Finite Group Databasebeta

← #33112760

Subgroups — #33112760

Order 18688.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613229C211yesmaximal, characteristic
2#22610651C211yesmaximal, characteristic, complemented
3#22610651C211yesmaximal, characteristic, complemented
4#22610646C211yesmaximal, characteristic, complemented
5#22610543C211yesmaximal, characteristic
6#22610543C211yesmaximal, characteristic
7#22610536C211yesmaximal, characteristic
8#22610492C211yesmaximal, characteristic, complemented
9#22610492C211yesmaximal, characteristic, complemented
10#22610485C211yesmaximal, characteristic, complemented
11#22610112C211yesmaximal, characteristic
12#22610112C211yesmaximal, characteristic
13#22610112C211yesmaximal, characteristic
14#22610076C211yesmaximal, characteristic, complemented
15C73×#1843C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C2×#14556520C2211yescharacteristic
18C2×#14556520C2211yescharacteristic
19C2×#14556520C2211yescharacteristic
20C2×#14556503C2211yescharacteristic
21C2×#14556503C2211yescharacteristic
22C2×#14556503C2211yescharacteristic
23C2×#14556501C2211yescharacteristic
24C2×#14556501C2211yescharacteristic
25C2×C8×Dic73C2211yescharacteristic
26C73⋊#401C411yescharacteristic
27#17988528C411yescharacteristic
28#17988528C411yescharacteristic
29#17988528C411yescharacteristic
30#17988516C411yescharacteristic
31#17988516C411yescharacteristic
32#17988516C411yescharacteristic
33#17988511C411yescharacteristic
34C4×#11924007C2211yescharacteristic
35C4×#11924007C2211yescharacteristic
36C4×#11924007C2211yescharacteristic
37C4×#11924005C2211yescharacteristic
38C4×#11924005C2211yescharacteristic
39C4×#11924005C2211yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55C2×C4⋊C8×C73C2211yescharacteristic
56C2×C4⋊C8×C73C2211yescharacteristic
57C2×C4⋊C8×C73C2211yescharacteristic
58#376×C73C2211yescharacteristic
59C22×C4×D73C2311yescharacteristic
60C2×#11924011—41no—
61C2×#11924011—41no—
62C2×#11924011—41no—
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C2×#11924007C2×C411yescharacteristic
68C2×#11924007C2×C411yescharacteristic
69C2×#11924007C2×C411yescharacteristic
70C2×#11924007C2×C411yescharacteristic
71C2×#11924007C2×C411yescharacteristic
72C2×#11924007C2×C411yescharacteristic
73C2×#11924005C2×C411yescharacteristic
74C2×#11924005C2×C411yescharacteristic
75C2×#11924005C2×C411yescharacteristic
76C2×#11924005C2×C411yescharacteristic
77C2×#11924005C2×C411yescharacteristic
78C2×#11924005C2×C411yescharacteristic
79C2×C4×Dic73C2311yescharacteristic
80C2×C4×Dic73C2311yescharacteristic
81C2×C4×Dic73C2311yescharacteristic
82#14556520—41no—
83#14556520—41no—
84#14556520—41no—
85#14556503—41no—
86#14556503—41no—
87#14556503—41no—
88#14556501—41no—
89#14556501—41no—
90C8×Dic73—41no—
91#14556498C2×C411yescharacteristic
92#14556498C2×C411yescharacteristic
93#14556498C2×C411yescharacteristic
94#14556498C2×C411yescharacteristic
95#14556498C2×C411yescharacteristic
96#14556498C2×C411yescharacteristic
97#14556498C2×C411yescharacteristic
98#14556498C2×C411yescharacteristic
99#14556498C2×C411yescharacteristic
100#14556498C2×C411yescharacteristic
101#14556498C2×C411yescharacteristic
102#14556498C2×C411yescharacteristic
103C22×C8×C73C2311yescharacteristic
104C22×C8×C73C2311yescharacteristic
105C22×C8×C73C2311yescharacteristic
106C22×C8×C73C2311yescharacteristic
107C2×C42×C73C2311yescharacteristic
108C2×C42×C73C2311yescharacteristic
109C2×C42×C73C2311yescharacteristic
110C4⋊C8×C73—41no—
111C4⋊C8×C73—41no—
112C4⋊C8×C73—41no—
113C4⋊C8×C73—41no—
114C4⋊C8×C73—41no—
115C4⋊C8×C73—41no—
116#95×C73C2×C411yescharacteristic
117#95×C73C2×C411yescharacteristic
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120C23×D73C22×C411yescharacteristic
121C22×Dic73C22×C411yescharacteristic
122C22×Dic73C22×C411yescharacteristic
123C22×Dic73C22×C411yescharacteristic
124C22×Dic73C22×C411yescharacteristic
125C22×Dic73C22×C411yescharacteristic
126C22×Dic73C22×C411yescharacteristic
127C22×Dic73C22×C411yescharacteristic
128C2×C4×D73—21no—
129C2×C4×D73—21no—
130C2×C4×D73—21no—
131C2×C4×D73—21no—
132C2×C4×D73—21no—
133C2×C4×D73—21no—
134#11924011—44no—
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—
147#11924007—22no—
148#11924007—22no—
149#11924007—41no—
150#11924007—41no—
151#11924007—41no—
152#11924007—41no—
153#11924005—22no—
154#11924005—41no—
155#11924005—41no—
156#11924005—41no—
157#11924005—41no—
158#11924005—41no—
159C4×Dic73—21no—
160C4×Dic73—21no—
161C4×Dic73—21no—
162C4×Dic73—21no—
163C4×Dic73—21no—
164C4×Dic73—21no—
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×C73C2411yescharacteristic
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C42×C73—21no—
185C42×C73—21no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C23×C73C23×C411yescharacteristic
191C22×D73—21no—
192C22×D73—21no—
193C22×D73—21no—
194C22×D73—21no—
195C22×D73—21no—
196C22×D73—21no—
197C22×D73—21no—
198C2×C4×C73—21no—
199C2×C4×C73—21no—
200C2×C4×C73—21no—
201C2×C4×C73—21no—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73H(5,𝔽2)11yescharacteristic
217C2×C4×C73H(5,𝔽2)11yescharacteristic
218C2×C4×C73H(5,𝔽2)11yescharacteristic
219C2×C4×C732−1+411yescharacteristic
220C2×C4×C732−1+411yescharacteristic
221C2×C4×C732−1+411yescharacteristic
222C2×Dic73—21no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73#13112yes—
243C4×D73—41no—
244C4×D73—41no—
245C4×D73—41no—
246C4×D73—41no—
247C8×C73—41no—
248C8×C73—41no—
249C8×C73—41no—
250C8×C73—41no—
251#10596831—41no—
252#10596831—41no—
253#10596831—41no—
254#10596831—41no—
255C22×C73#52011yescharacteristic
256C22×C73#52011yescharacteristic
257C22×C73#52011yescharacteristic
258C22×C73C2×#13111yescharacteristic
259C22×C73#56811yescharacteristic
260C22×C73#56811yescharacteristic
261C22×C73#56811yescharacteristic
262C2×D73—41no—
263C2×D73—41no—
264C2×D73—41no—
265C2×D73—41no—
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73—41no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73#56011yescharacteristic
276C4×C73#56311yescharacteristic
277C4×C73#56311yescharacteristic
278C4×C73#56311yescharacteristic
279Dic73—22no—
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283Dic73—41no—
284Dic73—41no—
285Dic73—41no—
286#23382—731nomaximal, Sylow
287C2×C73#238311yescharacteristic
288C2×C73#299211yescharacteristic
289C2×C73#299311yescharacteristic
290C2×C73#299311yescharacteristic
291C2×C73#299511yescharacteristic
292C2×C73#299511yescharacteristic
293C2×C73#299511yescharacteristic
294D73—81no—
295#2401—731no—
296#1940—731no—
297#1940—731no—
298#1939—731no—
299#1924—731no—
300#1924—731no—
301#1923—731no—
302#1917—731no—
303#1917—731no—
304#1916—731no—
305#1851—731no—
306#1851—731no—
307#1851—731no—
308#1843D7311yescharacteristic, complemented
309#1840—731no—
310C73#2338211yescharacteristic, complemented, Sylow
311C22×M16—731no—
312C2×C4⋊C8—731no—
313C2×C4⋊C8—731no—
314C2×C4⋊C8—731no—
315C2×C4⋊C8C2×D7311yescharacteristic
316C2×C4⋊C8C2×D7311yescharacteristic
317C2×C4⋊C8C2×D7311yescharacteristic
318C2×C4⋊C8C2×D7311yescharacteristic
319C2×C4⋊C8C2×D7311yescharacteristic
320C2×C4⋊C8C2×D7311yescharacteristic
321C2×C22⋊C8—731no—
322C2×C22⋊C8—731no—
323C2×C22⋊C8—731no—
324C2×#97—731no—
325C2×#97—731no—
326C2×C4×C8—731no—
327#401—731no—
328#400—731no—
329#400—731no—
330#400—731no—
331#397—731no—
332#397—731no—
333#397—731no—
334#396—731no—
335C4×C4⋊C4—731no—
336C4×C4⋊C4—731no—
337C4×C4⋊C4—731no—
338C4×C22⋊C4—731no—
339C4×C22⋊C4—731no—
340C4×C22⋊C4—731no—
341#376C2×D7311yescharacteristic
342#336—731no—
343#336—731no—
344#336—731no—
345#336—731no—
346#336—731no—
347#336—731no—
348#336—731no—
349#336—731no—
350#336—731no—
351#336—731no—
352#336—731no—
353#336—731no—
354C23×C4—731no—
355C2×M16—2921no—
356C2×M16—2921no—
357C2×M16—2921no—
358C22×C8—731no—
359C22×C8—731no—
360C22×C8—731no—
361C22×C8—731no—
362C22×C8C22×D7311yescharacteristic
363C22×C8C22×D7311yescharacteristic
364C22×C8C22×D7311yescharacteristic
365C22×C8C22×D7311yescharacteristic
366C2×C4⋊C4—731no—
367C2×C4⋊C4—731no—
368C2×C4⋊C4—731no—
369C2×C4⋊C4—731no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C22⋊C4—731no—
373C2×C22⋊C4—731no—
374C2×C22⋊C4—731no—
375C2×C22⋊C4—731no—
376C2×C22⋊C4—731no—
377C2×C22⋊C4—731no—
378C2×C42—731no—
379C2×C42—731no—
380C2×C42—731no—
381C2×C42C22×D7311yescharacteristic
382C2×C42C22×D7311yescharacteristic
383C2×C42C22×D7311yescharacteristic
384C4⋊C8—41no—
385C4⋊C8—41no—
386C4⋊C8—41no—
387C4⋊C8—41no—
388C4⋊C8—41no—
389C4⋊C8—41no—
390C4⋊C8—2921no—
391C4⋊C8—2921no—
392C4⋊C8—2921no—
393C22⋊C8—2921no—
394C22⋊C8—2921no—
395C22⋊C8—2921no—
396#97—2921no—
397#97—2921no—
398C4×C8—2921no—
399#95—731no—
400#95—731no—
401#95—731no—
402#95—731no—
403#95—731no—
404#95—731no—
405#95—731no—
406#95—731no—
407#95—731no—
408#95—731no—
409#95—731no—
410#95—731no—
411#95C4×D7311yescharacteristic
412#95C4×D7311yescharacteristic
413#95C4×D7311yescharacteristic
414#95C4×D7311yescharacteristic
415C24—731no—
416C22×C4—731no—
417C22×C4—731no—
418C22×C4—731no—
419C22×C4—731no—
420C22×C4—731no—
421C22×C4—731no—
422C22×C4—731no—
423C22×C4—1461no—
424C22×C4—1461no—
425C22×C4—1461no—
426C22×C4—1461no—
427C22×C4—1461no—
428C22×C4—1461no—
429C22×C4C2×C4×D7311yescharacteristic
430C22×C4C2×C4×D7311yescharacteristic
431C22×C4C2×C4×D7311yescharacteristic
432C22×C4C2×C4×D7311yescharacteristic
433C22×C4C2×C4×D7311yescharacteristic
434C22×C4C2×C4×D7311yescharacteristic
435C22×C4C23×D7311yescharacteristic
436M16—2924no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—1461no—
450C2×C8—1461no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C4⋊C4—2921no—
462C4⋊C4—2921no—
463C4⋊C4—2921no—
464C4⋊C4—2921no—
465C4⋊C4—1462no—
466C4⋊C4—1462no—
467C22⋊C4—2921no—
468C22⋊C4—2921no—
469C22⋊C4—2921no—
470C22⋊C4—2921no—
471C22⋊C4—2921no—
472C22⋊C4—1462no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—1461no—
480C42—1461no—
481C42—1461no—
482C42—1461no—
483C42—1461no—
484C42—1461no—
485C23—1461no—
486C23—1461no—
487C23—1461no—
488C23—1461no—
489C23—1461no—
490C23—1461no—
491C23—1461no—
492C23C22×C4×D7311yescharacteristic
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—2921no—
512C2×C4—2921no—
513C2×C4—2921no—
514C2×C4—2921no—
515C2×C4—732no—
516C2×C4—1461no—
517C2×C4—1461no—
518C2×C4—1461no—
519C2×C4—1461no—
520C2×C4—1461no—
521C2×C4—1461no—
522C2×C4—1461no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4—1461no—
530C2×C4—1461no—
531C2×C4—1461no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4#1455663611yescharacteristic
537C2×C4#1455663611yescharacteristic
538C2×C4#1455663611yescharacteristic
539C2×C4#1455663911yescharacteristic
540C2×C4#1455663911yescharacteristic
541C2×C4#1455663911yescharacteristic
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—2921no—
547C8—2921no—
548C8—2921no—
549C8—2921no—
550C22—2921no—
551C22—2921no—
552C22—2921no—
553C22—2921no—
554C22—2921no—
555C22—2921no—
556C22—2921no—
557C22#1798906811yescharacteristic
558C22#1798906811yescharacteristic
559C22#1798906811yescharacteristic
560C22#131×D7311yescharacteristic
561C22#1798935211yescharacteristic
562C22#1798935211yescharacteristic
563C22#1798935211yescharacteristic
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—2921no—
571C4—2921no—
572C4—2921no—
573C4—2921no—
574C4—2921no—
575C4—2921no—
576C4—1462no—
577C4#1798932411yescharacteristic
578C4#1798933611yescharacteristic
579C4#1798933611yescharacteristic
580C4#1798933611yescharacteristic
581C2—5841no—
582C2#2261312411yescharacteristic
583C2#2261906811yescharacteristic
584C2#2261907811yescharacteristic
585C2#2261907811yescharacteristic
586C2#2261909911yescharacteristic
587C2#2261909911yescharacteristic
588C2#2261909911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1843C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenter#1843D73
hypocenterC73#23382
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1843

Complements

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

NH ≅ G/Ntype
2. #22610651C2semidirect
3. #22610651C2semidirect
4. #22610646C2semidirect
8. #22610492C2semidirect
9. #22610492C2semidirect
10. #22610485C2semidirect
14. #22610076C2semidirect
15. C73×#1843C2semidirect
308. #1843D73semidirect
310. C73#23382semidirect

Maximal subgroups

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

subgroupindex
#226132292
#226106512
#226106462
#226105432
#226105362
#226104922
#226104852
#226101122
#226100762
C73×#18432
#2338273