Finite Group Databasebeta

← #33144271

Subgroups — #33144271

Order 18688.

744 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#22612902C211yesmaximal, characteristic
2#22611316C211yesmaximal, characteristic
3#22611302C211yesmaximal, characteristic
4#22611064C211yesmaximal, characteristic
5#22611064C211yesmaximal, characteristic
6#22610884C211yesmaximal, characteristic, complemented
7#22610880C211yesmaximal, characteristic, complemented
8#22610699C211yesmaximal, characteristic, complemented
9#22610655C211yesmaximal, characteristic, complemented
10#22610520C211yesmaximal, characteristic, complemented
11#22610506C211yesmaximal, characteristic, complemented
12#22610066C211yesmaximal, characteristic, complemented
13#22609928C211yesmaximal, characteristic
14#22609759C211yesmaximal, characteristic
15C73×#2551C211yesmaximal, characteristic, complemented
16C2×C4×D292C2211yescharacteristic
17C2×#14556524C2211yescharacteristic
18C2×#14556522C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556511C2211yescharacteristic
23C2×#14556511C2211yescharacteristic
24C2×#14556511C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556502C2211yescharacteristic
27#17988489C2211yescharacteristic
28#17988489C2211yescharacteristic
29#17988477—21no—
30#17988477—21no—
31#17988453C2211yescharacteristic
32#17988449—21no—
33C4×C4⋊Dic73C2211yescharacteristic
34C4×C4⋊Dic73C2211yescharacteristic
35#17988434—21no—
36#17988349C2211yescharacteristic
37#17988349C2211yescharacteristic
38#17988349C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48C2×C4⋊Q8×C73—21no—
49C2×C4⋊Q8×C73C2211yescharacteristic
50C2×C4⋊Q8×C73C2211yescharacteristic
51#395×C73—21no—
52#395×C73—21no—
53#389×C73—21no—
54#389×C73C2211yescharacteristic
55#389×C73C2211yescharacteristic
56#384×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59C22×D292C2311yescharacteristic
60C22×C4×D73—21no—
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C4×D292—22no—
66C4×D292Q814yescomplemented
67C2×C4⋊Dic73C2311yescharacteristic
68C2×C4⋊Dic73C2311yescharacteristic
69C2×C4⋊Dic73C2311yescharacteristic
70C2×#11924005—21no—
71C2×#11924005—21no—
72C2×#11924005—21no—
73C2×#11924005—21no—
74C2×#11924005—21no—
75C2×C4×Dic73—21no—
76C2×C4×Dic73—21no—
77#14556524—22no—
78#14556522—22no—
79C4⋊#10596831—22no—
80C4⋊#10596831—41no—
81C4⋊#10596831—41no—
82#14556511—22no—
83#14556511—22no—
84#14556511—41no—
85#14556511—41no—
86#14556502—22no—
87#14556498—21no—
88#14556498—21no—
89#14556498—21no—
90#14556498—21no—
91C22×Q8×C73—21no—
92C22×Q8×C73—21no—
93C4⋊Q8×C73—22no—
94C4⋊Q8×C73—22no—
95C4⋊Q8×C73—41no—
96C4⋊Q8×C73—41no—
97C4⋊Q8×C73—44no—
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×C73—21no—
104C2×C4⋊C4×C73D411yescharacteristic
105C2×C4⋊C4×C73D411yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C4⋊C4×C73C2311yescharacteristic
110C2×C42×C73—21no—
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114#95×C73—21no—
115#95×C73—21no—
116#95×C73—21no—
117#95×C73D411yescharacteristic
118#95×C73D411yescharacteristic
119C23×D73—21no—
120C2×D292—21no—
121C2×D292—21no—
122C2×D292—21no—
123C2×D292—21no—
124C2×D292—21no—
125C2×D292C2×Q812yes—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C2×C4×D73—24no—
130C2×C4×D73—81no—
131C2×C4×D73—81no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73C2×Q812yes—
150#11924005—24no—
151#11924005—42no—
152#11924005—42no—
153#11924005—81no—
154#11924005—81no—
155C4×Dic73—81no—
156C4×Dic73—81no—
157C2×Q8×C73—42no—
158C2×Q8×C73—42no—
159C2×Q8×C73—42no—
160C2×Q8×C73—42no—
161C2×Q8×C73—81no—
162C2×Q8×C73—81no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2411yescharacteristic
174C4⋊C4×C73—22no—
175C4⋊C4×C73—22no—
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—42no—
183C4⋊C4×C73—42no—
184C4⋊C4×C73—42no—
185C4⋊C4×C73—42no—
186C4⋊C4×C73—42no—
187C4⋊C4×C73—81no—
188C4⋊C4×C73#4112yes—
189C4⋊C4×C73#4112yes—
190C42×C73—21no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—42no—
195C42×C73C2×Q812yes—
196C42×C73#4112yes—
197C23×C73C22×D411yescharacteristic
198C22×D73—22no—
199C22×D73—41no—
200C22×D73—41no—
201C22×D73—41no—
202C22×D73—41no—
203C22×D73—41no—
204C22×D73—41no—
205Q8×C73—84no—
206Q8×C73—84no—
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—22no—
218C2×C4×C73—22no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
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—41no—
232C2×C4×C73—41no—
233C2×C4×C73C22⋊Q812yes—
234C2×C4×C73C22⋊Q812yes—
235C2×C4×C73AGL(1,ℤ/8)12yes—
236C2×C4×C73#13712yes—
237C2×C4×C73C22×Q811yescharacteristic
238C2×C4×C73C2×#4111yescharacteristic
239C2×C4×C73C2×#4111yescharacteristic
240C2×C4×C73C2×#4111yescharacteristic
241C2×C4×C73H(5,𝔽2)11yescharacteristic
242C2×C4×C732−1+411yescharacteristic
243C2×Dic73—22no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252D292—22no—
253D292—22no—
254D292—41no—
255D292—41no—
256C4×D73—84no—
257#10596831—41no—
258#10596831—41no—
259#10596831—41no—
260#10596831—41no—
261C22×C73C2×C22⋊Q811yescharacteristic
262C22×C73#54611yescharacteristic
263C22×C73#54811yescharacteristic
264C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C73C2×#13711yescharacteristic
266C22×C73#57611yescharacteristic
267C22×C73#57711yescharacteristic
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—22no—
278C4×C73—22no—
279C4×C73—42no—
280C4×C73—41no—
281C4×C73—42no—
282C4×C73—41no—
283C4×C73—81no—
284C4×C73—81no—
285C4×C73#53311yescharacteristic
286C4×C73#54411yescharacteristic
287C4×C73#55511yescharacteristic
288C4×C73#55611yescharacteristic
289Dic73—42no—
290Dic73—81no—
291Dic73—81no—
292#26036—731nomaximal, Sylow
293C2×C73#243911yescharacteristic
294C2×C73#307911yescharacteristic
295C2×C73#308111yescharacteristic
296C2×C73#331811yescharacteristic
297C2×C73#332011yescharacteristic
298C2×C73#337311yescharacteristic
299C2×C73#337511yescharacteristic
300D73—82no—
301#2551D7311yescharacteristic, complemented
302#2357—731no—
303#2067—731no—
304#2065—731no—
305#2023—731no—
306#2023—731no—
307#1988—731no—
308#1987—731no—
309#1949—731no—
310#1940—731no—
311#1921—731no—
312#1919—731no—
313#1836—731no—
314#1802—731no—
315#1762—731no—
316C73#2603611yescharacteristic, complemented, Sylow
317C2×C4⋊Q8—21no—
318C2×C4⋊Q8C2×D7311yescharacteristic
319C2×C4⋊Q8C2×D7311yescharacteristic
320C2×C4×D4—731no—
321C2×#107—731no—
322C2×#106—731no—
323C2×C4⋊C8—731no—
324C2×C4⋊C8—731no—
325C2×C4⋊C8—731no—
326C2×#102—731no—
327C2×#102—731no—
328C2×#102—731no—
329C2×#102—731no—
330C2×#97—731no—
331#395—21no—
332#395—21no—
333#390—731no—
334#390—731no—
335#389—21no—
336#389C2×D7311yescharacteristic
337#389C2×D7311yescharacteristic
338#388—1461no—
339#388—1461no—
340#384C2×D7311yescharacteristic
341#382—731no—
342#381—1461no—
343C4×C4⋊C4—731no—
344C4×C4⋊C4—731no—
345C4×C4⋊C4C2×D7311yescharacteristic
346C4×C4⋊C4C2×D7311yescharacteristic
347C4×C22⋊C4—1461no—
348#340—731no—
349#340—731no—
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—21no—
361C22×Q8—21no—
362C22×D4—731no—
363C23×C4—1461no—
364C22×C8—731no—
365C22×C8—731no—
366C22×C8—731no—
367C22×C8—731no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—41no—
371C4⋊Q8—41no—
372C4⋊Q8—44no—
373C4×D4—734no—
374C4×D4—1462no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—731no—
384C2×C4⋊C4C22⋊D7311yescharacteristic
385C2×C4⋊C4C22⋊D7311yescharacteristic
386C2×C4⋊C4C22×D7311yescharacteristic
387C2×C4⋊C4C22×D7311yescharacteristic
388C2×C4⋊C4C22×D7311yescharacteristic
389C2×C4⋊C4C22×D7311yescharacteristic
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C22⋊C4—1461no—
393C2×C22⋊C4—1461no—
394C2×C22⋊C4—1461no—
395C2×C42—21no—
396C2×C42—1461no—
397C2×C42—1461no—
398C2×C42C22×D7311yescharacteristic
399C2×C42C22×D7311yescharacteristic
400C2×C42C22×D7311yescharacteristic
401#107—1462no—
402#106—1462no—
403C4⋊C8—2921no—
404C4⋊C8—2921no—
405C4⋊C8—1462no—
406#102—2921no—
407#102—2921no—
408#102—1462no—
409#102—1462no—
410#97—1462no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—1461no—
415#95—1461no—
416#95—1461no—
417#95—1461no—
418#95C22⋊D7311yescharacteristic
419#95C22⋊D7311yescharacteristic
420C24—1461no—
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—42no—
425C2×Q8—81no—
426C2×Q8—81no—
427C2×D4—732no—
428C2×D4—1461no—
429C2×D4—1461no—
430C2×D4—1461no—
431C2×D4—1461no—
432C2×D4—1461no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—5841no—
438C22×C4—5841no—
439C22×C4—1461no—
440C22×C4—1461no—
441C22×C4—1461no—
442C22×C4—1464no—
443C22×C4C2×C22⋊D7311yescharacteristic
444C22×C4C2×C22⋊D7311yescharacteristic
445C22×C4C2×C22⋊D7311yescharacteristic
446C22×C4C2×C22⋊D7311yescharacteristic
447C22×C4C2×C22⋊D7311yescharacteristic
448C22×C4C2×C22⋊D7311yescharacteristic
449C22×C4C23×D7311yescharacteristic
450C2×C8—1461no—
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—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—81no—
476C4⋊C4—732no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4#1192402712yes—
483C4⋊C4#1192402912yes—
484C22⋊C4—2922no—
485C22⋊C4—2922no—
486C22⋊C4—5841no—
487C22⋊C4—5841no—
488C22⋊C4—1464no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—5841no—
495C42—5841no—
496C42Q8×D7312yes—
497C42#1192402912yes—
498C23—2921no—
499C23—2921no—
500C23—2921no—
501C23—2921no—
502C23—2921no—
503C23—2921no—
504C23—1462no—
505C23C22×C22⋊D7311yescharacteristic
506Q8—84no—
507Q8—84no—
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—22no—
526C2×C4—22no—
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—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—5844no—
547C2×C4—1462no—
548C2×C4#1455656712yes—
549C2×C4#1455656712yes—
550C2×C4#1455661712yes—
551C2×C4#1455662212yes—
552C2×C4C2×Q8×D7311yescharacteristic
553C2×C4C2×#1192402711yescharacteristic
554C2×C4C2×#1192402911yescharacteristic
555C2×C4C2×#1192402911yescharacteristic
556C2×C4#1455663611yescharacteristic
557C2×C4#1455663911yescharacteristic
558C8—2921no—
559C8—2921no—
560C8—2921no—
561C8—2921no—
562C22—2922no—
563C22—2922no—
564C22—2922no—
565C22—5841no—
566C22—5841no—
567C22—5841no—
568C22—5841no—
569C22C2×#1455656711yescharacteristic
570C22#1798923111yescharacteristic
571C22#1798924811yescharacteristic
572C22C2×#1455661711yescharacteristic
573C22C2×#1455662211yescharacteristic
574C22#1798939011yescharacteristic
575C22#1798939511yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—22no—
580C4—42no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—2922no—
587C4—5841no—
588C4—5841no—
589C4#1798914211yescharacteristic
590C4#1798921411yescharacteristic
591C4#1798930311yescharacteristic
592C4#1798931111yescharacteristic
593C2—5842no—
594C2#2261361811yescharacteristic
595C2#2261974011yescharacteristic
596C2#2261975611yescharacteristic
597C2#2262207211yescharacteristic
598C2#2262210211yescharacteristic
599C2#2262272311yescharacteristic
600C2#2262274511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2551C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenter#2551D73
hypocenterC73#26036
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2551

Complements

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

NH ≅ G/Ntype
6. #22610884C2semidirect
7. #22610880C2semidirect
8. #22610699C2semidirect
9. #22610655C2semidirect
10. #22610520C2semidirect
11. #22610506C2semidirect
12. #22610066C2semidirect
15. C73×#2551C2semidirect
66. C4×D292Q8semidirect
301. #2551D73semidirect
316. C73#26036semidirect

Maximal subgroups

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

subgroupindex
#226129022
#226113162
#226113022
#226110642
#226108842
#226108802
#226106992
#226106552
#226105202
#226105062
#226100662
#226099282
#226097592
C73×#25512
#2603673