Finite Group Databasebeta

← #33158802

Subgroups — #33158802

Order 18688.

742 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612967C211yesmaximal, characteristic
2#22611335C211yesmaximal, characteristic, complemented
3#22611316C211yesmaximal, characteristic, complemented
4#22611113C211yesmaximal, characteristic
5#22611113C211yesmaximal, characteristic
6#22610687C211yesmaximal, characteristic, complemented
7#22610661C211yesmaximal, characteristic, complemented
8#22610539C211yesmaximal, characteristic, complemented
9#22610523C211yesmaximal, characteristic, complemented
10#22610506C211yesmaximal, characteristic, complemented
11#22610191C211yesmaximal, characteristic, complemented
12#22610128C211yesmaximal, characteristic, complemented
13#22610023C211yesmaximal, characteristic, complemented
14C4×#14556511C211yesmaximal, characteristic, complemented
15C73×#2497C211yesmaximal, characteristic, complemented
16C2×#14556565C2211yescharacteristic
17C2×C4×D292C2211yescharacteristic
18C2×#14556550C2211yescharacteristic
19C2×#14556524C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556524C2211yescharacteristic
22C2×#14556522C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×#14556511C2211yescharacteristic
25C2×#14556511C2211yescharacteristic
26C2×#14556511C2211yescharacteristic
27C2×#14556511C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×C4×#10596831C2211yescharacteristic
31#17988489C2211yescharacteristic
32#17988487—21no—
33#17988485C2211yescharacteristic
34#17988476—21no—
35#17988463—21no—
36C4×C4⋊Dic73C2211yescharacteristic
37#17988434—21no—
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#396×C73—21no—
50#389×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#388×C73—21no—
53#387×C73—21no—
54#384×C73C2211yescharacteristic
55#380×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C22⋊C4×C73C2211yescharacteristic
59C22×D292C2311yescharacteristic
60C22×C22⋊D73—21no—
61C22×C4×D73—21no—
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66#14556565—22no—
67#14556565—22no—
68C4×D292—22no—
69C4×D292—41no—
70#14556550—22no—
71#14556550—41no—
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×#11924007—21no—
76C2×C22⋊Dic73—21no—
77C2×#11924005—21no—
78C2×#11924005—21no—
79C2×#11924005—21no—
80C2×#11924005—21no—
81C2×C4×Dic73—21no—
82C2×C4×Dic73—21no—
83#14556524—22no—
84#14556524—22no—
85#14556524—41no—
86#14556522—22no—
87C4⋊#10596831—22no—
88#14556511—22no—
89#14556511—22no—
90#14556511—22no—
91#14556511—41no—
92C22⋊#10596831—22no—
93C22⋊#10596831—41no—
94C4×#10596831—41no—
95#14556498—21no—
96#14556498—21no—
97C23×C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73D411yescharacteristic
109C2×C22⋊C4×C73D411yescharacteristic
110C2×C42×C73—21no—
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113#95×C73—21no—
114#95×C73—21no—
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73D411yescharacteristic
119#95×C73D411yescharacteristic
120C23×D73—21no—
121C2×D292—21no—
122C2×D292—21no—
123C2×D292—21no—
124C2×D292—21no—
125C2×D292—21no—
126C2×D292#4112yes—
127C2×C22⋊D73—24no—
128C2×C22⋊D73—81no—
129C2×C22⋊D73—81no—
130C22×Dic73—21no—
131C22×Dic73—21no—
132C22×Dic73—21no—
133C2×C4×D73—42no—
134C2×C4×D73—42no—
135C2×C4×D73—81no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
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#4112yes—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152C4⋊Dic73#4112yes—
153C4⋊Dic73#4112yes—
154#11924007—81no—
155C22⋊Dic73—42no—
156#11924005—24no—
157#11924005—42no—
158#11924005—42no—
159#11924005—81no—
160C4×Dic73—42no—
161C4×Dic73—81no—
162C24×C73C2×D411yescharacteristic
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2411yescharacteristic
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—42no—
188C4⋊C4×C73—81no—
189C4⋊C4×C73—81no—
190C4⋊C4×C73—81no—
191C22⋊C4×C73—22no—
192C22⋊C4×C73—22no—
193C22⋊C4×C73—81no—
194C22⋊C4×C73—81no—
195C42×C73—21no—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73—21no—
199C42×C73—81no—
200C23×C73—21no—
201C23×C73—21no—
202C23×C73—21no—
203C23×C73—21no—
204C23×C73—21no—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73C22×D411yescharacteristic
208C22×D73—22no—
209C22×D73—41no—
210C22×D73—41no—
211C22×D73—41no—
212C22×D73—41no—
213C22×D73—41no—
214C22×D73—41no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
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—41no—
229C2×C4×C73—41no—
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×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73#13512yes—
245C2×C4×C73#13712yes—
246C2×C4×C73C2×#4111yescharacteristic
247C2×C4×C73C2×#4111yescharacteristic
248C2×C4×C73C2×#4111yescharacteristic
249C2×C4×C73C2×#4111yescharacteristic
250C2×C4×C73H(5,𝔽2)11yescharacteristic
251C2×C4×C732−1+411yescharacteristic
252C22⋊D73—84no—
253C2×Dic73—22no—
254C2×Dic73—22no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
258C2×Dic73—41no—
259C2×Dic73—41no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262D292—22no—
263D292—22no—
264D292—41no—
265D292—41no—
266C4×D73—84no—
267#10596831—22no—
268#10596831—41no—
269#10596831—41no—
270#10596831—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73#52511yescharacteristic
279C22×C73#54611yescharacteristic
280C22×C73#54711yescharacteristic
281C22×C73C2×#13511yescharacteristic
282C22×C73C2×#13711yescharacteristic
283C22×C73#57611yescharacteristic
284C22×C73#57611yescharacteristic
285C2×D73—42no—
286C2×D73—42no—
287C2×D73—42no—
288C2×D73—81no—
289C2×D73—81no—
290C2×D73—81no—
291C2×D73—81no—
292C4×C73—22no—
293C4×C73—22no—
294C4×C73—41no—
295C4×C73—41no—
296C4×C73—41no—
297C4×C73—81no—
298C4×C73—81no—
299C4×C73—81no—
300C4×C73—81no—
301C4×C73#52911yescharacteristic
302C4×C73#53911yescharacteristic
303C4×C73#55311yescharacteristic
304C4×C73#55611yescharacteristic
305Dic73—42no—
306Dic73—42no—
307Dic73—81no—
308#27041—731nomaximal, Sylow
309C2×C73—81no—
310C2×C73#246611yescharacteristic
311C2×C73#310711yescharacteristic
312C2×C73#312211yescharacteristic
313C2×C73#330511yescharacteristic
314C2×C73#331411yescharacteristic
315C2×C73#333911yescharacteristic
316C2×C73#335711yescharacteristic
317D73—82no—
318#2497D7311yescharacteristic, complemented
319#2363—731no—
320#2071—731no—
321#2067—731no—
322#2033—731no—
323#2033—731no—
324#1947—731no—
325#1942—731no—
326#1923—731no—
327#1921—731no—
328#1919—731no—
329#1864—731no—
330#1854—731no—
331#1825—731no—
332C4×#102—731no—
333C73#2704111yescharacteristic, complemented, Sylow
334C2×#121—731no—
335C2×C4×D4—731no—
336C2×#117—731no—
337C2×#107—731no—
338C2×#107—731no—
339C2×#107—731no—
340C2×#106—731no—
341C2×C4⋊C8—731no—
342C2×#102—731no—
343C2×#102—731no—
344C2×#102—731no—
345C2×#102—731no—
346C2×C22⋊C8—731no—
347C2×C22⋊C8—731no—
348C2×C4×C8—731no—
349#400—21no—
350#396—21no—
351#390—731no—
352#390—1461no—
353#389—731no—
354#389C2×D7311yescharacteristic
355#389C2×D7311yescharacteristic
356#388—21no—
357#388—1461no—
358#387—21no—
359#386—1461no—
360#384C2×D7311yescharacteristic
361#380C2×D7311yescharacteristic
362#380C2×D7311yescharacteristic
363C4×C4⋊C4—731no—
364C4×C4⋊C4C2×D7311yescharacteristic
365C4×C22⋊C4—1461no—
366C4×C22⋊C4C2×D7311yescharacteristic
367#340—731no—
368#340—731no—
369#340—731no—
370#340—731no—
371#340—731no—
372#340—731no—
373#340—731no—
374#340—731no—
375#336—731no—
376#336—731no—
377C22×D4—731no—
378C22×D4—1461no—
379C23×C4—1461no—
380C23×C4C22×D7311yescharacteristic
381C22×C8—731no—
382C22×C8—731no—
383C22×C8—731no—
384C22×C8—731no—
385#121—1462no—
386#121—1462no—
387C4×D4—2921no—
388C4×D4—1462no—
389#117—2921no—
390#117—1462no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—731no—
396C2×C4⋊C4—731no—
397C2×C4⋊C4—731no—
398C2×C4⋊C4—1461no—
399C2×C4⋊C4C22×D7311yescharacteristic
400C2×C4⋊C4C22×D7311yescharacteristic
401C2×C4⋊C4C22×D7311yescharacteristic
402C2×C4⋊C4C22×D7311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—1461no—
406C2×C22⋊C4—1461no—
407C2×C22⋊C4—1461no—
408C2×C22⋊C4—1461no—
409C2×C22⋊C4—1461no—
410C2×C22⋊C4C22⋊D7311yescharacteristic
411C2×C22⋊C4C22⋊D7311yescharacteristic
412C2×C42—21no—
413C2×C42—1461no—
414C2×C42—1461no—
415C2×C42C22×D7311yescharacteristic
416C2×C42C22×D7311yescharacteristic
417#107—2921no—
418#107—1462no—
419#107—1462no—
420#106—1462no—
421C4⋊C8—1462no—
422#102—2921no—
423#102—1462no—
424#102—1462no—
425#102—1462no—
426C22⋊C8—2921no—
427C22⋊C8—1462no—
428C4×C8—2921no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—1461no—
435#95—1461no—
436#95C22⋊D7311yescharacteristic
437#95C22⋊D7311yescharacteristic
438C24—1461no—
439C24C2×C22⋊D7311yescharacteristic
440C2×D4—5841no—
441C2×D4—5841no—
442C2×D4—732no—
443C2×D4—1464no—
444C2×D4—1461no—
445C2×D4—1461no—
446C2×D4—1461no—
447C2×D4—1461no—
448C2×D4—1461no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—2922no—
460C22×C4—2922no—
461C22×C4—5841no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4—1461no—
465C22×C4C2×C22⋊D7311yescharacteristic
466C22×C4C2×C22⋊D7311yescharacteristic
467C22×C4C2×C22⋊D7311yescharacteristic
468C22×C4C2×C22⋊D7311yescharacteristic
469C22×C4C2×C22⋊D7311yescharacteristic
470C22×C4C23×D7311yescharacteristic
471C2×C8—732no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8—1461no—
478C2×C8—1461no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4—5841no—
496C4⋊C4—732no—
497C4⋊C4—732no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C22⋊C4—2922no—
507C22⋊C4—2922no—
508C22⋊C4—2922no—
509C22⋊C4—5841no—
510C22⋊C4—1464no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—81no—
516C42—2922no—
517C42—5841no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—2921no—
526C23—2921no—
527C23—2921no—
528C23—2921no—
529C23—2921no—
530C23—2921no—
531C23—1462no—
532C23C22×C22⋊D7311yescharacteristic
533D4—2921no—
534D4—2921no—
535D4—5844no—
536D4—1462no—
537D4—1462no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—2921no—
568C2×C4—2921no—
569C2×C4—2921no—
570C2×C4—2921no—
571C2×C4—2921no—
572C2×C4—2921no—
573C2×C4—2921no—
574C2×C4—5844no—
575C2×C4—1462no—
576C2×C4—1462no—
577C2×C4#1455661112yes—
578C2×C4#1455662212yes—
579C2×C4#41×D7311yescharacteristic
580C2×C4#41×D7311yescharacteristic
581C2×C4#41×D7311yescharacteristic
582C2×C4#41×D7311yescharacteristic
583C2×C4#1455663711yescharacteristic
584C2×C4#1455663811yescharacteristic
585C8—2921no—
586C8—2921no—
587C8—2921no—
588C8—1462no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—2922no—
597C22—2922no—
598C22—2922no—
599C22—5841no—
600C22—5841no—
601C22—5841no—
602C22—5841no—
603C22#1798909411yescharacteristic
604C22#1798922511yescharacteristic
605C22#1798923611yescharacteristic
606C22C2×#1455661111yescharacteristic
607C22C2×#1455662211yescharacteristic
608C22#1798939011yescharacteristic
609C22#1798939011yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—2922no—
620C4—2922no—
621C4—5841no—
622C4#1798912011yescharacteristic
623C4#1798917811yescharacteristic
624C4#1798928811yescharacteristic
625C4#1798930411yescharacteristic
626C2—81no—
627C2—5842no—
628C2#2261396311yescharacteristic
629C2#2261999611yescharacteristic
630C2#2262016911yescharacteristic
631C2#2262187511yescharacteristic
632C2#2262200611yescharacteristic
633C2#2262232711yescharacteristic
634C2#2262255711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2497C2
socleC23×C73C22×D4
prime radicalC2×#14556565C22
hypercenter#2497D73
hypocenterC73#27041
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2497

Complements

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

NH ≅ G/Ntype
2. #22611335C2semidirect
3. #22611316C2semidirect
6. #22610687C2semidirect
7. #22610661C2semidirect
8. #22610539C2semidirect
9. #22610523C2semidirect
10. #22610506C2semidirect
11. #22610191C2semidirect
12. #22610128C2semidirect
13. #22610023C2semidirect
14. C4×#14556511C2semidirect
15. C73×#2497C2semidirect
318. #2497D73semidirect
333. C73#27041semidirect

Maximal subgroups

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

subgroupindex
#226129672
#226113352
#226113162
#226111132
#226106872
#226106612
#226105392
#226105232
#226105062
#226101912
#226101282
#226100232
C4×#145565112
C73×#24972
#2704173