Finite Group Databasebeta

← #33093709

Subgroups — #33093709

Order 18688.

868 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988887C211yesmaximal, characteristic
2#22612672C211yesmaximal, characteristic, complemented
3#22610888C211yesmaximal, characteristic, complemented
4#22610689C211yesmaximal, characteristic, complemented
5#22610523C211yesmaximal, characteristic, complemented
6#22610516C211yesmaximal, characteristic, complemented
7#22610178C211yesmaximal, characteristic
8#22610178C211yesmaximal, characteristic
9#22609931C211yesmaximal, characteristic
10#22609829C211yesmaximal, characteristic, complemented
11C4×#14556524C211yesmaximal, characteristic, complemented
12#22609788C211yesmaximal, characteristic, complemented
13#22609756C211yesmaximal, characteristic
14C4×#14556512C211yesmaximal, characteristic
15C73×#2275C211yesmaximal, characteristic
16C2×#14556583C2211yescharacteristic
17#17988887C418yescomplemented
18C2×#14556524C2211yescharacteristic
19C2×#14556524C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×#14556512C2211yescharacteristic
25C2×#14556512C2211yescharacteristic
26C2×#14556512C2211yescharacteristic
27C2×#14556512C2211yescharacteristic
28C2×#14556502C2211yescharacteristic
29C2×C4×#10596831C2211yescharacteristic
30#17988485C2211yescharacteristic
31#17988485C2211yescharacteristic
32#17988484—21no—
33#17988484—21no—
34#17988474—21no—
35#17988474—21no—
36#17988457C2211yescharacteristic
37C4×C4⋊Dic73C2211yescharacteristic
38C4×C4⋊Dic73C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988342C2211yescharacteristic
49C2×C4×D4×C73C2211yescharacteristic
50C2×C4×D4×C73C2211yescharacteristic
51C2×C4×D4×C73C2211yescharacteristic
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55C4×C22⋊C4×C73—21no—
56C4×C22⋊C4×C73—21no—
57C4×C22⋊C4×C73—21no—
58#376×C73C2211yescharacteristic
59C2×#95×C73—21no—
60C22×#10596831C2311yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64#14556583—22no—
65#14556583C2×C414yescomplemented
66C2×C4⋊Dic73—21no—
67C2×C4⋊Dic73—21no—
68C2×C4⋊Dic73C2311yescharacteristic
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×#11924007—21no—
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×C4×Dic73—21no—
77C2×C4×Dic73—21no—
78#14556524—22no—
79#14556524—22no—
80#14556524C2×C414yescomplemented
81#14556522C2×C414yescomplemented
82C4⋊#10596831—22no—
83C4⋊#10596831C2×C414yescomplemented
84#14556512—22no—
85#14556512—22no—
86#14556512C2×C414yes—
87#14556512C2×C414yes—
88#14556502—22no—
89C4×#10596831—22no—
90#14556498—21no—
91#14556498—21no—
92#14556498—21no—
93#14556498—21no—
94C22×D4×C73C2311yescharacteristic
95C23×C4×C73—21no—
96C23×C4×C73—21no—
97C23×C4×C73—21no—
98C4×D4×C73—22no—
99C4×D4×C73—22no—
100C4×D4×C73—22no—
101C4×D4×C73—22no—
102C4×D4×C73C2×C414yes—
103C4×D4×C73Q814yes—
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73—21no—
112C2×C42×C73—21no—
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116#95×C73—21no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73D411yescharacteristic
120#95×C73D411yescharacteristic
121#95×C73D411yescharacteristic
122#95×C73D411yescharacteristic
123C22×Dic73—21no—
124C22×Dic73—21no—
125C22×Dic73—21no—
126C22×Dic73—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—
136C2×#10596831—21no—
137C2×#10596831C22×C412yes—
138C2×#10596831C22×C412yes—
139C4⋊Dic73—21no—
140C4⋊Dic73—21no—
141C4⋊Dic73—21no—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—81no—
146C4⋊Dic73—81no—
147C4⋊Dic73C22×C412yes—
148C4⋊Dic73C22×C412yes—
149#11924007—24no—
150#11924007—24no—
151#11924007—81no—
152#11924007—81no—
153C4×Dic73—81no—
154C4×Dic73—81no—
155C24×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73C22×C412yes—
160C2×D4×C73C2×Q812yes—
161C2×D4×C73#4112yes—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—24no—
166C22×C4×C73—24no—
167C22×C4×C73—24no—
168C22×C4×C73—81no—
169C22×C4×C73—81no—
170C22×C4×C73—81no—
171C22×C4×C73—81no—
172C22×C4×C73—81no—
173C22×C4×C73—81no—
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2411yescharacteristic
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73C22×C412yes—
185C4⋊C4×C73C2×Q812yes—
186C4⋊C4×C73#4112yes—
187C22⋊C4×C73—24no—
188C22⋊C4×C73—24no—
189C22⋊C4×C73—24no—
190C42×C73—21no—
191C42×C73—21no—
192C42×C73—81no—
193C42×C73—81no—
194C42×C73—81no—
195C42×C73C22×C412yes—
196C42×C73C2×Q812yes—
197C42×C73#4112yes—
198C42×C73#4112yes—
199C23×C73—22no—
200C23×C73—22no—
201C23×C73—22no—
202C23×C73—41no—
203C23×C73—41no—
204C23×C73—41no—
205C23×C73—41no—
206C23×C73C22×D411yescharacteristic
207D4×C73—22no—
208D4×C73—22no—
209D4×C73—22no—
210D4×C73C4×Q814yes—
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—21no—
218C2×C4×C73—21no—
219C2×C4×C73—22no—
220C2×C4×C73—22no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—22no—
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—84no—
235C2×C4×C73—84no—
236C2×C4×C73—84no—
237C2×C4×C73C4×D412yes—
238C2×C4×C73C4×D412yes—
239C2×C4×C73C22⋊Q812yes—
240C2×C4×C73C22⋊Q812yes—
241C2×C4×C73C23×C411yescharacteristic
242C2×C4×C73C22×Q811yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C2×C4×C73C2×#4111yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×Dic73—22no—
248C2×Dic73—22no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73—41no—
255C2×Dic73—41no—
256C2×Dic73—41no—
257C2×Dic73—41no—
258C2×Dic73—41no—
259#10596831—22no—
260#10596831—22no—
261#10596831—41no—
262#10596831—41no—
263C22×C73—24no—
264C22×C73—42no—
265C22×C73—42no—
266C22×C73—42no—
267C22×C73—42no—
268C22×C73—42no—
269C22×C73—42no—
270C22×C73C2×C4×D411yescharacteristic
271C22×C73C2×C22⋊Q811yescharacteristic
272C22×C73#52511yescharacteristic
273C22×C73#57611yescharacteristic
274C22×C73#57611yescharacteristic
275C22×C73#57711yescharacteristic
276C22×C73#57811yescharacteristic
277C4×C73—22no—
278C4×C73—22no—
279C4×C73—22no—
280C4×C73—22no—
281C4×C73—42no—
282C4×C73—41no—
283C4×C73—41no—
284C4×C73—42no—
285C4×C73—42no—
286C4×C73C2×C4×Q811yescharacteristic
287C4×C73C4×#4111yescharacteristic
288C4×C73#52911yescharacteristic
289C4×C73#53311yescharacteristic
290Dic73—42no—
291Dic73—42no—
292Dic73—81no—
293Dic73—81no—
294#21620—731nomaximal, Sylow
295C2×C73—44no—
296C2×C73C4×C22⋊Q811yescharacteristic
297C2×C73#294611yescharacteristic
298C2×C73#295111yescharacteristic
299C2×C73#308111yescharacteristic
300C2×C73#308311yescharacteristic
301C2×C73#312011yescharacteristic
302C2×C73#312211yescharacteristic
303C2×#478—731no—
304#2330—731no—
305#2275D7311yescharacteristic
306#1989—731no—
307#1947—731no—
308#1921—731no—
309#1920—731no—
310#1862—731no—
311#1862—731no—
312#1802—731no—
313#1776—731no—
314C4×#107—731no—
315#1768—731no—
316#1762—731no—
317C4×#102—731no—
318C73#2162011yescharacteristic, complemented, Sylow
319C2×#125—731no—
320C2×C4×D4C2×D7311yescharacteristic
321C2×C4×D4C2×D7311yescharacteristic
322C2×C4×D4C2×D7311yescharacteristic
323#478—738no—
324C2×#107—731no—
325C2×#107—731no—
326C2×#107—731no—
327C2×#106—731no—
328C2×C4⋊C8—731no—
329C2×C4⋊C8—731no—
330C2×#102—731no—
331C2×#102—731no—
332C2×#102—731no—
333C2×#102—731no—
334C2×#97—731no—
335C2×C4×C8—731no—
336#389—731no—
337#389—731no—
338#389—1461no—
339#389—1461no—
340#387—1461no—
341#387—1461no—
342#384—731no—
343C4×C4⋊C4—731no—
344C4×C4⋊C4—731no—
345C4×C4⋊C4C2×D7311yescharacteristic
346C4×C4⋊C4C2×D7311yescharacteristic
347C4×C4⋊C4C2×D7311yescharacteristic
348C4×C22⋊C4—21no—
349C4×C22⋊C4—21no—
350C4×C22⋊C4—21no—
351#376C2×D7311yescharacteristic
352C2×#95—21no—
353#340—731no—
354#340—731no—
355#340—731no—
356#340—731no—
357#340—731no—
358#340—731no—
359#340—731no—
360#340—731no—
361#336—731no—
362#336—731no—
363C22×D4C22×D7311yescharacteristic
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—21no—
367C22×C8—731no—
368C22×C8—731no—
369C22×C8—731no—
370C22×C8—731no—
371#125—734no—
372#125—1462no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4Dic14614yes—
378C4×D4C4×D7314yes—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—731no—
381C2×C4⋊C4—731no—
382C2×C4⋊C4—731no—
383C2×C4⋊C4—1461no—
384C2×C4⋊C4—1461no—
385C2×C4⋊C4—1461no—
386C2×C4⋊C4—1461no—
387C2×C4⋊C4—1461no—
388C2×C4⋊C4—1461no—
389C2×C4⋊C4C22×D7311yescharacteristic
390C2×C4⋊C4C22×D7311yescharacteristic
391C2×C4⋊C4C22×D7311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—1461no—
399C2×C42—1461no—
400C2×C42C22×D7311yescharacteristic
401C2×C42C22×D7311yescharacteristic
402C2×C42C22×D7311yescharacteristic
403#107—734no—
404#107—1462no—
405#107—1462no—
406#106—734no—
407C4⋊C8—734no—
408C4⋊C8—1462no—
409#102—734no—
410#102—734no—
411#102—1462no—
412#102—1462no—
413#97—1462no—
414C4×C8—1462no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—1461no—
419#95—1461no—
420#95—1461no—
421#95—1461no—
422#95C22⋊D7311yescharacteristic
423#95C22⋊D7311yescharacteristic
424#95C22⋊D7311yescharacteristic
425#95C22⋊D7311yescharacteristic
426C24—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4C2×C4×D7312yes—
431C2×D4C2×Dic14612yes—
432C2×D4#1192402812yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—81no—
440C22×C4—81no—
441C22×C4—81no—
442C22×C4—81no—
443C22×C4—81no—
444C22×C4—81no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4—1461no—
448C22×C4—1461no—
449C22×C4C2×C22⋊D7311yescharacteristic
450C22×C4C2×C22⋊D7311yescharacteristic
451C22×C4C2×C22⋊D7311yescharacteristic
452C22×C4C2×C22⋊D7311yescharacteristic
453C22×C4C2×C22⋊D7311yescharacteristic
454C22×C4C2×C22⋊D7311yescharacteristic
455C22×C4C23×D7311yescharacteristic
456C2×C8—732no—
457C2×C8—732no—
458C2×C8—1461no—
459C2×C8—1461no—
460C2×C8—1461no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—5841no—
472C4⋊C4—5841no—
473C4⋊C4—5841no—
474C4⋊C4—5841no—
475C4⋊C4—732no—
476C4⋊C4—732no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1464no—
482C4⋊C4—1464no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4C2×C4×D7312yes—
486C4⋊C4C2×Dic14612yes—
487C4⋊C4#1192402812yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C42—21no—
492C42—21no—
493C42—81no—
494C42—81no—
495C42—81no—
496C42—5841no—
497C42—5841no—
498C42C2×C4×D7312yes—
499C42C2×Dic14612yes—
500C42#1192402812yes—
501C42#1192402812yes—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23C22×C22⋊D7311yescharacteristic
510D4—22no—
511D4—22no—
512D4—22no—
513D4C4×Dic14614yes—
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—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4—84no—
539C2×C4—84no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—1462no—
551C2×C4—1462no—
552C2×C4C4×C22⋊D7312yes—
553C2×C4C4×C22⋊D7312yes—
554C2×C4#1455657012yes—
555C2×C4#1455657012yes—
556C2×C4C22×C4×D7311yescharacteristic
557C2×C4C22×Dic14611yescharacteristic
558C2×C4C2×#1192402811yescharacteristic
559C2×C4C2×#1192402811yescharacteristic
560C2×C4C2×#1192402811yescharacteristic
561C2×C4C2×#1192402811yescharacteristic
562C8—2921no—
563C8—2921no—
564C8—1462no—
565C8—1462no—
566C22—24no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22C2×C4×C22⋊D7311yescharacteristic
574C22C2×#1455657011yescharacteristic
575C22#1798909811yescharacteristic
576C22#1798939011yescharacteristic
577C22#1798939011yescharacteristic
578C22#1798939811yescharacteristic
579C22#1798940211yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—42no—
586C4—42no—
587C4—42no—
588C4—41no—
589C4—2922no—
590C4—2922no—
591C4—5841no—
592C4—5841no—
593C4C2×C4×Dic14611yescharacteristic
594C4C4×#1192402811yescharacteristic
595C4#1798912111yescharacteristic
596C4#1798914411yescharacteristic
597C2—44no—
598C2C4×#1455657011yescharacteristic
599C2#2261876311yescharacteristic
600C2#2261880411yescharacteristic
601C2#2261976211yescharacteristic
602C2#2261978211yescharacteristic
603C2#2262014511yescharacteristic
604C2#2262017411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2275C2
socleC23×C73C22×D4
prime radicalC22×D4×C73C23
cosocleC22×C4×C73C24
hypercenter#2275D73
hypocenterC73#21620
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ #376 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #22612672C2semidirect
3. #22610888C2semidirect
4. #22610689C2semidirect
5. #22610523C2semidirect
6. #22610516C2semidirect
10. #22609829C2semidirect
11. C4×#14556524C2semidirect
12. #22609788C2semidirect
17. #17988887C4semidirect
65. #14556583C2×C4semidirect
80. #14556524C2×C4semidirect
81. #14556522C2×C4semidirect
83. C4⋊#10596831C2×C4semidirect
318. C73#21620semidirect

Maximal subgroups

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

subgroupindex
C2×#179888872
#226126722
#226108882
#226106892
#226105232
#226105162
#226101782
#226099312
#226098292
C4×#145565242
#226097882
#226097562
C4×#145565122
C73×#22752
#2162073