Finite Group Databasebeta

← #33153996

Subgroups — #33153996

Order 18688.

680 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613025C211yesmaximal, characteristic, complemented
2#22611422C211yesmaximal, characteristic, complemented
3#22611167C211yesmaximal, characteristic
4#22611082C211yesmaximal, characteristic, complemented
5#22611077C211yesmaximal, characteristic
6#22610864C211yesmaximal, characteristic
7#22610631C211yesmaximal, characteristic
8#22610569C211yesmaximal, characteristic, complemented
9#22610548C211yesmaximal, characteristic
10#22610548C211yesmaximal, characteristic
11#22610520C211yesmaximal, characteristic, complemented
12#22610497C211yesmaximal, characteristic, complemented
13#22610185C211yesmaximal, characteristic, complemented
14#22609761C211yesmaximal, characteristic, complemented
15C73×#2448C211yesmaximal, characteristic
16C2×#14556583C2211yescharacteristic
17C2×#14556524C2211yescharacteristic
18C2×#14556524C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×#14556515C2211yescharacteristic
21C2×#14556515C2211yescharacteristic
22C2×#14556515C2211yescharacteristic
23C2×#14556515C2211yescharacteristic
24C2×#14556512C2211yescharacteristic
25C2×#14556512C2211yescharacteristic
26C2×#14556512C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556502C2211yescharacteristic
29#17988485C2211yescharacteristic
30#17988485C2211yescharacteristic
31#17988482—21no—
32#17988469—21no—
33#17988468—21no—
34C4×C4⋊Dic73C2211yescharacteristic
35C4×C4⋊Dic73C2211yescharacteristic
36C4×C4⋊Dic73C2211yescharacteristic
37#17988438—21no—
38#17988349C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48C2×#124×C73C2211yescharacteristic
49C2×C4×Q8×C73C2211yescharacteristic
50#399×C73—21no—
51#397×C73—21no—
52#391×C73C2211yescharacteristic
53#390×C73C2211yescharacteristic
54#390×C73C2211yescharacteristic
55#389×C73C2211yescharacteristic
56#388×C73—21no—
57#388×C73—21no—
58C4×C4⋊C4×C73C2211yescharacteristic
59C22×#10596831C2311yescharacteristic
60C22×#10596831C2311yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63#14556583—22no—
64#14556583—22no—
65C2×C4⋊Dic73C2311yescharacteristic
66C2×C4⋊Dic73C2311yescharacteristic
67C2×C4⋊Dic73C2311yescharacteristic
68C2×C4⋊Dic73C2311yescharacteristic
69C2×#11924007—21no—
70C2×#11924007—21no—
71C2×#11924007—21no—
72C2×#11924007—21no—
73C2×C4×Dic73—21no—
74C2×C4×Dic73—21no—
75C2×C4×Dic73—21no—
76#14556524—22no—
77#14556524—41no—
78C4⋊#10596831—41no—
79#14556515—22no—
80#14556515—22no—
81#14556515—22no—
82#14556515—22no—
83#14556512—22no—
84#14556512—22no—
85#14556512—22no—
86#14556512—41no—
87#14556502—41no—
88#14556498—21no—
89#14556498—21no—
90#14556498—21no—
91#14556498—21no—
92#14556498—21no—
93C22×Q8×C73C2311yescharacteristic
94C22×D4×C73C2311yescharacteristic
95#124×C73—22no—
96#124×C73—41no—
97C4×Q8×C73—22no—
98C4×Q8×C73—41no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73D411yescharacteristic
102C2×C4⋊C4×C73D411yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C42×C73—21no—
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73D411yescharacteristic
119#95×C73D411yescharacteristic
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73—21no—
124C2×#10596831—21no—
125C2×#10596831—21no—
126C2×#10596831—21no—
127C2×#10596831—21no—
128C2×#10596831—21no—
129C2×#10596831—21no—
130C2×#10596831—21no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C4⋊Dic73—21no—
137C4⋊Dic73—21no—
138C4⋊Dic73—21no—
139C4⋊Dic73—21no—
140C4⋊Dic73—21no—
141C4⋊Dic73#4112yes—
142C4⋊Dic73#4112yes—
143C4⋊Dic73#4112yes—
144#11924007—24no—
145#11924007—24no—
146#11924007—42no—
147#11924007—81no—
148C4×Dic73—42no—
149C4×Dic73—81no—
150C4×Dic73—81no—
151C24×C73—21no—
152C2×Q8×C73—21no—
153C2×Q8×C73—21no—
154C2×Q8×C73—21no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73#4112yes—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×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—21no—
175C4⋊C4×C73—21no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73—41no—
179C4⋊C4×C73—41no—
180C4⋊C4×C73—42no—
181C4⋊C4×C73—81no—
182C22⋊C4×C73—42no—
183C22⋊C4×C73—42no—
184C22⋊C4×C73—42no—
185C22⋊C4×C73—42no—
186C22⋊C4×C73—81no—
187C22⋊C4×C73—81no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—42no—
195C23×C73—41no—
196C23×C73—41no—
197C23×C73—41no—
198C23×C73—41no—
199C23×C73—41no—
200C23×C73—41no—
201C23×C73—41no—
202C23×C73C22×D411yescharacteristic
203Q8×C73—22no—
204Q8×C73—22no—
205Q8×C73—41no—
206Q8×C73—41no—
207D4×C73—41no—
208D4×C73—41no—
209D4×C73—41no—
210D4×C73—41no—
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—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73C2×#4111yescharacteristic
239C2×C4×C73C2×#4111yescharacteristic
240C2×C4×C73C2×#4111yescharacteristic
241C2×C4×C73C2×#4111yescharacteristic
242C2×C4×C73H(5,𝔽2)11yescharacteristic
243C2×C4×C732−1+411yescharacteristic
244C2×Dic73—22no—
245C2×Dic73—22no—
246C2×Dic73—22no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256#10596831—41no—
257#10596831—41no—
258#10596831—41no—
259#10596831—41no—
260C22×C73—81no—
261C22×C73—81no—
262C22×C73—81no—
263C22×C73—81no—
264C22×C73—81no—
265C22×C73—81no—
266C22×C73—81no—
267C22×C73#52511yescharacteristic
268C22×C73#54611yescharacteristic
269C22×C73#54811yescharacteristic
270C22×C73#57511yescharacteristic
271C22×C73#57511yescharacteristic
272C22×C73#57611yescharacteristic
273C22×C73#57811yescharacteristic
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—42no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—41no—
281C4×C73—81no—
282C4×C73—81no—
283C4×C73#52911yescharacteristic
284C4×C73#54211yescharacteristic
285C4×C73#55211yescharacteristic
286C4×C73#55911yescharacteristic
287Dic73—42no—
288Dic73—42no—
289Dic73—42no—
290Dic73—81no—
291#26719—731nomaximal, Sylow
292C2×C73—161no—
293C2×C73#245811yescharacteristic
294C2×C73#311111yescharacteristic
295C2×C73#312411yescharacteristic
296C2×C73#330911yescharacteristic
297C2×C73#332711yescharacteristic
298C2×C73#337011yescharacteristic
299C2×C73#337711yescharacteristic
300#2448D7311yescharacteristic
301#2370—731no—
302#2086—731no—
303#2042—731no—
304#2026—731no—
305#2025—731no—
306#1983—731no—
307#1936—731no—
308#1928—731no—
309#1925—731no—
310#1925—731no—
311#1921—731no—
312#1917—731no—
313#1863—731no—
314#1763—731no—
315C73#2671911yescharacteristic, complemented, Sylow
316C2×#125—731no—
317C2×#124C2×D7311yescharacteristic
318C2×C4×Q8C2×D7311yescharacteristic
319C2×#107—731no—
320C2×#107—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—
331#399—21no—
332#397—21no—
333#391C2×D7311yescharacteristic
334#390C2×D7311yescharacteristic
335#390C2×D7311yescharacteristic
336#389—731no—
337#389—731no—
338#389—1461no—
339#389C2×D7311yescharacteristic
340#388—21no—
341#388—21no—
342#387—1461no—
343#387—1461no—
344C4×C4⋊C4—731no—
345C4×C4⋊C4—731no—
346C4×C4⋊C4—731no—
347C4×C4⋊C4—1461no—
348C4×C4⋊C4C2×D7311yescharacteristic
349#340—731no—
350#340—731no—
351#340—731no—
352#340—731no—
353#340—731no—
354#340—731no—
355#336—731no—
356#336—731no—
357#336—731no—
358#336—731no—
359C22×Q8C22×D7311yescharacteristic
360C22×D4C22×D7311yescharacteristic
361C22×C8—731no—
362C22×C8—731no—
363C22×C8—731no—
364C22×C8—731no—
365#125—1462no—
366#125—1462no—
367#124—22no—
368#124—41no—
369C4×Q8—22no—
370C4×Q8—41no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—731no—
375C2×C4⋊C4—731no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4—1461no—
378C2×C4⋊C4—1461no—
379C2×C4⋊C4—1461no—
380C2×C4⋊C4—1461no—
381C2×C4⋊C4C22⋊D7311yescharacteristic
382C2×C4⋊C4C22⋊D7311yescharacteristic
383C2×C4⋊C4C22×D7311yescharacteristic
384C2×C4⋊C4C22×D7311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—21no—
392C2×C42—1461no—
393C2×C42—1461no—
394C2×C42—1461no—
395C2×C42C22×D7311yescharacteristic
396C2×C42C22×D7311yescharacteristic
397C2×C42C22×D7311yescharacteristic
398#107—2921no—
399#107—1462no—
400C4⋊C8—2921no—
401#103—1462no—
402#103—1462no—
403#103—1462no—
404#103—1462no—
405#102—2921no—
406#102—1462no—
407#102—1462no—
408#102—1462no—
409#97—2921no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—1461no—
414#95—1461no—
415#95—1461no—
416#95—1461no—
417#95—1461no—
418#95C22⋊D7311yescharacteristic
419#95C22⋊D7311yescharacteristic
420C24—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#1192402712yes—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—1461no—
437C22×C4—1461no—
438C22×C4—1461no—
439C22×C4—1461no—
440C22×C4C2×C22⋊D7311yescharacteristic
441C22×C4C2×C22⋊D7311yescharacteristic
442C22×C4C2×C22⋊D7311yescharacteristic
443C22×C4C2×C22⋊D7311yescharacteristic
444C22×C4C2×C22⋊D7311yescharacteristic
445C22×C4C2×C22⋊D7311yescharacteristic
446C22×C4C23×D7311yescharacteristic
447C2×C8—1461no—
448C2×C8—1461no—
449C2×C8—1461no—
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—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—42no—
466C4⋊C4—81no—
467C4⋊C4—2922no—
468C4⋊C4—5841no—
469C4⋊C4—732no—
470C4⋊C4—732no—
471C4⋊C4—732no—
472C4⋊C4—1464no—
473C4⋊C4—1464no—
474C4⋊C4—1461no—
475C4⋊C4—1461no—
476C4⋊C4—1461no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—42no—
492C42—2922no—
493C42—5841no—
494C42—5841no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23C22×C22⋊D7311yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511C2×C4—21no—
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—22no—
528C2×C4—21no—
529C2×C4—21no—
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—2921no—
547C2×C4—1462no—
548C2×C4—1462no—
549C2×C4—1462no—
550C2×C4#41×D7311yescharacteristic
551C2×C4#41×D7311yescharacteristic
552C2×C4#41×D7311yescharacteristic
553C2×C4C2×#1192402711yescharacteristic
554C2×C4#1455663611yescharacteristic
555C2×C4#1455663811yescharacteristic
556C8—2921no—
557C8—2921no—
558C8—2921no—
559C8—2921no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22#1798909411yescharacteristic
568C22#1798923111yescharacteristic
569C22#1798924411yescharacteristic
570C22#1798938511yescharacteristic
571C22#1798938511yescharacteristic
572C22#1798939011yescharacteristic
573C22#1798940211yescharacteristic
574C4—41no—
575C4—42no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—2922no—
584C4—2922no—
585C4—2922no—
586C4—5841no—
587C4#1798911411yescharacteristic
588C4#1798920511yescharacteristic
589C4#1798927411yescharacteristic
590C4#1798932111yescharacteristic
591C2—161no—
592C2#2261384911yescharacteristic
593C2#2262003411yescharacteristic
594C2#2262018711yescharacteristic
595C2#2262193711yescharacteristic
596C2#2262219911yescharacteristic
597C2#2262267811yescharacteristic
598C2#2262276711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2448C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
hypercenter#2448D73
hypocenterC73#26719
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2448

Complements

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

NH ≅ G/Ntype
1. #22613025C2semidirect
2. #22611422C2semidirect
4. #22611082C2semidirect
8. #22610569C2semidirect
11. #22610520C2semidirect
12. #22610497C2semidirect
13. #22610185C2semidirect
14. #22609761C2semidirect
315. C73#26719semidirect

Maximal subgroups

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

subgroupindex
#226130252
#226114222
#226111672
#226110822
#226110772
#226108642
#226106312
#226105692
#226105482
#226105202
#226104972
#226101852
#226097612
C73×#24482
#2671973