Finite Group Databasebeta

← #33144153

Subgroups — #33144153

Order 18688.

706 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#22614952C211yesmaximal, characteristic, complemented
2#22612902C211yesmaximal, characteristic
3#22611318C211yesmaximal, characteristic
4#22611304C211yesmaximal, characteristic
5#22611078C211yesmaximal, characteristic
6#22611068C211yesmaximal, characteristic
7#22610886C211yesmaximal, characteristic, complemented
8#22610882C211yesmaximal, characteristic, complemented
9#22610701C211yesmaximal, characteristic, complemented
10#22610524C211yesmaximal, characteristic, complemented
11#22610517C211yesmaximal, characteristic, complemented
12#22610062C211yesmaximal, characteristic, complemented
13#22609942C211yesmaximal, characteristic
14C4×#14556513C211yesmaximal, characteristic
15C73×#1939C211yesmaximal, characteristic, complemented
16C2×#14556591C2211yescharacteristic
17C2×#14556583C2211yescharacteristic
18C2×C4×D292C2211yescharacteristic
19C2×#14556525C2211yescharacteristic
20C2×#14556523C2211yescharacteristic
21C2×#14556513C2211yescharacteristic
22C2×#14556513C2211yescharacteristic
23C2×#14556513C2211yescharacteristic
24C2×#14556513C2211yescharacteristic
25#17988520—21no—
26#17988507—21no—
27#17988491—21no—
28#17988489C2211yescharacteristic
29#17988489C2211yescharacteristic
30#17988485C2211yescharacteristic
31#17988485C2211yescharacteristic
32#17988484—21no—
33#17988477—21no—
34#17988477—21no—
35#17988453C2211yescharacteristic
36#17988453C2211yescharacteristic
37#17988449—21no—
38C4×C4⋊Dic73C2211yescharacteristic
39C4×C4⋊Dic73C2211yescharacteristic
40C4×C4⋊Dic73C2211yescharacteristic
41#17988434—21no—
42#17988350C2211yescharacteristic
43#17988350C2211yescharacteristic
44#17988350C2211yescharacteristic
45#17988350C2211yescharacteristic
46#17988350C2211yescharacteristic
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988350C2211yescharacteristic
51#17988350C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55C2×C4×C8×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×Dic146—21no—
60C22×D292C2311yescharacteristic
61C22×C4×D73—21no—
62#14556591—22no—
63#14556591—41no—
64#14556583—22no—
65#14556583—41no—
66C4×D292—22no—
67C4×D292Q814yescomplemented
68C2×C4⋊Dic73—21no—
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×#11924007—21no—
77C2×#11924007—21no—
78C2×#11924007—21no—
79C2×#11924007—21no—
80C2×#11924005—21no—
81C2×#11924005—21no—
82C2×#11924005—21no—
83C2×#11924005—21no—
84C2×#11924005—21no—
85C2×C4×Dic73—21no—
86C2×C4×Dic73—21no—
87C2×C4×Dic73—21no—
88#14556525—22no—
89#14556523—22no—
90#14556513—22no—
91#14556513—22no—
92#14556513—41no—
93#14556513—41no—
94#14556498—21no—
95#14556498—21no—
96#14556498—21no—
97#14556498—21no—
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101#14556498—21no—
102#14556498—21no—
103C22×C8×C73C2311yescharacteristic
104C22×C8×C73C2311yescharacteristic
105C22×C8×C73C2311yescharacteristic
106C22×C8×C73C2311yescharacteristic
107C2×C4⋊C4×C73D411yescharacteristic
108C2×C4⋊C4×C73D411yescharacteristic
109C2×C42×C73C2311yescharacteristic
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112C4⋊C8×C73—22no—
113C4⋊C8×C73—41no—
114C4⋊C8×C73—41no—
115C4×C8×C73—22no—
116#95×C73D411yescharacteristic
117#95×C73D411yescharacteristic
118C23×D73—21no—
119C2×Dic146—42no—
120C2×Dic146—42no—
121C2×Dic146—81no—
122C2×D292—21no—
123C2×D292—21no—
124C2×D292—21no—
125C2×D292—21no—
126C2×D292—21no—
127C2×D292C2×Q812yes—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C2×C4×D73—24no—
136C2×C4×D73—81no—
137C2×C4×D73—81no—
138C4⋊Dic73—21no—
139C4⋊Dic73—21no—
140C4⋊Dic73—21no—
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—42no—
150C4⋊Dic73C2×Q812yes—
151C4⋊Dic73#4112yes—
152C4⋊Dic73#4112yes—
153#11924007—42no—
154#11924007—42no—
155#11924007—42no—
156#11924007—81no—
157#11924005—24no—
158#11924005—42no—
159#11924005—42no—
160#11924005—81no—
161#11924005—81no—
162C4×Dic73—81no—
163C4×Dic73—81no—
164C4×Dic73—81no—
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
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—
184C4⋊C4×C73—22no—
185C4⋊C4×C73—41no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73C2×Q812yes—
191C42×C73#4112yes—
192C23×C73C22×D411yescharacteristic
193C22×D73—22no—
194C22×D73—41no—
195C22×D73—41no—
196C22×D73—41no—
197C22×D73—41no—
198C22×D73—41no—
199C22×D73—41no—
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×C73C22⋊Q812yes—
216C2×C4×C73C22⋊Q812yes—
217C2×C4×C73#13512yes—
218C2×C4×C73C22×Q811yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C2×C4×C73C2×#4111yescharacteristic
221C2×C4×C73C2×#4111yescharacteristic
222C2×C4×C73H(5,𝔽2)11yescharacteristic
223C2×C4×C732−1+411yescharacteristic
224C2×Dic73—22no—
225C2×Dic73—22no—
226C2×Dic73—22no—
227C2×Dic73—41no—
228C2×Dic73—41no—
229C2×Dic73—41no—
230C2×Dic73—41no—
231C2×Dic73—41no—
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×Dic73—41no—
245D292—22no—
246D292—22no—
247D292—41no—
248D292—41no—
249C4×D73—84no—
250Dic146—84no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254C8×C73—41no—
255C22×C73C2×C22⋊Q811yescharacteristic
256C22×C73#54611yescharacteristic
257C22×C73#54811yescharacteristic
258C22×C73C2×#13511yescharacteristic
259C22×C73#57511yescharacteristic
260C22×C73#57611yescharacteristic
261C22×C73#57711yescharacteristic
262C2×D73—42no—
263C2×D73—42no—
264C2×D73—42no—
265C2×D73—81no—
266C2×D73—81no—
267C2×D73—81no—
268C2×D73—81no—
269C4×C73—22no—
270C4×C73—22no—
271C4×C73—22no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73#53311yescharacteristic
276C4×C73#54411yescharacteristic
277C4×C73#55511yescharacteristic
278C4×C73#55611yescharacteristic
279Dic73—42no—
280Dic73—42no—
281Dic73—42no—
282Dic73—81no—
283Dic73—81no—
284Dic73—81no—
285Dic73—81no—
286#26028—731nomaximal, Sylow
287C2×C73#243911yescharacteristic
288C2×C73#307611yescharacteristic
289C2×C73#308111yescharacteristic
290C2×C73#329711yescharacteristic
291C2×C73#332611yescharacteristic
292C2×C73#336511yescharacteristic
293C2×C73#337011yescharacteristic
294D73—82no—
295#2550—731no—
296#2357—731no—
297#2067—731no—
298#2065—731no—
299#2025—731no—
300#2023—731no—
301#1989—731no—
302#1988—731no—
303#1949—731no—
304#1939D7311yescharacteristic, complemented
305#1921—731no—
306#1920—731no—
307#1835—731no—
308#1804—731no—
309C4×#102—731no—
310C73#2602811yescharacteristic, complemented, Sylow
311C2×C4⋊Q8—731no—
312C2×#125—731no—
313C2×C4×D4—731no—
314C2×#107—731no—
315C2×#106—731no—
316C2×C4⋊C8C2×D7311yescharacteristic
317C2×C4⋊C8C2×D7311yescharacteristic
318C2×C4⋊C8C2×D7311yescharacteristic
319C2×#102—731no—
320C2×#102—731no—
321C2×#102—731no—
322C2×#102—731no—
323C2×C4×C8C2×D7311yescharacteristic
324#398—1461no—
325#395—1461no—
326#391—1461no—
327#390—731no—
328#390—731no—
329#389—731no—
330#389—731no—
331#389—1461no—
332#388—1461no—
333#388—1461no—
334#382—731no—
335#382—731no—
336#381—1461no—
337C4×C4⋊C4—731no—
338C4×C4⋊C4—731no—
339C4×C4⋊C4—731no—
340C4×C4⋊C4C2×D7311yescharacteristic
341C4×C22⋊C4—1461no—
342#340—731no—
343#340—731no—
344#340—731no—
345#340—731no—
346#340—731no—
347#340—731no—
348#340—731no—
349#340—731no—
350#340—731no—
351#340—731no—
352#336C2×D7311yescharacteristic
353#336C2×D7311yescharacteristic
354C22×Q8—1461no—
355C22×D4—731no—
356C23×C4—1461no—
357C22×C8C22×D7311yescharacteristic
358C22×C8C22×D7311yescharacteristic
359C22×C8C22×D7311yescharacteristic
360C22×C8C22×D7311yescharacteristic
361C4⋊Q8—2921no—
362C4⋊Q8—1462no—
363#125—2921no—
364#125—1462no—
365C4×D4—734no—
366C4×D4—1462no—
367C2×C4⋊C4—731no—
368C2×C4⋊C4—731no—
369C2×C4⋊C4—731no—
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⋊C4—1461no—
377C2×C4⋊C4—1461no—
378C2×C4⋊C4—1461no—
379C2×C4⋊C4D29211yescharacteristic
380C2×C4⋊C4D29211yescharacteristic
381C2×C22⋊C4—1461no—
382C2×C22⋊C4—1461no—
383C2×C22⋊C4—1461no—
384C2×C22⋊C4—1461no—
385C2×C22⋊C4—1461no—
386C2×C42—1461no—
387C2×C42—1461no—
388C2×C42—1461no—
389C2×C42C22×D7311yescharacteristic
390C2×C42C22×D7311yescharacteristic
391C2×C42C22×D7311yescharacteristic
392#107—1462no—
393#106—1462no—
394C4⋊C8—22no—
395C4⋊C8—41no—
396C4⋊C8—41no—
397#102—2921no—
398#102—2921no—
399#102—1462no—
400#102—1462no—
401C4×C8—22no—
402#95—1461no—
403#95—1461no—
404#95—1461no—
405#95—1461no—
406#95—1461no—
407#95—1461no—
408#95—1461no—
409#95—1461no—
410#95—1461no—
411#95D29211yescharacteristic
412#95D29211yescharacteristic
413C24—1461no—
414C2×Q8—2922no—
415C2×Q8—2922no—
416C2×Q8—5841no—
417C2×D4—732no—
418C2×D4—1461no—
419C2×D4—1461no—
420C2×D4—1461no—
421C2×D4—1461no—
422C2×D4—1461no—
423C22×C4—5841no—
424C22×C4—5841no—
425C22×C4—1461no—
426C22×C4—1461no—
427C22×C4—1461no—
428C22×C4—1461no—
429C22×C4—1461no—
430C22×C4—1461no—
431C22×C4—1461no—
432C22×C4—1464no—
433C22×C4C2×D29211yescharacteristic
434C22×C4C2×D29211yescharacteristic
435C22×C4C2×D29211yescharacteristic
436C22×C4C2×D29211yescharacteristic
437C22×C4C2×D29211yescharacteristic
438C22×C4C2×D29211yescharacteristic
439C22×C4C23×D7311yescharacteristic
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—21no—
450C2×C8—21no—
451C2×C8—21no—
452C4⋊C4—22no—
453C4⋊C4—41no—
454C4⋊C4—2922no—
455C4⋊C4—2922no—
456C4⋊C4—2922no—
457C4⋊C4—2922no—
458C4⋊C4—5841no—
459C4⋊C4—732no—
460C4⋊C4—732no—
461C4⋊C4—732no—
462C4⋊C4—1461no—
463C4⋊C4—1461no—
464C4⋊C4—1461no—
465C4⋊C4—1461no—
466C4⋊C4—1461no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C4⋊C4—1461no—
470C4⋊C4—1461no—
471C4⋊C4—1461no—
472C4⋊C4—1461no—
473C22⋊C4—2922no—
474C22⋊C4—2922no—
475C22⋊C4—5841no—
476C22⋊C4—5841no—
477C22⋊C4—1464no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—5841no—
483C42—5841no—
484C42—5841no—
485C42Q8×D7312yes—
486C42#1192402712yes—
487C23—2921no—
488C23—2921no—
489C23—2921no—
490C23—2921no—
491C23—2921no—
492C23—2921no—
493C23—1462no—
494C23C22×D29211yescharacteristic
495Q8—5844no—
496D4—2921no—
497D4—2921no—
498D4—1462no—
499D4—1462no—
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—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—2921no—
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—2921no—
529C2×C4—2921no—
530C2×C4—2921no—
531C2×C4—2921no—
532C2×C4—2921no—
533C2×C4—5844no—
534C2×C4—1462no—
535C2×C4—1462no—
536C2×C4—1462no—
537C2×C4#1455657112yes—
538C2×C4#1455657112yes—
539C2×C4#1455661312yes—
540C2×C4C2×Q8×D7311yescharacteristic
541C2×C4#41×D7311yescharacteristic
542C2×C4#41×D7311yescharacteristic
543C2×C4C2×#1192402711yescharacteristic
544C2×C4#1455663611yescharacteristic
545C2×C4#1455663911yescharacteristic
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—2922no—
551C22—2922no—
552C22—2922no—
553C22—5841no—
554C22—5841no—
555C22—5841no—
556C22—5841no—
557C22C2×#1455657111yescharacteristic
558C22#1798923211yescharacteristic
559C22#1798924911yescharacteristic
560C22C2×#1455661311yescharacteristic
561C22#1798938711yescharacteristic
562C22#1798939211yescharacteristic
563C22#1798939911yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—2922no—
571C4—2922no—
572C4—2922no—
573C4—5841no—
574C4—5841no—
575C4—5841no—
576C4—5841no—
577C4#1798914311yescharacteristic
578C4#1798921411yescharacteristic
579C4#1798930111yescharacteristic
580C4#1798930811yescharacteristic
581C2—5842no—
582C2#2261362011yescharacteristic
583C2#2261972111yescharacteristic
584C2#2261976311yescharacteristic
585C2#2262178311yescharacteristic
586C2#2262218611yescharacteristic
587C2#2262262911yescharacteristic
588C2#2262268611yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#1939C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#1939D73
hypocenterC73#26028
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. #22614952C2semidirect
7. #22610886C2semidirect
8. #22610882C2semidirect
9. #22610701C2semidirect
10. #22610524C2semidirect
11. #22610517C2semidirect
12. #22610062C2semidirect
15. C73×#1939C2semidirect
67. C4×D292Q8semidirect
304. #1939D73semidirect
310. C73#26028semidirect

Maximal subgroups

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

subgroupindex
#226149522
#226129022
#226113182
#226113042
#226110782
#226110682
#226108862
#226108822
#226107012
#226105242
#226105172
#226100622
#226099422
C4×#145565132
C73×#19392
#2602873