Finite Group Databasebeta

← #33095529

Subgroups — #33095529

Order 18688.

970 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989215C211yesmaximal, characteristic
2C2×#17988648C211yesmaximal, characteristic
3#22610903C211yesmaximal, characteristic, complemented
4#22610899C211yesmaximal, characteristic, complemented
5#22610895C211yesmaximal, characteristic, complemented
6#22610891C211yesmaximal, characteristic, complemented
7#22610888C211yesmaximal, characteristic, complemented
8#22610888C211yesmaximal, characteristic, complemented
9#22610883C211yesmaximal, characteristic, complemented
10#22610879C211yesmaximal, characteristic, complemented
11#22610023C211yesmaximal, characteristic
12#22610023C211yesmaximal, characteristic
13#22610019C211yesmaximal, characteristic
14#22610015C211yesmaximal, characteristic
15C73×#2314C211yesmaximal, characteristic
16#17989215—24no—
17#17989215C418yescomplemented
18C2×#14556591C2211yescharacteristic
19C2×#14556591C2211yescharacteristic
20C2×#14556590—21no—
21C2×#14556583C2211yescharacteristic
22C2×#14556583C2211yescharacteristic
23C2×#14556582—21no—
24C2×#14556568—21no—
25C2×#14556568—21no—
26C2×#14556550C2211yescharacteristic
27C22×C4⋊Dic73C2211yescharacteristic
28#17988648—24no—
29C2×C4⋊#10596831C2211yescharacteristic
30C2×C4⋊#10596831C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×C22⋊#10596831C2211yescharacteristic
33C2×#14556502C2211yescharacteristic
34C2×C4×#10596831C2211yescharacteristic
35#17988349C2211yescharacteristic
36#17988349C2211yescharacteristic
37#17988349C2211yescharacteristic
38#17988349C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51C2×#117×C73C2211yescharacteristic
52#388×C73—21no—
53#388×C73—21no—
54#387×C73—21no—
55#387×C73—21no—
56#384×C73C2211yescharacteristic
57#382×C73C2211yescharacteristic
58#380×C73C2211yescharacteristic
59#380×C73C2211yescharacteristic
60C4×C4⋊C4×C73C2211yescharacteristic
61C4×C4⋊C4×C73C2211yescharacteristic
62C22×Dic146—21no—
63C22×Dic146—21no—
64C23×Dic73—21no—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69#14556591—22no—
70#14556591—22no—
71#14556591C2×C414yes—
72#14556591C2×C414yes—
73#14556590—28no—
74#14556583—22no—
75#14556583—22no—
76#14556583C2×C414yes—
77#14556583C2×C414yes—
78#14556582—28no—
79#14556568—28no—
80#14556568—28no—
81#14556550—22no—
82#14556550C2×C414yes—
83C2×C4⋊Dic73—21no—
84C2×C4⋊Dic73—21no—
85C2×C4⋊Dic73—21no—
86C2×C4⋊Dic73—22no—
87C2×C4⋊Dic73C2×C414yes—
88C2×C4⋊Dic73C2311yescharacteristic
89C2×C4⋊Dic73C2311yescharacteristic
90C2×C4⋊Dic73C2311yescharacteristic
91C2×C4⋊Dic73C2311yescharacteristic
92C2×#11924007—21no—
93C2×#11924007—21no—
94C2×#11924007—21no—
95C2×#11924007—21no—
96C2×C22⋊Dic73—21no—
97C2×C4×Dic73—21no—
98C4⋊#10596831—22no—
99C4⋊#10596831—22no—
100C22⋊#10596831—22no—
101C22⋊#10596831—22no—
102#14556502—22no—
103C4×#10596831—22no—
104C23×C4×C73C2311yescharacteristic
105#117×C73C2×C414yes—
106#117×C73D414yes—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73D411yescharacteristic
110C2×C4⋊C4×C73D411yescharacteristic
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C22⋊C4×C73—21no—
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73D411yescharacteristic
118C2×C22⋊C4×C73D411yescharacteristic
119C2×C42×C73—21no—
120C2×C42×C73—21no—
121C2×C42×C73C2311yescharacteristic
122C2×C42×C73C2311yescharacteristic
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129C2×Dic146—24no—
130C2×Dic146—24no—
131C2×Dic146—81no—
132C2×Dic146—81no—
133C2×Dic146—81no—
134C2×Dic146—81no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73—21no—
139C22×Dic73—24no—
140C22×Dic73—81no—
141C22×Dic73—81no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C4⋊Dic73—24no—
155C4⋊Dic73—24no—
156C4⋊Dic73—24no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73C22×C412yes—
162C4⋊Dic73C22×C412yes—
163C4⋊Dic73C22×C412yes—
164C4⋊Dic73C22×C412yes—
165#11924007—24no—
166#11924007—24no—
167#11924007—24no—
168#11924007—24no—
169C22⋊Dic73—24no—
170C4×Dic73—24no—
171C24×C73C2×D411yescharacteristic
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73C22×C412yes—
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73C2×D412yes—
187C22×C4×C73C2411yescharacteristic
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—81no—
197C4⋊C4×C73—81no—
198C4⋊C4×C73C22⋊C414yes—
199C4⋊C4×C73C22⋊C414yes—
200C22⋊C4×C73—81no—
201C22⋊C4×C73—81no—
202C22⋊C4×C73C22⋊C414yes—
203C22⋊C4×C73C22⋊C414yes—
204C42×C73—81no—
205C42×C73—81no—
206C42×C73C22×C412yes—
207C42×C73C22×C412yes—
208C42×C73C2×D412yes—
209C42×C73C2×D412yes—
210C23×C73—21no—
211C23×C73—21no—
212C23×C73—21no—
213C23×C73—21no—
214C23×C73—21no—
215C23×C73—21no—
216C23×C73C2×C22⋊C412yes—
217C23×C73C22×D411yescharacteristic
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—22no—
229C2×C4×C73—22no—
230C2×C4×C73—22no—
231C2×C4×C73—22no—
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×C73C2×C22⋊C412yes—
245C2×C4×C73C2×C22⋊C412yes—
246C2×C4×C73C2×C22⋊C412yes—
247C2×C4×C73C2×C22⋊C412yes—
248C2×C4×C73C2×C22⋊C412yes—
249C2×C4×C73C23×C411yescharacteristic
250C2×C4×C73C22×D411yescharacteristic
251C2×C4×C732−1+411yescharacteristic
252C2×C4×C732−1+411yescharacteristic
253C2×C4×C732−1+411yescharacteristic
254C2×C4×C732−1+411yescharacteristic
255C2×Dic73—22no—
256C2×Dic73—22no—
257C2×Dic73—22no—
258C2×Dic73—22no—
259C2×Dic73—41no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267C2×Dic73—84no—
268Dic146—84no—
269Dic146—84no—
270#10596831—41no—
271#10596831—41no—
272#10596831—41no—
273#10596831—41no—
274C22×C73—22no—
275C22×C73—22no—
276C22×C73—22no—
277C22×C73—41no—
278C22×C73—41no—
279C22×C73—41no—
280C22×C73—41no—
281C22×C73C22×C22⋊C411yescharacteristic
282C22×C73#53611yescharacteristic
283C22×C73#53611yescharacteristic
284C22×C73#57611yescharacteristic
285C22×C73#57711yescharacteristic
286C22×C73#57711yescharacteristic
287C22×C73#57811yescharacteristic
288C4×C73—22no—
289C4×C73—22no—
290C4×C73—22no—
291C4×C73—22no—
292C4×C73—22no—
293C4×C73—81no—
294C4×C73—81no—
295C4×C73—81no—
296C4×C73—81no—
297C4×C73#51911yescharacteristic
298C4×C73#51911yescharacteristic
299C4×C73#53611yescharacteristic
300C4×C73#53611yescharacteristic
301Dic73—42no—
302Dic73—42no—
303Dic73—42no—
304Dic73—42no—
305#21843—731nomaximal, Sylow
306C2×C73—42no—
307C2×C73#231011yescharacteristic
308C2×C73#289711yescharacteristic
309C2×C73#289811yescharacteristic
310C2×C73#324111yescharacteristic
311C2×C73#324211yescharacteristic
312C2×C73#324311yescharacteristic
313C2×C73#324411yescharacteristic
314C2×#544—731no—
315C2×#433—731no—
316#2314D7311yescharacteristic
317#1993—731no—
318#1992—731no—
319#1991—731no—
320#1990—731no—
321#1989—731no—
322#1989—731no—
323#1988—731no—
324#1987—731no—
325#1825—731no—
326#1825—731no—
327#1824—731no—
328#1823—731no—
329C73#2184311yescharacteristic, complemented, Sylow
330#544—738no—
331#544—1464no—
332C2×C4⋊Q8—731no—
333C2×C4⋊Q8—731no—
334C2×C4⋊Q8—1461no—
335C2×#125—731no—
336C2×#125—731no—
337C2×#125—1461no—
338C2×C22⋊Q8—1461no—
339C2×C22⋊Q8—1461no—
340C2×#117—731no—
341C2×#117C2×D7311yescharacteristic
342C22×C4⋊C4—731no—
343#433—1464no—
344C2×C4⋊C8—731no—
345C2×C4⋊C8—731no—
346C2×C22⋊C8—731no—
347C2×C22⋊C8—731no—
348C2×#97—731no—
349C2×C4×C8—731no—
350#388—21no—
351#388—21no—
352#387—21no—
353#387—21no—
354#384C2×D7311yescharacteristic
355#382C2×D7311yescharacteristic
356#380C2×D7311yescharacteristic
357#380C2×D7311yescharacteristic
358C4×C4⋊C4C2×D7311yescharacteristic
359C4×C4⋊C4C2×D7311yescharacteristic
360#340—731no—
361#340—731no—
362#340—731no—
363#340—731no—
364#340—731no—
365#340—731no—
366#340—731no—
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#340—731no—
376C22×Q8—1461no—
377C22×Q8—1461no—
378C23×C4—1461no—
379C23×C4C22×D7311yescharacteristic
380C22×C8—731no—
381C22×C8—731no—
382C22×C8—731no—
383C22×C8—731no—
384C4⋊Q8—734no—
385C4⋊Q8—734no—
386C4⋊Q8—1468no—
387C4⋊Q8—1462no—
388C4⋊Q8—1462no—
389#125—734no—
390#125—734no—
391#125—1468no—
392#125—1462no—
393#125—1462no—
394C22⋊Q8—1468no—
395C22⋊Q8—1468no—
396#117—734no—
397#117—1462no—
398#117C4×D7314yes—
399#117D29214yes—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—734no—
403C2×C4⋊C4—731no—
404C2×C4⋊C4—731no—
405C2×C4⋊C4—731no—
406C2×C4⋊C4—731no—
407C2×C4⋊C4—1461no—
408C2×C4⋊C4—1461no—
409C2×C4⋊C4—1461no—
410C2×C4⋊C4—1461no—
411C2×C4⋊C4—1461no—
412C2×C4⋊C4—1461no—
413C2×C4⋊C4—1461no—
414C2×C4⋊C4—1462no—
415C2×C4⋊C4C22⋊D7311yescharacteristic
416C2×C4⋊C4C22⋊D7311yescharacteristic
417C2×C4⋊C4C22×D7311yescharacteristic
418C2×C4⋊C4C22×D7311yescharacteristic
419C2×C4⋊C4C22×D7311yescharacteristic
420C2×C4⋊C4C22×D7311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—1461no—
424C2×C22⋊C4C22⋊D7311yescharacteristic
425C2×C22⋊C4C22⋊D7311yescharacteristic
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—1461no—
429C2×C42C22×D7311yescharacteristic
430C2×C42C22×D7311yescharacteristic
431C4⋊C8—1462no—
432C4⋊C8—1462no—
433C22⋊C8—1462no—
434C22⋊C8—1462no—
435#97—1462no—
436C4×C8—1462no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443C24C2×C22⋊D7311yescharacteristic
444C2×Q8—5841no—
445C2×Q8—5841no—
446C2×Q8—5841no—
447C2×Q8—5841no—
448C2×Q8—1464no—
449C2×Q8—1464no—
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—5841no—
459C22×C4—5841no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4—1464no—
465C22×C4C2×C4×D7312yes—
466C22×C4C2×C22⋊D7311yescharacteristic
467C22×C4C2×C22⋊D7311yescharacteristic
468C22×C4C2×C22⋊D7311yescharacteristic
469C22×C4C2×C22⋊D7311yescharacteristic
470C22×C4C2×C22⋊D7311yescharacteristic
471C22×C4C2×D29212yes—
472C22×C4C23×D7311yescharacteristic
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—
483C2×C8—1461no—
484C2×C8—1461no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4—732no—
496C4⋊C4—732no—
497C4⋊C4—732no—
498C4⋊C4—732no—
499C4⋊C4—1464no—
500C4⋊C4—1464no—
501C4⋊C4—1464no—
502C4⋊C4—1464no—
503C4⋊C4—1464no—
504C4⋊C4—1464no—
505C4⋊C4—1464no—
506C4⋊C4—1461no—
507C4⋊C4—1461no—
508C4⋊C4—1461no—
509C4⋊C4—1461no—
510C4⋊C4#1192400514yes—
511C4⋊C4#1192400514yes—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C22⋊C4—1464no—
515C22⋊C4#1192400514yes—
516C22⋊C4#1192400514yes—
517C42—81no—
518C42—81no—
519C42—1464no—
520C42C2×C4×D7312yes—
521C42C2×C4×D7312yes—
522C42C2×D29212yes—
523C42C2×D29212yes—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23C2×#1192400512yes—
531C23C22×C22⋊D7311yescharacteristic
532Q8—5844no—
533Q8—5844no—
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—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
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—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—2921no—
564C2×C4—2921no—
565C2×C4—2921no—
566C2×C4—2921no—
567C2×C4—2921no—
568C2×C4—5844no—
569C2×C4—1462no—
570C2×C4—1462no—
571C2×C4—1462no—
572C2×C4—1462no—
573C2×C4C2×#1192400512yes—
574C2×C4C2×#1192400512yes—
575C2×C4C2×#1192400512yes—
576C2×C4C2×#1192400512yes—
577C2×C4C2×#1192400512yes—
578C2×C4C22×C4×D7311yescharacteristic
579C2×C4C22×D29211yescharacteristic
580C2×C4#1455663811yescharacteristic
581C2×C4#1455663811yescharacteristic
582C2×C4#1455663811yescharacteristic
583C2×C4#1455663811yescharacteristic
584C8—2921no—
585C8—2921no—
586C8—2921no—
587C8—2921no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C22×#1192400511yescharacteristic
596C22#1798915811yescharacteristic
597C22#1798915811yescharacteristic
598C22#1798939011yescharacteristic
599C22#1798939511yescharacteristic
600C22#1798939811yescharacteristic
601C22#1798940211yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—22no—
606C4—22no—
607C4—81no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4—2922no—
612C4—2922no—
613C4—2922no—
614C4—2922no—
615C4#1798906411yescharacteristic
616C4#1798906411yescharacteristic
617C4#1798916311yescharacteristic
618C4#1798916311yescharacteristic
619C2—42no—
620C2#2261251511yescharacteristic
621C2#2261845411yescharacteristic
622C2#2261846111yescharacteristic
623C2#2262117811yescharacteristic
624C2#2262119311yescharacteristic
625C2#2262120811yescharacteristic
626C2#2262122311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2314C2
socleC23×C73C22×D4
prime radicalC24×C73C2×D4
cosocleC22×C4×C73C24
hypercenter#2314D73
hypocenterC73#21843
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #22610903C2semidirect
4. #22610899C2semidirect
5. #22610895C2semidirect
6. #22610891C2semidirect
7. #22610888C2semidirect
8. #22610888C2semidirect
9. #22610883C2semidirect
10. #22610879C2semidirect
17. #17989215C4semidirect
329. C73#21843semidirect

Maximal subgroups

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

subgroupindex
C2×#179892152
C2×#179886482
#226109032
#226108992
#226108952
#226108912
#226108882
#226108832
#226108792
#226100232
#226100192
#226100152
C73×#23142
#2184373