Finite Group Databasebeta

← #33097993

Subgroups — #33097993

Order 18688.

786 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988715C211yesmaximal, characteristic, complemented
2C4×#14556570C211yesmaximal, characteristic
3#22610871C211yesmaximal, characteristic, complemented
4#22610654C211yesmaximal, characteristic, complemented
5#22610651C211yesmaximal, characteristic, complemented
6#22610646C211yesmaximal, characteristic, complemented
7#22610547C211yesmaximal, characteristic
8#22610541C211yesmaximal, characteristic
9#22610540C211yesmaximal, characteristic
10#22610534C211yesmaximal, characteristic
11#22610492C211yesmaximal, characteristic, complemented
12#22610485C211yesmaximal, characteristic, complemented
13#22609911C211yesmaximal, characteristic
14#22609803C211yesmaximal, characteristic, complemented
15C2×#432×C73C211yesmaximal, characteristic
16C2×#14556570C411yescharacteristic
17C2×C4×Dic146C2211yescharacteristic
18#17988715—24no—
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×#14556501C2211yescharacteristic
28C2×#14556501C2211yescharacteristic
29C2×C8×Dic73C2211yescharacteristic
30C2×C8×Dic73C2211yescharacteristic
31#17988493C411yescharacteristic
32#17988485C411yescharacteristic
33#17988471C411yescharacteristic
34#17988471C411yescharacteristic
35#17988460C411yescharacteristic
36#17988460C411yescharacteristic
37#17988447C411yescharacteristic
38C4×#11924007C2211yescharacteristic
39C4×#11924007C2211yescharacteristic
40C4×C4⋊Dic73C2211yescharacteristic
41C4×C22⋊Dic73C2211yescharacteristic
42C4×C22⋊Dic73C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53C22×C42×C73C2211yescharacteristic
54#432×C73—24no—
55C2×C4⋊C8×C73C2211yescharacteristic
56C2×C4⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×#97×C73C2211yescharacteristic
60C2×#97×C73C2211yescharacteristic
61C22×Dic146C2×C411yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66#14556570—24no—
67C4×Dic146—22no—
68C4×Dic146—22no—
69C2×C4⋊Dic73C2×C411yescharacteristic
70C2×C4⋊Dic73C2×C411yescharacteristic
71C2×C4⋊Dic73C2×C411yescharacteristic
72C2×#11924007C2×C411yescharacteristic
73C2×#11924007C2×C411yescharacteristic
74C2×#11924007C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×C22⋊Dic73C2×C411yescharacteristic
79C2×C22⋊Dic73C2×C411yescharacteristic
80C2×C22⋊Dic73C2×C411yescharacteristic
81C2×C22⋊Dic73C2×C411yescharacteristic
82C2×C4×Dic73C2311yescharacteristic
83C2×C4×Dic73C2311yescharacteristic
84C2×C4×Dic73C2311yescharacteristic
85C2×C4×Dic73C2311yescharacteristic
86C4⋊#10596831—22no—
87C4⋊#10596831—22no—
88#14556520—22no—
89#14556520—22no—
90#14556520—41no—
91#14556520—41no—
92C22⋊#10596831—41no—
93C22⋊#10596831—41no—
94#14556501—22no—
95#14556501—41no—
96C8×Dic73—22no—
97C8×Dic73—41no—
98#14556498C2×C411yescharacteristic
99#14556498C2×C411yescharacteristic
100#14556498C2×C411yescharacteristic
101#14556498C2×C411yescharacteristic
102#14556498C2×C411yescharacteristic
103#14556498C2×C411yescharacteristic
104#14556498C2×C411yescharacteristic
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107#14556498C2×C411yescharacteristic
108C23×C4×C73C2×C411yescharacteristic
109C23×C4×C73C2×C411yescharacteristic
110C23×C4×C73C2311yescharacteristic
111C22×C8×C73C2311yescharacteristic
112C22×C8×C73C2311yescharacteristic
113C22×C8×C73C2311yescharacteristic
114C22×C8×C73C2311yescharacteristic
115C2×C42×C73—22no—
116C2×C42×C73—22no—
117C2×C42×C73C2×C411yescharacteristic
118C2×C42×C73C2×C411yescharacteristic
119C2×C42×C73C2311yescharacteristic
120C2×C42×C73C2311yescharacteristic
121C4⋊C8×C73—22no—
122C4⋊C8×C73—22no—
123C22⋊C8×C73—22no—
124C22⋊C8×C73—22no—
125#97×C73—22no—
126#97×C73D414yes—
127C2×Dic146—22no—
128C2×Dic146—22no—
129C2×Dic146—41no—
130C22×Dic73C22×C411yescharacteristic
131C22×Dic73C22×C411yescharacteristic
132C22×Dic73C22×C411yescharacteristic
133C22×Dic73C22×C411yescharacteristic
134C22×Dic73C22×C411yescharacteristic
135C22×Dic73C22×C411yescharacteristic
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
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—
150C4⋊Dic73—22no—
151C4⋊Dic73—22no—
152C4⋊Dic73—41no—
153#11924007—22no—
154#11924007—22no—
155#11924007—22no—
156#11924007—22no—
157#11924007—22no—
158#11924007—22no—
159C22⋊Dic73—22no—
160C22⋊Dic73—41no—
161C22⋊Dic73—41no—
162C22⋊Dic73M1614yes—
163C4×Dic73—21no—
164C4×Dic73—21no—
165C4×Dic73—21no—
166C4×Dic73—21no—
167C4×Dic73—21no—
168C4×Dic73—21no—
169C4×Dic73—21no—
170C4×Dic73—21no—
171C24×C73C22×C411yescharacteristic
172C22×C4×C73—22no—
173C22×C4×C73—22no—
174C22×C4×C73—22no—
175C22×C4×C73—22no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—41no—
183C22×C4×C73—41no—
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C2411yescharacteristic
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73C2×D412yes—
201C2×C8×C73C2×D412yes—
202C42×C73—22no—
203C42×C73—22no—
204C42×C73—21no—
205C42×C73—21no—
206C42×C73C2×D412yes—
207C42×C73#4112yes—
208C23×C73—21no—
209C23×C73—21no—
210C23×C73—21no—
211C23×C73—21no—
212C23×C73—21no—
213C23×C73—21no—
214C23×C73C2×M1612yes—
215C23×C73C23×C411yescharacteristic
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—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—44no—
229C2×C4×C73—44no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73C4×D412yes—
235C2×C4×C73C4×D412yes—
236C2×C4×C73#13112yes—
237C2×C4×C73C22×D411yescharacteristic
238C2×C4×C73C2×#4111yescharacteristic
239C2×C4×C73H(5,𝔽2)11yescharacteristic
240C2×C4×C732−1+411yescharacteristic
241C2×C4×C732−1+411yescharacteristic
242C2×C4×C732−1+411yescharacteristic
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265C2×Dic73C2×M1612yes—
266C2×Dic73C2×M1612yes—
267Dic146—44no—
268C8×C73—22no—
269C8×C73—22no—
270C8×C73—41no—
271C8×C73—41no—
272#10596831—41no—
273#10596831—41no—
274#10596831—41no—
275#10596831—41no—
276C22×C73—22no—
277C22×C73—22no—
278C22×C73—22no—
279C22×C73—41no—
280C22×C73—41no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73C2×C4×D411yescharacteristic
284C22×C73#51911yescharacteristic
285C22×C73#52011yescharacteristic
286C22×C73C22×M1611yescharacteristic
287C22×C73C2×#13111yescharacteristic
288C22×C73#56811yescharacteristic
289C22×C73#56811yescharacteristic
290C4×C73—22no—
291C4×C73—22no—
292C4×C73—22no—
293C4×C73—41no—
294C4×C73—41no—
295C4×C73#53611yescharacteristic
296C4×C73#53711yescharacteristic
297C4×C73#54111yescharacteristic
298C4×C73#54211yescharacteristic
299Dic73—22no—
300Dic73—22no—
301Dic73—41no—
302Dic73—41no—
303Dic73—41no—
304Dic73—41no—
305Dic73—41no—
306Dic73—41no—
307#22108—731nomaximal, Sylow
308C2×C73—42no—
309C2×C73#232311yescharacteristic
310C2×C73#293311yescharacteristic
311C2×C73D4×M1611yescharacteristic
312C2×C73#298311yescharacteristic
313C2×C73#298511yescharacteristic
314C2×C73#299011yescharacteristic
315C2×C73#299511yescharacteristic
316C2×#446—731no—
317C2×#432D7311yescharacteristic
318C4×C22⋊Q8—731no—
319#1985—731no—
320#1940—731no—
321#1940—731no—
322#1939—731no—
323#1924—731no—
324#1924—731no—
325#1923—731no—
326#1923—731no—
327#1917—731no—
328#1916—731no—
329#1797—731no—
330#1771—731no—
331C73#2210811yescharacteristic, complemented, Sylow
332C2×C22⋊Q8—731no—
333C2×C4×Q8—731no—
334C22×C42C2×D7311yescharacteristic
335#446—1464no—
336#432—24no—
337C2×C4⋊C8—731no—
338C2×C4⋊C8—731no—
339C2×C4⋊C8—731no—
340C2×C4⋊C8—731no—
341C2×C4⋊C8—731no—
342C2×C4⋊C8—731no—
343C2×C4⋊C8C2×D7311yescharacteristic
344C2×C4⋊C8C2×D7311yescharacteristic
345C2×C22⋊C8—731no—
346C2×C22⋊C8—731no—
347C2×C22⋊C8C2×D7311yescharacteristic
348C2×C22⋊C8C2×D7311yescharacteristic
349C2×#97—731no—
350C2×#97—731no—
351C2×#97C2×D7311yescharacteristic
352C2×#97C2×D7311yescharacteristic
353C2×C4×C8—731no—
354C2×C4×C8—731no—
355#391—731no—
356#389—731no—
357#387—731no—
358#387—731no—
359#385—731no—
360#385—731no—
361#380—731no—
362C4×C4⋊C4—731no—
363C4×C4⋊C4—731no—
364C4×C4⋊C4—731no—
365C4×C22⋊C4—731no—
366C4×C22⋊C4—731no—
367#336—731no—
368#336—731no—
369#336—731no—
370#336—731no—
371#336—731no—
372#336—731no—
373#336—731no—
374#336—731no—
375#336—731no—
376#336—731no—
377C22×Q8—731no—
378C23×C4C4×D7311yescharacteristic
379C23×C4C4×D7311yescharacteristic
380C23×C4C22×D7311yescharacteristic
381C22×C8—731no—
382C22×C8—731no—
383C22×C8—731no—
384C22×C8—731no—
385C22×C8C22×D7311yescharacteristic
386C22×C8C22×D7311yescharacteristic
387C22×C8C22×D7311yescharacteristic
388C22×C8C22×D7311yescharacteristic
389C22⋊Q8—1464no—
390C4×Q8—1462no—
391C4×Q8—1462no—
392C2×C4⋊C4—731no—
393C2×C4⋊C4—731no—
394C2×C4⋊C4—731no—
395C2×C4⋊C4—731no—
396C2×C4⋊C4—731no—
397C2×C4⋊C4—731no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4—731no—
400C2×C4⋊C4—731no—
401C2×C22⋊C4—731no—
402C2×C22⋊C4—731no—
403C2×C22⋊C4—731no—
404C2×C22⋊C4—731no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—731no—
408C2×C42—731no—
409C2×C42—731no—
410C2×C42—731no—
411C2×C42C4×D7311yescharacteristic
412C2×C42C4×D7311yescharacteristic
413C2×C42C22×D7311yescharacteristic
414C2×C42C22×D7311yescharacteristic
415C4⋊C8—22no—
416C4⋊C8—22no—
417C4⋊C8—2921no—
418C4⋊C8—2921no—
419C4⋊C8—1462no—
420C4⋊C8—1462no—
421C4⋊C8—1462no—
422C4⋊C8—1462no—
423C22⋊C8—22no—
424C22⋊C8—22no—
425C22⋊C8—2921no—
426C22⋊C8—2921no—
427#97—22no—
428#97—2921no—
429#97—1462no—
430#97C22⋊D7314yes—
431C4×C8—2921no—
432C4×C8—1462no—
433#95—731no—
434#95—731no—
435#95—731no—
436#95—731no—
437#95—731no—
438#95—731no—
439#95—731no—
440#95—731no—
441#95—731no—
442#95—731no—
443C24C2×C4×D7311yescharacteristic
444C2×Q8—2921no—
445C2×Q8—1462no—
446C2×Q8—1462no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—731no—
460C22×C4—731no—
461C22×C4—731no—
462C22×C4—731no—
463C22×C4—731no—
464C22×C4—731no—
465C22×C4—731no—
466C22×C4—731no—
467C22×C4C2×C4×D7311yescharacteristic
468C22×C4C2×C4×D7311yescharacteristic
469C22×C4C2×C4×D7311yescharacteristic
470C22×C4C2×C4×D7311yescharacteristic
471C22×C4C2×C4×D7311yescharacteristic
472C22×C4C23×D7311yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8—1461no—
494C2×C8—1461no—
495C2×C8C2×C22⋊D7312yes—
496C2×C8C2×C22⋊D7312yes—
497C4⋊C4—2921no—
498C4⋊C4—1462no—
499C4⋊C4—1462no—
500C4⋊C4—1462no—
501C4⋊C4—1462no—
502C4⋊C4—1462no—
503C4⋊C4—1462no—
504C4⋊C4—1462no—
505C4⋊C4—1462no—
506C22⋊C4—2921no—
507C22⋊C4—2921no—
508C22⋊C4—734no—
509C22⋊C4—1462no—
510C42—22no—
511C42—22no—
512C42—21no—
513C42—21no—
514C42—1461no—
515C42—1461no—
516C42—1461no—
517C42—1461no—
518C42—1461no—
519C42—1461no—
520C42—1461no—
521C42—1461no—
522C42C2×C22⋊D7312yes—
523C42#1192402812yes—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23M16×D7312yes—
531C23C22×C4×D7311yescharacteristic
532Q8—2924no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—732no—
552C2×C4—732no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4—1461no—
556C2×C4—1461no—
557C2×C4—1461no—
558C2×C4—1461no—
559C2×C4—1461no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4—1461no—
573C2×C4—1461no—
574C2×C4—1461no—
575C2×C4C4×C22⋊D7312yes—
576C2×C4C4×C22⋊D7312yes—
577C2×C4#1455659912yes—
578C2×C4C22×C22⋊D7311yescharacteristic
579C2×C4C2×#1192402811yescharacteristic
580C2×C4#1455663711yescharacteristic
581C2×C4#1455663811yescharacteristic
582C2×C4#1455663811yescharacteristic
583C2×C4#1455663811yescharacteristic
584C8—22no—
585C8—22no—
586C8—41no—
587C8—41no—
588C8—2921no—
589C8—2921no—
590C8—2921no—
591C8—2921no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22C2×C4×C22⋊D7311yescharacteristic
600C22#1798906411yescharacteristic
601C22#1798906711yescharacteristic
602C22C2×M16×D7311yescharacteristic
603C22C2×#1455659911yescharacteristic
604C22#1798935311yescharacteristic
605C22#1798935311yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—41no—
610C4—41no—
611C4—2921no—
612C4—2921no—
613C4—2921no—
614C4—2921no—
615C4—2921no—
616C4—2921no—
617C4—1462no—
618C4—1462no—
619C4#1798915811yescharacteristic
620C4#1798916511yescharacteristic
621C4#1798919911yescharacteristic
622C4#1798920811yescharacteristic
623C2—42no—
624C2#2261261311yescharacteristic
625C2#2261865611yescharacteristic
626C2M16×C22⋊D7311yescharacteristic
627C2#2261901511yescharacteristic
628C2#2261902811yescharacteristic
629C2#2261905811yescharacteristic
630C2#2261910311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#432×C73C2
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenterC2×#432D73
hypocenterC73#22108
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#17988715C2semidirect
3. #22610871C2semidirect
4. #22610654C2semidirect
5. #22610651C2semidirect
6. #22610646C2semidirect
11. #22610492C2semidirect
12. #22610485C2semidirect
14. #22609803C2semidirect
331. C73#22108semidirect

Maximal subgroups

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

subgroupindex
C2×#179887152
C4×#145565702
#226108712
#226106542
#226106512
#226106462
#226105472
#226105412
#226105402
#226105342
#226104922
#226104852
#226099112
#226098032
C2×#432×C732
#2210873