Finite Group Databasebeta

← #32992429

Subgroups — #32992429

Order 18688.

918 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988603C211yesmaximal, characteristic
2#22618448C211yesmaximal, characteristic
3C2×#17988555C211yesmaximal, characteristic
4C2×#17988358C211yesmaximal, characteristic, complemented
5C2×#17988351C211yesmaximal, characteristic, complemented
6#22609647C211yesmaximal, characteristic, complemented
7C73×#2873C211yesmaximal, characteristic, complemented
8C22×#11924028C2211yescharacteristic
9C22×#11924012C2211yescharacteristic
10C23×#10596831C2211yescharacteristic
11C2×#14556550C2211yescharacteristic
12#17988603—22no—
13#17988603C414yescomplemented
14C2×#14556517—22no—
15#17988595C412yescomplemented
16#17988591C412yescomplemented
17#17988586—22no—
18#17988581—22no—
19#17988555—22no—
20#17988555C414yescomplemented
21C2×#14556503—22no—
22#17988358—22no—
23#17988351—22no—
24#17988349—22no—
25C22×M16×C73C2211yescharacteristic
26C22×M16×C73C2211yescharacteristic
27C2×#117×C73C2211yescharacteristic
28#405×C73—22no—
29#405×C73—22no—
30C4×M16×C73—22no—
31C2×#11924028—21no—
32C2×#11924028—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×#11924028C2×C412yes—
42C2×#11924028C2×C412yes—
43C22×Dic146C2×C411yescharacteristic
44C22×D292C2×C411yescharacteristic
45C22×C22⋊D73—21no—
46C22×C4×D73—21no—
47C2×#11924012—21no—
48C2×#11924012—21no—
49C2×#11924012—21no—
50C2×#11924012—21no—
51C2×#11924012—21no—
52C2×#11924012C2×C412yes—
53C22×#10596831—21no—
54C22×#10596831—21no—
55C22×#10596831—21no—
56C22×#10596831—21no—
57C22×#10596831—21no—
58C22×#10596831—21no—
59C22×#10596831—21no—
60C22×#10596831C2×C412yes—
61#14556550—21no—
62#14556550—21no—
63#14556550—21no—
64#14556550C2×C412yes—
65C2×C4⋊Dic73—21no—
66C2×C22⋊Dic73—21no—
67C2×C4×Dic73—21no—
68#14556517—28no—
69#14556514—24no—
70#14556511—24no—
71#14556503—28no—
72C23×C4×C73C2311yescharacteristic
73C2×M16×C73—21no—
74C2×M16×C73—21no—
75C2×M16×C73—21no—
76C2×M16×C73—21no—
77C2×M16×C73—21no—
78C2×M16×C73—21no—
79C2×M16×C73—21no—
80C2×M16×C73C2×C412yes—
81C2×M16×C73C2×C412yes—
82C2×M16×C73D412yes—
83C2×M16×C73D412yes—
84C2×M16×C73D412yes—
85C22×C8×C73—21no—
86C22×C8×C73D412yes—
87#117×C73—21no—
88#117×C73—21no—
89#117×C73C2×C412yes—
90#117×C73D412yes—
91C2×C4⋊C4×C73D412yes—
92C2×C22⋊C4×C73—21no—
93C2×C42×C73—21no—
94#97×C73—24no—
95C4×C8×C73—24no—
96C23×D73—21no—
97#11924028—22no—
98#11924028—22no—
99#11924028—22no—
100#11924028—22no—
101#11924028—22no—
102#11924028—22no—
103#11924028—22no—
104#11924028—22no—
105#11924028—41no—
106#11924028—41no—
107#11924028—41no—
108#11924028—41no—
109#11924028—41no—
110#11924028—41no—
111#11924028—41no—
112#11924028—41no—
113C2×Dic146—21no—
114C2×Dic146—21no—
115C2×Dic146—21no—
116C2×Dic146—21no—
117C2×Dic146—21no—
118C2×Dic146C4212yes—
119C2×D292—21no—
120C2×D292—21no—
121C2×D292—21no—
122C2×D292—21no—
123C2×D292—21no—
124C2×D292C4212yes—
125C2×C22⋊D73—22no—
126C2×C22⋊D73—22no—
127C2×C22⋊D73—41no—
128C2×C22⋊D73—41no—
129C2×C22⋊D73—41no—
130C2×C22⋊D73—41no—
131C22×Dic73—21no—
132C22×Dic73—41no—
133C2×C4×D73—22no—
134C2×C4×D73—22no—
135C2×C4×D73—41no—
136C2×C4×D73—41no—
137C2×C4×D73—41no—
138C2×C4×D73—41no—
139#11924012—22no—
140#11924012—22no—
141#11924012—41no—
142#11924012—41no—
143C2×#10596831—22no—
144C2×#10596831—22no—
145C2×#10596831—22no—
146C2×#10596831—22no—
147C2×#10596831—41no—
148C2×#10596831—41no—
149C2×#10596831—41no—
150C2×#10596831—41no—
151C2×#10596831—41no—
152C2×#10596831—41no—
153C4⋊Dic73—22no—
154C4⋊Dic73—41no—
155C22⋊Dic73—22no—
156C22⋊Dic73—41no—
157C4×Dic73—22no—
158C4×Dic73—41no—
159C24×C73#4111yescharacteristic
160C22×C4×C73—22no—
161C22×C4×C73C22×C411yescharacteristic
162C22×C4×C73C22×C411yescharacteristic
163C22×C4×C73C22×C411yescharacteristic
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73#4111yescharacteristic
171C22×C4×C73#4111yescharacteristic
172C22×C4×C73#4111yescharacteristic
173C22×C4×C73#4111yescharacteristic
174C22×C4×C73#4111yescharacteristic
175M16×C73—22no—
176M16×C73—22no—
177M16×C73—22no—
178M16×C73—22no—
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—22no—
187C2×C8×C73—22no—
188C2×C8×C73C22⋊C414yes—
189C4⋊C4×C73—22no—
190C4⋊C4×C73C22⋊C414yes—
191C22⋊C4×C73—22no—
192C22⋊C4×C73—22no—
193C42×C73—22no—
194C42×C73—22no—
195C23×C73—42no—
196C23×C73#11711yescharacteristic
197C23×C73C4×D411yescharacteristic
198C23×C73C4×D411yescharacteristic
199C23×C73#12111yescharacteristic
200C23×C73#12311yescharacteristic
201C23×C73#12411yescharacteristic
202C23×C73#12611yescharacteristic
203C22×D73—22no—
204C22×D73—44no—
205C22×D73—41no—
206C22×D73—41no—
207C2×C4×C73—24no—
208C2×C4×C73—82no—
209C2×C4×C73C2×C4211yescharacteristic
210C2×C4×C73C2×C22⋊C411yescharacteristic
211C2×C4×C73C2×C22⋊C411yescharacteristic
212C2×C4×C73C2×C22⋊C411yescharacteristic
213C2×C4×C73#11711yescharacteristic
214C2×C4×C73#11711yescharacteristic
215C2×C4×C73C4×D411yescharacteristic
216C2×C4×C73C4×D411yescharacteristic
217C2×C4×C73C4×D411yescharacteristic
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C4×D411yescharacteristic
220C2×C4×C73C4×D411yescharacteristic
221C2×C4×C73C4×D411yescharacteristic
222C2×C4×C73C4×D411yescharacteristic
223C2×C4×C73C4×D411yescharacteristic
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73#12011yescharacteristic
226C2×C4×C73#12111yescharacteristic
227C2×C4×C73#12111yescharacteristic
228C2×C4×C73#12111yescharacteristic
229C2×C4×C73#12111yescharacteristic
230C2×C4×C73#12111yescharacteristic
231C2×C4×C73#12311yescharacteristic
232C2×C4×C73#12311yescharacteristic
233C2×C4×C73#12411yescharacteristic
234C2×C4×C73#12411yescharacteristic
235C2×C4×C73#12611yescharacteristic
236C2×C4×C73#12711yescharacteristic
237C22⋊D73—42no—
238C22⋊D73—42no—
239C22⋊D73—42no—
240C22⋊D73—42no—
241C2×Dic73—22no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—42no—
245C2×Dic73—82no—
246D292—22no—
247D292—22no—
248D292—41no—
249D292—41no—
250C4×D73—42no—
251C4×D73—42no—
252C4×D73—42no—
253C4×D73—42no—
254Dic146—22no—
255Dic146—22no—
256Dic146—41no—
257Dic146—41no—
258C8×C73—24no—
259C8×C73—24no—
260#10596831—42no—
261#10596831—42no—
262C22×C73—22no—
263C22×C73—22no—
264C22×C73—22no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73—41no—
268C22×C73—41no—
269C22×C73C4×C22⋊C411yescharacteristic
270C22×C73#38611yescharacteristic
271C22×C73#38811yescharacteristic
272C22×C73#38811yescharacteristic
273C22×C73#38811yescharacteristic
274C22×C73#38811yescharacteristic
275C22×C73#39011yescharacteristic
276C2×D73—44no—
277C2×D73—42no—
278C2×D73—82no—
279C2×D73—82no—
280C4×C73—44no—
281C4×C73C4×C22⋊C411yescharacteristic
282C4×C73C4×C22⋊C411yescharacteristic
283C4×C73#38611yescharacteristic
284C4×C73#38611yescharacteristic
285C4×C73#38811yescharacteristic
286C4×C73#38811yescharacteristic
287C4×C73#39011yescharacteristic
288C4×C73#39011yescharacteristic
289Dic73—42no—
290Dic73—82no—
291#10956—731nomaximal, Sylow
292C2×C73—21no—
293C2×C73—21no—
294C2×C73—21no—
295C2×C73—21no—
296C2×C73—21no—
297C2×C73—21no—
298C2×C73#143711yescharacteristic
299C2×C73#188112yes—
300D73—82no—
301C2×#421—731no—
302#2896—731no—
303C2×#408—731no—
304#2873D7311yescharacteristic, complemented
305C2×#344—731no—
306C2×#341—731no—
307#1735—731no—
308C73#1095611yescharacteristic, complemented, Sylow
309C22×#41—731no—
310C22×M16—731no—
311C22×M16C2×D7311yescharacteristic
312C22×M16C2×D7311yescharacteristic
313C23×C8—731no—
314C2×#117—731no—
315C2×#117C2×D7311yescharacteristic
316#421—734no—
317#421—1462no—
318C2×#104—1462no—
319#419—732no—
320#418—732no—
321#417—1462no—
322#416—1462no—
323#408—734no—
324#408—1462no—
325C2×C22⋊C8—1462no—
326#405—22no—
327#405—22no—
328C4×M16—22no—
329#344—1462no—
330#341—1462no—
331#340—1462no—
332C2×#41—732no—
333C2×#41—732no—
334C2×#41—1461no—
335C2×#41—1461no—
336C2×#41—1461no—
337C2×#41—1461no—
338C2×#41—1461no—
339C2×#41—1461no—
340C2×#41—1461no—
341C2×#41—1461no—
342C2×#41—1461no—
343C2×#41—1461no—
344C22×Q8—731no—
345C22×D4—731no—
346C22×D4—1461no—
347C23×C4—1461no—
348C23×C4C22×D7311yescharacteristic
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—732no—
357C2×M16—1461no—
358C2×M16—1461no—
359C2×M16—1461no—
360C2×M16—1461no—
361C2×M16—1461no—
362C2×M16C4×D7312yes—
363C2×M16C4×D7312yes—
364C2×M16D29212yes—
365C2×M16D29212yes—
366C2×M16C22⋊D7312yes—
367C22×C8—21no—
368C22×C8—732no—
369C22×C8—1461no—
370C22×C8—1461no—
371C22×C8—1461no—
372C22×C8—1461no—
373C22×C8—1461no—
374C22×C8—1461no—
375C22×C8—1461no—
376C22×C8C22⋊D7312yes—
377#117—21no—
378#117—21no—
379#117—732no—
380#117—1461no—
381#117—1461no—
382#117—1461no—
383#117C4×D7312yes—
384#117C22⋊D7312yes—
385C2×C4⋊C4—1461no—
386C2×C4⋊C4D29212yes—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—1461no—
389C2×C42—21no—
390C2×C42—1461no—
391#104—1468no—
392#103—1464no—
393#102—1464no—
394C22⋊C8—1468no—
395#97—24no—
396C4×C8—24no—
397C24—1461no—
398C24#1192402811yescharacteristic
399#41—2921no—
400#41—2921no—
401#41—2921no—
402#41—2921no—
403#41—2921no—
404#41—2921no—
405#41—2921no—
406#41—2921no—
407#41—1462no—
408#41—1462no—
409#41—1462no—
410#41—1462no—
411#41—1462no—
412#41—1462no—
413#41—1462no—
414#41—1462no—
415C2×Q8—732no—
416C2×Q8—1461no—
417C2×Q8—1461no—
418C2×Q8—1461no—
419C2×Q8—1461no—
420C2×Q8—1461no—
421C2×D4—2921no—
422C2×D4—2921no—
423C2×D4—2921no—
424C2×D4—2921no—
425C2×D4—732no—
426C2×D4—1462no—
427C2×D4—1462no—
428C2×D4—1461no—
429C2×D4—1461no—
430C2×D4—1461no—
431C2×D4—1461no—
432C2×D4—1461no—
433C22×C4—22no—
434C22×C4—2921no—
435C22×C4—2921no—
436C22×C4—2921no—
437C22×C4—2921no—
438C22×C4—2921no—
439C22×C4—1461no—
440C22×C4—1462no—
441C22×C4—1462no—
442C22×C4C2×C4×D7311yescharacteristic
443C22×C4C2×C4×D7311yescharacteristic
444C22×C4C2×C4×D7311yescharacteristic
445C22×C4C2×C22⋊D7311yescharacteristic
446C22×C4C2×C22⋊D7311yescharacteristic
447C22×C4C2×C22⋊D7311yescharacteristic
448C22×C4C2×D29211yescharacteristic
449C22×C4C2×D29211yescharacteristic
450C22×C4C2×D29211yescharacteristic
451C22×C4#1192402811yescharacteristic
452C22×C4#1192402811yescharacteristic
453C22×C4#1192402811yescharacteristic
454C22×C4#1192402811yescharacteristic
455C22×C4#1192402811yescharacteristic
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—2921no—
464M16—2921no—
465M16—1462no—
466M16—1462no—
467M16#1192400514yes—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—2921no—
474C2×C8—2921no—
475C2×C8—2921no—
476C2×C8—2921no—
477C2×C8—2921no—
478C2×C8—2921no—
479C2×C8—1462no—
480C2×C8—1462no—
481C2×C8—1462no—
482C2×C8—1462no—
483C2×C8#1192400514yes—
484C4⋊C4—22no—
485C4⋊C4—2921no—
486C4⋊C4—1462no—
487C4⋊C4#1192400514yes—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—2921no—
491C22⋊C4—1462no—
492C42—22no—
493C42—22no—
494C42—2921no—
495C42—1462no—
496C23—42no—
497C23—2924no—
498C23—2921no—
499C23—2921no—
500C23—1462no—
501C23#1455654811yescharacteristic
502C23C4×C22⋊D7311yescharacteristic
503C23C4×D29211yescharacteristic
504C23#1455656511yescharacteristic
505C23#1455657411yescharacteristic
506C23#1455657911yescharacteristic
507C23#1455658511yescharacteristic
508Q8—2921no—
509Q8—2921no—
510Q8—1462no—
511Q8—1462no—
512D4—2922no—
513D4—2922no—
514D4—2922no—
515D4—2922no—
516D4—2921no—
517D4—2921no—
518D4—1462no—
519D4—1462no—
520C2×C4—24no—
521C2×C4—82no—
522C2×C4—2921no—
523C2×C4—2921no—
524C2×C4—2922no—
525C2×C4—2922no—
526C2×C4—2922no—
527C2×C4—2922no—
528C2×C4—2922no—
529C2×C4—5842no—
530C2×C4—1462no—
531C2×C4C42×D7311yescharacteristic
532C2×C4C2×#1192400511yescharacteristic
533C2×C4C2×#1192400511yescharacteristic
534C2×C4C2×#1192400511yescharacteristic
535C2×C4#1455654811yescharacteristic
536C2×C4#1455654811yescharacteristic
537C2×C4C4×C22⋊D7311yescharacteristic
538C2×C4C4×C22⋊D7311yescharacteristic
539C2×C4C4×C22⋊D7311yescharacteristic
540C2×C4C4×C22⋊D7311yescharacteristic
541C2×C4C4×C22⋊D7311yescharacteristic
542C2×C4C4×D29211yescharacteristic
543C2×C4C4×D29211yescharacteristic
544C2×C4C4×D29211yescharacteristic
545C2×C4C4×D29211yescharacteristic
546C2×C4C4×D29211yescharacteristic
547C2×C4#1455656011yescharacteristic
548C2×C4#1455656511yescharacteristic
549C2×C4#1455656511yescharacteristic
550C2×C4#1455656511yescharacteristic
551C2×C4#1455656511yescharacteristic
552C2×C4#1455656511yescharacteristic
553C2×C4#1455657411yescharacteristic
554C2×C4#1455657411yescharacteristic
555C2×C4#1455657911yescharacteristic
556C2×C4#1455657911yescharacteristic
557C2×C4#1455658511yescharacteristic
558C2×C4#1455658811yescharacteristic
559C8—24no—
560C8—24no—
561C8—2922no—
562C8—2922no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—2924no—
571C22—2922no—
572C22—5842no—
573C22—5842no—
574C22C4×#1192400511yescharacteristic
575C22#1798846611yescharacteristic
576C22#1798847811yescharacteristic
577C22#1798847811yescharacteristic
578C22#1798847811yescharacteristic
579C22#1798847811yescharacteristic
580C22#1798848911yescharacteristic
581C4—44no—
582C4—2922no—
583C4—5842no—
584C4C4×#1192400511yescharacteristic
585C4C4×#1192400511yescharacteristic
586C4#1798846611yescharacteristic
587C4#1798846611yescharacteristic
588C4#1798847811yescharacteristic
589C4#1798847811yescharacteristic
590C4#1798848911yescharacteristic
591C4#1798848911yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—5842no—
599C2#2260816911yescharacteristic
600C2#2261029312yes—
subgroupG/H
centerC2×C4#14556560
commutatorC2×C4×C73C2×C42
FrattiniC23×C4C22×D73
FittingC73×#2873C2
socleC22×C73#386
prime radicalC22×#11924028C22
cosocleC23×C4×C73C23
hypercenter#2873D73
hypocenterC73#10956
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2873

Complements

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

NH ≅ G/Ntype
4. C2×#17988358C2semidirect
5. C2×#17988351C2semidirect
6. #22609647C2semidirect
7. C73×#2873C2semidirect
13. #17988603C4semidirect
15. #17988595C4semidirect
16. #17988591C4semidirect
20. #17988555C4semidirect
304. #2873D73semidirect
308. C73#10956semidirect

Maximal subgroups

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

subgroupindex
C2×#179886032
#226184482
C2×#179885552
C2×#179883582
C2×#179883512
#226096472
C73×#28732
#1095673