Finite Group Databasebeta

← #33088901

Subgroups — #33088901

Order 18688.

906 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988644C211yesmaximal, characteristic, complemented
2C2×#17988543C211yesmaximal, characteristic, complemented
3#22610546C211yesmaximal, characteristic, complemented
4#22610539C211yesmaximal, characteristic, complemented
5#22610497C211yesmaximal, characteristic, complemented
6#22610490C211yesmaximal, characteristic, complemented
7#22610229C211yesmaximal, characteristic
8#22610224C211yesmaximal, characteristic
9#22610116C211yesmaximal, characteristic, complemented
10#22610111C211yesmaximal, characteristic, complemented
11#22609788C211yesmaximal, characteristic, complemented
12#22609697C211yesmaximal, characteristic, complemented
13C4×C22⋊#10596831C211yesmaximal, characteristic, complemented
14#22609683C211yesmaximal, characteristic, complemented
15C73×#2290C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18#17988644—24no—
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29#17988543—24no—
30C2×#14556502C2211yescharacteristic
31C2×#14556502C2211yescharacteristic
32C2×#14556502C2211yescharacteristic
33C2×C4×#10596831C2211yescharacteristic
34C2×C4×#10596831C2211yescharacteristic
35C2×C4×#10596831C2211yescharacteristic
36#17988342C2211yescharacteristic
37#17988342C2211yescharacteristic
38#17988342C2211yescharacteristic
39#17988342C2211yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46C2×C4×D4×C73C2211yescharacteristic
47C2×#117×C73C2211yescharacteristic
48C22×C42×C73C2211yescharacteristic
49#388×C73C411yescharacteristic
50#388×C73C411yescharacteristic
51#387×C73C411yescharacteristic
52#387×C73C411yescharacteristic
53#386×C73C411yescharacteristic
54#386×C73C411yescharacteristic
55#385×C73C411yescharacteristic
56#385×C73C411yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C22⋊C4×C73C2211yescharacteristic
59C4×C22⋊C4×C73C2211yescharacteristic
60#376×C73C2211yescharacteristic
61C2×#11924012—22no—
62C2×#11924012—22no—
63C2×#11924012—22no—
64C22×#10596831—22no—
65C22×#10596831—22no—
66C22×#10596831—22no—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C4⋊#10596831—22no—
76C4⋊#10596831—22no—
77C4⋊#10596831—22no—
78C4⋊#10596831—22no—
79C22⋊#10596831—22no—
80C22⋊#10596831—22no—
81C22⋊#10596831—22no—
82C22⋊#10596831—22no—
83C22⋊#10596831—22no—
84C22⋊#10596831—22no—
85#14556502—22no—
86#14556502—22no—
87#14556502D414yescomplemented
88C4×#10596831—22no—
89C4×#10596831—22no—
90C4×#10596831—22no—
91C22×D4×C73C2×C411yescharacteristic
92C23×C4×C73C2×C411yescharacteristic
93C23×C4×C73C2×C411yescharacteristic
94C23×C4×C73C2311yescharacteristic
95C23×C4×C73C2311yescharacteristic
96C4×D4×C73—22no—
97C4×D4×C73—22no—
98#117×C73—22no—
99#117×C73—22no—
100C2×C4⋊C4×C73C2×C411yescharacteristic
101C2×C4⋊C4×C73C2×C411yescharacteristic
102C2×C4⋊C4×C73C2×C411yescharacteristic
103C2×C4⋊C4×C73C2×C411yescharacteristic
104C2×C4⋊C4×C73C2×C411yescharacteristic
105C2×C22⋊C4×C73C2×C411yescharacteristic
106C2×C22⋊C4×C73C2×C411yescharacteristic
107C2×C22⋊C4×C73C2×C411yescharacteristic
108C2×C22⋊C4×C73C2×C411yescharacteristic
109C2×C22⋊C4×C73C2×C411yescharacteristic
110C2×C22⋊C4×C73C2×C411yescharacteristic
111C2×C22⋊C4×C73C2×C411yescharacteristic
112C2×C22⋊C4×C73C2×C411yescharacteristic
113C2×C42×C73—22no—
114C2×C42×C73—22no—
115C2×C42×C73C2×C411yescharacteristic
116C2×C42×C73C2×C411yescharacteristic
117C2×C42×C73C2311yescharacteristic
118C2×C42×C73C2311yescharacteristic
119C2×C42×C73C2311yescharacteristic
120C2×C42×C73C2311yescharacteristic
121C2×C42×C73C2311yescharacteristic
122#95×C73C2×C411yescharacteristic
123#95×C73C2×C411yescharacteristic
124#95×C73C2×C411yescharacteristic
125#95×C73C2×C411yescharacteristic
126#95×C73C2×C411yescharacteristic
127#95×C73C2×C411yescharacteristic
128#95×C73C2×C411yescharacteristic
129#95×C73C2×C411yescharacteristic
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132#11924012—28no—
133C2×#10596831—28no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831C2×D412yes—
155C2×#10596831C2×D412yes—
156C2×#10596831#4112yes—
157C2×#10596831#4112yes—
158C24×C73C22×C411yescharacteristic
159C24×C73C22×C411yescharacteristic
160C2×D4×C73—22no—
161C2×D4×C73—22no—
162C2×D4×C73—41no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—22no—
168C22×C4×C73—22no—
169C22×C4×C73—22no—
170C22×C4×C73—22no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—41no—
178C22×C4×C73—41no—
179C22×C4×C73C22×C411yescharacteristic
180C22×C4×C73C22×C411yescharacteristic
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C22×C411yescharacteristic
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73#4112yes—
192C22×C4×C73#4112yes—
193C22×C4×C73C2411yescharacteristic
194C4⋊C4×C73—22no—
195C4⋊C4×C73—22no—
196C4⋊C4×C73—22no—
197C4⋊C4×C73—22no—
198C4⋊C4×C73—41no—
199C22⋊C4×C73—22no—
200C22⋊C4×C73—22no—
201C22⋊C4×C73—22no—
202C22⋊C4×C73—22no—
203C22⋊C4×C73—22no—
204C22⋊C4×C73—22no—
205C22⋊C4×C73—41no—
206C22⋊C4×C73—41no—
207C42×C73—22no—
208C42×C73—22no—
209C42×C73—21no—
210C42×C73—21no—
211C42×C73—21no—
212C42×C73—21no—
213C42×C73—21no—
214C42×C73—21no—
215C42×C73—21no—
216C42×C73—21no—
217C42×C73C2×D412yes—
218C42×C73#4112yes—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73#11712yes—
232C23×C73#13112yes—
233C23×C73C23×C411yescharacteristic
234D4×C73—44no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—22no—
244C2×C4×C73—22no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
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—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—44no—
272C2×C4×C73—44no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73#11712yes—
278C2×C4×C73C4×D412yes—
279C2×C4×C73C4×D412yes—
280C2×C4×C73#13112yes—
281C2×C4×C73C22×D411yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×C4×C73C2×#4111yescharacteristic
285C2×C4×C73C2×#4111yescharacteristic
286C2×C4×C73C2×#4111yescharacteristic
287#10596831—22no—
288#10596831—22no—
289#10596831—22no—
290#10596831—22no—
291#10596831—41no—
292#10596831—41no—
293#10596831—41no—
294#10596831—41no—
295C22×C73—22no—
296C22×C73—22no—
297C22×C73—22no—
298C22×C73—22no—
299C22×C73—22no—
300C22×C73—22no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73—41no—
304C22×C73—41no—
305C22×C73—41no—
306C22×C73—41no—
307C22×C73—41no—
308C22×C73—41no—
309C22×C73C2×#11711yescharacteristic
310C22×C73C2×C4×D411yescharacteristic
311C22×C73C4×#4111yescharacteristic
312C22×C73C2×#13111yescharacteristic
313C22×C73C2×#13111yescharacteristic
314C22×C73#56811yescharacteristic
315C22×C73#56811yescharacteristic
316C4×C73—22no—
317C4×C73—22no—
318C4×C73—22no—
319C4×C73—22no—
320C4×C73—41no—
321C4×C73—41no—
322C4×C73—41no—
323C4×C73—41no—
324C4×C73—41no—
325C4×C73—41no—
326C4×C73—41no—
327C4×C73—41no—
328C4×C73#52511yescharacteristic
329C4×C73#52511yescharacteristic
330C4×C73#52911yescharacteristic
331C4×C73#52911yescharacteristic
332#21112—731nomaximal, Sylow
333C2×C73—42no—
334C2×C73—42no—
335C2×C73#229011yescharacteristic
336C2×C73#292411yescharacteristic
337C2×C73#292511yescharacteristic
338C2×C73#293311yescharacteristic
339C2×C73#293311yescharacteristic
340C2×C73#296611yescharacteristic
341C2×C73#296711yescharacteristic
342C2×#432—731no—
343C2×#405—731no—
344#2290D7311yescharacteristic
345#1924—731no—
346#1923—731no—
347#1917—731no—
348#1916—731no—
349#1870—731no—
350#1869—731no—
351#1851—731no—
352#1850—731no—
353#1768—731no—
354#1750—731no—
355C4×C22⋊C8—731no—
356#1746—731no—
357C73#2111211yescharacteristic, complemented, Sylow
358C22×M16—731no—
359C23×C8—731no—
360C2×C4×D4C2×D7311yescharacteristic
361C2×#117C2×D7311yescharacteristic
362C22×C42C2×D7311yescharacteristic
363#432—1464no—
364C2×C4⋊C8—731no—
365C2×C4⋊C8—731no—
366C2×C4⋊C8—731no—
367C2×C4⋊C8—731no—
368C2×C22⋊C8—731no—
369C2×C22⋊C8—731no—
370C2×C22⋊C8—731no—
371C2×C22⋊C8—731no—
372C2×C22⋊C8—731no—
373C2×C22⋊C8—731no—
374#405—1464no—
375C2×#97—731no—
376C2×#97—731no—
377C2×#97—731no—
378C2×C4×C8—731no—
379C2×C4×C8—731no—
380C2×C4×C8—731no—
381#388Dic7311yescharacteristic
382#388Dic7311yescharacteristic
383#387Dic7311yescharacteristic
384#387Dic7311yescharacteristic
385#386Dic7311yescharacteristic
386#386Dic7311yescharacteristic
387#385Dic7311yescharacteristic
388#385Dic7311yescharacteristic
389C4×C4⋊C4C2×D7311yescharacteristic
390C4×C22⋊C4C2×D7311yescharacteristic
391C4×C22⋊C4C2×D7311yescharacteristic
392#376C2×D7311yescharacteristic
393#336—731no—
394#336—731no—
395#336—731no—
396#336—731no—
397#336—731no—
398#336—731no—
399#336—731no—
400#336—731no—
401#336—731no—
402#336—731no—
403C22×D4C2×Dic7311yescharacteristic
404C23×C4C2×Dic7311yescharacteristic
405C23×C4C2×Dic7311yescharacteristic
406C23×C4C22×D7311yescharacteristic
407C23×C4C22×D7311yescharacteristic
408C2×M16—1462no—
409C2×M16—1462no—
410C2×M16—1462no—
411C22×C8—731no—
412C22×C8—731no—
413C22×C8—731no—
414C22×C8—731no—
415C22×C8—731no—
416C22×C8—731no—
417C22×C8—731no—
418C22×C8—731no—
419C22×C8—1462no—
420C22×C8—1462no—
421C22×C8—1462no—
422C4×D4—22no—
423C4×D4—22no—
424#117—22no—
425#117—22no—
426C2×C4⋊C4C2×Dic7311yescharacteristic
427C2×C4⋊C4C2×Dic7311yescharacteristic
428C2×C4⋊C4C2×Dic7311yescharacteristic
429C2×C4⋊C4C2×Dic7311yescharacteristic
430C2×C4⋊C4C2×Dic7311yescharacteristic
431C2×C22⋊C4C2×Dic7311yescharacteristic
432C2×C22⋊C4C2×Dic7311yescharacteristic
433C2×C22⋊C4C2×Dic7311yescharacteristic
434C2×C22⋊C4C2×Dic7311yescharacteristic
435C2×C22⋊C4C2×Dic7311yescharacteristic
436C2×C22⋊C4C2×Dic7311yescharacteristic
437C2×C22⋊C4C2×Dic7311yescharacteristic
438C2×C22⋊C4C2×Dic7311yescharacteristic
439C2×C42—22no—
440C2×C42—22no—
441C2×C42C2×Dic7311yescharacteristic
442C2×C42C2×Dic7311yescharacteristic
443C2×C42C22×D7311yescharacteristic
444C2×C42C22×D7311yescharacteristic
445C2×C42C22×D7311yescharacteristic
446C2×C42C22×D7311yescharacteristic
447C2×C42C22×D7311yescharacteristic
448C4⋊C8—1462no—
449C4⋊C8—1462no—
450C4⋊C8—1462no—
451C4⋊C8—1462no—
452C22⋊C8—1462no—
453C22⋊C8—1462no—
454C22⋊C8—1462no—
455C22⋊C8—1462no—
456C22⋊C8—1462no—
457C22⋊C8—1462no—
458#97—734no—
459#97—1462no—
460#97—1462no—
461C4×C8—1462no—
462C4×C8—1462no—
463C4×C8—1462no—
464#95C2×Dic7311yescharacteristic
465#95C2×Dic7311yescharacteristic
466#95C2×Dic7311yescharacteristic
467#95C2×Dic7311yescharacteristic
468#95C2×Dic7311yescharacteristic
469#95C2×Dic7311yescharacteristic
470#95C2×Dic7311yescharacteristic
471#95C2×Dic7311yescharacteristic
472#95C2×Dic7311yescharacteristic
473#95C2×Dic7311yescharacteristic
474C24C22×Dic7311yescharacteristic
475C24C22×Dic7311yescharacteristic
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—41no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4C22×Dic7311yescharacteristic
496C22×C4C22×Dic7311yescharacteristic
497C22×C4C22×Dic7311yescharacteristic
498C22×C4C22×Dic7311yescharacteristic
499C22×C4C22×Dic7311yescharacteristic
500C22×C4C22×Dic7311yescharacteristic
501C22×C4C22×Dic7311yescharacteristic
502C22×C4C22×Dic7311yescharacteristic
503C22×C4C22×Dic7311yescharacteristic
504C22×C4C22×Dic7311yescharacteristic
505C22×C4C22×Dic7311yescharacteristic
506C22×C4C22×Dic7311yescharacteristic
507C22×C4#1192402812yes—
508C22×C4#1192402812yes—
509C22×C4C23×D7311yescharacteristic
510M16—1468no—
511C2×C8—732no—
512C2×C8—732no—
513C2×C8—732no—
514C2×C8—732no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C2×C8—1461no—
520C2×C8—1461no—
521C2×C8—1461no—
522C2×C8—1461no—
523C2×C8—1461no—
524C2×C8—1461no—
525C2×C8—1461no—
526C2×C8—1461no—
527C2×C8—1468no—
528C2×C8—1461no—
529C2×C8—1461no—
530C2×C8—1461no—
531C2×C8—1461no—
532C2×C8—1461no—
533C2×C8—1461no—
534C2×C8—1461no—
535C2×C8—1461no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—41no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C42—22no—
550C42—22no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42D4×D7312yes—
560C42#1192402712yes—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#1455655012yes—
574C23#1455659812yes—
575C23C23×Dic7311yescharacteristic
576D4—44no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—44no—
614C2×C4—44no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4#1455655012yes—
620C2×C4D4×Dic7312yes—
621C2×C4D4×Dic7312yes—
622C2×C4#1455659812yes—
623C2×C4C2×D4×D7311yescharacteristic
624C2×C4#41×D7311yescharacteristic
625C2×C4#41×D7311yescharacteristic
626C2×C4C2×#1192402711yescharacteristic
627C2×C4C2×#1192402811yescharacteristic
628C2×C4C2×#1192402811yescharacteristic
629C8—2921no—
630C8—2921no—
631C8—2921no—
632C8—2921no—
633C8—1462no—
634C8—1462no—
635C8—1462no—
636C8—1462no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×#1455655011yescharacteristic
652C22C2×D4×Dic7311yescharacteristic
653C22#41×Dic7311yescharacteristic
654C22C2×#1455659811yescharacteristic
655C22C2×#1455659811yescharacteristic
656C22#1798935411yescharacteristic
657C22#1798935411yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4#1798909611yescharacteristic
671C4#1798909611yescharacteristic
672C4#1798911711yescharacteristic
673C4#1798911711yescharacteristic
674C2—42no—
675C2—42no—
676C2#2261237611yescharacteristic
677C2#2261858911yescharacteristic
678C2#2261859711yescharacteristic
679C2#2261865811yescharacteristic
680C2#2261865811yescharacteristic
681C2#2261890711yescharacteristic
682C2#2261891811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#2290C2
prime radicalC22×D4×C73C2×C4
cosocleC22×C4×C73C24
hypercenter#2290D73
hypocenterC73#21112
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
1. C2×#17988644C2semidirect
2. C2×#17988543C2semidirect
3. #22610546C2semidirect
4. #22610539C2semidirect
5. #22610497C2semidirect
6. #22610490C2semidirect
9. #22610116C2semidirect
10. #22610111C2semidirect
11. #22609788C2semidirect
12. #22609697C2semidirect
13. C4×C22⋊#10596831C2semidirect
14. #22609683C2semidirect
87. #14556502D4semidirect
357. C73#21112semidirect

Maximal subgroups

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

subgroupindex
C2×#179886442
C2×#179885432
#226105462
#226105392
#226104972
#226104902
#226102292
#226102242
#226101162
#226101112
#226097882
#226096972
C4×C22⋊#105968312
#226096832
C73×#22902
#2111273