Finite Group Databasebeta

← #33096491

Subgroups — #33096491

Order 18688.

774 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988647C211yesmaximal, characteristic
2C2×#17988612C211yesmaximal, characteristic
3#22612428C211yesmaximal, characteristic
4#22610653C211yesmaximal, characteristic, complemented
5#22610653C211yesmaximal, characteristic, complemented
6#22610648C211yesmaximal, characteristic, complemented
7#22610648C211yesmaximal, characteristic, complemented
8#22610115C211yesmaximal, characteristic
9#22610115C211yesmaximal, characteristic
10#22610110C211yesmaximal, characteristic
11#22610110C211yesmaximal, characteristic
12#22610084C211yesmaximal, characteristic, complemented
13#22610083C211yesmaximal, characteristic, complemented
14#22610050C211yesmaximal, characteristic, complemented
15C73×#1831C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×#14556548C2211yescharacteristic
19#17988647—24no—
20#17988612—24no—
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×C4⋊#10596831C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×C4⋊#10596831C2211yescharacteristic
27C2×#14556520C2211yescharacteristic
28C2×#14556520C2211yescharacteristic
29C2×#14556520C2211yescharacteristic
30C2×#14556520C2211yescharacteristic
31C2×#14556520C2211yescharacteristic
32C2×#14556520C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556503C2211yescharacteristic
35C2×#14556501C2211yescharacteristic
36C2×C8×Dic73C2211yescharacteristic
37#17988478C411yescharacteristic
38#17988478C411yescharacteristic
39#17988478C411yescharacteristic
40#17988478C411yescharacteristic
41#17988471C411yescharacteristic
42#17988471C411yescharacteristic
43#17988471C411yescharacteristic
44#17988471C411yescharacteristic
45C4×#11924007C2211yescharacteristic
46C4×#11924007C2211yescharacteristic
47C4×#11924005C2211yescharacteristic
48C4×#11924005C2211yescharacteristic
49#17988433C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55C2×C4⋊C8×C73C2211yescharacteristic
56C43×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×C4×D73C2311yescharacteristic
62C2×#11924011—22no—
63C2×#11924011—41no—
64C2×#11924011—41no—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C2×C8×D73—22no—
70C2×C8×D73—41no—
71C2×C8×D73—41no—
72#14556548D414yes—
73#14556548Q814yes—
74C2×#11924007C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×#11924005C2×C411yescharacteristic
81C2×#11924005C2×C411yescharacteristic
82C2×#11924005C2×C411yescharacteristic
83C2×#11924005C2×C411yescharacteristic
84C2×#11924005C2×C411yescharacteristic
85C2×#11924005C2×C411yescharacteristic
86C2×C4×Dic73C2311yescharacteristic
87C2×C4×Dic73C2311yescharacteristic
88C2×C4×Dic73C2311yescharacteristic
89C4⋊#10596831—22no—
90C4⋊#10596831—22no—
91C4⋊#10596831—41no—
92C4⋊#10596831—41no—
93C4⋊#10596831—41no—
94C4⋊#10596831—41no—
95#14556520—22no—
96#14556520—22no—
97#14556520—41no—
98#14556520—41no—
99#14556520—41no—
100#14556520—41no—
101#14556503—22no—
102#14556503—22no—
103#14556501—22no—
104C8×Dic73—22no—
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107#14556498C2×C411yescharacteristic
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117C22×C8×C73C2311yescharacteristic
118C22×C8×C73C2311yescharacteristic
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C2×C42×C73C2×C411yescharacteristic
122C2×C42×C73C2×C411yescharacteristic
123C2×C42×C73C2×C411yescharacteristic
124C2×C42×C73C2×C411yescharacteristic
125C2×C42×C73C2311yescharacteristic
126C2×C42×C73C2311yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C4⋊C8×C73—22no—
129C4⋊C8×C73—22no—
130C23×D73C22×C411yescharacteristic
131C22×Dic73C22×C411yescharacteristic
132C22×Dic73C22×C411yescharacteristic
133C22×Dic73C22×C411yescharacteristic
134C22×Dic73C22×C411yescharacteristic
135C22×Dic73C22×C411yescharacteristic
136C22×Dic73C22×C411yescharacteristic
137C22×Dic73C22×C411yescharacteristic
138C2×C4×D73—21no—
139C2×C4×D73—21no—
140C2×C4×D73—21no—
141C2×C4×D73—21no—
142C2×C4×D73C2×D412yes—
143C2×C4×D73C2×Q812yes—
144#11924011—44no—
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×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C8×D73—44no—
158#11924007—22no—
159#11924007—22no—
160#11924007—41no—
161#11924007—41no—
162#11924007C4⋊C414yes—
163#11924007C4⋊C414yes—
164#11924005—22no—
165#11924005—22no—
166#11924005—41no—
167#11924005—41no—
168#11924005C4⋊C414yes—
169#11924005C4⋊C414yes—
170C4×Dic73—21no—
171C4×Dic73—21no—
172C4×Dic73—21no—
173C4×Dic73—21no—
174C4×Dic73C2×D412yes—
175C4×Dic73C2×Q812yes—
176C22×C4×C73C22×C411yescharacteristic
177C22×C4×C73C22×C411yescharacteristic
178C22×C4×C73C22×C411yescharacteristic
179C22×C4×C73C22×C411yescharacteristic
180C22×C4×C73C22×C411yescharacteristic
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C2411yescharacteristic
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C42×C73—22no—
196C42×C73—22no—
197C42×C73—21no—
198C42×C73—21no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73—41no—
202C42×C73—41no—
203C42×C73C2×D412yes—
204C42×C73C2×Q812yes—
205C23×C73C23×C411yescharacteristic
206C22×D73—21no—
207C22×D73—21no—
208C22×D73—21no—
209C22×D73—21no—
210C22×D73—21no—
211C22×D73—21no—
212C22×D73C2×C4⋊C412yes—
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—21no—
226C2×C4×C73—21no—
227C2×C4×C73C2×C4⋊C412yes—
228C2×C4×C73C2×C4⋊C412yes—
229C2×C4×C73#13112yes—
230C2×C4×C73#13112yes—
231C2×C4×C73C22×D411yescharacteristic
232C2×C4×C73C22×Q811yescharacteristic
233C2×C4×C73H(5,𝔽2)11yescharacteristic
234C2×C4×C73H(5,𝔽2)11yescharacteristic
235C2×C4×C732−1+411yescharacteristic
236C2×C4×C732−1+411yescharacteristic
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
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×Dic73C2×C4⋊C412yes—
256C2×Dic73C2×C4⋊C412yes—
257C2×Dic73C2×C4⋊C412yes—
258C4×D73—22no—
259C4×D73—22no—
260C4×D73—22no—
261C4×D73—22no—
262C8×C73—41no—
263C8×C73—41no—
264C8×C73—41no—
265C8×C73—41no—
266#10596831—41no—
267#10596831—41no—
268#10596831—41no—
269#10596831—41no—
270C22×C73C22×C4⋊C411yescharacteristic
271C22×C73#52011yescharacteristic
272C22×C73#52011yescharacteristic
273C22×C73C2×#13111yescharacteristic
274C22×C73C2×#13111yescharacteristic
275C22×C73#56811yescharacteristic
276C22×C73#56811yescharacteristic
277C2×D73—22no—
278C2×D73—22no—
279C2×D73—22no—
280C2×D73—41no—
281C2×D73—41no—
282C2×D73—41no—
283C2×D73—41no—
284C4×C73—22no—
285C4×C73—22no—
286C4×C73—22no—
287C4×C73—22no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73#53511yescharacteristic
291C4×C73#53611yescharacteristic
292C4×C73#54411yescharacteristic
293C4×C73#54411yescharacteristic
294Dic73—22no—
295Dic73—22no—
296Dic73—22no—
297Dic73—41no—
298Dic73—41no—
299Dic73—41no—
300Dic73—41no—
301#21980—731nomaximal, Sylow
302C2×C73#231711yescharacteristic
303C2×C73#290611yescharacteristic
304C2×C73#290611yescharacteristic
305C2×C73#299211yescharacteristic
306C2×C73#299311yescharacteristic
307C2×C73#299411yescharacteristic
308C2×C73#299511yescharacteristic
309D73—42no—
310C2×#433—731no—
311C2×#424—731no—
312#2298—731no—
313#1940—731no—
314#1940—731no—
315#1939—731no—
316#1939—731no—
317#1851—731no—
318#1851—731no—
319#1850—731no—
320#1850—731no—
321#1843—731no—
322#1842—731no—
323#1832—731no—
324#1831D7311yescharacteristic, complemented
325C73#2198011yescharacteristic, complemented, Sylow
326C22×M16—731no—
327C23×C8—731no—
328C2×#117—731no—
329#433—1464no—
330#424—1464no—
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×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×#97—731no—
348C2×C4×C8—731no—
349#388—731no—
350#388—731no—
351#388—731no—
352#388—731no—
353#387—731no—
354#387—731no—
355#387—731no—
356#387—731no—
357C4×C4⋊C4—731no—
358C4×C4⋊C4—731no—
359C4×C22⋊C4—731no—
360C4×C22⋊C4—731no—
361#376—731no—
362C43C2×D7311yescharacteristic
363#336—731no—
364#336—731no—
365#336—731no—
366#336—731no—
367#336C2×D7311yescharacteristic
368#336C2×D7311yescharacteristic
369#336C2×D7311yescharacteristic
370#336C2×D7311yescharacteristic
371C23×C4—731no—
372C2×M16—2921no—
373C2×M16—2921no—
374C2×M16—1462no—
375C22×C8—2921no—
376C22×C8—2921no—
377C22×C8—731no—
378C22×C8—731no—
379C22×C8—731no—
380C22×C8—731no—
381C22×C8—1462no—
382C22×C8C22×D7311yescharacteristic
383C22×C8C22×D7311yescharacteristic
384C22×C8C22×D7311yescharacteristic
385C22×C8C22×D7311yescharacteristic
386#117—734no—
387#117—734no—
388C2×C4⋊C4—731no—
389C2×C4⋊C4—731no—
390C2×C4⋊C4—731no—
391C2×C4⋊C4—731no—
392C2×C4⋊C4—731no—
393C2×C4⋊C4—731no—
394C2×C22⋊C4—731no—
395C2×C22⋊C4—731no—
396C2×C22⋊C4—731no—
397C2×C22⋊C4—731no—
398C2×C22⋊C4—731no—
399C2×C22⋊C4—731no—
400C2×C42—731no—
401C2×C42—731no—
402C2×C42—731no—
403C2×C42C4×D7311yescharacteristic
404C2×C42C4×D7311yescharacteristic
405C2×C42C4×D7311yescharacteristic
406C2×C42C4×D7311yescharacteristic
407C2×C42C22×D7311yescharacteristic
408C2×C42C22×D7311yescharacteristic
409C2×C42C22×D7311yescharacteristic
410C4⋊C8—22no—
411C4⋊C8—22no—
412C4⋊C8—2921no—
413C4⋊C8—2921no—
414C4⋊C8—2921no—
415C4⋊C8—2921no—
416C4⋊C8—2921no—
417C4⋊C8—2921no—
418C4⋊C8—2921no—
419C4⋊C8—2921no—
420C4⋊C8—1462no—
421C4⋊C8—1462no—
422C4⋊C8—1462no—
423C4⋊C8—1462no—
424C22⋊C8—1462no—
425C22⋊C8—1462no—
426#97—1462no—
427C4×C8—1462no—
428#95—731no—
429#95—731no—
430#95—731no—
431#95—731no—
432#95—731no—
433#95—731no—
434#95—731no—
435#95—731no—
436#95—731no—
437#95—731no—
438#95—731no—
439#95—731no—
440C24—731no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—732no—
445C22×C4—732no—
446C22×C4—731no—
447C22×C4—731no—
448C22×C4—731no—
449C22×C4—731no—
450C22×C4—1461no—
451C22×C4—1461no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4C2×C4×D7311yescharacteristic
455C22×C4C2×C4×D7311yescharacteristic
456C22×C4C2×C4×D7311yescharacteristic
457C22×C4C2×C4×D7311yescharacteristic
458C22×C4C2×C4×D7311yescharacteristic
459C22×C4C2×C4×D7311yescharacteristic
460C22×C4C23×D7311yescharacteristic
461M16—2924no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—2924no—
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—2921no—
488C4⋊C4—2921no—
489C4⋊C4—734no—
490C4⋊C4—734no—
491C4⋊C4—1462no—
492C4⋊C4—1462no—
493C22⋊C4—2921no—
494C22⋊C4—2921no—
495C22⋊C4—734no—
496C22⋊C4—734no—
497C22⋊C4—1462no—
498C22⋊C4—1462no—
499C42—22no—
500C42—22no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—41no—
506C42—41no—
507C42—732no—
508C42—732no—
509C42—1461no—
510C42—1461no—
511C42—1461no—
512C42—1461no—
513C42D4×D7312yes—
514C42Q8×D7312yes—
515C23—732no—
516C23—1461no—
517C23—1461no—
518C23—1461no—
519C23—1461no—
520C23—1461no—
521C23—1461no—
522C23C22×C4×D7311yescharacteristic
523C2×C4—21no—
524C2×C4—21no—
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—732no—
538C2×C4—732no—
539C2×C4—732no—
540C2×C4—1461no—
541C2×C4—1461no—
542C2×C4—1461no—
543C2×C4—1461no—
544C2×C4—1461no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1461no—
548C2×C4—1461no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4—1461no—
556C2×C4—1461no—
557C2×C4—1461no—
558C2×C4—1462no—
559C2×C4—1462no—
560C2×C4—1462no—
561C2×C4—1462no—
562C2×C4C4⋊C4×D7312yes—
563C2×C4C4⋊C4×D7312yes—
564C2×C4#1455659712yes—
565C2×C4#1455659912yes—
566C2×C4C2×D4×D7311yescharacteristic
567C2×C4C2×Q8×D7311yescharacteristic
568C2×C4#1455663711yescharacteristic
569C2×C4#1455663711yescharacteristic
570C2×C4#1455663811yescharacteristic
571C2×C4#1455663811yescharacteristic
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—2921no—
577C8—2921no—
578C8—2921no—
579C8—2921no—
580C22—2921no—
581C22—2921no—
582C22—2921no—
583C22—2921no—
584C22—1462no—
585C22—1462no—
586C22—1462no—
587C22C2×C4⋊C4×D7311yescharacteristic
588C22#1798906711yescharacteristic
589C22#1798906711yescharacteristic
590C22C2×#1455659711yescharacteristic
591C22C2×#1455659911yescharacteristic
592C22#1798935311yescharacteristic
593C22#1798935311yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—2921no—
601C4—2921no—
602C4—2921no—
603C4—2921no—
604C4—1462no—
605C4—1462no—
606C4—1462no—
607C4#1798915511yescharacteristic
608C4#1798915711yescharacteristic
609C4#1798921711yescharacteristic
610C4#1798921711yescharacteristic
611C2—2922no—
612C2#2261255611yescharacteristic
613C2#2261849611yescharacteristic
614C2#2261850011yescharacteristic
615C2#2261907211yescharacteristic
616C2#2261908211yescharacteristic
617C2#2261909311yescharacteristic
618C2#2261910311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1831C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1831D73
hypocenterC73#21980
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1831

Complements

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

NH ≅ G/Ntype
4. #22610653C2semidirect
5. #22610653C2semidirect
6. #22610648C2semidirect
7. #22610648C2semidirect
12. #22610084C2semidirect
13. #22610083C2semidirect
14. #22610050C2semidirect
15. C73×#1831C2semidirect
324. #1831D73semidirect
325. C73#21980semidirect

Maximal subgroups

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

subgroupindex
C2×#179886472
C2×#179886122
#226124282
#226106532
#226106482
#226101152
#226101102
#226100842
#226100832
#226100502
C73×#18312
#2198073