Finite Group Databasebeta

← #33103779

Subgroups — #33103779

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#22612335C211yesmaximal, characteristic
2#22610648C211yesmaximal, characteristic, complemented
3#22610646C211yesmaximal, characteristic, complemented
4#22610494C211yesmaximal, characteristic, complemented
5#22610490C211yesmaximal, characteristic, complemented
6#22610489C211yesmaximal, characteristic, complemented
7#22609914C211yesmaximal, characteristic
8#22609912C211yesmaximal, characteristic
9#22609910C211yesmaximal, characteristic
10#22609799C211yesmaximal, characteristic, complemented
11#22609792C211yesmaximal, characteristic, complemented
12#22609700C211yesmaximal, characteristic
13#22609696C211yesmaximal, characteristic
14#22609688C211yesmaximal, characteristic
15C73×#1917C211yesmaximal, characteristic, complemented
16C2×#14556548C2211yescharacteristic
17C2×#14556548C2211yescharacteristic
18C2×C42×D73C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556503C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556501C2211yescharacteristic
29C2×C4×#10596831C2211yescharacteristic
30C2×C8×Dic73C2211yescharacteristic
31C2×C8×Dic73C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33#17988456C411yescharacteristic
34#17988456C411yescharacteristic
35#17988451C411yescharacteristic
36#17988451C411yescharacteristic
37#17988446C411yescharacteristic
38#17988446C411yescharacteristic
39#17988444C411yescharacteristic
40#17988444C411yescharacteristic
41C4×#11924007C2211yescharacteristic
42C4×#11924007C2211yescharacteristic
43C4×C4⋊Dic73C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×#97×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55#336×C73C2211yescharacteristic
56#336×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×C4×D73C2×C411yescharacteristic
60C22×C4×D73C2×C411yescharacteristic
61C22×C4×D73C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66#14556548—41no—
67#14556548—41no—
68#14556548—41no—
69#14556548—41no—
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×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×#11924005C2×C411yescharacteristic
81C2×#11924005C2×C411yescharacteristic
82C2×#11924005C2×C411yescharacteristic
83C2×#11924005C2×C411yescharacteristic
84C2×C4×Dic73C2×C411yescharacteristic
85C2×C4×Dic73C2×C411yescharacteristic
86C2×C4×Dic73C2311yescharacteristic
87C2×C4×Dic73C2311yescharacteristic
88C2×C4×Dic73C2311yescharacteristic
89C42×D73—22no—
90C42×D73—22no—
91C4⋊#10596831—41no—
92#14556520—22no—
93#14556520—22no—
94#14556520—41no—
95#14556520—41no—
96#14556503—22no—
97#14556503—22no—
98#14556503—22no—
99#14556503Q814yes—
100#14556501—41no—
101C4×#10596831—41no—
102C8×Dic73—22no—
103C8×Dic73—22no—
104C8×Dic73—41no—
105#14556498C2×C411yescharacteristic
106#14556498C2×C411yescharacteristic
107#14556498C2×C411yescharacteristic
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111C22×C8×C73C2311yescharacteristic
112C22×C8×C73C2311yescharacteristic
113C22×C8×C73C2311yescharacteristic
114C22×C8×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2×C411yescharacteristic
116C2×C4⋊C4×C73C2×C411yescharacteristic
117C2×C42×C73C2311yescharacteristic
118C2×C42×C73C2311yescharacteristic
119C2×C42×C73C2311yescharacteristic
120C4⋊C8×C73—41no—
121#97×C73—41no—
122#95×C73C2×C411yescharacteristic
123#95×C73C2×C411yescharacteristic
124C23×D73C22×C411yescharacteristic
125C22×Dic73C22×C411yescharacteristic
126C22×Dic73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
128C22×Dic73C22×C411yescharacteristic
129C22×Dic73C22×C411yescharacteristic
130C22×Dic73C22×C411yescharacteristic
131C22×Dic73C22×C411yescharacteristic
132C2×C4×D73—21no—
133C2×C4×D73—21no—
134C2×C4×D73—21no—
135C2×C4×D73—21no—
136C2×C4×D73—22no—
137C2×C4×D73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—41no—
142C2×C4×D73C2×Q812yes—
143C2×C4×D73#4112yes—
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×#10596831—21no—
155C2×#10596831C2×Q812yes—
156C4⋊Dic73—22no—
157C4⋊Dic73—41no—
158#11924007—22no—
159#11924007—22no—
160#11924007—22no—
161#11924007—22no—
162#11924007—41no—
163#11924007—41no—
164#11924007—41no—
165#11924007—41no—
166#11924005—41no—
167#11924005—41no—
168#11924005—41no—
169#11924005—41no—
170C4×Dic73—21no—
171C4×Dic73—21no—
172C4×Dic73—21no—
173C4×Dic73—21no—
174C4×Dic73—22no—
175C4×Dic73—22no—
176C4×Dic73#4112yes—
177C4×Dic73#4112yes—
178C22×C4×C73C22×C411yescharacteristic
179C22×C4×C73C22×C411yescharacteristic
180C22×C4×C73C22×C411yescharacteristic
181C22×C4×C73C22×C411yescharacteristic
182C22×C4×C73C22×C411yescharacteristic
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C2411yescharacteristic
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—
195C2×C8×C73—21no—
196C2×C8×C73C2×Q812yes—
197C4⋊C4×C73—22no—
198C4⋊C4×C73—41no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73—21no—
205C23×C73C23×C411yescharacteristic
206C22×D73—21no—
207C22×D73—21no—
208C22×D73—21no—
209C22×D73—21no—
210C22×D73—21no—
211C22×D73—21no—
212C22×D73C4×Q812yes—
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×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73#13112yes—
231C2×C4×C73C22×Q811yescharacteristic
232C2×C4×C73C2×#4111yescharacteristic
233C2×C4×C73C2×#4111yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C2×C4×C73H(5,𝔽2)11yescharacteristic
236C2×C4×C73H(5,𝔽2)11yescharacteristic
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#11712yes—
254C2×Dic73#11712yes—
255C2×Dic73C4×Q812yes—
256C2×Dic73#13112yes—
257C2×Dic73#13112yes—
258C4×D73—22no—
259C4×D73—22no—
260C4×D73—22no—
261C4×D73—22no—
262C4×D73—44no—
263C4×D73—44no—
264C8×C73—22no—
265C8×C73—41no—
266C8×C73—41no—
267C8×C73—41no—
268#10596831—22no—
269#10596831—41no—
270#10596831—41no—
271#10596831—41no—
272C22×C73C2×#11711yescharacteristic
273C22×C73C2×C4×Q811yescharacteristic
274C22×C73#51811yescharacteristic
275C22×C73C2×#13111yescharacteristic
276C22×C73C2×#13111yescharacteristic
277C22×C73C2×#13111yescharacteristic
278C22×C73#56811yescharacteristic
279C2×D73—22no—
280C2×D73—22no—
281C2×D73—22no—
282C2×D73—41no—
283C2×D73—41no—
284C2×D73—41no—
285C2×D73—41no—
286C4×C73—22no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73—41no—
291C4×C73—41no—
292C4×C73#55311yescharacteristic
293C4×C73#55311yescharacteristic
294C4×C73#55411yescharacteristic
295C4×C73#55411yescharacteristic
296Dic73—22no—
297Dic73—22no—
298Dic73—41no—
299Dic73—41no—
300Dic73—41no—
301Dic73—41no—
302Dic73#43314yes—
303#22626—731nomaximal, Sylow
304C2×C73#234511yescharacteristic
305C2×C73C2×#43311yescharacteristic
306C2×C73#292411yescharacteristic
307C2×C73#296011yescharacteristic
308C2×C73#296211yescharacteristic
309C2×C73#297911yescharacteristic
310C2×C73#298111yescharacteristic
311D73—42no—
312#2285—731no—
313#1939—731no—
314#1939—731no—
315#1917—731no—
316#1917D7311yescharacteristic, complemented
317#1916—731no—
318#1916—731no—
319#1798—731no—
320#1798—731no—
321#1797—731no—
322#1770—731no—
323C8×C4⋊C4—731no—
324#1750—731no—
325#1750—731no—
326C4×C22⋊C8—731no—
327C73#2262611yescharacteristic, complemented, Sylow
328C2×#117—731no—
329C2×#117—731no—
330C22×C42—731no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C2×C4⋊C8—731no—
336C2×C4⋊C8C2×D7311yescharacteristic
337C2×C22⋊C8—731no—
338C2×C22⋊C8—731no—
339C2×C22⋊C8—731no—
340C2×C22⋊C8—731no—
341C2×#97—731no—
342C2×#97C2×D7311yescharacteristic
343C2×C4×C8—731no—
344C2×C4×C8—731no—
345C2×C4×C8—731no—
346C2×C4×C8—731no—
347#384—731no—
348#384—731no—
349#382—731no—
350#382—731no—
351#380—731no—
352#380—731no—
353#380—731no—
354#380—731no—
355C4×C4⋊C4—731no—
356C4×C4⋊C4—731no—
357C4×C4⋊C4—731no—
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#336C2×D7311yescharacteristic
368#336C2×D7311yescharacteristic
369#336C2×D7311yescharacteristic
370#336C2×D7311yescharacteristic
371C23×C4—731no—
372C23×C4—731no—
373C23×C4—731no—
374C22×C8—731no—
375C22×C8—731no—
376C22×C8—731no—
377C22×C8—731no—
378C22×C8C22×D7311yescharacteristic
379C22×C8C22×D7311yescharacteristic
380C22×C8C22×D7311yescharacteristic
381C22×C8C22×D7311yescharacteristic
382#117—2921no—
383#117—2921no—
384#117—2921no—
385#117—2921no—
386C2×C4⋊C4—731no—
387C2×C4⋊C4—731no—
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×C4⋊C4—731no—
395C2×C4⋊C4—731no—
396C2×C4⋊C4C4×D7311yescharacteristic
397C2×C4⋊C4C4×D7311yescharacteristic
398C2×C22⋊C4—731no—
399C2×C22⋊C4—731no—
400C2×C22⋊C4—731no—
401C2×C22⋊C4—731no—
402C2×C42—731no—
403C2×C42—731no—
404C2×C42—731no—
405C2×C42—731no—
406C2×C42—731no—
407C2×C42—1462no—
408C2×C42—1462no—
409C2×C42C22×D7311yescharacteristic
410C2×C42C22×D7311yescharacteristic
411C2×C42C22×D7311yescharacteristic
412C4⋊C8—41no—
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—41no—
423#97—2921no—
424C4×C8—2921no—
425C4×C8—2921no—
426C4×C8—1462no—
427C4×C8—1462no—
428#95—731no—
429#95—731no—
430#95—731no—
431#95—731no—
432#95—731no—
433#95—731no—
434#95C4×D7311yescharacteristic
435#95C4×D7311yescharacteristic
436C24—731no—
437C22×C4—2921no—
438C22×C4—731no—
439C22×C4—731no—
440C22×C4—731no—
441C22×C4—732no—
442C22×C4—732no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—731no—
446C22×C4—731no—
447C22×C4—1462no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4C2×C4×D7311yescharacteristic
457C22×C4C2×C4×D7311yescharacteristic
458C22×C4C2×C4×D7311yescharacteristic
459C22×C4C2×C4×D7311yescharacteristic
460C22×C4C2×C4×D7311yescharacteristic
461C22×C4C2×C4×D7311yescharacteristic
462C22×C4C23×D7311yescharacteristic
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—732no—
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×C8Q8×D7312yes—
487C4⋊C4—22no—
488C4⋊C4—41no—
489C4⋊C4—2921no—
490C4⋊C4—2921no—
491C4⋊C4—2921no—
492C4⋊C4—2921no—
493C4⋊C4—2921no—
494C4⋊C4—1462no—
495C4⋊C4—1462no—
496C4⋊C4—1462no—
497C4⋊C4—1462no—
498C4⋊C4—1462no—
499C22⋊C4—2921no—
500C22⋊C4—2921no—
501C22⋊C4—2921no—
502C22⋊C4—2921no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—732no—
510C42—732no—
511C42—1462no—
512C42—1462no—
513C42—1461no—
514C42—1461no—
515C42—1461no—
516C42—1461no—
517C23—732no—
518C23—1461no—
519C23—1461no—
520C23—1461no—
521C23—1461no—
522C23—1461no—
523C23—1461no—
524C23C22×C4×D7311yescharacteristic
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—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—2924no—
543C2×C4—2924no—
544C2×C4—732no—
545C2×C4—732no—
546C2×C4—732no—
547C2×C4—732no—
548C2×C4—732no—
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—1461no—
559C2×C4—1461no—
560C2×C4—1461no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1462no—
566C2×C4—1462no—
567C2×C4—1462no—
568C2×C4—1462no—
569C2×C4#1455659912yes—
570C2×C4C2×Q8×D7311yescharacteristic
571C2×C4#41×D7311yescharacteristic
572C2×C4#41×D7311yescharacteristic
573C2×C4#41×D7311yescharacteristic
574C2×C4#1455663611yescharacteristic
575C2×C4#1455663711yescharacteristic
576C8—22no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—2921no—
581C8—2921no—
582C8—2921no—
583C8—1462no—
584C22—2921no—
585C22—2921no—
586C22—2921no—
587C22—2921no—
588C22—1462no—
589C22—1462no—
590C22—1462no—
591C22#117×D7311yescharacteristic
592C22C4×Q8×D7311yescharacteristic
593C22#1798905911yescharacteristic
594C22#131×D7311yescharacteristic
595C22#131×D7311yescharacteristic
596C22C2×#1455659911yescharacteristic
597C22#1798935311yescharacteristic
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—2921no—
605C4—2921no—
606C4—2921no—
607C4—2921no—
608C4—734no—
609C4—1462no—
610C4—1462no—
611C4#1798928211yescharacteristic
612C4#1798928811yescharacteristic
613C4#1798929111yescharacteristic
614C4#1798929311yescharacteristic
615C2—2922no—
616C2#2261280511yescharacteristic
617C2#433×D7311yescharacteristic
618C2#2261859011yescharacteristic
619C2#2261886211yescharacteristic
620C2#2261887611yescharacteristic
621C2#2261899611yescharacteristic
622C2#2261900311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1917C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1917D73
hypocenterC73#22626
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #22610648C2semidirect
3. #22610646C2semidirect
4. #22610494C2semidirect
5. #22610490C2semidirect
6. #22610489C2semidirect
10. #22609799C2semidirect
11. #22609792C2semidirect
15. C73×#1917C2semidirect
316. #1917D73semidirect
327. C73#22626semidirect

Maximal subgroups

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

subgroupindex
#226123352
#226106482
#226106462
#226104942
#226104902
#226104892
#226099142
#226099122
#226099102
#226097992
#226097922
#226097002
#226096962
#226096882
C73×#19172
#2262673