Finite Group Databasebeta

← #32992456

Subgroups — #32992456

Order 18688.

926 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988569C211yesmaximal, characteristic
2C2×#17988560C211yesmaximal, characteristic
3C2×#17988553C211yesmaximal, characteristic
4C2×#17988359C211yesmaximal, characteristic, complemented
5C2×#17988357C211yesmaximal, characteristic, complemented
6#22609627C211yesmaximal, characteristic, complemented
7C2×#405×C73C211yesmaximal, characteristic, complemented
8C22×#11924028C2211yescharacteristic
9C22×#11924012C2211yescharacteristic
10C22×#11924012C2211yescharacteristic
11C2×#14556550C2211yescharacteristic
12#17988569—22no—
13#17988569—22no—
14C2×#14556509C412yescomplemented
15C2×#14556507C412yescomplemented
16#17988560—22no—
17#17988560—22no—
18C2×#14556505C414yes—
19#17988553—22no—
20#17988553—21no—
21#17988553—21no—
22C2×#14556503C414yescomplemented
23#17988359—22no—
24#17988357—22no—
25#17988341—22no—
26C22×M16×C73C2211yescharacteristic
27C23×C8×C73C2211yescharacteristic
28C2×#117×C73C2211yescharacteristic
29#405×C73—22no—
30#405×C73—22no—
31C2×#97×C73—21no—
32C2×C4×C8×C73—21no—
33C2×#11924028—21no—
34C2×#11924028—21no—
35C2×#11924028—21no—
36C2×#11924028—21no—
37C2×#11924028—21no—
38C2×#11924028—21no—
39C2×#11924028—21no—
40C2×#11924028—21no—
41C2×#11924028—21no—
42C2×#11924028—21no—
43C2×#11924028—21no—
44C2×#11924028—21no—
45C22×Dic146C2×C411yescharacteristic
46C22×D292C2×C411yescharacteristic
47C22×C22⋊D73C2×C412yes—
48C22×C4×D73C2×C412yes—
49C2×#11924012—21no—
50C2×#11924012—21no—
51C2×#11924012—21no—
52C2×#11924012—21no—
53C2×#11924012—21no—
54C2×#11924012—21no—
55C2×#11924012—21no—
56C2×#11924012—21no—
57C2×#11924012—21no—
58C2×#11924012—21no—
59C2×#11924012—21no—
60C2×#11924012C2×C412yes—
61C22×#10596831—21no—
62C22×#10596831C2×C412yes—
63#14556550—21no—
64#14556550—21no—
65#14556550—21no—
66#14556550—21no—
67C2×C4⋊Dic73—21no—
68C2×C22⋊Dic73C2×C412yes—
69C2×C4×Dic73—21no—
70#14556509—24no—
71#14556507—24no—
72#14556505—28no—
73#14556503—24no—
74#14556503—24no—
75C23×C4×C73C2311yescharacteristic
76C2×M16×C73—21no—
77C2×M16×C73—21no—
78C2×M16×C73—21no—
79C2×M16×C73C2×C412yes—
80C2×M16×C73D412yes—
81C2×M16×C73D412yes—
82C22×C8×C73—21no—
83C22×C8×C73—21no—
84C22×C8×C73—21no—
85C22×C8×C73—21no—
86C22×C8×C73—21no—
87C22×C8×C73C2×C412yes—
88C22×C8×C73D412yes—
89C22×C8×C73D411yescharacteristic
90C22×C8×C73D411yescharacteristic
91#117×C73—21no—
92#117×C73—21no—
93#117×C73D412yes—
94#117×C73D412yes—
95C2×C4⋊C4×C73—21no—
96C2×C22⋊C4×C73C2×C412yes—
97C2×C42×C73—21no—
98#97×C73—24no—
99C4×C8×C73—24no—
100C23×D73C4212yes—
101#11924028—41no—
102#11924028—41no—
103#11924028—41no—
104#11924028—41no—
105#11924028—41no—
106#11924028—41no—
107#11924028—41no—
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—
117C2×Dic146—21no—
118C2×Dic146—21no—
119C2×Dic146—21no—
120C2×Dic146—21no—
121C2×Dic146—21no—
122C2×Dic146—21no—
123C2×D292—21no—
124C2×D292—21no—
125C2×D292—21no—
126C2×D292—21no—
127C2×D292—21no—
128C2×D292—21no—
129C2×C22⋊D73—22no—
130C2×C22⋊D73—22no—
131C2×C22⋊D73—22no—
132C2×C22⋊D73—22no—
133C2×C22⋊D73—22no—
134C2×C22⋊D73—22no—
135C22×Dic73—22no—
136C22×Dic73C4212yes—
137C2×C4×D73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C2×C4×D73—22no—
143#11924012—22no—
144#11924012—22no—
145#11924012—41no—
146#11924012—41no—
147#11924012—41no—
148#11924012—41no—
149#11924012—41no—
150#11924012—41no—
151C2×#10596831—22no—
152C2×#10596831—22no—
153C2×#10596831—22no—
154C2×#10596831—22no—
155C2×#10596831—41no—
156C2×#10596831—41no—
157C4⋊Dic73—41no—
158C4⋊Dic73—41no—
159C22⋊Dic73—22no—
160C22⋊Dic73—22no—
161C4×Dic73—41no—
162C4×Dic73—41no—
163C24×C73C22×C411yescharacteristic
164C22×C4×C73—22no—
165C22×C4×C73C22×C411yescharacteristic
166C22×C4×C73C22×C411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73#4111yescharacteristic
174C22×C4×C73#4111yescharacteristic
175C22×C4×C73#4111yescharacteristic
176C22×C4×C73#4111yescharacteristic
177C22×C4×C73#4111yescharacteristic
178C22×C4×C73#4111yescharacteristic
179M16×C73—22no—
180M16×C73—22no—
181M16×C73—22no—
182M16×C73C22⋊C414yes—
183C2×C8×C73—22no—
184C2×C8×C73—22no—
185C2×C8×C73—22no—
186C2×C8×C73—21no—
187C2×C8×C73—22no—
188C2×C8×C73—21no—
189C2×C8×C73—22no—
190C2×C8×C73—22no—
191C2×C8×C73—22no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73C22⋊C412yes—
195C2×C8×C73C22⋊C412yes—
196C4⋊C4×C73—22no—
197C4⋊C4×C73—22no—
198C22⋊C4×C73—22no—
199C22⋊C4×C73C22⋊C414yes—
200C42×C73—22no—
201C42×C73—22no—
202C23×C73—42no—
203C23×C73C2×C4211yescharacteristic
204C23×C73C2×C22⋊C411yescharacteristic
205C23×C73#11711yescharacteristic
206C23×C73C4×D411yescharacteristic
207C23×C73C4×D411yescharacteristic
208C23×C73C4×D411yescharacteristic
209C23×C73C4×D411yescharacteristic
210C22×D73—22no—
211C22×D73—22no—
212C22×D73—22no—
213C22×D73—44no—
214C2×C4×C73—24no—
215C2×C4×C73—44no—
216C2×C4×C73C2×C22⋊C411yescharacteristic
217C2×C4×C73C2×C22⋊C411yescharacteristic
218C2×C4×C73#11711yescharacteristic
219C2×C4×C73#11711yescharacteristic
220C2×C4×C73C4×D411yescharacteristic
221C2×C4×C73C4×D411yescharacteristic
222C2×C4×C73C4×D411yescharacteristic
223C2×C4×C73C4×D411yescharacteristic
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C4×D411yescharacteristic
228C2×C4×C73#12011yescharacteristic
229C2×C4×C73#12111yescharacteristic
230C2×C4×C73#12111yescharacteristic
231C2×C4×C73#12111yescharacteristic
232C2×C4×C73#12111yescharacteristic
233C2×C4×C73#12111yescharacteristic
234C2×C4×C73#12111yescharacteristic
235C2×C4×C73#12311yescharacteristic
236C2×C4×C73#12311yescharacteristic
237C2×C4×C73#12311yescharacteristic
238C2×C4×C73#12411yescharacteristic
239C2×C4×C73#12411yescharacteristic
240C2×C4×C73#12411yescharacteristic
241C2×C4×C73#12611yescharacteristic
242C2×C4×C73#12611yescharacteristic
243C2×C4×C73#12711yescharacteristic
244C22⋊D73—42no—
245C22⋊D73—42no—
246C22⋊D73—42no—
247C22⋊D73—42no—
248C2×Dic73—22no—
249C2×Dic73—22no—
250C2×Dic73—22no—
251C2×Dic73—44no—
252C2×Dic73—42no—
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—22no—
266C8×C73—22no—
267C8×C73—24no—
268#10596831—42no—
269#10596831—42no—
270C22×C73—22no—
271C22×C73—22no—
272C22×C73—22no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73C4×C22⋊C411yescharacteristic
278C22×C73C4×C22⋊C411yescharacteristic
279C22×C73C4×C22⋊C411yescharacteristic
280C22×C73#38611yescharacteristic
281C22×C73#38811yescharacteristic
282C22×C73#38811yescharacteristic
283C22×C73#39011yescharacteristic
284C2×D73—42no—
285C2×D73—44no—
286C2×D73—82no—
287C2×D73—82no—
288C4×C73—44no—
289C4×C73#38611yescharacteristic
290C4×C73#38611yescharacteristic
291C4×C73#38811yescharacteristic
292C4×C73#38811yescharacteristic
293C4×C73#38811yescharacteristic
294C4×C73#38811yescharacteristic
295C4×C73#39011yescharacteristic
296C4×C73#39011yescharacteristic
297Dic73—42no—
298Dic73—82no—
299#10961—731nomaximal, Sylow
300C2×C73—21no—
301C2×C73—21no—
302C2×C73—21no—
303C2×C73—21no—
304C2×C73—21no—
305C2×C73—21no—
306C2×C73#143711yescharacteristic
307C2×C73#175712yes—
308D73—82no—
309C2×#413—731no—
310C2×#410—731no—
311C2×#408—731no—
312C2×#405D7311yescharacteristic, complemented
313C2×#344—731no—
314C2×#344—731no—
315#1729—731no—
316C73#1096111yescharacteristic, complemented, Sylow
317C22×#41—731no—
318C22×M16—731no—
319C22×M16—731no—
320C22×M16C2×D7311yescharacteristic
321C23×C8C2×D7311yescharacteristic
322C2×#117—731no—
323C2×#117C2×D7311yescharacteristic
324#413—1462no—
325#413—1462no—
326C2×#101—732no—
327C2×#100—732no—
328#410—1462no—
329#410—1462no—
330C2×#99—734no—
331#408—1462no—
332#408—1461no—
333#408—1461no—
334C2×C22⋊C8—734no—
335#405—22no—
336#405—22no—
337C2×#97—21no—
338C2×C4×C8—21no—
339#344—1462no—
340#344—1462no—
341#336—1462no—
342C2×#41—1461no—
343C2×#41—1461no—
344C2×#41—1461no—
345C2×#41—1461no—
346C2×#41—1461no—
347C2×#41—1461no—
348C2×#41—1461no—
349C2×#41—1461no—
350C2×#41—1461no—
351C2×#41—1461no—
352C2×#41—1461no—
353C2×#41—1461no—
354C22×Q8—731no—
355C22×D4—732no—
356C22×D4—731no—
357C23×C4—732no—
358C23×C4C22×D7311yescharacteristic
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—732no—
363C2×M16—1461no—
364C2×M16—1461no—
365C2×M16—1461no—
366C2×M16—1461no—
367C2×M16—1461no—
368C2×M16—1461no—
369C2×M16—1461no—
370C2×M16—1461no—
371C2×M16—1461no—
372C2×M16—1461no—
373C2×M16—1461no—
374C2×M16C4×D7312yes—
375C2×M16D29212yes—
376C2×M16C22⋊D7312yes—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—732no—
383C22×C8—1461no—
384C22×C8C4×D7312yes—
385C22×C8D29212yes—
386C22×C8C22⋊D7311yescharacteristic
387C22×C8C22⋊D7311yescharacteristic
388#117—21no—
389#117—21no—
390#117—1461no—
391#117—1461no—
392#117—1461no—
393#117—1461no—
394#117D29212yes—
395#117C22⋊D7312yes—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—1461no—
398C2×C22⋊C4—732no—
399C2×C22⋊C4C4×D7312yes—
400C2×C42—21no—
401C2×C42—1461no—
402#101—1464no—
403#100—1464no—
404#99—1468no—
405C22⋊C8—1464no—
406C22⋊C8—1464no—
407#97—24no—
408C4×C8—24no—
409C24—732no—
410C24C2×C4×D7311yescharacteristic
411#41—2921no—
412#41—2921no—
413#41—2921no—
414#41—2921no—
415#41—2921no—
416#41—2921no—
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—
427C2×Q8—1461no—
428C2×Q8—1461no—
429C2×Q8—1461no—
430C2×Q8—1461no—
431C2×Q8—1461no—
432C2×Q8—1461no—
433C2×D4—1462no—
434C2×D4—1462no—
435C2×D4—1462no—
436C2×D4—1462no—
437C2×D4—1462no—
438C2×D4—1462no—
439C2×D4—1461no—
440C2×D4—1461no—
441C2×D4—1461no—
442C2×D4—1461no—
443C2×D4—1461no—
444C2×D4—1461no—
445C22×C4—22no—
446C22×C4—732no—
447C22×C4—1462no—
448C22×C4—1462no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4—1462no—
452C22×C4—1462no—
453C22×C4—1462no—
454C22×C4C2×C4×D7311yescharacteristic
455C22×C4C2×C4×D7311yescharacteristic
456C22×C4C2×C22⋊D7311yescharacteristic
457C22×C4C2×C22⋊D7311yescharacteristic
458C22×C4C2×C22⋊D7311yescharacteristic
459C22×C4C2×D29211yescharacteristic
460C22×C4C2×D29211yescharacteristic
461C22×C4C2×D29211yescharacteristic
462C22×C4#1192402811yescharacteristic
463C22×C4#1192402811yescharacteristic
464C22×C4#1192402811yescharacteristic
465C22×C4#1192402811yescharacteristic
466C22×C4#1192402811yescharacteristic
467C22×C4#1192402811yescharacteristic
468M16—22no—
469M16—22no—
470M16—22no—
471M16—2921no—
472M16—2921no—
473M16—2921no—
474M16—2921no—
475M16—2921no—
476M16—2921no—
477M16—1462no—
478M16—1462no—
479M16#1192400514yes—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—21no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—2921no—
492C2×C8—2921no—
493C2×C8—1462no—
494C2×C8—1462no—
495C2×C8—1462no—
496C2×C8—1462no—
497C2×C8#1192400512yes—
498C2×C8#1192400512yes—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—2921no—
502C4⋊C4—2921no—
503C22⋊C4—22no—
504C22⋊C4—1462no—
505C22⋊C4—1462no—
506C22⋊C4#1192400514yes—
507C42—22no—
508C42—22no—
509C42—2921no—
510C42—2921no—
511C23—42no—
512C23—2924no—
513C23—1462no—
514C23—1462no—
515C23—1462no—
516C23C42×D7311yescharacteristic
517C23C2×#1192400511yescharacteristic
518C23#1455654811yescharacteristic
519C23C4×C22⋊D7311yescharacteristic
520C23C4×C22⋊D7311yescharacteristic
521C23C4×D29211yescharacteristic
522C23C4×D29211yescharacteristic
523Q8—2921no—
524Q8—2921no—
525Q8—2921no—
526Q8—2921no—
527D4—2922no—
528D4—2922no—
529D4—2922no—
530D4—2922no—
531D4—2921no—
532D4—2921no—
533D4—2921no—
534D4—2921no—
535C2×C4—24no—
536C2×C4—44no—
537C2×C4—2922no—
538C2×C4—2922no—
539C2×C4—2922no—
540C2×C4—2922no—
541C2×C4—2924no—
542C2×C4—2922no—
543C2×C4—1462no—
544C2×C4—1462no—
545C2×C4—1462no—
546C2×C4C2×#1192400511yescharacteristic
547C2×C4C2×#1192400511yescharacteristic
548C2×C4#1455654811yescharacteristic
549C2×C4#1455654811yescharacteristic
550C2×C4C4×C22⋊D7311yescharacteristic
551C2×C4C4×C22⋊D7311yescharacteristic
552C2×C4C4×C22⋊D7311yescharacteristic
553C2×C4C4×C22⋊D7311yescharacteristic
554C2×C4C4×D29211yescharacteristic
555C2×C4C4×D29211yescharacteristic
556C2×C4C4×D29211yescharacteristic
557C2×C4C4×D29211yescharacteristic
558C2×C4#1455656011yescharacteristic
559C2×C4#1455656511yescharacteristic
560C2×C4#1455656511yescharacteristic
561C2×C4#1455656511yescharacteristic
562C2×C4#1455656511yescharacteristic
563C2×C4#1455656511yescharacteristic
564C2×C4#1455656511yescharacteristic
565C2×C4#1455657411yescharacteristic
566C2×C4#1455657411yescharacteristic
567C2×C4#1455657411yescharacteristic
568C2×C4#1455657911yescharacteristic
569C2×C4#1455657911yescharacteristic
570C2×C4#1455657911yescharacteristic
571C2×C4#1455658511yescharacteristic
572C2×C4#1455658511yescharacteristic
573C2×C4#1455658811yescharacteristic
574C8—22no—
575C8—22no—
576C8—24no—
577C8—2922no—
578C8—2922no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—2922no—
587C22—2924no—
588C22—5842no—
589C22—5842no—
590C22C4×#1192400511yescharacteristic
591C22C4×#1192400511yescharacteristic
592C22C4×#1192400511yescharacteristic
593C22#1798846611yescharacteristic
594C22#1798847811yescharacteristic
595C22#1798847811yescharacteristic
596C22#1798848911yescharacteristic
597C4—44no—
598C4—2922no—
599C4—5842no—
600C4#1798846611yescharacteristic
601C4#1798846611yescharacteristic
602C4#1798847811yescharacteristic
603C4#1798847811yescharacteristic
604C4#1798847811yescharacteristic
605C4#1798847811yescharacteristic
606C4#1798848911yescharacteristic
607C4#1798848911yescharacteristic
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—5842no—
615C2#2260816911yescharacteristic
616C2#2260973212yes—
subgroupG/H
centerC2×C4C2×#11924005
commutatorC23×C73C2×C42
FrattiniC23×C4C22×D73
FittingC2×#405×C73C2
socleC22×C73C4×C22⋊C4
prime radicalC22×#11924028C22
cosocleC23×C4×C73C23
hypercenterC2×#405D73
hypocenterC73#10961
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
4. C2×#17988359C2semidirect
5. C2×#17988357C2semidirect
6. #22609627C2semidirect
7. C2×#405×C73C2semidirect
14. C2×#14556509C4semidirect
15. C2×#14556507C4semidirect
22. C2×#14556503C4semidirect
312. C2×#405D73semidirect
316. C73#10961semidirect

Maximal subgroups

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

subgroupindex
C2×#179885692
C2×#179885602
C2×#179885532
C2×#179883592
C2×#179883572
#226096272
C2×#405×C732
#1096173