Finite Group Databasebeta

← #33144288

Subgroups — #33144288

Order 18688.

692 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22614966C211yesmaximal, characteristic, complemented
2#22612902C211yesmaximal, characteristic
3#22611318C211yesmaximal, characteristic
4#22611304C211yesmaximal, characteristic
5#22611078C211yesmaximal, characteristic
6#22611078C211yesmaximal, characteristic
7#22610886C211yesmaximal, characteristic, complemented
8#22610886C211yesmaximal, characteristic, complemented
9#22610701C211yesmaximal, characteristic, complemented
10#22610517C211yesmaximal, characteristic, complemented
11#22610503C211yesmaximal, characteristic, complemented
12#22610065C211yesmaximal, characteristic, complemented
13#22609932C211yesmaximal, characteristic
14#22609757C211yesmaximal, characteristic
15C73×#1940C211yesmaximal, characteristic, complemented
16C2×#14556583C2211yescharacteristic
17C2×#14556583C2211yescharacteristic
18C2×C4×D292C2211yescharacteristic
19C2×#14556525C2211yescharacteristic
20C2×#14556523C2211yescharacteristic
21C2×#14556513C2211yescharacteristic
22C2×#14556513C2211yescharacteristic
23C2×#14556513C2211yescharacteristic
24C2×#14556513C2211yescharacteristic
25#17988521—21no—
26#17988521—21no—
27#17988489C2211yescharacteristic
28#17988489C2211yescharacteristic
29#17988485C2211yescharacteristic
30#17988485C2211yescharacteristic
31#17988483—21no—
32#17988477—21no—
33#17988477—21no—
34#17988457C2211yescharacteristic
35#17988456—21no—
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×#97×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×D292C2311yescharacteristic
60C22×C4×D73—21no—
61#14556583—22no—
62#14556583—22no—
63#14556583—41no—
64#14556583—41no—
65C4×D292—22no—
66C4×D292Q814yes—
67C2×C4⋊Dic73—21no—
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×#11924007—21no—
81C2×#11924007—21no—
82C2×#11924005—21no—
83C2×#11924005—21no—
84C2×#11924005—21no—
85C2×#11924005—21no—
86C2×#11924005—21no—
87C2×C4×Dic73—21no—
88C2×C4×Dic73—21no—
89C2×C4×Dic73—21no—
90#14556525—22no—
91#14556523—22no—
92#14556513—22no—
93#14556513—22no—
94#14556513—41no—
95#14556513—41no—
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—
115#97×C73—22no—
116#95×C73D411yescharacteristic
117#95×C73D411yescharacteristic
118C23×D73—21no—
119C2×D292—21no—
120C2×D292—21no—
121C2×D292—21no—
122C2×D292—21no—
123C2×D292—21no—
124C2×D292C2×Q812yes—
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C2×C4×D73—24no—
133C2×C4×D73—81no—
134C2×C4×D73—81no—
135C4⋊Dic73—21no—
136C4⋊Dic73—21no—
137C4⋊Dic73—21no—
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—42no—
147C4⋊Dic73—81no—
148C4⋊Dic73C2×Q812yes—
149C4⋊Dic73#4112yes—
150C4⋊Dic73#4112yes—
151#11924007—42no—
152#11924007—42no—
153#11924007—42no—
154#11924007—42no—
155#11924007—81no—
156#11924007—81no—
157#11924005—24no—
158#11924005—42no—
159#11924005—42no—
160#11924005—81no—
161#11924005—81no—
162C4×Dic73—42no—
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—41no—
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×C73—21no—
216C2×C4×C73C22⋊Q812yes—
217C2×C4×C73C22⋊Q812yes—
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—
250C8×C73—41no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254C22×C73C2×C22⋊Q811yescharacteristic
255C22×C73#54611yescharacteristic
256C22×C73#54811yescharacteristic
257C22×C73#57511yescharacteristic
258C22×C73#57511yescharacteristic
259C22×C73#57611yescharacteristic
260C22×C73#57711yescharacteristic
261C2×D73—42no—
262C2×D73—42no—
263C2×D73—42no—
264C2×D73—81no—
265C2×D73—81no—
266C2×D73—81no—
267C2×D73—81no—
268C4×C73—22no—
269C4×C73—22no—
270C4×C73—41no—
271C4×C73—41no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73#53311yescharacteristic
275C4×C73#54411yescharacteristic
276C4×C73#55511yescharacteristic
277C4×C73#55611yescharacteristic
278Dic73—42no—
279Dic73—42no—
280Dic73—42no—
281Dic73—81no—
282Dic73—81no—
283Dic73—81no—
284Dic73—81no—
285#26037—731nomaximal, Sylow
286C2×C73#243911yescharacteristic
287C2×C73#308011yescharacteristic
288C2×C73#308111yescharacteristic
289C2×C73#330711yescharacteristic
290C2×C73#330911yescharacteristic
291C2×C73#337011yescharacteristic
292C2×C73#337111yescharacteristic
293D73—82no—
294#2552—731no—
295#2357—731no—
296#2067—731no—
297#2065—731no—
298#2025—731no—
299#2025—731no—
300#1989—731no—
301#1989—731no—
302#1949—731no—
303#1940D7311yescharacteristic, complemented
304#1920—731no—
305#1918—731no—
306#1836—731no—
307#1802—731no—
308#1762—731no—
309C73#2603711yescharacteristic, complemented, Sylow
310C2×#125—731no—
311C2×#125—731no—
312C2×C4×D4—731no—
313C2×#107—731no—
314C2×#106—731no—
315C2×C4⋊C8C2×D7311yescharacteristic
316C2×C4⋊C8C2×D7311yescharacteristic
317C2×C4⋊C8C2×D7311yescharacteristic
318C2×#102—731no—
319C2×#102—731no—
320C2×#102—731no—
321C2×#102—731no—
322C2×#97C2×D7311yescharacteristic
323#398—1461no—
324#398—1461no—
325#390—731no—
326#390—731no—
327#389—731no—
328#389—731no—
329#389—1461no—
330#388—1461no—
331#388—1461no—
332#384—731no—
333#384—1461no—
334#382—731no—
335#381—1461no—
336C4×C4⋊C4—731no—
337C4×C4⋊C4—731no—
338C4×C4⋊C4—731no—
339C4×C4⋊C4C2×D7311yescharacteristic
340C4×C22⋊C4—1461no—
341#340—731no—
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#336C2×D7311yescharacteristic
352#336C2×D7311yescharacteristic
353C22×D4—731no—
354C23×C4—1461no—
355C22×C8C22×D7311yescharacteristic
356C22×C8C22×D7311yescharacteristic
357C22×C8C22×D7311yescharacteristic
358C22×C8C22×D7311yescharacteristic
359#125—2921no—
360#125—2921no—
361#125—1462no—
362#125—1462no—
363C4×D4—734no—
364C4×D4—1462no—
365C2×C4⋊C4—731no—
366C2×C4⋊C4—731no—
367C2×C4⋊C4—731no—
368C2×C4⋊C4—731no—
369C2×C4⋊C4—731no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—1461no—
373C2×C4⋊C4—1461no—
374C2×C4⋊C4—1461no—
375C2×C4⋊C4—1461no—
376C2×C4⋊C4—1461no—
377C2×C4⋊C4—1461no—
378C2×C4⋊C4—1461no—
379C2×C4⋊C4—1461no—
380C2×C4⋊C4D29211yescharacteristic
381C2×C4⋊C4D29211yescharacteristic
382C2×C22⋊C4—1461no—
383C2×C22⋊C4—1461no—
384C2×C22⋊C4—1461no—
385C2×C22⋊C4—1461no—
386C2×C22⋊C4—1461no—
387C2×C42—1461no—
388C2×C42—1461no—
389C2×C42—1461no—
390C2×C42C22×D7311yescharacteristic
391C2×C42C22×D7311yescharacteristic
392C2×C42C22×D7311yescharacteristic
393#107—1462no—
394#106—1462no—
395C4⋊C8—22no—
396C4⋊C8—41no—
397C4⋊C8—41no—
398#102—2921no—
399#102—2921no—
400#102—1462no—
401#102—1462no—
402#97—22no—
403#95—1461no—
404#95—1461no—
405#95—1461no—
406#95—1461no—
407#95—1461no—
408#95—1461no—
409#95—1461no—
410#95D29211yescharacteristic
411#95D29211yescharacteristic
412C24—1461no—
413C2×D4—732no—
414C2×D4—1461no—
415C2×D4—1461no—
416C2×D4—1461no—
417C2×D4—1461no—
418C2×D4—1461no—
419C22×C4—5841no—
420C22×C4—5841no—
421C22×C4—1461no—
422C22×C4—1461no—
423C22×C4—1461no—
424C22×C4—1461no—
425C22×C4—1461no—
426C22×C4—1461no—
427C22×C4—1461no—
428C22×C4—1464no—
429C22×C4C2×D29211yescharacteristic
430C22×C4C2×D29211yescharacteristic
431C22×C4C2×D29211yescharacteristic
432C22×C4C2×D29211yescharacteristic
433C22×C4C2×D29211yescharacteristic
434C22×C4C2×D29211yescharacteristic
435C22×C4C23×D7311yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—2922no—
451C4⋊C4—2922no—
452C4⋊C4—2922no—
453C4⋊C4—2922no—
454C4⋊C4—2922no—
455C4⋊C4—5841no—
456C4⋊C4—5841no—
457C4⋊C4—5841no—
458C4⋊C4—732no—
459C4⋊C4—732no—
460C4⋊C4—732no—
461C4⋊C4—1461no—
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—
472C22⋊C4—2922no—
473C22⋊C4—2922no—
474C22⋊C4—5841no—
475C22⋊C4—5841no—
476C22⋊C4—1464no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—2922no—
482C42—5841no—
483C42—5841no—
484C42Q8×D7312yes—
485C42#1192402712yes—
486C23—2921no—
487C23—2921no—
488C23—2921no—
489C23—2921no—
490C23—2921no—
491C23—2921no—
492C23—1462no—
493C23C22×D29211yescharacteristic
494D4—2921no—
495D4—2921no—
496D4—1462no—
497D4—1462no—
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—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—2921no—
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—5844no—
533C2×C4—1462no—
534C2×C4—1462no—
535C2×C4—1462no—
536C2×C4#1455657112yes—
537C2×C4#1455657112yes—
538C2×C4C2×Q8×D7311yescharacteristic
539C2×C4#41×D7311yescharacteristic
540C2×C4#41×D7311yescharacteristic
541C2×C4C2×#1192402711yescharacteristic
542C2×C4#1455663611yescharacteristic
543C2×C4#1455663911yescharacteristic
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C22—2922no—
549C22—2922no—
550C22—2922no—
551C22—5841no—
552C22—5841no—
553C22—5841no—
554C22—5841no—
555C22C2×#1455657111yescharacteristic
556C22#1798923211yescharacteristic
557C22#1798924911yescharacteristic
558C22#1798938711yescharacteristic
559C22#1798938711yescharacteristic
560C22#1798939211yescharacteristic
561C22#1798939911yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—2922no—
569C4—2922no—
570C4—2922no—
571C4—5841no—
572C4—5841no—
573C4—5841no—
574C4—5841no—
575C4#1798914311yescharacteristic
576C4#1798921411yescharacteristic
577C4#1798930111yescharacteristic
578C4#1798930811yescharacteristic
579C2—5842no—
580C2#2261362011yescharacteristic
581C2#2261975411yescharacteristic
582C2#2261976311yescharacteristic
583C2#2262190911yescharacteristic
584C2#2262193911yescharacteristic
585C2#2262268611yescharacteristic
586C2#2262270111yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#1940C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#1940D73
hypocenterC73#26037
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. #22614966C2semidirect
7. #22610886C2semidirect
8. #22610886C2semidirect
9. #22610701C2semidirect
10. #22610517C2semidirect
11. #22610503C2semidirect
12. #22610065C2semidirect
15. C73×#1940C2semidirect
303. #1940D73semidirect
309. C73#26037semidirect

Maximal subgroups

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

subgroupindex
#226149662
#226129022
#226113182
#226113042
#226110782
#226108862
#226107012
#226105172
#226105032
#226100652
#226099322
#226097572
C73×#19402
#2603773