Finite Group Databasebeta

← #33114708

Subgroups — #33114708

Order 18688.

960 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988636C211yesmaximal, characteristic, complemented
2C2×#17988635C211yesmaximal, characteristic, complemented
3C2×#17988569C211yesmaximal, characteristic
4C2×#17988569C211yesmaximal, characteristic
5C2×#17988569C211yesmaximal, characteristic
6#22611331C214yesmaximal, complemented
7#22611328C214yesmaximal, complemented
8C2×#17988345C211yesmaximal, characteristic, complemented
9C2×#430×C73C211yesmaximal, characteristic, complemented
10C22×#11924028C2211yescharacteristic
11C22×#11924012C2211yescharacteristic
12C22×#11924012C2211yescharacteristic
13C22×#11924012C2211yescharacteristic
14#17988636—22no—
15#17988636C2214yes—
16#17988635—22no—
17#17988635C2214yes—
18C2×#14556527—22no—
19C2×#14556526—22no—
20#17988569—22no—
21#17988569—22no—
22#17988569—22no—
23#17988569—22no—
24#17988569—22no—
25#17988569—22no—
26C2×#14556509C2212yes—
27C2×#14556509C2212yes—
28C2×#14556509C2212yes—
29C2×#14556507C2212yes—
30C2×#14556507C2212yes—
31C2×#14556507C2212yes—
32#17988345C2214yes—
33C22×M16×C73C2211yescharacteristic
34C22×M16×C73C2211yescharacteristic
35C22×M16×C73C2211yescharacteristic
36#430×C73—22no—
37#430×C73C2214yes—
38C2×#108×C73—22no—
39C2×#11924028—21no—
40C2×#11924028—21no—
41C2×#11924028—21no—
42C2×#11924028—21no—
43C2×#11924028—21no—
44C2×#11924028—21no—
45C2×#11924028—21no—
46C2×#11924028—21no—
47C2×#11924028—21no—
48C2×#11924028—21no—
49C2×#11924028—21no—
50C2×#11924028—21no—
51C22×Dic146C2311yescharacteristic
52C22×D292C2311yescharacteristic
53C22×C22⋊D73Q812yes—
54C22×C4×D73Q812yes—
55C2×#11924012—21no—
56C2×#11924012—21no—
57C2×#11924012—21no—
58C2×#11924012—21no—
59C2×#11924012—21no—
60C2×#11924012—21no—
61C2×#11924012—21no—
62C2×#11924012—21no—
63C2×#11924012—21no—
64C2×#11924012—21no—
65C2×#11924012—21no—
66C2×#11924012—21no—
67C2×#11924012—21no—
68C2×#11924012D412yes—
69C2×#11924012D412yes—
70C2×#11924012C2312yes—
71C2×#11924012C2312yes—
72C2×#11924012C2312yes—
73C22×#10596831—21no—
74C22×#10596831—21no—
75C22×#10596831—21no—
76#14556527—28no—
77#14556526—28no—
78#14556509—24no—
79#14556509—24no—
80#14556509—24no—
81#14556507—24no—
82#14556507—24no—
83#14556507—24no—
84C23×C4×C73C2311yescharacteristic
85C2×M16×C73—21no—
86C2×M16×C73—21no—
87C2×M16×C73—21no—
88C2×M16×C73—21no—
89C2×M16×C73—21no—
90C2×M16×C73—21no—
91C2×M16×C73—21no—
92C2×M16×C73—21no—
93C2×M16×C73—21no—
94C2×M16×C73—21no—
95C2×M16×C73—21no—
96C2×M16×C73D412yes—
97C2×M16×C73D412yes—
98C2×M16×C73D412yes—
99C2×M16×C73D412yes—
100C2×M16×C73C2312yes—
101C2×M16×C73C2312yes—
102C2×M16×C73C2312yes—
103C22×C8×C73—21no—
104C22×C8×C73—21no—
105C22×C8×C73—21no—
106#108×C73—28no—
107C23×D73C2×Q812yes—
108#11924028—41no—
109#11924028—41no—
110#11924028—41no—
111#11924028—41no—
112#11924028—41no—
113#11924028—41no—
114#11924028—41no—
115#11924028—41no—
116#11924028—41no—
117#11924028—41no—
118#11924028—41no—
119#11924028—41no—
120#11924028—41no—
121#11924028—41no—
122#11924028—41no—
123#11924028—41no—
124C2×Dic146—21no—
125C2×Dic146—21no—
126C2×Dic146—21no—
127C2×Dic146—21no—
128C2×Dic146—21no—
129C2×Dic146—21no—
130C2×D292—21no—
131C2×D292—21no—
132C2×D292—21no—
133C2×D292—21no—
134C2×D292—21no—
135C2×D292—21no—
136C2×C22⋊D73—22no—
137C2×C22⋊D73—22no—
138C2×C22⋊D73—22no—
139C2×C22⋊D73—22no—
140C2×C22⋊D73—22no—
141C2×C22⋊D73—22no—
142C22×Dic73C2×Q812yes—
143C2×C4×D73—22no—
144C2×C4×D73—22no—
145C2×C4×D73—22no—
146C2×C4×D73—22no—
147C2×C4×D73—22no—
148C2×C4×D73—22no—
149#11924012—22no—
150#11924012—22no—
151#11924012—22no—
152#11924012—22no—
153#11924012—22no—
154#11924012—22no—
155#11924012—22no—
156#11924012—41no—
157#11924012—41no—
158#11924012—41no—
159#11924012—41no—
160#11924012C2×D414yes—
161C2×#10596831—22no—
162C2×#10596831—22no—
163C2×#10596831—22no—
164C2×#10596831—22no—
165C2×#10596831—22no—
166C2×#10596831—41no—
167C2×#10596831—41no—
168C2×#10596831—41no—
169C2×#10596831—41no—
170C24×C73C2×Q811yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×Q811yescharacteristic
178C22×C4×C73#4111yescharacteristic
179C22×C4×C73#4111yescharacteristic
180C22×C4×C73#4111yescharacteristic
181C22×C4×C73#4111yescharacteristic
182C22×C4×C73#4111yescharacteristic
183C22×C4×C73#4111yescharacteristic
184C22×C4×C73C2411yescharacteristic
185M16×C73—22no—
186M16×C73—22no—
187M16×C73—22no—
188M16×C73—22no—
189M16×C73—22no—
190M16×C73—22no—
191M16×C73—22no—
192M16×C73—22no—
193M16×C73—41no—
194M16×C73—41no—
195M16×C73C2×D414yes—
196M16×C73C2×D414yes—
197C2×C8×C73—22no—
198C2×C8×C73—22no—
199C2×C8×C73—22no—
200C2×C8×C73—22no—
201C2×C8×C73—22no—
202C2×C8×C73—22no—
203C2×C8×C73—22no—
204C2×C8×C73—41no—
205C2×C8×C73—41no—
206C23×C73—81no—
207C23×C73C22⋊Q811yescharacteristic
208C23×C73C22⋊Q811yescharacteristic
209C23×C73C22⋊Q811yescharacteristic
210C23×C73C22⋊Q811yescharacteristic
211C23×C73C22⋊Q811yescharacteristic
212C23×C73C22⋊Q811yescharacteristic
213C23×C73C22×Q811yescharacteristic
214C22×D73—22no—
215C22×D73—22no—
216C22×D73—22no—
217C22×D73—82no—
218C2×C4×C73#12111yescharacteristic
219C2×C4×C73#12111yescharacteristic
220C2×C4×C73#12111yescharacteristic
221C2×C4×C73#12111yescharacteristic
222C2×C4×C73#12111yescharacteristic
223C2×C4×C73#12111yescharacteristic
224C2×C4×C73#12111yescharacteristic
225C2×C4×C73#12111yescharacteristic
226C2×C4×C73#12111yescharacteristic
227C2×C4×C73#12111yescharacteristic
228C2×C4×C73#12111yescharacteristic
229C2×C4×C73#12111yescharacteristic
230C2×C4×C73C22⋊Q811yescharacteristic
231C2×C4×C73C22⋊Q811yescharacteristic
232C2×C4×C73C22⋊Q811yescharacteristic
233C2×C4×C73C22⋊Q811yescharacteristic
234C2×C4×C73C22⋊Q811yescharacteristic
235C2×C4×C73C22⋊Q811yescharacteristic
236C2×C4×C73#12611yescharacteristic
237C2×C4×C73#12611yescharacteristic
238C2×C4×C73#12611yescharacteristic
239C2×C4×C73#12611yescharacteristic
240C2×C4×C73C22×D411yescharacteristic
241C2×C4×C73C22×D411yescharacteristic
242C2×C4×C73C22×D411yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C2×C4×C73C2×#4111yescharacteristic
246C22⋊D73—42no—
247C22⋊D73—42no—
248C22⋊D73—42no—
249C22⋊D73—42no—
250C2×Dic73—22no—
251C2×Dic73—22no—
252C2×Dic73—22no—
253D292—41no—
254D292—41no—
255D292—41no—
256D292—41no—
257C4×D73—42no—
258C4×D73—42no—
259C4×D73—42no—
260C4×D73—42no—
261Dic146—41no—
262Dic146—41no—
263Dic146—41no—
264Dic146—41no—
265C8×C73—24no—
266C8×C73—24no—
267C8×C73—42no—
268#10596831—24no—
269#10596831—42no—
270#10596831—42no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73#39611yescharacteristic
279C22×C73#39611yescharacteristic
280C22×C73#39611yescharacteristic
281C22×C73#39611yescharacteristic
282C22×C73C2×C22⋊Q811yescharacteristic
283C22×C73C2×C22⋊Q811yescharacteristic
284C22×C73C2×C22⋊Q811yescharacteristic
285C2×D73—42no—
286C2×D73—82no—
287C2×D73—82no—
288C2×D73—82no—
289C4×C73#39611yescharacteristic
290C4×C73#39611yescharacteristic
291C4×C73#39611yescharacteristic
292C4×C73#39611yescharacteristic
293C4×C73C2×#12111yescharacteristic
294C4×C73C2×#12111yescharacteristic
295C4×C73C2×#12111yescharacteristic
296C4×C73C2×#12611yescharacteristic
297Dic73—42no—
298#23622—731nomaximal, Sylow
299C2×C73—21no—
300C2×C73—21no—
301C2×C73—21no—
302C2×C73—21no—
303C2×C73—21no—
304C2×C73—21no—
305C2×C73—21no—
306C2×C73C2×#39611yescharacteristic
307D73—82no—
308C2×#430—731no—
309C2×#430—731no—
310C2×#430D7311yescharacteristic, complemented
311C2×#413—731no—
312C2×#413—731no—
313C2×#413—731no—
314#2070—734no—
315#2069—734no—
316C2×#338—731no—
317C73#2362211yescharacteristic, complemented, Sylow
318C22×#41—731no—
319C22×M16—731no—
320C22×M16—731no—
321C22×M16—731no—
322C22×M16C2×D7311yescharacteristic
323C22×M16C2×D7311yescharacteristic
324C22×M16C2×D7311yescharacteristic
325#430—22no—
326#430—734no—
327#430—734no—
328#430—1462no—
329#430—1462no—
330#430C2×D7314yes—
331C2×#108—22no—
332C2×#108—1462no—
333C2×#108—1462no—
334#413—1462no—
335#413—1462no—
336#413—1462no—
337#413—1462no—
338#413—1462no—
339#413—1462no—
340C2×#101—732no—
341C2×#101—732no—
342C2×#101—732no—
343C2×#100—732no—
344C2×#100—732no—
345C2×#100—732no—
346#338—734no—
347C2×#41—1461no—
348C2×#41—1461no—
349C2×#41—1461no—
350C2×#41—1461no—
351C2×#41—1461no—
352C2×#41—1461no—
353C2×#41—1461no—
354C2×#41—1461no—
355C2×#41—1461no—
356C2×#41—1461no—
357C2×#41—1461no—
358C2×#41—1461no—
359C22×Q8—731no—
360C22×D4—732no—
361C22×D4—731no—
362C23×C4—732no—
363C23×C4C22×D7311yescharacteristic
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—732no—
376C2×M16—732no—
377C2×M16—732no—
378C2×M16—732no—
379C2×M16—732no—
380C2×M16—1461no—
381C2×M16—1461no—
382C2×M16—1461no—
383C2×M16—1461no—
384C2×M16—1461no—
385C2×M16—1461no—
386C2×M16—1461no—
387C2×M16—1461no—
388C2×M16—1461no—
389C2×M16—1461no—
390C2×M16—1461no—
391C2×M16—1461no—
392C2×M16—1461no—
393C2×M16D29212yes—
394C2×M16D29212yes—
395C2×M16C22⋊D7312yes—
396C2×M16C22⋊D7312yes—
397C2×M16C22×D7312yes—
398C2×M16C22×D7312yes—
399C2×M16C22×D7312yes—
400C22×C8—21no—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—1461no—
404C22×C8—1461no—
405C22×C8—1461no—
406#108—28no—
407#108—1468no—
408#108—1468no—
409#101—1464no—
410#101—1464no—
411#101—1464no—
412#100—1464no—
413#100—1464no—
414#100—1464no—
415C24—732no—
416C24Q8×D7311yescharacteristic
417#41—2921no—
418#41—2921no—
419#41—2921no—
420#41—2921no—
421#41—2921no—
422#41—2921no—
423#41—2921no—
424#41—2921no—
425#41—2921no—
426#41—2921no—
427#41—2921no—
428#41—2921no—
429#41—2921no—
430#41—2921no—
431#41—2921no—
432#41—2921no—
433C2×Q8—1461no—
434C2×Q8—1461no—
435C2×Q8—1461no—
436C2×Q8—1461no—
437C2×Q8—1461no—
438C2×Q8—1461no—
439C2×D4—1462no—
440C2×D4—1462no—
441C2×D4—1462no—
442C2×D4—1462no—
443C2×D4—1462no—
444C2×D4—1462no—
445C2×D4—1461no—
446C2×D4—1461no—
447C2×D4—1461no—
448C2×D4—1461no—
449C2×D4—1461no—
450C2×D4—1461no—
451C22×C4—732no—
452C22×C4—1462no—
453C22×C4—1462no—
454C22×C4—1462no—
455C22×C4—1462no—
456C22×C4—1462no—
457C22×C4—1462no—
458C22×C4D4×D7311yescharacteristic
459C22×C4D4×D7311yescharacteristic
460C22×C4C2×C22⋊D7311yescharacteristic
461C22×C4C2×C22⋊D7311yescharacteristic
462C22×C4C2×D29211yescharacteristic
463C22×C4C2×D29211yescharacteristic
464C22×C4Q8×D7311yescharacteristic
465C22×C4#1192402711yescharacteristic
466C22×C4#1192402711yescharacteristic
467C22×C4#1192402811yescharacteristic
468C22×C4#1192402811yescharacteristic
469C22×C4#1192402911yescharacteristic
470C22×C4#1192402911yescharacteristic
471C22×C4C23×D7311yescharacteristic
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—41no—
481M16—41no—
482M16—2921no—
483M16—2921no—
484M16—2921no—
485M16—2921no—
486M16—734no—
487M16—1462no—
488M16—1462no—
489M16—1462no—
490M16—1462no—
491M16—1462no—
492M16—1462no—
493M16—1462no—
494M16C2×C22⋊D7314yes—
495M16C2×D29214yes—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—2921no—
506C2×C8—2921no—
507C2×C8—2921no—
508C2×C8—2921no—
509C2×C8—1462no—
510C2×C8—1462no—
511C2×C8—1462no—
512C2×C8—1462no—
513C2×C8—1462no—
514C23—81no—
515C23—5842no—
516C23—1462no—
517C23—1462no—
518C23—1462no—
519C23#1455656711yescharacteristic
520C23#1455656711yescharacteristic
521C23#1455656911yescharacteristic
522C23#1455656911yescharacteristic
523C23#1455657111yescharacteristic
524C23#1455657111yescharacteristic
525C23C2×Q8×D7311yescharacteristic
526Q8—2921no—
527Q8—2921no—
528Q8—2921no—
529Q8—2921no—
530D4—2922no—
531D4—2922no—
532D4—2922no—
533D4—2922no—
534D4—2921no—
535D4—2921no—
536D4—2921no—
537D4—2921no—
538C2×C4—2922no—
539C2×C4—2922no—
540C2×C4—2922no—
541C2×C4—2922no—
542C2×C4—1462no—
543C2×C4—1462no—
544C2×C4—1462no—
545C2×C4#1455656311yescharacteristic
546C2×C4#1455656311yescharacteristic
547C2×C4#1455656311yescharacteristic
548C2×C4#1455656311yescharacteristic
549C2×C4#1455656511yescharacteristic
550C2×C4#1455656511yescharacteristic
551C2×C4#1455656511yescharacteristic
552C2×C4#1455656511yescharacteristic
553C2×C4#1455656611yescharacteristic
554C2×C4#1455656611yescharacteristic
555C2×C4#1455656611yescharacteristic
556C2×C4#1455656611yescharacteristic
557C2×C4#1455656711yescharacteristic
558C2×C4#1455656711yescharacteristic
559C2×C4#1455656911yescharacteristic
560C2×C4#1455656911yescharacteristic
561C2×C4#1455657111yescharacteristic
562C2×C4#1455657111yescharacteristic
563C2×C4#1455658611yescharacteristic
564C2×C4#1455658611yescharacteristic
565C2×C4#1455658611yescharacteristic
566C2×C4#1455658611yescharacteristic
567C2×C4C2×D4×D7311yescharacteristic
568C2×C4C22×C22⋊D7311yescharacteristic
569C2×C4C22×D29211yescharacteristic
570C2×C4C2×#1192402711yescharacteristic
571C2×C4C2×#1192402811yescharacteristic
572C2×C4C2×#1192402911yescharacteristic
573C8—24no—
574C8—24no—
575C8—42no—
576C8—2922no—
577C8—2922no—
578C8—1464no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—2922no—
587C22—5842no—
588C22—5842no—
589C22—5842no—
590C22#1798850911yescharacteristic
591C22#1798850911yescharacteristic
592C22#1798850911yescharacteristic
593C22#1798850911yescharacteristic
594C22C2×#1455656711yescharacteristic
595C22C2×#1455656911yescharacteristic
596C22C2×#1455657111yescharacteristic
597C4—2922no—
598C4#1798850911yescharacteristic
599C4#1798850911yescharacteristic
600C4#1798850911yescharacteristic
601C4#1798850911yescharacteristic
602C4C2×#1455656311yescharacteristic
603C4C2×#1455656511yescharacteristic
604C4C2×#1455656611yescharacteristic
605C4C2×#1455658611yescharacteristic
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—5842no—
614C2C2×#1798850911yescharacteristic
subgroupG/H
centerC4#17988509
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#430×C73C2
socleC2×C73C2×#396
prime radicalC22×#11924028C22
hypercenterC2×#430D73
hypocenterC73#23622
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
1. C2×#17988636C2semidirect
2. C2×#17988635C2semidirect
6. #22611331C2semidirect
7. #22611328C2semidirect
8. C2×#17988345C2semidirect
9. C2×#430×C73C2semidirect
310. C2×#430D73semidirect
317. C73#23622semidirect

Maximal subgroups

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

subgroupindex
C2×#179886362
C2×#179886352
C2×#179885692
#226113312
#226113282
C2×#179883452
C2×#430×C732
#2362273