Finite Group Databasebeta

← #33096357

Subgroups — #33096357

Order 18688.

818 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C8×D73C211yesmaximal, characteristic
2#22612327C211yesmaximal, characteristic
3#22612324C211yesmaximal, characteristic
4#22610702C211yesmaximal, characteristic, complemented
5#22610701C211yesmaximal, characteristic, complemented
6#22610700C211yesmaximal, characteristic, complemented
7#22610699C211yesmaximal, characteristic, complemented
8#22610698C211yesmaximal, characteristic, complemented
9#22610697C211yesmaximal, characteristic, complemented
10#22610696C211yesmaximal, characteristic, complemented
11#22609959C211yesmaximal, characteristic
12#22609957C211yesmaximal, characteristic
13#22609955C211yesmaximal, characteristic
14#22609953C211yesmaximal, characteristic
15C73×#1949C211yesmaximal, characteristic, complemented
16C22×C8×D73C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×C42×D73C2211yescharacteristic
19C2×#14556525C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556524C2211yescharacteristic
22C2×#14556523C2211yescharacteristic
23C2×#14556522C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×#14556520C2211yescharacteristic
27C2×#14556520C2211yescharacteristic
28C4⋊C8×D73C418yescomplemented
29#17988454—21no—
30#17988454—21no—
31#17988453C2211yescharacteristic
32#17988452C2211yescharacteristic
33#17988452C2211yescharacteristic
34#17988449—21no—
35#17988449—21no—
36#17988444C2211yescharacteristic
37#17988444C2211yescharacteristic
38#17988444C2211yescharacteristic
39#17988444C2211yescharacteristic
40C4⋊C4×Dic73C2211yescharacteristic
41C4⋊C4×Dic73C2211yescharacteristic
42C4×C4⋊Dic73C2211yescharacteristic
43C4×#11924005—21no—
44#17988434—21no—
45#17988433—21no—
46#17988432—21no—
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53C2×#107×C73C2211yescharacteristic
54C2×#106×C73C2211yescharacteristic
55C2×C4⋊C8×C73C2211yescharacteristic
56#382×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60C22×C4×D73D411yescharacteristic
61C22×C4×D73D411yescharacteristic
62C22×C4×D73C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C2×C8×D73—41no—
66C2×C8×D73—41no—
67C2×C8×D73—41no—
68C2×C8×D73—41no—
69C2×C8×D73C2×C414yes—
70C2×C8×D73C2×C414yes—
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×#11924005—21no—
76C2×#11924005—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79C2×C4×Dic73—21no—
80C2×C4×Dic73—21no—
81C2×C4×Dic73—21no—
82C2×C4×Dic73D411yescharacteristic
83C2×C4×Dic73D411yescharacteristic
84C2×C4×Dic73C2311yescharacteristic
85C42×D73C2×C414yes—
86C42×D73Q814yes—
87#14556525—41no—
88#14556524—41no—
89#14556524—41no—
90#14556523—41no—
91#14556522—41no—
92#14556522—41no—
93C4⋊#10596831C2×C414yes—
94#14556520C2×C414yes—
95#14556520C2×C414yes—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109C22×C8×C73C2311yescharacteristic
110C22×C8×C73C2311yescharacteristic
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C42×C73—21no—
116C2×C42×C73C2311yescharacteristic
117#107×C73—41no—
118#106×C73—41no—
119C4⋊C8×C73C2×C414yes—
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—22no—
132C2×C4×D73—22no—
133C2×C4×D73—21no—
134C2×C4×D73—21no—
135C2×C4×D73—21no—
136C2×C4×D73—21no—
137C2×C4×D73—41no—
138C2×C4×D73—41no—
139C2×C4×D73C4⋊C414yes—
140C2×C4×D73C4⋊C414yes—
141C2×C4×D73C22×C412yes—
142C2×C4×D73C2×Q812yes—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831C22×C412yes—
148C2×#10596831C22×C412yes—
149C8×D73—44no—
150C8×D73—44no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159#11924005—42no—
160#11924005—42no—
161#11924005—42no—
162#11924005—42no—
163C4×Dic73—42no—
164C4×Dic73—42no—
165C4×Dic73—42no—
166C4×Dic73C4⋊C414yes—
167C4×Dic73C4⋊C414yes—
168C4×Dic73C22×C412yes—
169C4×Dic73C2×Q812yes—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2411yescharacteristic
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73C22×C412yes—
182C2×C8×C73C22×C412yes—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C42×C73—42no—
192C42×C73C22×C412yes—
193C42×C73C2×Q812yes—
194C23×C73C22×D411yescharacteristic
195C22×D73—21no—
196C22×D73—21no—
197C22×D73—21no—
198C22×D73—21no—
199C22×D73C2×C4⋊C412yes—
200C22×D73#13512yes—
201C22×D73#13512yes—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—41no—
207C2×C4×C73—41no—
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×C73C2×C4⋊C412yes—
219C2×C4×C73C2×C4⋊C412yes—
220C2×C4×C73C23×C411yescharacteristic
221C2×C4×C73C22×Q811yescharacteristic
222C2×C4×C73H(5,𝔽2)11yescharacteristic
223C2×C4×C73H(5,𝔽2)11yescharacteristic
224C2×C4×C732−1+411yescharacteristic
225C2×C4×C732−1+411yescharacteristic
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—41no—
233C2×Dic73—41no—
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×Dic73C2×C4⋊C412yes—
245C2×Dic73C2×C4⋊C412yes—
246C2×Dic73C2×C4⋊C412yes—
247C4×D73—28no—
248C4×D73—22no—
249C4×D73—22no—
250C4×D73—22no—
251C4×D73—22no—
252C4×D73—44no—
253C8×C73—22no—
254C8×C73—22no—
255#10596831—22no—
256#10596831—22no—
257C22×C73C22×C4⋊C411yescharacteristic
258C22×C73#53711yescharacteristic
259C22×C73#53711yescharacteristic
260C22×C73C2×#13511yescharacteristic
261C22×C73C2×#13511yescharacteristic
262C22×C73#57511yescharacteristic
263C22×C73#57511yescharacteristic
264C2×D73—22no—
265C2×D73—22no—
266C2×D73—22no—
267C2×D73—22no—
268C2×D73—22no—
269C2×D73—22no—
270C2×D73#42714yes—
271C4×C73—22no—
272C4×C73—22no—
273C4×C73—81no—
274C4×C73—81no—
275C4×C73—81no—
276C4×C73—81no—
277C4×C73#51811yescharacteristic
278C4×C73#51911yescharacteristic
279C4×C73#54411yescharacteristic
280C4×C73#54411yescharacteristic
281Dic73—22no—
282Dic73—22no—
283Dic73—22no—
284Dic73—81no—
285Dic73—81no—
286Dic73—81no—
287Dic73—81no—
288#21960—731nomaximal, Sylow
289C2×C73#231611yescharacteristic
290C2×C73C2×#42711yescharacteristic
291C2×C73#291111yescharacteristic
292C2×C73#325011yescharacteristic
293C2×C73#325011yescharacteristic
294C2×C73#325011yescharacteristic
295C2×C73#325011yescharacteristic
296D73—24no—
297C22×C4⋊C8—731no—
298#2283—731no—
299#2283—731no—
300#1949—731no—
301#1949—731no—
302#1949—731no—
303#1949—731no—
304#1949—731no—
305#1949—731no—
306#1949—731no—
307#1949D7311yescharacteristic, complemented
308#1808—731no—
309#1808—731no—
310#1807—731no—
311#1807—731no—
312C73#2196011yescharacteristic, complemented, Sylow
313C23×C8—731no—
314C23×C8—731no—
315C22×C42—731no—
316C2×#107—731no—
317C2×#107—731no—
318C2×#107—731no—
319C2×#107C2×D7311yescharacteristic
320C2×#106—731no—
321C2×#106—731no—
322C2×#106—731no—
323C2×#106C2×D7311yescharacteristic
324C2×C4⋊C8—731no—
325C2×C4⋊C8—731no—
326C2×C4⋊C8—731no—
327C2×C4⋊C8—738no—
328C2×C4⋊C8C2×D7311yescharacteristic
329#383—1461no—
330#383—1461no—
331#382—731no—
332#382—731no—
333#382—731no—
334#382C2×D7311yescharacteristic
335#381—1461no—
336#381—1461no—
337#380—731no—
338#380—731no—
339#380—731no—
340#380—731no—
341C4×C4⋊C4—731no—
342C4×C4⋊C4—731no—
343C4×C4⋊C4—731no—
344C4×C4⋊C4C2×D7311yescharacteristic
345C4×C22⋊C4—1461no—
346C4×C22⋊C4—1461no—
347#376—1461no—
348#376—1461no—
349#340—731no—
350#340—731no—
351#340—731no—
352#340—731no—
353#340—731no—
354#340—731no—
355#340C2×D7311yescharacteristic
356#340C2×D7311yescharacteristic
357C23×C4—731no—
358C23×C4—731no—
359C23×C4—731no—
360C22×C8—2921no—
361C22×C8—2921no—
362C22×C8—2921no—
363C22×C8—2921no—
364C22×C8—734no—
365C22×C8—734no—
366C22×C8—731no—
367C22×C8—731no—
368C22×C8C22×D7311yescharacteristic
369C22×C8C22×D7311yescharacteristic
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4C22×D7311yescharacteristic
375C2×C4⋊C4C22×D7311yescharacteristic
376C2×C4⋊C4C22×D7311yescharacteristic
377C2×C4⋊C4C22×D7311yescharacteristic
378C2×C22⋊C4—1461no—
379C2×C22⋊C4—1461no—
380C2×C22⋊C4—1461no—
381C2×C22⋊C4—1461no—
382C2×C42—21no—
383C2×C42—731no—
384C2×C42—731no—
385C2×C42—731no—
386C2×C42—734no—
387C2×C42—734no—
388C2×C42—1461no—
389C2×C42—1461no—
390C2×C42—1461no—
391C2×C42C22×D7311yescharacteristic
392#107—41no—
393#107—2921no—
394#107—2921no—
395#107—2921no—
396#106—41no—
397#106—2921no—
398#106—2921no—
399#106—2921no—
400C4⋊C8—734no—
401C4⋊C8—734no—
402C4⋊C8—734no—
403C4⋊C8C4×D7314yes—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—1461no—
408#95—1461no—
409#95—1461no—
410#95—1461no—
411#95—1461no—
412#95—1461no—
413#95—1461no—
414#95—1461no—
415#95—1461no—
416#95—1461no—
417#95—1461no—
418#95—1461no—
419#95—1461no—
420C24—731no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—2921no—
426C22×C4—2921no—
427C22×C4—734no—
428C22×C4—731no—
429C22×C4—731no—
430C22×C4—731no—
431C22×C4—734no—
432C22×C4—732no—
433C22×C4—732no—
434C22×C4—1462no—
435C22×C4—1462no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4—1461no—
440C22×C4—1461no—
441C22×C4—1461no—
442C22×C4—1461no—
443C22×C4—1461no—
444C22×C4D4×D7311yescharacteristic
445C22×C4D4×D7311yescharacteristic
446C22×C4C23×D7311yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—2924no—
452C2×C8—2924no—
453C2×C8—732no—
454C2×C8—732no—
455C2×C8—1461no—
456C2×C8—1461no—
457C2×C8—1461no—
458C2×C8—1461no—
459C2×C8C2×C4×D7312yes—
460C2×C8C2×C4×D7312yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C4⋊C4—1461no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C22⋊C4—2922no—
478C22⋊C4—2922no—
479C22⋊C4—2922no—
480C22⋊C4—2922no—
481C42—42no—
482C42—2922no—
483C42—2922no—
484C42—2922no—
485C42—734no—
486C42—734no—
487C42—732no—
488C42—732no—
489C42C2×C4×D7312yes—
490C42Q8×D7312yes—
491C23—732no—
492C23—732no—
493C23—732no—
494C23—1461no—
495C23—1461no—
496C23—1461no—
497C23—1461no—
498C23C2×D4×D7311yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
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—2924no—
516C2×C4—2921no—
517C2×C4—2921no—
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—732no—
529C2×C4—732no—
530C2×C4—732no—
531C2×C4—1468no—
532C2×C4—1461no—
533C2×C4—1461no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4—1462no—
539C2×C4—1462no—
540C2×C4—1462no—
541C2×C4—1462no—
542C2×C4C4⋊C4×D7312yes—
543C2×C4C4⋊C4×D7312yes—
544C2×C4C22×C4×D7311yescharacteristic
545C2×C4C2×Q8×D7311yescharacteristic
546C2×C4#1455663611yescharacteristic
547C2×C4#1455663711yescharacteristic
548C2×C4#1455663811yescharacteristic
549C2×C4#1455663911yescharacteristic
550C8—22no—
551C8—22no—
552C8—1462no—
553C8—1462no—
554C22—734no—
555C22—1462no—
556C22—1462no—
557C22—1462no—
558C22—1462no—
559C22—1462no—
560C22—1462no—
561C22C2×C4⋊C4×D7311yescharacteristic
562C22#1798916611yescharacteristic
563C22#1798916711yescharacteristic
564C22#135×D7311yescharacteristic
565C22#135×D7311yescharacteristic
566C22#1798938311yescharacteristic
567C22#1798938611yescharacteristic
568C4—22no—
569C4—22no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—5841no—
575C4—5841no—
576C4—5841no—
577C4—5841no—
578C4—1462no—
579C4—1462no—
580C4—1462no—
581C4#1798905911yescharacteristic
582C4#1798906311yescharacteristic
583C4#1798921411yescharacteristic
584C4#1798921711yescharacteristic
585C2—1464no—
586C2#2261254611yescharacteristic
587C2#427×D7311yescharacteristic
588C2#2261851811yescharacteristic
589C2#2262128011yescharacteristic
590C2#2262128111yescharacteristic
591C2#2262128211yescharacteristic
592C2#2262128511yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1949C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1949D73
hypocenterC73#21960
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #22610702C2semidirect
5. #22610701C2semidirect
6. #22610700C2semidirect
7. #22610699C2semidirect
8. #22610698C2semidirect
9. #22610697C2semidirect
10. #22610696C2semidirect
15. C73×#1949C2semidirect
28. C4⋊C8×D73C4semidirect
307. #1949D73semidirect
312. C73#21960semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D732
#226123272
#226123242
#226107022
#226107012
#226107002
#226106992
#226106982
#226106972
#226106962
#226099592
#226099572
#226099552
#226099532
C73×#19492
#2196073