Finite Group Databasebeta

← #11906319

Subgroups — #11906319

Order 1152.

1590 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#554C211yesmaximal, characteristic, complemented
2D9×C4⋊Q8C211yesmaximal, characteristic, complemented
3#10589824C211yesmaximal, characteristic, complemented
4#10589791C212yesmaximal, complemented
5#10589787C212yesmaximal, complemented
6#10589737C212yesmaximal, complemented
7#10589734C214yesmaximal, complemented
8#10589725C214yesmaximal, complemented
9#10589724C212yesmaximal, complemented
10#10589680C211yesmaximal, characteristic, complemented
11Q8×Dic18C211yesmaximal, characteristic, complemented
12#10589648C212yesmaximal
13#10589645C211yesmaximal, characteristic, complemented
14D4×Dic18C212yesmaximal, complemented
15C4×#3699C211yesmaximal, characteristic
16#10589613C212yesmaximal, complemented
17C2×#63450C212yesmaximal, complemented
18#86926—31nomaximal
19C2×Q8×D9C2212yes—
20C2×#3699C2211yescharacteristic
21C22×Dic18C2214yes—
22C9×C4⋊Q8C2211yescharacteristic
23C9×#125C2212yes—
24C9×C22⋊Q8C2212yes—
25C9×C22⋊Q8C2214yes—
26C4×Q8×C9C2211yescharacteristic
27C4×D4×C9C2211yescharacteristic
28C4×D4×C9C2212yes—
29C2×C9×C4⋊C4C2212yes—
30#63508C2211yescharacteristic
31Q8×Dic9C2212yes—
32#63506C2211yescharacteristic
33#63506C2212yes—
34#63506C2214yes—
35D4×Dic9C2211yescharacteristic
36D4×Dic9C2212yes—
37C4×#611C2214yes—
38C4×#611C2212yes—
39C2×C4⋊Dic9C2212yes—
40#63486C2212yes—
41#63486C2214yes—
42C2×Dic9⋊C4C2214yes—
43C2×C4×Dic9C2212yes—
44#63459C2214yes—
45#63459C2211yescharacteristic
46#63458C2212yes—
47#63458C2214yes—
48#63454C2211yescharacteristic
49C4⋊C4×D9C2212yes—
50C4⋊C4×D9C2212yes—
51#63452C2212yes—
52#63451C2214yes—
53#63451C2212yes—
54#63451C2214yes—
55#63451C2214yes—
56#63450C2212yes—
57#63450C2214yes—
58#63450C2214yes—
59#63450C2214yes—
60#63450C2212yes—
61#63450C2212yes—
62#63450C2212yes—
63#63450C2211yescharacteristic
64#63450C2212yes—
65#63449C2214yes—
66#63449C2212yes—
67#63449C2211yescharacteristic
68#63449C2212yes—
69#611⋊C4C2212yes—
70#611⋊C4C2214yes—
71#63440C2214yes—
72#63440C2214yes—
73#63440C2214yes—
74#63439C2214yes—
75#63439C2212yes—
76#63434C2212yes—
77C42×D9C2211yescharacteristic
78#63431C2212yes—
79#63431C2211yescharacteristic
80C4×Dic18C2212yes—
81C4×Dic18C2212yes—
82C4×Dic18C2211yescharacteristic
83C4×Dic18C2211yescharacteristic
84C3×#554D311yescharacteristic
85D3×C4⋊Q8—31no—
86#5722—31no—
87#5689—32no—
88#5685—32no—
89#5635—32no—
90#5632—34no—
91#5623—34no—
92#5622—32no—
93#5578—31no—
94Q8×Dic6—31no—
95#5546—32no—
96#5543—31no—
97D4×Dic6—32no—
98C4×#237—31no—
99#5511—32no—
100C2×#888—32no—
101C2×Q8×C9C2311yescharacteristic
102C2×Q8×C9C2312yes—
103C2×D4×C9C2311yescharacteristic
104C22×C4×C9C2312yes—
105C22×C4×C9C2314yes—
106C2×#611C2312yes—
107C22×Dic9C2312yes—
108C22×Dic9C2314yes—
109C22×Dic9C2312yes—
110Q8×D9—44no—
111#3699Q818yescomplemented
112C2×C4×D9C2311yescharacteristic
113C2×C4×D9C2311yescharacteristic
114C2×C4×D9C2314yes—
115C2×C4×D9C2311yescharacteristic
116C2×Dic18—48no—
117C2×Dic18C2311yescharacteristic
118C2×Dic18C2312yes—
119C2×Dic18C2314yes—
120C2×Dic18C2312yes—
121C2×Dic18C2314yes—
122C2×Dic18C2314yes—
123C2×Dic18C2311yescharacteristic
124C9×C4⋊C4C2311yescharacteristic
125C9×C4⋊C4C2314yes—
126C9×C4⋊C4C2312yes—
127C9×C4⋊C4C2311yescharacteristic
128C9×C4⋊C4C2312yes—
129C9×C4⋊C4C2312yes—
130C9×C4⋊C4C2314yes—
131C9×C22⋊C4C2314yes—
132C9×C22⋊C4C2312yes—
133C42×C9C2312yes—
134C42×C9C2311yescharacteristic
135#3676C2314yes—
136#3676C2312yes—
137(C2×D9)⋊C4C2312yes—
138(C2×D9)⋊C4C2312yes—
139(C2×D9)⋊C4C2312yes—
140C4⋊Dic9C2311yescharacteristic
141C4⋊Dic9C2312yes—
142C4⋊Dic9C2314yes—
143C4⋊Dic9C2312yes—
144C4⋊Dic9C2311yescharacteristic
145C4⋊Dic9C2312yes—
146C4⋊Dic9C2314yes—
147Dic9⋊C4C2314yes—
148Dic9⋊C4C2312yes—
149Dic9⋊C4C2312yes—
150Dic9⋊C4C2312yes—
151Dic9⋊C4C2312yes—
152Dic9⋊C4C2312yes—
153Dic9⋊C4C2314yes—
154Dic9⋊C4C2314yes—
155Dic9⋊C4C2314yes—
156Dic9⋊C4C2314yes—
157Dic9⋊C4C2312yes—
158Dic9⋊C4C2312yes—
159Dic9⋊C4C2314yes—
160C4×Dic9C2314yes—
161C4×Dic9C2312yes—
162C4×Dic9C2311yescharacteristic
163C4×Dic9C2312yes—
164C4×Dic9C2311yescharacteristic
165C4×Dic9C2311yescharacteristic
166C4×Dic9C2314yes—
167C4×Dic9C2312yes—
168C4×Dic9C2312yes—
169#3503—91noSylow
170C2×D3×Q8—32no—
171C2×#237—31no—
172C22×Dic6—34no—
173C3×C4⋊Q8C2×D311yescharacteristic
174C3×#125C2×D312yes—
175C3×C22⋊Q8C2×D314yes—
176C3×C22⋊Q8C2×D312yes—
177C3×C4×Q8C2×D311yescharacteristic
178C3×C4×D4C2×D311yescharacteristic
179C3×C4×D4C2×D312yes—
180C2×C3×C4⋊C4C2×D312yes—
181#946—31no—
182Q8×Dic3—32no—
183#944—34no—
184#944—32no—
185#944—31no—
186D4×Dic3—31no—
187D4×Dic3—32no—
188C4×#67—34no—
189C4×#67—32no—
190C2×C4⋊Dic3—32no—
191#924—34no—
192#924—32no—
193C2×Dic3⋊C4—34no—
194C2×C4×Dic3—32no—
195#897—34no—
196#897—31no—
197#896—32no—
198#896—34no—
199#892—31no—
200D3×C4⋊C4—32no—
201D3×C4⋊C4—32no—
202#890—32no—
203#889—34no—
204#889—34no—
205#889—34no—
206#889—32no—
207#888—34no—
208#888—34no—
209#888—32no—
210#888—32no—
211#888—32no—
212#888—34no—
213#888—32no—
214#888—31no—
215#888—32no—
216#887—34no—
217#887—31no—
218#887—32no—
219#887—32no—
220#67⋊C4—32no—
221#67⋊C4—34no—
222#878—34no—
223#878—34no—
224#878—34no—
225#877—32no—
226#877—34no—
227#872—32no—
228C42×D3—31no—
229#869—32no—
230#869—31no—
231C4×Dic6—32no—
232C4×Dic6—32no—
233C4×Dic6—31no—
234C4×Dic6—31no—
235C23×C9C2412yes—
236C22×D9C2411yescharacteristic
237Q8×C9—22no—
238Q8×C9—42no—
239D4×C9C2×Q814yescomplemented
240C2×C4×C9—24no—
241C2×C4×C9—44no—
242C2×C4×C9C2412yes—
243C2×C4×C9C2412yes—
244C2×C4×C9C2411yescharacteristic
245C2×C4×C9C2414yes—
246C2×C4×C9C2412yes—
247C2×C4×C9C2411yescharacteristic
248C2×C4×C9C2411yescharacteristic
249#611C2×Q818yescomplemented
250C2×Dic9—24no—
251C2×Dic9—44no—
252C2×Dic9C2×Q818yescomplemented
253C2×Dic9C2412yes—
254C2×Dic9C2411yescharacteristic
255C2×Dic9C2412yes—
256C2×Dic9C2412yes—
257C2×Dic9C2414yes—
258C2×Dic9C2412yes—
259C2×Dic9C2411yescharacteristic
260C2×Dic9C2411yescharacteristic
261C4×D9—22no—
262C4×D9—22no—
263C4×D9—44no—
264C4×D9C2×Q814yescomplemented
265Dic18—22no—
266Dic18—24no—
267Dic18—28no—
268Dic18—44no—
269Dic18—44no—
270Dic18—42no—
271Dic18C2×Q814yescomplemented
272Q82—91no—
273Q82—91no—
274#557—92no—
275#554—92no—
276#554—91no—
277#554—92no—
278#554D911yescharacteristic, complemented
279D4×Q8—94no—
280D4×Q8—92no—
281#544—92no—
282#544—94no—
283#533—92no—
284#533—91no—
285C2×C4⋊Q8—91no—
286C2×C4⋊Q8—92no—
287#520—92no—
288C4×#41—91no—
289C2×C3×Q8C22×D311yescharacteristic
290C2×C3×Q8C22×D312yes—
291C2×C3×D4C22×D311yescharacteristic
292C22×C3×C4C22×D312yes—
293C22×C3×C4C22×D314yes—
294C2×#67—32no—
295C22×Dic3—32no—
296C22×Dic3—32no—
297C22×Dic3—34no—
298D3×Q8—124no—
299#237—38no—
300C2×C4×D3—31no—
301C2×C4×D3—31no—
302C2×C4×D3—31no—
303C2×C4×D3—34no—
304C2×Dic6—31no—
305C2×Dic6—31no—
306C2×Dic6—32no—
307C2×Dic6—34no—
308C2×Dic6—32no—
309C2×Dic6—34no—
310C2×Dic6—34no—
311C2×Dic6—128no—
312C3×C4⋊C4C22×D312yes—
313C3×C4⋊C4C22×D312yes—
314C3×C4⋊C4C22×D314yes—
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C4⋊C4C22×D314yes—
318C3×C4⋊C4C22×D312yes—
319C3×C22⋊C4C22×D314yes—
320C3×C22⋊C4C22×D312yes—
321C3×C42C22×D311yescharacteristic
322C3×C42C22×D312yes—
323#217—34no—
324#217—32no—
325(C2×D3)⋊C4—32no—
326(C2×D3)⋊C4—32no—
327(C2×D3)⋊C4—32no—
328C4⋊Dic3—31no—
329C4⋊Dic3—32no—
330C4⋊Dic3—31no—
331C4⋊Dic3—32no—
332C4⋊Dic3—34no—
333C4⋊Dic3—32no—
334C4⋊Dic3—34no—
335Dic3⋊C4—32no—
336Dic3⋊C4—32no—
337Dic3⋊C4—32no—
338Dic3⋊C4—32no—
339Dic3⋊C4—34no—
340Dic3⋊C4—32no—
341Dic3⋊C4—32no—
342Dic3⋊C4—32no—
343Dic3⋊C4—34no—
344Dic3⋊C4—34no—
345Dic3⋊C4—34no—
346Dic3⋊C4—34no—
347Dic3⋊C4—34no—
348C4×Dic3—31no—
349C4×Dic3—32no—
350C4×Dic3—34no—
351C4×Dic3—32no—
352C4×Dic3—31no—
353C4×Dic3—31no—
354C4×Dic3—34no—
355C4×Dic3—32no—
356C4×Dic3—32no—
357C22×C9—22no—
358C22×C9—22no—
359C22×C9C22×Q814yes—
360C22×C9C2511yescharacteristic
361C2×D9—21no—
362C2×D9—21no—
363C2×D9C22×Q812yes—
364C4×C9—22no—
365C4×C9—24no—
366C4×C9—21no—
367C4×C9—22no—
368C4×C9—22no—
369C4×C9C22×Q812yes—
370C4×C92−1+412yes—
371Dic9—24no—
372Dic9—22no—
373Dic9—22no—
374Dic9—22no—
375Dic9—21no—
376Dic9C22×Q814yes—
377Dic9C22×Q812yes—
378Dic9H(5,𝔽2)12yes—
379C2×#41—91no—
380C22×Q8—92no—
381C22×Q8—94no—
382C4⋊Q8—92no—
383C4⋊Q8—91no—
384C4⋊Q8—94no—
385C4⋊Q8—92no—
386C4⋊Q8—91no—
387C4⋊Q8—94no—
388C4⋊Q8—94no—
389C4⋊Q8—92no—
390C4⋊Q8—92no—
391C4⋊Q8—92no—
392C4⋊Q8—94no—
393C4⋊Q8—92no—
394C4⋊Q8—91no—
395C4⋊Q8—92no—
396C4⋊Q8C2×D911yescharacteristic
397#125—92no—
398#125—94no—
399#125—94no—
400#125—94no—
401#125—92no—
402#125C2×D912yes—
403C22⋊Q8—91no—
404C22⋊Q8—92no—
405C22⋊Q8—94no—
406C22⋊Q8—92no—
407C22⋊Q8—91no—
408C22⋊Q8—94no—
409C22⋊Q8—94no—
410C22⋊Q8—94no—
411C22⋊Q8—94no—
412C22⋊Q8—94no—
413C22⋊Q8C2×D912yes—
414C22⋊Q8C2×D914yes—
415C4×Q8—92no—
416C4×Q8—91no—
417C4×Q8—92no—
418C4×Q8—94no—
419C4×Q8—92no—
420C4×Q8—91no—
421C4×Q8—92no—
422C4×Q8—92no—
423C4×Q8—91no—
424C4×Q8C2×D911yescharacteristic
425C4×D4—91no—
426C4×D4—92no—
427C4×D4—92no—
428C4×D4—94no—
429C4×D4—92no—
430C4×D4—94no—
431C4×D4C2×D911yescharacteristic
432C4×D4C2×D912yes—
433#117—91no—
434#117—92no—
435#117—94no—
436#117—92no—
437C2×C4⋊C4—94no—
438C2×C4⋊C4—92no—
439C2×C4⋊C4—92no—
440C2×C4⋊C4—92no—
441C2×C4⋊C4C2×D912yes—
442C2×C42—92no—
443C2×C42—91no—
444C23×C3C23×D312yes—
445C22×D3—31no—
446C3×Q8—22no—
447C3×Q8—42no—
448C3×D4D3×Q814yes—
449C2×C3×C4—24no—
450C2×C3×C4—44no—
451C2×C3×C4C23×D312yes—
452C2×C3×C4C23×D312yes—
453C2×C3×C4C23×D311yescharacteristic
454C2×C3×C4C23×D314yes—
455C2×C3×C4C23×D312yes—
456C2×C3×C4C23×D311yescharacteristic
457C2×C3×C4C23×D311yescharacteristic
458#67—38no—
459C2×Dic3—38no—
460C2×Dic3—32no—
461C2×Dic3—31no—
462C2×Dic3—31no—
463C2×Dic3—32no—
464C2×Dic3—31no—
465C2×Dic3—32no—
466C2×Dic3—32no—
467C2×Dic3—34no—
468C2×Dic3—64no—
469C2×Dic3—124no—
470C4×D3—34no—
471C4×D3—62no—
472C4×D3—62no—
473C4×D3—124no—
474Dic6—34no—
475Dic6—64no—
476Dic6—68no—
477Dic6—62no—
478Dic6—124no—
479Dic6—124no—
480Dic6—122no—
481C2×C9—24no—
482C2×C9C23×Q811yescharacteristic
483C2×C9C2×H(5,𝔽2)11yescharacteristic
484C2×C9C2×2−1+411yescharacteristic
485D9—22no—
486#41—98no—
487C2×Q8—91no—
488C2×Q8—91no—
489C2×Q8—94no—
490C2×Q8—92no—
491C2×Q8—94no—
492C2×Q8—94no—
493C2×Q8—92no—
494C2×Q8—368no—
495C2×Q8—364no—
496C2×Q8C22×D911yescharacteristic
497C2×Q8C22×D912yes—
498C2×D4—92no—
499C2×D4C22×D911yescharacteristic
500C22×C4—92no—
501C22×C4—91no—
502C22×C4—92no—
503C22×C4—94no—
504C22×C4—91no—
505C22×C4—91no—
506C22×C4—94no—
507C22×C4C22×D912yes—
508C22×C4C22×D914yes—
509C4⋊C4—94no—
510C4⋊C4—92no—
511C4⋊C4—91no—
512C4⋊C4—92no—
513C4⋊C4—94no—
514C4⋊C4—94no—
515C4⋊C4—92no—
516C4⋊C4—94no—
517C4⋊C4—94no—
518C4⋊C4—92no—
519C4⋊C4—92no—
520C4⋊C4—92no—
521C4⋊C4—91no—
522C4⋊C4—92no—
523C4⋊C4—94no—
524C4⋊C4—92no—
525C4⋊C4—92no—
526C4⋊C4—94no—
527C4⋊C4—92no—
528C4⋊C4—94no—
529C4⋊C4C22×D912yes—
530C4⋊C4C22×D912yes—
531C4⋊C4C22×D911yescharacteristic
532C4⋊C4C22×D914yes—
533C4⋊C4C22×D911yescharacteristic
534C4⋊C4C22×D914yes—
535C4⋊C4C22×D912yes—
536C22⋊C4—94no—
537C22⋊C4—92no—
538C22⋊C4—92no—
539C22⋊C4—92no—
540C22⋊C4—92no—
541C22⋊C4C22×D914yes—
542C22⋊C4C22×D912yes—
543C42—91no—
544C42—91no—
545C42—92no—
546C42—92no—
547C42—92no—
548C42—91no—
549C42—94no—
550C42—94no—
551C42—92no—
552C42C22×D911yescharacteristic
553C42C22×D912yes—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3C2×D3×Q814yes—
557C22×C3C24×D311yescharacteristic
558C2×D3—32no—
559C2×D3—61no—
560C2×D3—61no—
561C3×C4—22no—
562C3×C4—22no—
563C3×C4—22no—
564C3×C4—24no—
565C3×C4—21no—
566C3×C4C2×D3×Q812yes—
567C3×C4#101012yes—
568Dic3—34no—
569Dic3—32no—
570Dic3—32no—
571Dic3—62no—
572Dic3—61no—
573Dic3—64no—
574Dic3—62no—
575Dic3—62no—
576C9#350311yescharacteristic, complemented, Sylow
577C23—91no—
578C23C23×D912yes—
579Q8—22no—
580Q8—42no—
581Q8—94no—
582Q8—184no—
583Q8—188no—
584Q8—182no—
585Q8—364no—
586Q8—364no—
587Q8—362no—
588D4—98no—
589D4Q8×D914yescomplemented
590C2×C4—24no—
591C2×C4—44no—
592C2×C4—92no—
593C2×C4—91no—
594C2×C4—91no—
595C2×C4—98no—
596C2×C4—94no—
597C2×C4—92no—
598C2×C4—91no—
599C2×C4—92no—
600C2×C4—94no—
601C2×C4—92no—
602C2×C4—182no—
603C2×C4—184no—
604C2×C4—182no—
605C2×C4—364no—
606C2×C4—364no—
607C2×C4C23×D912yes—
608C2×C4C23×D912yes—
609C2×C4C23×D911yescharacteristic
610C2×C4C23×D914yes—
611C2×C4C23×D912yes—
612C2×C4C23×D911yescharacteristic
613C2×C4C23×D911yescharacteristic
614C2×C3—24no—
615C2×C3C22×D3×Q811yescharacteristic
616C2×C3C2×#101011yescharacteristic
617C2×C3D3×H(5,𝔽2)11yescharacteristic
618D3—62no—
619C22—22no—
620C22—22no—
621C22—92no—
622C22—181no—
623C22—181no—
624C22C2×Q8×D914yes—
625C22C24×D911yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—24no—
630C4—21no—
631C4—92no—
632C4—94no—
633C4—92no—
634C4—181no—
635C4—182no—
636C4—182no—
637C4—184no—
638C4—182no—
639C4C2×Q8×D912yes—
640C4#6371612yes—
641C3#8692611yescharacteristic
642C2—24no—
643C2—182no—
644C2C22×Q8×D911yescharacteristic
645C2C2×#6371611yescharacteristic
646C2D9×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#554C2
prime radicalC2×#3699C22
hypercenter#554D9
hypocenterC9#3503
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C9×#554C2semidirect
2. D9×C4⋊Q8C2semidirect
3. #10589824C2semidirect
4. #10589791C2semidirect
5. #10589787C2semidirect
6. #10589737C2semidirect
7. #10589734C2semidirect
8. #10589725C2semidirect
9. #10589724C2semidirect
10. #10589680C2semidirect
11. Q8×Dic18C2semidirect
13. #10589645C2semidirect
14. D4×Dic18C2semidirect
16. #10589613C2semidirect
17. C2×#63450C2semidirect
111. #3699Q8semidirect
239. D4×C9C2×Q8semidirect
249. #611C2×Q8semidirect
252. C2×Dic9C2×Q8semidirect
264. C4×D9C2×Q8semidirect
271. Dic18C2×Q8semidirect
278. #554D9semidirect
576. C9#3503semidirect
589. D4Q8×D9semidirect

Maximal subgroups

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

subgroupindex
C9×#5542
D9×C4⋊Q82
#105898242
#105897912
#105897872
#105897372
#105897342
#105897252
#105897242
#105896802
Q8×Dic182
#105896482
#105896452
D4×Dic182
C4×#36992
#105896132
C2×#634502
#869263