Finite Group Databasebeta

← #34028251

Subgroups — #34028251

Order 18688.

880 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989636C211yesmaximal, characteristic, complemented
2C2×#17989605C211yesmaximal, characteristic
3#22626102C211yesmaximal, characteristic, complemented
4#22626030C211yesmaximal, characteristic, complemented
5#22626003C211yesmaximal, characteristic
6#22626003C211yesmaximal, characteristic
7#22626002C211yesmaximal, characteristic
8#22626002C211yesmaximal, characteristic
9#22625986C211yesmaximal, characteristic, complemented
10#22625984C211yesmaximal, characteristic, complemented
11#22625723C211yesmaximal, characteristic, complemented
12#22625723C211yesmaximal, characteristic, complemented
13C4⋊C4×#10596833C211yesmaximal, characteristic, complemented
14C4×#14556648C211yesmaximal, characteristic
15#22612465C211yesmaximal, characteristic
16#17989636—24no—
17#17989605—24no—
18C2×#14556658C2211yescharacteristic
19C2×#14556658C2211yescharacteristic
20C2×#14556658C2211yescharacteristic
21C2×#14556658C2211yescharacteristic
22C2×C4⋊#10596833C2211yescharacteristic
23C2×C4⋊#10596833C2211yescharacteristic
24C2×#14556648C2211yescharacteristic
25C2×#14556648C2211yescharacteristic
26C2×#14556648C2211yescharacteristic
27C2×#14556648C2211yescharacteristic
28C2×C4×#10596833C2211yescharacteristic
29C2×C4×#10596833C2211yescharacteristic
30C2×C4×#10596833C2211yescharacteristic
31C2×C4×#10596833C2211yescharacteristic
32C2×C4×#10596833C2211yescharacteristic
33C2×C4×#10596833C2211yescharacteristic
34C2×C4×#10596833C2211yescharacteristic
35C2×C4×#10596833C2211yescharacteristic
36#17989453C2211yescharacteristic
37#17989453C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44#17989453C2211yescharacteristic
45#17989453C2211yescharacteristic
46C2×#14556569C411yescharacteristic
47C2×#14556556C2211yescharacteristic
48C2×C42×D73C2211yescharacteristic
49#17988491C411yescharacteristic
50#17988484C411yescharacteristic
51#17988471C411yescharacteristic
52#17988461C411yescharacteristic
53#17988458C411yescharacteristic
54#17988446C411yescharacteristic
55C4⋊C4×Dic73C2211yescharacteristic
56#17988438C2211yescharacteristic
57#17988438C2211yescharacteristic
58#17988434C2211yescharacteristic
59#17988434C2211yescharacteristic
60#387×C73C411yescharacteristic
61C22×#10596833C2311yescharacteristic
62C22×#10596833C2311yescharacteristic
63C22×#10596833C2311yescharacteristic
64C22×#10596833C2311yescharacteristic
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69#14556658—22no—
70#14556658—22no—
71#14556658—22no—
72#14556658D414yes—
73C4⋊#10596833—22no—
74C4⋊#10596833—22no—
75#14556648—22no—
76#14556648—22no—
77#14556648—22no—
78#14556648—22no—
79C4×#10596833—22no—
80C4×#10596833—22no—
81C4×#10596833—22no—
82C4×#10596833—22no—
83C4×#10596833—22no—
84C4×#10596833—22no—
85C4×#10596833—22no—
86C4×#10596833—22no—
87C22×Dic146C2×C411yescharacteristic
88C22×C4×D73C2×C411yescharacteristic
89C22×C4×D73C2×C411yescharacteristic
90C22×C4×D73C2311yescharacteristic
91#14556569C818yescomplemented
92#14556556—22no—
93#14556556—22no—
94C2×C4⋊Dic73C2×C411yescharacteristic
95C2×#11924007C2×C411yescharacteristic
96C2×#11924007C2×C411yescharacteristic
97C2×#11924007C2×C411yescharacteristic
98C2×#11924007C2×C411yescharacteristic
99C2×#11924007C2×C411yescharacteristic
100C2×#11924007C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×#11924005C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×#11924005C2×C411yescharacteristic
105C2×C4×Dic73C2×C411yescharacteristic
106C2×C4×Dic73C2311yescharacteristic
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109C2×C4×Dic73C2311yescharacteristic
110C2×C4×Dic73C2311yescharacteristic
111C2×C4×Dic73C2311yescharacteristic
112C42×D73—22no—
113C42×D73—22no—
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120C2×C4⋊C4×C73C2×C411yescharacteristic
121C2×C4⋊C4×C73C2×C411yescharacteristic
122C2×C42×C73C2×C411yescharacteristic
123#95×C73C2×C411yescharacteristic
124#95×C73C2×C411yescharacteristic
125#95×C73C2×C411yescharacteristic
126#95×C73C2×C411yescharacteristic
127C2×#10596833—21no—
128C2×#10596833—21no—
129C2×#10596833—21no—
130C2×#10596833—21no—
131C2×#10596833—21no—
132C2×#10596833—21no—
133C2×#10596833—21no—
134C2×#10596833—21no—
135C2×#10596833—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833C2×D412yes—
148C2×#10596833C2×D412yes—
149C2×#10596833#4112yes—
150C2×#10596833#4112yes—
151C23×D73C22×C411yescharacteristic
152C2×Dic146—22no—
153C2×Dic146—22no—
154C2×Dic146C2×C814yes—
155C22×Dic73C22×C411yescharacteristic
156C22×Dic73C22×C411yescharacteristic
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C22×C411yescharacteristic
160C22×Dic73C22×C411yescharacteristic
161C22×Dic73C2411yescharacteristic
162C2×C4×D73—22no—
163C2×C4×D73—22no—
164C2×C4×D73—22no—
165C2×C4×D73—22no—
166C2×C4×D73—21no—
167C2×C4×D73—21no—
168C2×C4×D73—21no—
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73—41no—
173C2×C4×D73C2×C814yes—
174C4⋊Dic73—22no—
175#11924007—22no—
176#11924007—22no—
177#11924007—22no—
178#11924007—22no—
179#11924007C2×C814yes—
180#11924007C2×C814yes—
181#11924005—41no—
182#11924005—41no—
183#11924005C2×C814yes—
184#11924005C2×C814yes—
185C4×Dic73—22no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73C2×D412yes—
197C4×Dic73#4112yes—
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200C22×C4×C73C22×C411yescharacteristic
201C22×C4×C73C22×C411yescharacteristic
202C22×C4×C73C22×C411yescharacteristic
203C22×C4×C73C22×C411yescharacteristic
204C22×C4×C73C22×C411yescharacteristic
205C4⋊C4×C73—22no—
206C4⋊C4×C73C2×C814yes—
207C42×C73—22no—
208C23×C73C23×C411yescharacteristic
209C22×D73—21no—
210C22×D73—21no—
211C22×D73—21no—
212C22×D73—21no—
213C22×D73—21no—
214C22×D73—21no—
215C22×D73C22×C812yes—
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—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73C4×D412yes—
234C2×C4×C73C22×C812yes—
235C2×C4×C73C22×C812yes—
236C2×C4×C73C22×C812yes—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245C2×Dic73—21no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73C4×D412yes—
250C2×Dic73C22×C812yes—
251C2×Dic73C22×C812yes—
252C2×Dic73C22×C812yes—
253C2×Dic73#13112yes—
254C2×Dic73#13112yes—
255C2×Dic73C22×D411yescharacteristic
256C2×Dic73C2×#4111yescharacteristic
257C2×Dic73C2×#4111yescharacteristic
258C2×Dic73C2×#4111yescharacteristic
259C2×Dic732−1+411yescharacteristic
260C2×Dic732−1+411yescharacteristic
261C4×D73—28no—
262C4×D73—44no—
263C4×D73—41no—
264C4×D73—41no—
265C4×D73—41no—
266C4×D73—41no—
267Dic146—28no—
268#10596833—22no—
269#10596833—22no—
270#10596833—22no—
271#10596833—22no—
272#10596833—41no—
273#10596833—41no—
274#10596833—41no—
275#10596833—41no—
276C22×C73C2×C4×D411yescharacteristic
277C22×C73C4×#4111yescharacteristic
278C22×C73#51911yescharacteristic
279C22×C73C23×C811yescharacteristic
280C22×C73C2×#13111yescharacteristic
281C22×C73C2×#13111yescharacteristic
282C22×C73#56811yescharacteristic
283C2×D73—22no—
284C2×D73—22no—
285C2×D73—22no—
286C2×D73—41no—
287C2×D73—41no—
288C2×D73—41no—
289C2×D73—41no—
290C4×C73—22no—
291C4×C73—22no—
292C4×C73—22no—
293C4×C73—22no—
294C4×C73—41no—
295C4×C73—41no—
296C4×C73—41no—
297Dic73—22no—
298Dic73—22no—
299Dic73—22no—
300Dic73—41no—
301Dic73—41no—
302Dic73C8×D414yes—
303Dic73#54711yescharacteristic
304Dic73#54811yescharacteristic
305Dic73#55211yescharacteristic
306Dic73#55611yescharacteristic
307#23050—731nomaximal, Sylow
308C2×C73#236211yescharacteristic
309C2×C73C2×C8×D411yescharacteristic
310C2×C73#293311yescharacteristic
311C2×C73C8×#4111yescharacteristic
312C2×C73#296911yescharacteristic
313C2×C73#298211yescharacteristic
314C2×C73#298611yescharacteristic
315D73—42no—
316C2×C8×Q8—731no—
317C2×#431—731no—
318C4×C22⋊Q8—731no—
319#1984—731no—
320#1939—731no—
321#1923—731no—
322#1923—731no—
323#1923—731no—
324#1923—731no—
325#1916—731no—
326#1916—731no—
327C8×C4⋊C4—731no—
328C8×C4⋊C4—731no—
329C8×C4⋊C4—731no—
330C4×C22⋊C8—731no—
331C73#2305011yescharacteristic, complemented, Sylow
332C2×C22⋊Q8—731no—
333C2×C4×Q8—731no—
334C22×C42—731no—
335C8×Q8—1464no—
336#431—1464no—
337C2×C4⋊C8—731no—
338C2×C4⋊C8—731no—
339C2×C4⋊C8—731no—
340C2×C4⋊C8—731no—
341C2×C4⋊C8—731no—
342C2×C4⋊C8—731no—
343C2×C22⋊C8—731no—
344C2×C22⋊C8—731no—
345C2×C22⋊C8—731no—
346C2×C22⋊C8—731no—
347C2×C4×C8—731no—
348C2×C4×C8—731no—
349C2×C4×C8—731no—
350C2×C4×C8—731no—
351C2×C4×C8—731no—
352C2×C4×C8—731no—
353C2×C4×C8—731no—
354C2×C4×C8—731no—
355#391—731no—
356#389—731no—
357#387—731no—
358#387#6440811yescharacteristic
359#385—731no—
360#385—731no—
361#380—731no—
362C4×C4⋊C4—731no—
363C4×C4⋊C4—731no—
364C4×C4⋊C4—731no—
365C4×C22⋊C4—731no—
366C4×C22⋊C4—731no—
367#336—731no—
368#336—731no—
369#336—731no—
370#336—731no—
371#336—731no—
372#336—731no—
373#336—731no—
374#336—731no—
375#336—731no—
376#336—731no—
377C22×Q8—731no—
378C23×C4—731no—
379C23×C4—731no—
380C23×C4—731no—
381C22×C8—731no—
382C22×C8—731no—
383C22×C8—731no—
384C22×C8—731no—
385C22×C8—731no—
386C22×C8—731no—
387C22×C8—731no—
388C22×C8—731no—
389C22⋊Q8—738no—
390C4×Q8—1462no—
391C4×Q8—1462no—
392C2×C4⋊C4—731no—
393C2×C4⋊C4—731no—
394C2×C4⋊C4—731no—
395C2×C4⋊C4—731no—
396C2×C4⋊C4—731no—
397C2×C4⋊C4—731no—
398C2×C4⋊C4—731no—
399C2×C4⋊C4C2×#6440811yescharacteristic
400C2×C4⋊C4C2×#6440811yescharacteristic
401C2×C22⋊C4—731no—
402C2×C22⋊C4—731no—
403C2×C22⋊C4—731no—
404C2×C22⋊C4—731no—
405C2×C42—731no—
406C2×C42—731no—
407C2×C42—731no—
408C2×C42—731no—
409C2×C42—731no—
410C2×C42—731no—
411C2×C42—731no—
412C2×C42—1462no—
413C2×C42—1462no—
414C2×C42C2×#6440811yescharacteristic
415C4⋊C8—734no—
416C4⋊C8—1462no—
417C4⋊C8—1462no—
418C4⋊C8—1462no—
419C4⋊C8—1462no—
420C4⋊C8—1462no—
421C22⋊C8—1462no—
422C22⋊C8—1462no—
423C22⋊C8—1462no—
424C22⋊C8—1462no—
425C4×C8—1462no—
426C4×C8—1462no—
427C4×C8—1462no—
428C4×C8—1462no—
429C4×C8—1462no—
430C4×C8—1462no—
431C4×C8—1462no—
432C4×C8—1462no—
433#95—731no—
434#95—731no—
435#95—731no—
436#95—731no—
437#95—731no—
438#95—731no—
439#95C2×#6440811yescharacteristic
440#95C2×#6440811yescharacteristic
441#95C2×#6440811yescharacteristic
442#95C2×#6440811yescharacteristic
443C24—731no—
444C2×Q8—734no—
445C2×Q8—1462no—
446C2×Q8—1462no—
447C22×C4—2921no—
448C22×C4—731no—
449C22×C4—731no—
450C22×C4—731no—
451C22×C4—731no—
452C22×C4—731no—
453C22×C4—734no—
454C22×C4—731no—
455C22×C4—731no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4—1461no—
460C22×C4—1462no—
461C22×C4—1461no—
462C22×C4—1461no—
463C22×C4—1462no—
464C22×C4—1462no—
465C22×C4—1462no—
466C22×C4C22×#6440811yescharacteristic
467C22×C4C22×#6440811yescharacteristic
468C22×C4C22×#6440811yescharacteristic
469C22×C4C22×#6440811yescharacteristic
470C22×C4C22×#6440811yescharacteristic
471C22×C4C22×#6440811yescharacteristic
472C22×C4C22×#6440811yescharacteristic
473C2×C8—732no—
474C2×C8—732no—
475C2×C8—732no—
476C2×C8—732no—
477C2×C8—1461no—
478C2×C8—1461no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8—1461no—
494C2×C8—1461no—
495C2×C8—1461no—
496C2×C8—1461no—
497C4⋊C4—22no—
498C4⋊C4—734no—
499C4⋊C4—734no—
500C4⋊C4—1462no—
501C4⋊C4—1462no—
502C4⋊C4—1462no—
503C4⋊C4—1462no—
504C4⋊C4—1462no—
505C4⋊C4#1192403614yes—
506C22⋊C4—2921no—
507C22⋊C4—2921no—
508C22⋊C4—734no—
509C22⋊C4—734no—
510C42—22no—
511C42—732no—
512C42—732no—
513C42—1461no—
514C42—1461no—
515C42—1461no—
516C42—1461no—
517C42—1461no—
518C42—1461no—
519C42—1461no—
520C42—1461no—
521C42—1462no—
522C42—1461no—
523C42—1461no—
524C23—732no—
525C23—1461no—
526C23—1461no—
527C23—1461no—
528C23—1461no—
529C23—1461no—
530C23—1461no—
531C23C23×#6440811yescharacteristic
532Q8—1468no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
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—2924no—
551C2×C4—2921no—
552C2×C4—2921no—
553C2×C4—2921no—
554C2×C4—2921no—
555C2×C4—731no—
556C2×C4—731no—
557C2×C4—732no—
558C2×C4—731no—
559C2×C4—731no—
560C2×C4—731no—
561C2×C4—731no—
562C2×C4—732no—
563C2×C4—732no—
564C2×C4—732no—
565C2×C4—732no—
566C2×C4—732no—
567C2×C4—1468no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1461no—
572C2×C4—1461no—
573C2×C4—1461no—
574C2×C4—1461no—
575C2×C4—1461no—
576C2×C4—1461no—
577C2×C4—1461no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4D4×#6440812yes—
581C2×C4C2×#1192403612yes—
582C2×C4C2×#1192403612yes—
583C2×C4C2×#1192403612yes—
584C8—2921no—
585C8—2921no—
586C8—2921no—
587C8—2921no—
588C8—1462no—
589C8—1462no—
590C8—1462no—
591C8—1462no—
592C22—2921no—
593C22—2921no—
594C22—2921no—
595C22—2921no—
596C22—1462no—
597C22—1462no—
598C22—1462no—
599C22C2×D4×#6440811yescharacteristic
600C22#41×#6440811yescharacteristic
601C22#1798965511yescharacteristic
602C22C22×#1192403611yescharacteristic
603C22D73⋊#13111yescharacteristic
604C22D73⋊#13111yescharacteristic
605C22#1798966611yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—22no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—2921no—
614C4—2921no—
615C4—734no—
616C4—731no—
617C4—731no—
618C4—731no—
619C4—731no—
620C4—1462no—
621C4—1462no—
622C4—1462no—
623C2—2922no—
624C2#2262645711yescharacteristic
625C2D4×#1192403611yescharacteristic
626C2#2262666511yescharacteristic
627C2#2262673511yescharacteristic
628C2#2262676611yescharacteristic
629C2#2262682511yescharacteristic
630C2#2262684111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutatorC22×C73C23×C8
Fitting#387×C73C4
socleC23×C73C23×C4
prime radicalC23×D73C22×C4
cosocleC22×Dic73C24
hypercenter#387#64408
hypocenterC73#23050
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#17989636C2semidirect
3. #22626102C2semidirect
4. #22626030C2semidirect
9. #22625986C2semidirect
10. #22625984C2semidirect
11. #22625723C2semidirect
12. #22625723C2semidirect
13. C4⋊C4×#10596833C2semidirect
91. #14556569C8semidirect
331. C73#23050semidirect

Maximal subgroups

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

subgroupindex
C2×#179896362
C2×#179896052
#226261022
#226260302
#226260032
#226260022
#226259862
#226259842
#226257232
C4⋊C4×#105968332
C4×#145566482
#226124652
#2305073