Finite Group Databasebeta

← #33096591

Subgroups — #33096591

Order 18688.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988646C211yesmaximal, characteristic
2#22612556C211yesmaximal, characteristic
3#22612541C211yesmaximal, characteristic
4#22610700C211yesmaximal, characteristic, complemented
5#22610696C211yesmaximal, characteristic, complemented
6#22610691C211yesmaximal, characteristic, complemented
7#22610686C211yesmaximal, characteristic, complemented
8#22610129C211yesmaximal, characteristic
9#22610127C211yesmaximal, characteristic
10#22610122C211yesmaximal, characteristic
11#22610117C211yesmaximal, characteristic
12#22610100C211yesmaximal, characteristic, complemented
13#22610064C211yesmaximal, characteristic, complemented
14#22610059C211yesmaximal, characteristic, complemented
15C73×#1846C211yesmaximal, characteristic, complemented
16C2×#14556549C2211yescharacteristic
17C2×#14556548C2211yescharacteristic
18C2×C4⋊C4×D73C2211yescharacteristic
19#17988646C418yescomplemented
20C2×#14556524C2211yescharacteristic
21C2×#14556524C2211yescharacteristic
22C2×#14556522C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556502C2211yescharacteristic
29#17988484—21no—
30#17988484—21no—
31#17988479—21no—
32#17988479—21no—
33#17988474—21no—
34#17988474—21no—
35#17988461—21no—
36#17988461—21no—
37#17988457C2211yescharacteristic
38#17988457C2211yescharacteristic
39#17988456C2211yescharacteristic
40#17988452C2211yescharacteristic
41#17988444C2211yescharacteristic
42#17988444C2211yescharacteristic
43C4⋊C4×Dic73C2211yescharacteristic
44C4⋊C4×Dic73C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53C2×#107×C73C2211yescharacteristic
54C2×#107×C73C2211yescharacteristic
55C2×#106×C73C2211yescharacteristic
56C2×#106×C73C2211yescharacteristic
57C2×C4×C8×C73C2211yescharacteristic
58#382×C73C2211yescharacteristic
59#382×C73C2211yescharacteristic
60C22×C4×D73—21no—
61C22×C4×D73C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64#14556549—41no—
65#14556549—41no—
66#14556548C2×C414yes—
67#14556548Q814yes—
68C2×C4⋊Dic73—21no—
69C2×C4⋊Dic73—21no—
70C2×C4⋊Dic73—21no—
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×#11924007—21no—
77C2×#11924007—21no—
78C2×#11924007—21no—
79C2×#11924007D411yescharacteristic
80C2×#11924007D411yescharacteristic
81C4⋊C4×D73—41no—
82C4⋊C4×D73—41no—
83C2×#11924005—21no—
84C2×#11924005—21no—
85C2×#11924005—21no—
86C2×#11924005D411yescharacteristic
87C2×#11924005D411yescharacteristic
88C2×C4×Dic73—21no—
89C2×C4×Dic73—21no—
90C2×C4×Dic73—21no—
91C2×C4×Dic73C2311yescharacteristic
92#14556524—41no—
93#14556524—41no—
94#14556522—41no—
95#14556522—41no—
96#14556520C2×C414yescomplemented
97#14556520C2×C414yescomplemented
98#14556503C2×C414yes—
99#14556503C2×C414yes—
100#14556502C2×C414yescomplemented
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C2×C4⋊C4×C73C2311yescharacteristic
110C2×C4⋊C4×C73C2311yescharacteristic
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114#107×C73—41no—
115#107×C73—41no—
116#106×C73—41no—
117#106×C73—41no—
118C4×C8×C73C2×C414yescomplemented
119#95×C73—21no—
120#95×C73—21no—
121#95×C73—21no—
122#95×C73—21no—
123C23×D73C2×D411yescharacteristic
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73C2×D411yescharacteristic
129C22×Dic73C2×D411yescharacteristic
130C22×Dic73C2×D411yescharacteristic
131C2×C4×D73—21no—
132C2×C4×D73—21no—
133C2×C4×D73—21no—
134C2×C4×D73—21no—
135C2×C4×D73—42no—
136C2×C4×D73—81no—
137C2×C4×D73—81no—
138C2×C4×D73C22×C412yes—
139C2×C4×D73C2×Q812yes—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831C22×C412yes—
145C2×#10596831C22×C412yes—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—81no—
155C4⋊Dic73—81no—
156C4⋊Dic73—81no—
157C4⋊Dic73—81no—
158#11924007—42no—
159#11924007—81no—
160#11924007—81no—
161#11924007C4⋊C414yes—
162#11924007C4⋊C414yes—
163#11924005—42no—
164#11924005—81no—
165#11924005—81no—
166#11924005C4⋊C414yes—
167#11924005C4⋊C414yes—
168C4×Dic73—42no—
169C4×Dic73—81no—
170C4×Dic73—81no—
171C4×Dic73C22×C412yes—
172C4×Dic73C2×Q812yes—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2411yescharacteristic
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73C22×C412yes—
185C2×C8×C73C22×C412yes—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C42×C73C22×C412yes—
195C42×C73C2×Q812yes—
196C23×C73C22×D411yescharacteristic
197C22×D73—21no—
198C22×D73—21no—
199C22×D73—21no—
200C22×D73—21no—
201C22×D73—21no—
202C22×D73—21no—
203C22×D73C2×C4⋊C412yes—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—41no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—41no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73C2×C4⋊C412yes—
221C2×C4×C73C2×C4⋊C412yes—
222C2×C4×C73C23×C411yescharacteristic
223C2×C4×C73C22×Q811yescharacteristic
224C2×C4×C73H(5,𝔽2)11yescharacteristic
225C2×C4×C73H(5,𝔽2)11yescharacteristic
226C2×C4×C732−1+411yescharacteristic
227C2×C4×C732−1+411yescharacteristic
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—41no—
235C2×Dic73—41no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73C2×C4⋊C412yes—
247C2×Dic73C2×C4⋊C412yes—
248C2×Dic73C2×C4⋊C412yes—
249C4×D73—22no—
250C4×D73—22no—
251C4×D73—22no—
252C4×D73—22no—
253C4×D73—84no—
254C8×C73—22no—
255C8×C73—22no—
256#10596831—22no—
257#10596831—22no—
258C22×C73C22×C4⋊C411yescharacteristic
259C22×C73#53511yescharacteristic
260C22×C73#53611yescharacteristic
261C22×C73#57611yescharacteristic
262C22×C73#57711yescharacteristic
263C22×C73#57711yescharacteristic
264C22×C73#57811yescharacteristic
265C2×D73—22no—
266C2×D73—22no—
267C2×D73—22no—
268C2×D73—41no—
269C2×D73—41no—
270C2×D73—41no—
271C2×D73—41no—
272C4×C73—22no—
273C4×C73—22no—
274C4×C73—81no—
275C4×C73—81no—
276C4×C73—81no—
277C4×C73—81no—
278C4×C73#52011yescharacteristic
279C4×C73#52011yescharacteristic
280C4×C73#54411yescharacteristic
281C4×C73#54411yescharacteristic
282Dic73—22no—
283Dic73—22no—
284Dic73—22no—
285Dic73—81no—
286Dic73—81no—
287Dic73—81no—
288Dic73—81no—
289#21992—731nomaximal, Sylow
290C2×C73#231711yescharacteristic
291C2×C73#291211yescharacteristic
292C2×C73#291311yescharacteristic
293C2×C73#322411yescharacteristic
294C2×C73#322511yescharacteristic
295C2×C73#324111yescharacteristic
296C2×C73#324211yescharacteristic
297D73—42no—
298C2×#433—731no—
299#2317—731no—
300#2314—731no—
301#1949—731no—
302#1949—731no—
303#1948—731no—
304#1947—731no—
305#1854—731no—
306#1854—731no—
307#1853—731no—
308#1852—731no—
309#1847—731no—
310#1846D7311yescharacteristic, complemented
311#1836—731no—
312#1834—731no—
313C73#2199211yescharacteristic, complemented, Sylow
314C2×#117—731no—
315C2×#117—731no—
316C22×C4⋊C4—731no—
317#433—738no—
318C2×#107—731no—
319C2×#107—731no—
320C2×#107C2×D7311yescharacteristic
321C2×#107C2×D7311yescharacteristic
322C2×#106—731no—
323C2×#106—731no—
324C2×#106C2×D7311yescharacteristic
325C2×#106C2×D7311yescharacteristic
326C2×C4⋊C8—731no—
327C2×C4⋊C8—731no—
328C2×C22⋊C8—731no—
329C2×C22⋊C8—731no—
330C2×#97—731no—
331C2×C4×C8C2×D7311yescharacteristic
332#389—1461no—
333#389—1461no—
334#388—1461no—
335#388—1461no—
336#387—1461no—
337#387—1461no—
338#385—1461no—
339#385—1461no—
340#384—731no—
341#384—731no—
342#384—731no—
343#382—731no—
344#382C2×D7311yescharacteristic
345#382C2×D7311yescharacteristic
346#380—731no—
347#380—731no—
348C4×C4⋊C4—731no—
349C4×C4⋊C4—731no—
350#340—731no—
351#340—731no—
352#340—731no—
353#340—731no—
354#340—731no—
355#340—731no—
356#340—731no—
357#340—731no—
358C23×C4—731no—
359C23×C4—1461no—
360C22×C8—731no—
361C22×C8—731no—
362C22×C8C22×D7311yescharacteristic
363C22×C8C22×D7311yescharacteristic
364#117—2921no—
365#117—2921no—
366#117—734no—
367#117—734no—
368C2×C4⋊C4—2921no—
369C2×C4⋊C4—2921no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—731no—
375C2×C4⋊C4—731no—
376C2×C4⋊C4—1461no—
377C2×C4⋊C4—1461no—
378C2×C4⋊C4—1461no—
379C2×C4⋊C4—1461no—
380C2×C4⋊C4—1461no—
381C2×C4⋊C4—1461no—
382C2×C4⋊C4—1461no—
383C2×C4⋊C4C22×D7311yescharacteristic
384C2×C4⋊C4C22×D7311yescharacteristic
385C2×C4⋊C4C22×D7311yescharacteristic
386C2×C4⋊C4C22×D7311yescharacteristic
387C2×C22⋊C4—731no—
388C2×C22⋊C4—731no—
389C2×C22⋊C4—1461no—
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C42—731no—
393C2×C42—1461no—
394C2×C42—1461no—
395C2×C42—1461no—
396C2×C42C22×D7311yescharacteristic
397#107—41no—
398#107—41no—
399#107—2921no—
400#107—2921no—
401#106—41no—
402#106—41no—
403#106—2921no—
404#106—2921no—
405C4⋊C8—734no—
406C4⋊C8—734no—
407C22⋊C8—734no—
408C22⋊C8—734no—
409#97—734no—
410C4×C8C4×D7314yescomplemented
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—1461no—
416#95—1461no—
417#95—1461no—
418#95—1461no—
419#95—1461no—
420#95—1461no—
421C24—731no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—2922no—
427C22×C4—5841no—
428C22×C4—5841no—
429C22×C4—731no—
430C22×C4—731no—
431C22×C4—731no—
432C22×C4—732no—
433C22×C4—732no—
434C22×C4—1461no—
435C22×C4—1461no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4—1461no—
440C22×C4—1461no—
441C22×C4—1461no—
442C22×C4D4×D7311yescharacteristic
443C22×C4D4×D7311yescharacteristic
444C22×C4C23×D7311yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—732no—
450C2×C8—732no—
451C2×C8—1461no—
452C2×C8—1461no—
453C2×C8—1461no—
454C2×C8—1461no—
455C2×C8C2×C4×D7312yes—
456C2×C8C2×C4×D7312yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—2922no—
466C4⋊C4—5841no—
467C4⋊C4—5841no—
468C4⋊C4—5841no—
469C4⋊C4—5841no—
470C4⋊C4—5841no—
471C4⋊C4—5841no—
472C4⋊C4—734no—
473C4⋊C4—734no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C22⋊C4—2922no—
483C22⋊C4—5841no—
484C22⋊C4—5841no—
485C22⋊C4—734no—
486C22⋊C4—734no—
487C42—2922no—
488C42—5841no—
489C42—5841no—
490C42—732no—
491C42—732no—
492C42C2×C4×D7312yes—
493C42Q8×D7312yes—
494C23—732no—
495C23—1461no—
496C23—1461no—
497C23—1461no—
498C23—1461no—
499C23—1461no—
500C23—1461no—
501C23C2×D4×D7311yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—2921no—
519C2×C4—2921no—
520C2×C4—2921no—
521C2×C4—2921no—
522C2×C4—2921no—
523C2×C4—2921no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—2921no—
527C2×C4—2921no—
528C2×C4—2921no—
529C2×C4—2921no—
530C2×C4—5844no—
531C2×C4—732no—
532C2×C4—732no—
533C2×C4—732no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4—1461no—
539C2×C4—1461no—
540C2×C4—1462no—
541C2×C4—1462no—
542C2×C4—1462no—
543C2×C4—1462no—
544C2×C4C4⋊C4×D7312yes—
545C2×C4C4⋊C4×D7312yes—
546C2×C4C22×C4×D7311yescharacteristic
547C2×C4C2×Q8×D7311yescharacteristic
548C2×C4#1455663611yescharacteristic
549C2×C4#1455663611yescharacteristic
550C2×C4#1455663911yescharacteristic
551C2×C4#1455663911yescharacteristic
552C8—22no—
553C8—22no—
554C8—1462no—
555C8—1462no—
556C22—2921no—
557C22—2921no—
558C22—2921no—
559C22—2921no—
560C22—1462no—
561C22—1462no—
562C22—1462no—
563C22C2×C4⋊C4×D7311yescharacteristic
564C22#1798915011yescharacteristic
565C22#1798916211yescharacteristic
566C22#1798938911yescharacteristic
567C22#1798939411yescharacteristic
568C22#1798939411yescharacteristic
569C22#1798940111yescharacteristic
570C4—22no—
571C4—22no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—5841no—
577C4—5841no—
578C4—5841no—
579C4—5841no—
580C4—1462no—
581C4—1462no—
582C4—1462no—
583C4#1798906811yescharacteristic
584C4#1798906811yescharacteristic
585C4#1798921411yescharacteristic
586C4#1798921411yescharacteristic
587C2—2922no—
588C2#2261255211yescharacteristic
589C2#2261852311yescharacteristic
590C2#2261852811yescharacteristic
591C2#2262101811yescharacteristic
592C2#2262103311yescharacteristic
593C2#2262118711yescharacteristic
594C2#2262120211yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1846C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1846D73
hypocenterC73#21992
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1846

Complements

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

NH ≅ G/Ntype
4. #22610700C2semidirect
5. #22610696C2semidirect
6. #22610691C2semidirect
7. #22610686C2semidirect
12. #22610100C2semidirect
13. #22610064C2semidirect
14. #22610059C2semidirect
15. C73×#1846C2semidirect
19. #17988646C4semidirect
96. #14556520C2×C4semidirect
97. #14556520C2×C4semidirect
100. #14556502C2×C4semidirect
118. C4×C8×C73C2×C4semidirect
310. #1846D73semidirect
313. C73#21992semidirect
410. C4×C8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886462
#226125562
#226125412
#226107002
#226106962
#226106912
#226106862
#226101292
#226101272
#226101222
#226101172
#226101002
#226100642
#226100592
C73×#18462
#2199273