22⋊C4—731no—
428C4×C22⋊C4—731no—
429C4×C22⋊C4C2×D7311yescharacteristic
430#336—731no—
431#336—731no—
432#336—731no—
433#336—731no—
434#336—731no—
435#336—731no—
436#336C2×D7311yescharacteristic, complemented
437#336C2×D7311yescharacteristic, complemented
438C25—731no—
439C23×C4—2921no—
440C23×C4—2921no—
441C23×C4—2921no—
442C23×C4—2921no—
443C23×C4—731no—
444C23×C4—731no—
445C23×C4—731no—
446C23×C4—731no—
447C23×C4—731no—
448C23×C4—1462no—
449C23×C4—1462no—
450C23×C4C22×D7311yescharacteristic
451C22×C8—731no—
452C22×C8—731no—
453C22×C8—731no—
454C22×C8—731no—
455C22×C8C22×D7311yescharacteristic
456C22×C8C22×D7311yescharacteristic
457C22×C8C22×D7311yescharacteristic
458C22×C8C22×D7311yescharacteristic
459#117—2921no—
460#117—2921no—
461#117—2921no—
462#117—2921no—
463C2×C4⋊C4—731no—
464C2×C4⋊C4—731no—
465C2×C4⋊C4—731no—
466C2×C4⋊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⋊C4—731no—
474C2×C22⋊C4—731no—
475C2×C22⋊C4—731no—
476C2×C22⋊C4—731no—
477C2×C22⋊C4C4×D7311yescharacteristic
478C2×C22⋊C4C4×D7311yescharacteristic
479C2×C42—731no—
480C2×C42—731no—
481C2×C42C22×D7311yescharacteristic
482C2×C42C22×D7311yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—2921no—
485C4⋊C8—2921no—
486C4⋊C8—2921no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—2921no—
490C22⋊C8—2921no—
491C22⋊C8—2921no—
492C22⋊C8—2921no—
493C22⋊C8—2921no—
494C22⋊C8—2921no—
495C22⋊C8—1462no—
496C22⋊C8—1462no—
497C22⋊C8—1462no—
498C22⋊C8—1462no—
499#97—2921no—
500#97—2921no—
501C4×C8—41no—
502C4×C8—2921no—
503#95—731no—
504#95—731no—
505#95—731no—
506#95—731no—
507#95—731no—
508#95—731no—
509#95C4×D7311yescharacteristic
510#95C4×D7311yescharacteristic
511C24—2921no—
512C24—2921no—
513C24—2921no—
514C24—2921no—
515C24—731no—
516C24—731no—
517C24—1462no—
518C24—1462no—
519C24—1462no—
520C24C2×C4×D7311yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—2921no—
528C22×C4—2921no—
529C22×C4—2921no—
530C22×C4—2921no—
531C22×C4—2924no—
532C22×C4—2924no—
533C22×C4—2924no—
534C22×C4—2924no—
535C22×C4—2921no—
536C22×C4—2921no—
537C22×C4—731no—
538C22×C4—732no—
539C22×C4—732no—
540C22×C4—731no—
541C22×C4—731no—
542C22×C4—731no—
543C22×C4—731no—
544C22×C4—731no—
545C22×C4—1462no—
546C22×C4—1462no—
547C22×C4—1462no—
548C22×C4—1461no—
549C22×C4—1461no—
550C22×C4—1461no—
551C22×C4—1461no—
552C22×C4—1461no—
553C22×C4—1461no—
554C22×C4—1461no—
555C22×C4—1461no—
556C22×C4—1461no—
557C22×C4—1461no—
558C22×C4C2×C4×D7311yescharacteristic
559C22×C4C2×C4×D7311yescharacteristic
560C22×C4C2×C4×D7311yescharacteristic
561C22×C4C2×C4×D7311yescharacteristic
562C22×C4C2×C4×D7311yescharacteristic
563C22×C4C23×D7311yescharacteristic
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C2×C8—1461no—
580C2×C8—1461no—
581C2×C8—1461no—
582C2×C8—1461no—
583C2×C8—1461no—
584C2×C8—1461no—
585C2×C8—1461no—
586C2×C8—1461no—
587C2×C8—1461no—
588C4⋊C4—2921no—
589C4⋊C4—2921no—
590C4⋊C4—2921no—
591C4⋊C4—2921no—
592C22⋊C4—22no—
593C22⋊C4—41no—
594C22⋊C4—2921no—
595C22⋊C4—2921no—
596C22⋊C4—2921no—
597C22⋊C4—2921no—
598C22⋊C4—2921no—
599C22⋊C4—2921no—
600C22⋊C4—2921no—
601C22⋊C4—1462no—
602C22⋊C4—1462no—
603C22⋊C4—1462no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—1461no—
609C42—1461no—
610C42—1461no—
611C42—1461no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—2924no—
619C23—2924no—
620C23—2924no—
621C23—2924no—
622C23—2924no—
623C23—2924no—
624C23—2924no—
625C23—732no—
626C23—732no—
627C23—1461no—
628C23—1461no—
629C23—1461no—
630C23—1461no—
631C23—1461no—
632C23—1461no—
633C23—1461no—
634C23—1461no—
635C23—1461no—
636C23—1461no—
637C23—1461no—
638C23—1461no—
639C23#1455659712yes—
640C23C22×C4×D7311yescharacteristic
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—2924no—
661C2×C4—2924no—
662C2×C4—2924no—
663C2×C4—2921no—
664C2×C4—2921no—
665C2×C4—2921no—
666C2×C4—2921no—
667C2×C4—732no—
668C2×C4—1461no—
669C2×C4—1461no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1461no—
675C2×C4—1461no—
676C2×C4—1461no—
677C2×C4—1461no—
678C2×C4—1461no—
679C2×C4—1461no—
680C2×C4—1461no—
681C2×C4—1461no—
682C2×C4—1461no—
683C2×C4—1461no—
684C2×C4—1461no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4#41×D7311yescharacteristic
690C2×C4#41×D7311yescharacteristic
691C2×C4#1455663611yescharacteristic
692C2×C4#1455663611yescharacteristic
693C2×C4#1455663711yescharacteristic
694C2×C4#1455663711yescharacteristic
695C8—41no—
696C8—41no—
697C8—41no—
698C8—41no—
699C8—2921no—
700C8—2921no—
701C8—2921no—
702C8—2921no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—29216no—
711C22—2921no—
712C22—2921no—
713C22—2921no—
714C22—2921no—
715C22—2921no—
716C22—2921no—
717C22—2921no—
718C22—2921no—
719C22—1462no—
720C22—1462no—
721C22—1462no—
722C22—1462no—
723C22—1462no—
724C22—1462no—
725C22#117×D7311yescharacteristic
726C22#1798905911yescharacteristic
727C22#1798905911yescharacteristic
728C22#131×D7311yescharacteristic
729C22C2×#1455659711yescharacteristic
730C22#1798935211yescharacteristic
731C22#1798935311yescharacteristic
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—2921no—
738C4—2921no—
739C4—2921no—
740C4—2921no—
741C4—2921no—
742C4—1462no—
743C4#1798916911yescharacteristic
744C4#1798917111yescharacteristic
745C4#1798917311yescharacteristic
746C4#1798917611yescharacteristic
747C2—42no—
748C2—2922no—
749C2—2922no—
750C2#2261252511yescharacteristic
751C2#2261858411yescharacteristic
752C2#2261858711yescharacteristic
753C2#2261897311yescharacteristic
754C2#2261897811yescharacteristic
755C2#2261898411yescharacteristic
756C2#2261898811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1923C2
prime radicalC24×D73C2×C4
cosocleC22×C4×C73C24
hypercenter#1923D73
hypocenterC73#21908
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #22610547C2semidirect
3. #22610546C2semidirect
4. #22610545C2semidirect
5. #22610542C2semidirect
6. #22610537C2semidirect
7. #22610536C2semidirect
8. #22610534C2semidirect
9. #22609914C2semidirect
10. #22609912C2semidirect
13. #22609698C2semidirect
14. #22609696C2semidirect
15. C73×#1923C2semidirect
19. C2×C4⋊#10596831C22semidirect
20. C2×#14556520C22semidirect
21. C2×#14556520C22semidirect
32. C2×#14556502C22semidirect
33. C2×#14556501C22semidirect
34. C2×C8×Dic73C22semidirect
46. #17988342C22semidirect
47. #17988342C22semidirect
48. #17988341C22semidirect
49. #17988341C22semidirect
50. #17988341C22semidirect
51. #17988341C22semidirect
52. C2×C4⋊C8×C73C22semidirect
55. C2×C4×C8×C73C22semidirect
57. #336×C73C22semidirect
58. #336×C73C22semidirect
387. #1923D73semidirect
394. C73#21908semidirect
401. C2×C4⋊C8C2×D73semidirect
417. C2×C4×C8C2×D73semidirect
436. #336C2×D73semidirect
437. #336C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226123122
#226105472
#226105462
#226105452
#226105422
#226105372
#226105362
#226105342
#226099142
#226099122
#226098402
#226096982
#226096962
C73×#19232
#2190873