Finite Group Databasebeta

← #33103823

Subgroups — #33103823

Order 18688.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610655C211yesmaximal, characteristic, complemented
2#22610650C211yesmaximal, characteristic, complemented
3#22610497C211yesmaximal, characteristic, complemented
4#22610490C211yesmaximal, characteristic, complemented
5#22610490C211yesmaximal, characteristic, complemented
6#22610490C211yesmaximal, characteristic, complemented
7#22609915C211yesmaximal, characteristic
8#22609915C211yesmaximal, characteristic
9#22609911C211yesmaximal, characteristic
10#22609806C211yesmaximal, characteristic, complemented
11C4⋊C4×#10596831C211yesmaximal, characteristic, complemented
12#22609697C211yesmaximal, characteristic
13#22609697C211yesmaximal, characteristic
14C4×C22⋊#10596831C211yesmaximal, characteristic
15C73×#2296C211yesmaximal, characteristic
16C2×C4⋊#10596831C2211yescharacteristic
17C2×C4⋊#10596831C2211yescharacteristic
18C2×C4⋊#10596831C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C22⋊#10596831C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×#14556502C2211yescharacteristic
27C2×#14556502C2211yescharacteristic
28C2×C4×#10596831C2211yescharacteristic
29C2×C4×#10596831C2211yescharacteristic
30C2×C4×#10596831C2211yescharacteristic
31C2×C4×#10596831C2211yescharacteristic
32#17988342C2211yescharacteristic
33#17988342C2211yescharacteristic
34#17988342C2211yescharacteristic
35#17988342C2211yescharacteristic
36#17988342C2211yescharacteristic
37#17988342C2211yescharacteristic
38#17988342C2211yescharacteristic
39#17988342C2211yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44C2×#117×C73C2211yescharacteristic
45C2×#117×C73C2211yescharacteristic
46C22×C42×C73C2211yescharacteristic
47#389×C73C411yescharacteristic
48#389×C73C411yescharacteristic
49#389×C73C411yescharacteristic
50#389×C73C411yescharacteristic
51#385×C73C411yescharacteristic
52#385×C73C411yescharacteristic
53#385×C73C411yescharacteristic
54#385×C73C411yescharacteristic
55C4×C4⋊C4×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59C22×#10596831C2311yescharacteristic
60C22×#10596831C2311yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C4⋊#10596831—22no—
68C4⋊#10596831—22no—
69C4⋊#10596831—41no—
70C4⋊#10596831—41no—
71C4⋊#10596831—41no—
72C4⋊#10596831—41no—
73C22⋊#10596831—22no—
74C22⋊#10596831—22no—
75C22⋊#10596831—22no—
76C22⋊#10596831Q814yes—
77#14556502—22no—
78#14556502—41no—
79C4×#10596831—22no—
80C4×#10596831—41no—
81C4×#10596831—41no—
82C4×#10596831—41no—
83C23×C4×C73C2×C411yescharacteristic
84C23×C4×C73C2×C411yescharacteristic
85C23×C4×C73C2311yescharacteristic
86#117×C73—22no—
87#117×C73—22no—
88#117×C73—41no—
89#117×C73—41no—
90C2×C4⋊C4×C73C2×C411yescharacteristic
91C2×C4⋊C4×C73C2×C411yescharacteristic
92C2×C4⋊C4×C73C2×C411yescharacteristic
93C2×C4⋊C4×C73C2×C411yescharacteristic
94C2×C4⋊C4×C73C2×C411yescharacteristic
95C2×C4⋊C4×C73C2×C411yescharacteristic
96C2×C4⋊C4×C73C2×C411yescharacteristic
97C2×C4⋊C4×C73C2×C411yescharacteristic
98C2×C4⋊C4×C73C2×C411yescharacteristic
99C2×C4⋊C4×C73C2×C411yescharacteristic
100C2×C4⋊C4×C73C2×C411yescharacteristic
101C2×C4⋊C4×C73C2×C411yescharacteristic
102C2×C22⋊C4×C73C2×C411yescharacteristic
103C2×C22⋊C4×C73C2×C411yescharacteristic
104C2×C22⋊C4×C73C2×C411yescharacteristic
105C2×C22⋊C4×C73C2×C411yescharacteristic
106C2×C42×C73—41no—
107C2×C42×C73—41no—
108C2×C42×C73C2×C411yescharacteristic
109C2×C42×C73C2×C411yescharacteristic
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116#95×C73C2×C411yescharacteristic
117#95×C73C2×C411yescharacteristic
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120#95×C73C2×C411yescharacteristic
121#95×C73C2×C411yescharacteristic
122#95×C73C2×C411yescharacteristic
123#95×C73C2×C411yescharacteristic
124C2×#10596831—21no—
125C2×#10596831—21no—
126C2×#10596831—21no—
127C2×#10596831—21no—
128C2×#10596831—21no—
129C2×#10596831—21no—
130C2×#10596831—21no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
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×#10596831C2×Q812yes—
147C2×#10596831C2×Q812yes—
148C24×C73C22×C411yescharacteristic
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—22no—
154C22×C4×C73—22no—
155C22×C4×C73—22no—
156C22×C4×C73—41no—
157C22×C4×C73—41no—
158C22×C4×C73—41no—
159C22×C4×C73C22×C411yescharacteristic
160C22×C4×C73C22×C411yescharacteristic
161C22×C4×C73C22×C411yescharacteristic
162C22×C4×C73C22×C411yescharacteristic
163C22×C4×C73C22×C411yescharacteristic
164C22×C4×C73C22×C411yescharacteristic
165C22×C4×C73C22×C411yescharacteristic
166C22×C4×C73C22×C411yescharacteristic
167C22×C4×C73C22×C411yescharacteristic
168C22×C4×C73C22×C411yescharacteristic
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C22×C411yescharacteristic
171C22×C4×C73C22×C411yescharacteristic
172C22×C4×C73C2×Q812yes—
173C22×C4×C73#4112yes—
174C22×C4×C73C2411yescharacteristic
175C4⋊C4×C73—22no—
176C4⋊C4×C73—22no—
177C4⋊C4×C73—22no—
178C4⋊C4×C73—22no—
179C4⋊C4×C73—22no—
180C4⋊C4×C73—22no—
181C4⋊C4×C73—22no—
182C4⋊C4×C73—22no—
183C4⋊C4×C73—41no—
184C4⋊C4×C73—41no—
185C4⋊C4×C73—41no—
186C4⋊C4×C73—41no—
187C22⋊C4×C73—22no—
188C22⋊C4×C73—22no—
189C22⋊C4×C73—41no—
190C22⋊C4×C73—41no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—21no—
195C42×C73—21no—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73—21no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73—41no—
202C42×C73—41no—
203C42×C73#4112yes—
204C42×C73#4112yes—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73—21no—
208C23×C73—21no—
209C23×C73—21no—
210C23×C73—21no—
211C23×C73C4×Q812yes—
212C23×C73C23×C411yescharacteristic
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—22no—
226C2×C4×C73—22no—
227C2×C4×C73—22no—
228C2×C4×C73—22no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
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—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—44no—
251C2×C4×C73—44no—
252C2×C4×C73#11712yes—
253C2×C4×C73#11712yes—
254C2×C4×C73C4×Q812yes—
255C2×C4×C73#13112yes—
256C2×C4×C73#13112yes—
257C2×C4×C73#13112yes—
258C2×C4×C73C22×Q811yescharacteristic
259C2×C4×C73C2×#4111yescharacteristic
260C2×C4×C73C2×#4111yescharacteristic
261C2×C4×C73C2×#4111yescharacteristic
262C2×C4×C73H(5,𝔽2)11yescharacteristic
263C2×C4×C73H(5,𝔽2)11yescharacteristic
264#10596831—22no—
265#10596831—22no—
266#10596831—41no—
267#10596831—41no—
268#10596831—41no—
269#10596831—41no—
270#10596831—41no—
271#10596831—41no—
272C22×C73—22no—
273C22×C73—22no—
274C22×C73—22no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73—41no—
279C22×C73C2×#11711yescharacteristic
280C22×C73C2×C4×Q811yescharacteristic
281C22×C73#51811yescharacteristic
282C22×C73C2×#13111yescharacteristic
283C22×C73C2×#13111yescharacteristic
284C22×C73C2×#13111yescharacteristic
285C22×C73#56811yescharacteristic
286C4×C73—22no—
287C4×C73—22no—
288C4×C73—22no—
289C4×C73—22no—
290C4×C73—22no—
291C4×C73—22no—
292C4×C73—41no—
293C4×C73—41no—
294C4×C73—41no—
295C4×C73—41no—
296C4×C73—41no—
297C4×C73—41no—
298C4×C73—41no—
299C4×C73#55311yescharacteristic
300C4×C73#55311yescharacteristic
301C4×C73#55411yescharacteristic
302C4×C73#55411yescharacteristic
303#22630—731nomaximal, Sylow
304C2×C73—42no—
305C2×C73#234511yescharacteristic
306C2×C73#292211yescharacteristic
307C2×C73#292511yescharacteristic
308C2×C73#296011yescharacteristic
309C2×C73#296211yescharacteristic
310C2×C73#297611yescharacteristic
311C2×C73#297711yescharacteristic
312#2296D7311yescharacteristic
313#1940—731no—
314#1939—731no—
315#1917—731no—
316#1916—731no—
317#1916—731no—
318#1916—731no—
319#1798—731no—
320#1798—731no—
321#1797—731no—
322#1771—731no—
323C8×C4⋊C4—731no—
324#1750—731no—
325#1750—731no—
326C4×C22⋊C8—731no—
327C73#2263011yescharacteristic, complemented, Sylow
328C2×#117C2×D7311yescharacteristic
329C2×#117C2×D7311yescharacteristic
330C22×C42C2×D7311yescharacteristic
331C2×C4⋊C8—731no—
332C2×C4⋊C8—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C2×C4⋊C8—731no—
336C2×C4⋊C8—731no—
337C2×C22⋊C8—731no—
338C2×C22⋊C8—731no—
339C2×C22⋊C8—731no—
340C2×C22⋊C8—731no—
341C2×#97—731no—
342C2×#97—731no—
343C2×C4×C8—731no—
344C2×C4×C8—731no—
345C2×C4×C8—731no—
346C2×C4×C8—731no—
347#389Dic7311yescharacteristic
348#389Dic7311yescharacteristic
349#389Dic7311yescharacteristic
350#389Dic7311yescharacteristic
351#385Dic7311yescharacteristic
352#385Dic7311yescharacteristic
353#385Dic7311yescharacteristic
354#385Dic7311yescharacteristic
355C4×C4⋊C4C2×D7311yescharacteristic
356C4×C4⋊C4C2×D7311yescharacteristic
357C4×C4⋊C4C2×D7311yescharacteristic
358C4×C4⋊C4C2×D7311yescharacteristic
359#336—731no—
360#336—731no—
361#336—731no—
362#336—731no—
363#336—731no—
364#336—731no—
365#336—731no—
366#336—731no—
367#336—731no—
368#336—731no—
369#336—731no—
370#336—731no—
371C23×C4C2×Dic7311yescharacteristic
372C23×C4C2×Dic7311yescharacteristic
373C23×C4C22×D7311yescharacteristic
374C22×C8—731no—
375C22×C8—731no—
376C22×C8—731no—
377C22×C8—731no—
378C22×C8—731no—
379C22×C8—731no—
380C22×C8—731no—
381C22×C8—731no—
382#117—22no—
383#117—22no—
384#117—41no—
385#117—41no—
386C2×C4⋊C4C2×Dic7311yescharacteristic
387C2×C4⋊C4C2×Dic7311yescharacteristic
388C2×C4⋊C4C2×Dic7311yescharacteristic
389C2×C4⋊C4C2×Dic7311yescharacteristic
390C2×C4⋊C4C2×Dic7311yescharacteristic
391C2×C4⋊C4C2×Dic7311yescharacteristic
392C2×C4⋊C4C2×Dic7311yescharacteristic
393C2×C4⋊C4C2×Dic7311yescharacteristic
394C2×C4⋊C4C2×Dic7311yescharacteristic
395C2×C4⋊C4C2×Dic7311yescharacteristic
396C2×C4⋊C4C2×Dic7311yescharacteristic
397C2×C4⋊C4C2×Dic7311yescharacteristic
398C2×C22⋊C4C2×Dic7311yescharacteristic
399C2×C22⋊C4C2×Dic7311yescharacteristic
400C2×C22⋊C4C2×Dic7311yescharacteristic
401C2×C22⋊C4C2×Dic7311yescharacteristic
402C2×C42—41no—
403C2×C42—41no—
404C2×C42C2×Dic7311yescharacteristic
405C2×C42C2×Dic7311yescharacteristic
406C2×C42C22×D7311yescharacteristic
407C2×C42C22×D7311yescharacteristic
408C2×C42C22×D7311yescharacteristic
409C2×C42C22×D7311yescharacteristic
410C2×C42C22×D7311yescharacteristic
411C2×C42C22×D7311yescharacteristic
412C4⋊C8—2921no—
413C4⋊C8—2921no—
414C4⋊C8—2921no—
415C4⋊C8—2921no—
416C4⋊C8—1462no—
417C4⋊C8—1462no—
418C22⋊C8—734no—
419C22⋊C8—1462no—
420C22⋊C8—1462no—
421C22⋊C8—1462no—
422#97—2921no—
423#97—1462no—
424C4×C8—2921no—
425C4×C8—2921no—
426C4×C8—2921no—
427C4×C8—1462no—
428#95C2×Dic7311yescharacteristic
429#95C2×Dic7311yescharacteristic
430#95C2×Dic7311yescharacteristic
431#95C2×Dic7311yescharacteristic
432#95C2×Dic7311yescharacteristic
433#95C2×Dic7311yescharacteristic
434#95C2×Dic7311yescharacteristic
435#95C2×Dic7311yescharacteristic
436C24C22×Dic7311yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4C22×Dic7311yescharacteristic
448C22×C4C22×Dic7311yescharacteristic
449C22×C4C22×Dic7311yescharacteristic
450C22×C4C22×Dic7311yescharacteristic
451C22×C4C22×Dic7311yescharacteristic
452C22×C4C22×Dic7311yescharacteristic
453C22×C4C22×Dic7311yescharacteristic
454C22×C4C22×Dic7311yescharacteristic
455C22×C4C22×Dic7311yescharacteristic
456C22×C4C22×Dic7311yescharacteristic
457C22×C4C22×Dic7311yescharacteristic
458C22×C4C22×Dic7311yescharacteristic
459C22×C4C22×Dic7311yescharacteristic
460C22×C4Q8×D7312yes—
461C22×C4#1192402912yes—
462C22×C4C23×D7311yescharacteristic
463C2×C8—732no—
464C2×C8—732no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8—1461no—
478C2×C8—1461no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—41no—
514C42—41no—
515C42#1192402812yes—
516C42#1192402812yes—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23Q8×Dic7312yes—
524C23C23×Dic7311yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4#1455655012yes—
565C2×C4#1455655012yes—
566C2×C4Q8×Dic7312yes—
567C2×C4#1455659812yes—
568C2×C4#1455659812yes—
569C2×C4#1455659812yes—
570C2×C4C2×Q8×D7311yescharacteristic
571C2×C4C2×#1192402811yescharacteristic
572C2×C4C2×#1192402811yescharacteristic
573C2×C4C2×#1192402911yescharacteristic
574C2×C4#1455663611yescharacteristic
575C2×C4#1455663611yescharacteristic
576C8—2921no—
577C8—2921no—
578C8—2921no—
579C8—2921no—
580C8—2921no—
581C8—2921no—
582C8—1462no—
583C8—1462no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C2×#1455655011yescharacteristic
592C22C2×Q8×Dic7311yescharacteristic
593C22#1798906211yescharacteristic
594C22C2×#1455659811yescharacteristic
595C22C2×#1455659811yescharacteristic
596C22C2×#1455659811yescharacteristic
597C22#1798935411yescharacteristic
598C4—22no—
599C4—22no—
600C4—22no—
601C4—22no—
602C4—22no—
603C4—22no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4#1798928511yescharacteristic
612C4#1798928511yescharacteristic
613C4#1798929211yescharacteristic
614C4#1798929211yescharacteristic
615C2—42no—
616C2#2261280811yescharacteristic
617C2#2261857511yescharacteristic
618C2#2261859711yescharacteristic
619C2#2261886611yescharacteristic
620C2#2261888011yescharacteristic
621C2#2261897911yescharacteristic
622C2#2261898711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#2296C2
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenter#2296D73
hypocenterC73#22630
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #2296

Complements

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

NH ≅ G/Ntype
1. #22610655C2semidirect
2. #22610650C2semidirect
3. #22610497C2semidirect
4. #22610490C2semidirect
5. #22610490C2semidirect
6. #22610490C2semidirect
10. #22609806C2semidirect
11. C4⋊C4×#10596831C2semidirect
327. C73#22630semidirect

Maximal subgroups

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

subgroupindex
#226106552
#226106502
#226104972
#226104902
#226099152
#226099112
#226098062
C4⋊C4×#105968312
#226096972
C4×C22⋊#105968312
C73×#22962
#2263073