Finite Group Databasebeta

← #33185757

Subgroups — #33185757

Order 18688.

690 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612642C211yesmaximal, characteristic
2#22611494C211yesmaximal, characteristic, complemented
3#22611489C211yesmaximal, characteristic, complemented
4#22611172C211yesmaximal, characteristic
5#22611172C211yesmaximal, characteristic
6#22610627C211yesmaximal, characteristic
7#22610620C211yesmaximal, characteristic, complemented
8#22610613C211yesmaximal, characteristic
9#22610606C211yesmaximal, characteristic, complemented
10#22609943C211yesmaximal, characteristic, complemented
11#22609938C211yesmaximal, characteristic
12#22609933C211yesmaximal, characteristic, complemented
13#22609928C211yesmaximal, characteristic
14#22609788C211yesmaximal, characteristic, complemented
15C73×#2647C211yesmaximal, characteristic, complemented
16C2×#14556579C2211yescharacteristic
17C2×C4×Dic146C2211yescharacteristic
18C2×C4×D292C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×#14556514C2211yescharacteristic
22C2×#14556514C2211yescharacteristic
23C2×#14556514C2211yescharacteristic
24C2×#14556514C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×#14556511C2211yescharacteristic
29C2×#14556502C2211yescharacteristic
30C2×C4×#10596831C2211yescharacteristic
31#17988493C2211yescharacteristic
32#17988489C2211yescharacteristic
33#17988479—21no—
34#17988479—21no—
35#17988461—21no—
36#17988461—21no—
37#17988457C2211yescharacteristic
38#17988349C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48#400×C73—21no—
49#400×C73—21no—
50#398×C73—21no—
51#398×C73—21no—
52#389×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#389×C73C2211yescharacteristic
55#389×C73C2211yescharacteristic
56#384×C73C2211yescharacteristic
57#382×C73C2211yescharacteristic
58#376×C73C2211yescharacteristic
59C22×Dic146C2311yescharacteristic
60C22×D292C2311yescharacteristic
61C22×C4×D73—21no—
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66#14556579—22no—
67#14556579—22no—
68C4×Dic146—22no—
69C4×Dic146—22no—
70C4×D292—22no—
71C4×D292—22no—
72C2×C4⋊Dic73—21no—
73C2×C4⋊Dic73—21no—
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×#11924007—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×#11924005—21no—
81C2×#11924005—21no—
82C2×C4×Dic73—21no—
83C4⋊#10596831—22no—
84C4⋊#10596831—22no—
85#14556514—22no—
86#14556514—22no—
87#14556514—41no—
88#14556514—41no—
89#14556511—22no—
90#14556511—22no—
91#14556511—41no—
92#14556511—41no—
93#14556502—41no—
94C4×#10596831—41no—
95#14556498—21no—
96#14556498—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—21no—
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C42×C73C2311yescharacteristic
108C2×C42×C73C2311yescharacteristic
109C2×C42×C73C2311yescharacteristic
110#95×C73—21no—
111#95×C73—21no—
112#95×C73—21no—
113#95×C73—21no—
114#95×C73—21no—
115#95×C73—21no—
116#95×C73D411yescharacteristic
117#95×C73D411yescharacteristic
118#95×C73D411yescharacteristic
119#95×C73D411yescharacteristic
120C23×D73—21no—
121C2×Dic146—21no—
122C2×Dic146—21no—
123C2×Dic146—21no—
124C2×Dic146—21no—
125C2×Dic146—21no—
126C2×Dic146#4112yes—
127C2×D292—21no—
128C2×D292—21no—
129C2×D292—21no—
130C2×D292—21no—
131C2×D292—21no—
132C2×D292#4112yes—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C2×C4×D73—42no—
137C2×C4×D73—81no—
138C2×C4×D73—81no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—81no—
156C4⋊Dic73—81no—
157#11924007—42no—
158#11924005—24no—
159#11924005—24no—
160#11924005—42no—
161#11924005—81no—
162#11924005—81no—
163C4×Dic73—42no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2411yescharacteristic
175C4⋊C4×C73—21no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—81no—
184C4⋊C4×C73—81no—
185C4⋊C4×C73—81no—
186C4⋊C4×C73—81no—
187C4⋊C4×C73—81no—
188C4⋊C4×C73—81no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73#4112yes—
194C42×C73#4112yes—
195C23×C73C22×D411yescharacteristic
196C22×D73—22no—
197C22×D73—41no—
198C22×D73—41no—
199C22×D73—41no—
200C22×D73—41no—
201C22×D73—41no—
202C22×D73—41no—
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×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
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×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73#12412yes—
232C2×C4×C73#12412yes—
233C2×C4×C73C2×#4111yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C2×C4×C73C2×#4111yescharacteristic
236C2×C4×C73C2×#4111yescharacteristic
237C2×C4×C73H(5,𝔽2)11yescharacteristic
238C2×C4×C732−1+411yescharacteristic
239C2×Dic73—22no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248D292—22no—
249D292—22no—
250D292—41no—
251D292—41no—
252C4×D73—84no—
253Dic146—22no—
254Dic146—22no—
255Dic146—41no—
256Dic146—41no—
257#10596831—41no—
258#10596831—41no—
259#10596831—41no—
260#10596831—41no—
261C22×C73#52511yescharacteristic
262C22×C73C2×#12411yescharacteristic
263C22×C73#53711yescharacteristic
264C22×C73#57611yescharacteristic
265C22×C73#57711yescharacteristic
266C22×C73#57711yescharacteristic
267C22×C73#57811yescharacteristic
268C2×D73—42no—
269C2×D73—42no—
270C2×D73—42no—
271C2×D73—81no—
272C2×D73—81no—
273C2×D73—81no—
274C2×D73—81no—
275C4×C73—22no—
276C4×C73—22no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—81no—
282C4×C73—81no—
283C4×C73—81no—
284C4×C73—81no—
285C4×C73#55211yescharacteristic
286C4×C73#55211yescharacteristic
287C4×C73#55311yescharacteristic
288C4×C73#55311yescharacteristic
289Dic73—42no—
290Dic73—81no—
291Dic73—81no—
292#29134—731nomaximal, Sylow
293C2×C73#256211yescharacteristic
294C2×C73#311911yescharacteristic
295C2×C73#312011yescharacteristic
296C2×C73#313611yescharacteristic
297C2×C73#313711yescharacteristic
298C2×C73#326211yescharacteristic
299C2×C73#326311yescharacteristic
300D73—82no—
301#2647D7311yescharacteristic, complemented
302#2326—731no—
303#2100—731no—
304#2099—731no—
305#2042—731no—
306#2042—731no—
307#1936—731no—
308#1935—731no—
309#1934—731no—
310#1933—731no—
311#1805—731no—
312#1804—731no—
313#1803—731no—
314#1802—731no—
315#1768—731no—
316C73#2913411yescharacteristic, complemented, Sylow
317C2×#124—731no—
318C2×C4×Q8—731no—
319C2×C4×D4—731no—
320C2×C4⋊C8—731no—
321C2×C4⋊C8—731no—
322C2×#103—731no—
323C2×#103—731no—
324C2×#103—731no—
325C2×#103—731no—
326C2×#102—731no—
327C2×#102—731no—
328C2×#102—731no—
329C2×#102—731no—
330C2×#97—731no—
331C2×C4×C8—731no—
332#400—21no—
333#400—21no—
334#398—21no—
335#398—21no—
336#391—731no—
337#390—731no—
338#389C2×D7311yescharacteristic
339#389C2×D7311yescharacteristic
340#389C2×D7311yescharacteristic
341#389C2×D7311yescharacteristic
342#388—1461no—
343#388—1461no—
344#385—1461no—
345#385—1461no—
346#384—731no—
347#384C2×D7311yescharacteristic
348#382C2×D7311yescharacteristic
349#376C2×D7311yescharacteristic
350#340—731no—
351#340—731no—
352#340—731no—
353#340—731no—
354#340—731no—
355#340—731no—
356#340—731no—
357#340—731no—
358#336—731no—
359#336—731no—
360C22×Q8—731no—
361C22×D4—731no—
362C23×C4—1461no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—731no—
366C22×C8—731no—
367#124—1462no—
368#124—1462no—
369C4×Q8—1462no—
370C4×Q8—1462no—
371C4×D4—1462no—
372C4×D4—1462no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—731no—
381C2×C4⋊C4—1461no—
382C2×C4⋊C4—1461no—
383C2×C4⋊C4—1461no—
384C2×C4⋊C4C22×D7311yescharacteristic
385C2×C4⋊C4C22×D7311yescharacteristic
386C2×C4⋊C4C22×D7311yescharacteristic
387C2×C4⋊C4C22×D7311yescharacteristic
388C2×C22⋊C4—1461no—
389C2×C22⋊C4—1461no—
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C22⋊C4—1461no—
393C2×C42—1461no—
394C2×C42C22×D7311yescharacteristic
395C2×C42C22×D7311yescharacteristic
396C2×C42C22×D7311yescharacteristic
397C4⋊C8—1462no—
398C4⋊C8—1462no—
399#103—2921no—
400#103—2921no—
401#103—1462no—
402#103—1462no—
403#102—2921no—
404#102—2921no—
405#102—1462no—
406#102—1462no—
407#97—2921no—
408C4×C8—2921no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—1461no—
416#95—1461no—
417#95C22⋊D7311yescharacteristic
418#95C22⋊D7311yescharacteristic
419#95C22⋊D7311yescharacteristic
420#95C22⋊D7311yescharacteristic
421C24—1461no—
422C2×Q8—732no—
423C2×Q8—1461no—
424C2×Q8—1461no—
425C2×Q8—1461no—
426C2×Q8—1461no—
427C2×Q8—1461no—
428C2×D4—732no—
429C2×D4—1461no—
430C2×D4—1461no—
431C2×D4—1461no—
432C2×D4—1461no—
433C2×D4—1461no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—2922no—
439C22×C4—5841no—
440C22×C4—5841no—
441C22×C4—1461no—
442C22×C4—1461no—
443C22×C4—1461no—
444C22×C4C2×C22⋊D7311yescharacteristic
445C22×C4C2×C22⋊D7311yescharacteristic
446C22×C4C2×C22⋊D7311yescharacteristic
447C22×C4C2×C22⋊D7311yescharacteristic
448C22×C4C2×C22⋊D7311yescharacteristic
449C22×C4C2×C22⋊D7311yescharacteristic
450C22×C4C23×D7311yescharacteristic
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—
461C2×C8—1461no—
462C2×C8—1461no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—2922no—
478C4⋊C4—5841no—
479C4⋊C4—5841no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C22⋊C4—2922no—
485C22⋊C4—5841no—
486C22⋊C4—5841no—
487C22⋊C4—1464no—
488C22⋊C4—1464no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—2922no—
494C42#1192402912yes—
495C42#1192402912yes—
496C23—2921no—
497C23—2921no—
498C23—2921no—
499C23—2921no—
500C23—2921no—
501C23—2921no—
502C23—1462no—
503C23C22×C22⋊D7311yescharacteristic
504Q8—2921no—
505Q8—2921no—
506Q8—1462no—
507Q8—1462no—
508D4—2921no—
509D4—2921no—
510D4—1462no—
511D4—1462no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—5844no—
549C2×C4—1462no—
550C2×C4#1455658012yes—
551C2×C4#1455658012yes—
552C2×C4#41×D7311yescharacteristic
553C2×C4#41×D7311yescharacteristic
554C2×C4C2×#1192402911yescharacteristic
555C2×C4C2×#1192402911yescharacteristic
556C2×C4#1455663711yescharacteristic
557C2×C4#1455663811yescharacteristic
558C8—2921no—
559C8—2921no—
560C8—2921no—
561C8—2921no—
562C22—2922no—
563C22—2922no—
564C22—2922no—
565C22—5841no—
566C22—5841no—
567C22—5841no—
568C22—5841no—
569C22#1798909411yescharacteristic
570C22C2×#1455658011yescharacteristic
571C22#1798916511yescharacteristic
572C22#1798939011yescharacteristic
573C22#1798939511yescharacteristic
574C22#1798939811yescharacteristic
575C22#1798940211yescharacteristic
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—2922no—
587C4—5841no—
588C4—5841no—
589C4#1798927511yescharacteristic
590C4#1798927511yescharacteristic
591C4#1798929011yescharacteristic
592C4#1798929011yescharacteristic
593C2—5842no—
594C2#2261509811yescharacteristic
595C2#2262012411yescharacteristic
596C2#2262013911yescharacteristic
597C2#2262029011yescharacteristic
598C2#2262030111yescharacteristic
599C2#2262138711yescharacteristic
600C2#2262139611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2647C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#2647D73
hypocenterC73#29134
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ #376 ◁ #2647

Complements

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

NH ≅ G/Ntype
2. #22611494C2semidirect
3. #22611489C2semidirect
7. #22610620C2semidirect
9. #22610606C2semidirect
10. #22609943C2semidirect
12. #22609933C2semidirect
14. #22609788C2semidirect
15. C73×#2647C2semidirect
301. #2647D73semidirect
316. C73#29134semidirect

Maximal subgroups

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

subgroupindex
#226126422
#226114942
#226114892
#226111722
#226106272
#226106202
#226106132
#226106062
#226099432
#226099382
#226099332
#226099282
#226097882
C73×#26472
#2913473