Finite Group Databasebeta

← #33096391

Subgroups — #33096391

Order 18688.

754 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
1C2×#17988614C211yesmaximal, characteristic
2#22612540C211yesmaximal, characteristic
3#22610699C211yesmaximal, characteristic, complemented
4#22610699C211yesmaximal, characteristic, complemented
5#22610697C211yesmaximal, characteristic, complemented
6#22610697C211yesmaximal, characteristic, complemented
7#22610694C211yesmaximal, characteristic, complemented
8#22610692C211yesmaximal, characteristic, complemented
9#22610689C211yesmaximal, characteristic, complemented
10#22610687C211yesmaximal, characteristic, complemented
11#22609962C211yesmaximal, characteristic
12#22609962C211yesmaximal, characteristic
13#22609958C211yesmaximal, characteristic
14#22609954C211yesmaximal, characteristic
15C73×#2314C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556524C2211yescharacteristic
19C2×#14556524C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556524C2211yescharacteristic
22C2×#14556522C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26#17988614C418yescomplemented
27C2×C4⋊#10596831C2211yescharacteristic
28C2×C4⋊#10596831C2211yescharacteristic
29C2×C4⋊#10596831C2211yescharacteristic
30C2×C4⋊#10596831C2211yescharacteristic
31#17988480—21no—
32#17988480—21no—
33#17988473—21no—
34#17988473—21no—
35#17988457C2211yescharacteristic
36#17988453C2211yescharacteristic
37#17988447C2211yescharacteristic
38#17988447C2211yescharacteristic
39C4×C4⋊Dic73C2211yescharacteristic
40C4×C4⋊Dic73C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49C2×#117×C73C2211yescharacteristic
50#388×C73—21no—
51#388×C73—21no—
52#387×C73—21no—
53#387×C73—21no—
54#384×C73C2211yescharacteristic
55#382×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59C4×C4⋊C4×C73C2211yescharacteristic
60C2×#11924012—41no—
61C2×#11924012—41no—
62C2×#11924012C2×C414yes—
63C22×#10596831—41no—
64C22×#10596831—41no—
65C22×#10596831C2×C414yes—
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C2×C4⋊Dic73—21no—
71C2×C4⋊Dic73—21no—
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×C22⋊Dic73—21no—
77C2×C22⋊Dic73—21no—
78C2×C4×Dic73—21no—
79C2×C4×Dic73—21no—
80#14556524—41no—
81#14556524—41no—
82#14556524—41no—
83#14556524—41no—
84#14556522—41no—
85#14556522—41no—
86#14556522—41no—
87#14556522—41no—
88C4⋊#10596831C2×C414yes—
89C4⋊#10596831C2×C414yes—
90C4⋊#10596831C2×C414yes—
91C4⋊#10596831C2×C414yes—
92#14556498—21no—
93#14556498—21no—
94#14556498—21no—
95#14556498—21no—
96#14556498—21no—
97#14556498—21no—
98C23×C4×C73C2311yescharacteristic
99#117×C73C2×C414yes—
100#117×C73Q814yes—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—21no—
103C2×C4⋊C4×C73D411yescharacteristic
104C2×C4⋊C4×C73D411yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73D411yescharacteristic
112C2×C22⋊C4×C73D411yescharacteristic
113C2×C42×C73—21no—
114C2×C42×C73—21no—
115C2×C42×C73C2311yescharacteristic
116C2×C42×C73C2311yescharacteristic
117#95×C73—21no—
118#95×C73—21no—
119#95×C73—21no—
120#95×C73—21no—
121#95×C73—21no—
122#95×C73—21no—
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—21no—
127#11924012—44no—
128C2×#10596831—21no—
129C2×#10596831—21no—
130C2×#10596831—21no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—44no—
137C2×#10596831C22×C412yes—
138C2×#10596831C22×C412yes—
139C2×#10596831C22×C412yes—
140C2×#10596831C22×C412yes—
141C4⋊Dic73—21no—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—81no—
150C4⋊Dic73—81no—
151C22⋊Dic73—81no—
152C22⋊Dic73—81no—
153C4×Dic73—81no—
154C4×Dic73—81no—
155C24×C73C2×D411yescharacteristic
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73C22×C412yes—
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×Q812yes—
171C22×C4×C73C2411yescharacteristic
172C4⋊C4×C73—21no—
173C4⋊C4×C73—21no—
174C4⋊C4×C73—21no—
175C4⋊C4×C73—21no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—81no—
181C4⋊C4×C73—81no—
182C4⋊C4×C73C4⋊C414yes—
183C4⋊C4×C73C4⋊C414yes—
184C22⋊C4×C73—81no—
185C22⋊C4×C73—81no—
186C22⋊C4×C73C4⋊C414yes—
187C22⋊C4×C73C4⋊C414yes—
188C42×C73—81no—
189C42×C73—81no—
190C42×C73C22×C412yes—
191C42×C73C22×C412yes—
192C42×C73C2×Q812yes—
193C42×C73C2×Q812yes—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73—21no—
197C23×C73—21no—
198C23×C73—21no—
199C23×C73—21no—
200C23×C73C2×C4⋊C412yes—
201C23×C73C22×D411yescharacteristic
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—22no—
213C2×C4×C73—22no—
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73C2×C4⋊C412yes—
229C2×C4×C73C2×C4⋊C412yes—
230C2×C4×C73C2×C4⋊C412yes—
231C2×C4×C73C2×C4⋊C412yes—
232C2×C4×C73C2×C4⋊C412yes—
233C2×C4×C73C23×C411yescharacteristic
234C2×C4×C73C22×Q811yescharacteristic
235C2×C4×C73H(5,𝔽2)11yescharacteristic
236C2×C4×C73H(5,𝔽2)11yescharacteristic
237C2×C4×C732−1+411yescharacteristic
238C2×C4×C732−1+411yescharacteristic
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251#10596831—22no—
252#10596831—22no—
253#10596831—22no—
254#10596831—22no—
255C22×C73—22no—
256C22×C73—22no—
257C22×C73—22no—
258C22×C73—41no—
259C22×C73—41no—
260C22×C73—41no—
261C22×C73—41no—
262C22×C73C22×C4⋊C411yescharacteristic
263C22×C73#53711yescharacteristic
264C22×C73#53711yescharacteristic
265C22×C73#57611yescharacteristic
266C22×C73#57711yescharacteristic
267C22×C73#57711yescharacteristic
268C22×C73#57811yescharacteristic
269C4×C73—22no—
270C4×C73—22no—
271C4×C73—22no—
272C4×C73—22no—
273C4×C73—22no—
274C4×C73—81no—
275C4×C73—81no—
276C4×C73—81no—
277C4×C73—81no—
278C4×C73#51811yescharacteristic
279C4×C73#51911yescharacteristic
280C4×C73#54411yescharacteristic
281C4×C73#54411yescharacteristic
282Dic73—81no—
283Dic73—81no—
284Dic73—81no—
285Dic73—81no—
286#21966—731nomaximal, Sylow
287C2×C73—42no—
288C2×C73#231611yescharacteristic
289C2×C73#291211yescharacteristic
290C2×C73#291311yescharacteristic
291C2×C73#325711yescharacteristic
292C2×C73#325711yescharacteristic
293C2×C73#325811yescharacteristic
294C2×C73#325811yescharacteristic
295C2×#424—731no—
296#2314—731no—
297#2314D7311yescharacteristic
298#1949—731no—
299#1949—731no—
300#1949—731no—
301#1949—731no—
302#1948—731no—
303#1948—731no—
304#1947—731no—
305#1947—731no—
306#1809—731no—
307#1809—731no—
308#1808—731no—
309#1807—731no—
310C73#2196611yescharacteristic, complemented, Sylow
311C22×M16—731no—
312C23×C8—731no—
313C2×#117C2×D7311yescharacteristic
314C2×#107—731no—
315C2×#107—731no—
316C2×#107—731no—
317C2×#107—731no—
318C2×#106—731no—
319C2×#106—731no—
320C2×#106—731no—
321C2×#106—731no—
322#424—738no—
323C2×C4⋊C8—731no—
324C2×C4⋊C8—731no—
325C2×C4⋊C8—731no—
326C2×C4⋊C8—731no—
327#388—21no—
328#388—21no—
329#388—1461no—
330#388—1461no—
331#387—21no—
332#387—21no—
333#387—1461no—
334#387—1461no—
335#384—731no—
336#384C2×D7311yescharacteristic
337#382—731no—
338#382C2×D7311yescharacteristic
339#380—731no—
340#380—731no—
341#380C2×D7311yescharacteristic
342#380C2×D7311yescharacteristic
343C4×C4⋊C4—731no—
344C4×C4⋊C4—731no—
345C4×C4⋊C4C2×D7311yescharacteristic
346C4×C4⋊C4C2×D7311yescharacteristic
347#340—731no—
348#340—731no—
349#340—731no—
350#340—731no—
351#340—731no—
352#340—731no—
353#340—731no—
354#340—731no—
355C23×C4C22×D7311yescharacteristic
356C2×M16—2921no—
357C2×M16—2921no—
358C2×M16—734no—
359C22×C8—2921no—
360C22×C8—2921no—
361C22×C8—734no—
362C22×C8—731no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—731no—
366#117Dic14614yes—
367#117C4×D7314yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—1461no—
375C2×C4⋊C4—1461no—
376C2×C4⋊C4C22⋊D7311yescharacteristic
377C2×C4⋊C4C22⋊D7311yescharacteristic
378C2×C4⋊C4C22×D7311yescharacteristic
379C2×C4⋊C4C22×D7311yescharacteristic
380C2×C4⋊C4C22×D7311yescharacteristic
381C2×C4⋊C4C22×D7311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—1461no—
385C2×C22⋊C4—1461no—
386C2×C22⋊C4C22⋊D7311yescharacteristic
387C2×C22⋊C4C22⋊D7311yescharacteristic
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—1461no—
391C2×C42—1461no—
392C2×C42C22×D7311yescharacteristic
393C2×C42C22×D7311yescharacteristic
394#107—2921no—
395#107—2921no—
396#107—2921no—
397#107—2921no—
398#106—2921no—
399#106—2921no—
400#106—2921no—
401#106—2921no—
402C4⋊C8—734no—
403C4⋊C8—734no—
404C4⋊C8—734no—
405C4⋊C8—734no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—1461no—
413#95—1461no—
414#95—1461no—
415#95—1461no—
416#95—1461no—
417#95—1461no—
418C24C2×C22⋊D7311yescharacteristic
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—1461no—
428C22×C4—1461no—
429C22×C4—1461no—
430C22×C4—1461no—
431C22×C4C2×C4×D7312yes—
432C22×C4C2×C22⋊D7311yescharacteristic
433C22×C4C2×C22⋊D7311yescharacteristic
434C22×C4C2×C22⋊D7311yescharacteristic
435C22×C4C2×C22⋊D7311yescharacteristic
436C22×C4C2×C22⋊D7311yescharacteristic
437C22×C4C2×Dic14612yes—
438C22×C4C23×D7311yescharacteristic
439M16—2924no—
440C2×C8—2924no—
441C2×C8—732no—
442C2×C8—732no—
443C2×C8—732no—
444C2×C8—732no—
445C2×C8—1461no—
446C2×C8—1461no—
447C2×C8—1461no—
448C2×C8—1461no—
449C2×C8—1461no—
450C2×C8—1461no—
451C2×C8—1461no—
452C2×C8—1461no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—5841no—
464C4⋊C4—5841no—
465C4⋊C4—1461no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4#1192400714yes—
474C4⋊C4#1192400714yes—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C22⋊C4—5841no—
478C22⋊C4—5841no—
479C22⋊C4#1192400714yes—
480C22⋊C4#1192400714yes—
481C42—81no—
482C42—81no—
483C42—5841no—
484C42—5841no—
485C42C2×C4×D7312yes—
486C42C2×C4×D7312yes—
487C42C2×Dic14612yes—
488C42C2×Dic14612yes—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23C2×#1192400712yes—
496C23C22×C22⋊D7311yescharacteristic
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—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—2921no—
524C2×C4—2921no—
525C2×C4—2921no—
526C2×C4—2921no—
527C2×C4—2921no—
528C2×C4—2921no—
529C2×C4—2921no—
530C2×C4—2921no—
531C2×C4—2921no—
532C2×C4—2921no—
533C2×C4—2921no—
534C2×C4—2921no—
535C2×C4C2×#1192400712yes—
536C2×C4C2×#1192400712yes—
537C2×C4C2×#1192400712yes—
538C2×C4C2×#1192400712yes—
539C2×C4C2×#1192400712yes—
540C2×C4C22×C4×D7311yescharacteristic
541C2×C4C22×Dic14611yescharacteristic
542C2×C4#1455663711yescharacteristic
543C2×C4#1455663711yescharacteristic
544C2×C4#1455663811yescharacteristic
545C2×C4#1455663811yescharacteristic
546C8—1462no—
547C8—1462no—
548C8—1462no—
549C8—1462no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C22×#1192400711yescharacteristic
558C22#1798916511yescharacteristic
559C22#1798916511yescharacteristic
560C22#1798939011yescharacteristic
561C22#1798939511yescharacteristic
562C22#1798939811yescharacteristic
563C22#1798940211yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—22no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—5841no—
574C4—5841no—
575C4—5841no—
576C4—5841no—
577C4#1798906111yescharacteristic
578C4#1798906411yescharacteristic
579C4#1798921511yescharacteristic
580C4#1798921511yescharacteristic
581C2—42no—
582C2#2261254711yescharacteristic
583C2#2261852411yescharacteristic
584C2#2261852911yescharacteristic
585C2#2262133611yescharacteristic
586C2#2262134211yescharacteristic
587C2#2262135111yescharacteristic
588C2#2262135711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2314C2
socleC23×C73C22×D4
prime radicalC24×C73C2×D4
cosocleC22×C4×C73C24
hypercenter#2314D73
hypocenterC73#21966
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #22610699C2semidirect
4. #22610699C2semidirect
5. #22610697C2semidirect
6. #22610697C2semidirect
7. #22610694C2semidirect
8. #22610692C2semidirect
9. #22610689C2semidirect
10. #22610687C2semidirect
26. #17988614C4semidirect
310. C73#21966semidirect

Maximal subgroups

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

subgroupindex
C2×#179886142
#226125402
#226106992
#226106972
#226106942
#226106922
#226106892
#226106872
#226099622
#226099582
#226099542
C73×#23142
#2196673