Finite Group Databasebeta

← #11909842

Subgroups — #11909842

Order 1152.

1488 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Q8×C9C211yesmaximal, characteristic, complemented
2Q8×#611C211yesmaximal, characteristic, complemented
3Q8×#611C211yesmaximal, characteristic, complemented
4#10589914C211yesmaximal, characteristic, complemented
5C2×Q8×Dic9C211yesmaximal, characteristic, complemented
6#10589833C213yesmaximal, complemented
7#10589823C213yesmaximal, complemented
8#10589744C213yesmaximal, complemented
9#10589743C213yesmaximal, complemented
10#10589727C213yesmaximal, complemented
11#10589724C213yesmaximal, complemented
12#10589674C211yesmaximal, characteristic, complemented
13#10589671C211yesmaximal, characteristic, complemented
14#10589643C213yesmaximal, complemented
15#10589640C213yesmaximal
16#86752—31nomaximal
17C22×Q8×C9C2211yescharacteristic
18C22×Q8×C9C2211yescharacteristic
19C2×Q8×D9C2211yescharacteristic
20C9×C4⋊Q8C2213yes—
21C9×C22⋊Q8C2213yes—
22C9×C22⋊Q8C2213yes—
23C4×Q8×C9C2211yescharacteristic
24C4×D4×C9C2213yes—
25#63508C2213yes—
26#63508C2213yes—
27Q8×Dic9C2213yes—
28Q8×Dic9C2213yes—
29Q8×Dic9C2213yes—
30Q8×Dic9C2213yes—
31Q8×Dic9C2211yescharacteristic
32Q8×Dic9C2211yescharacteristic
33Q8×Dic9C2211yescharacteristic
34#63506C2213yes—
35#63506C2213yes—
36#63501C2211yescharacteristic
37#63497C2213yes—
38C4×#611C2213yes—
39C4×#611C2213yes—
40#63488C2213yes—
41#63488C2213yes—
42C2×C4⋊Dic9C2213yes—
43#63486C2213yes—
44#63486C2213yes—
45C2×C4×Dic9C2213yes—
46#63460C2216yes—
47#63460C2213yes—
48#63454C2213yes—
49#63452C2216yes—
50#63452C2213yes—
51#63451C2216yes—
52#63451C2213yes—
53#63451C2216yes—
54#63450C2213yes—
55#63449C2213yes—
56#63449C2216yes—
57#63448C2213yes—
58#63447C2213yes—
59#63441C2213yes—
60#63441C2216yes—
61#63440C2213yes—
62#63439C2216yes—
63#63434C2213yes—
64#63432C2213yes—
65C4×Dic18C2213yes—
66C4×Dic18C2213yes—
67C3×D4×Q8D311yescharacteristic
68Q8×#67—31no—
69Q8×#67—31no—
70#5812—31no—
71C2×Q8×Dic3—31no—
72#5731—33no—
73#5721—33no—
74#5642—33no—
75#5641—33no—
76#5625—33no—
77#5622—33no—
78#5572—31no—
79#5569—31no—
80#5541—33no—
81#5538—33no—
82C2×Q8×C9—24no—
83C2×Q8×C9—24no—
84C2×Q8×C9C2313yes—
85C2×Q8×C9C2313yes—
86C2×Q8×C9C2311yescharacteristic
87C2×D4×C9C2311yescharacteristic
88C22×C4×C9C2313yes—
89C22×C4×C9C2313yes—
90C2×#611C2311yescharacteristic
91C2×#611C2311yescharacteristic
92C22×Dic9C2313yes—
93C22×Dic9C2311yescharacteristic
94Q8×D9—24no—
95C2×C4×D9C2313yes—
96C2×Dic18C2313yes—
97C2×Dic18C2313yes—
98C9×C4⋊C4C2313yes—
99C9×C4⋊C4C2313yes—
100C9×C4⋊C4C2316yes—
101C9×C22⋊C4C2313yes—
102C9×C22⋊C4C2313yes—
103C42×C9C2313yes—
104#3676C2313yes—
105#3676C2311yescharacteristic
106#3676C2313yes—
107#3676C2313yes—
108(C2×D9)⋊C4C2313yes—
109(C2×D9)⋊C4C2313yes—
110(C2×D9)⋊C4C2311yescharacteristic
111(C2×D9)⋊C4C2313yes—
112C4⋊Dic9C2313yes—
113C4⋊Dic9C2313yes—
114C4⋊Dic9C2313yes—
115C4⋊Dic9C2313yes—
116C4⋊Dic9C2313yes—
117C4⋊Dic9C2316yes—
118C4⋊Dic9C2313yes—
119Dic9⋊C4C2313yes—
120Dic9⋊C4C2313yes—
121Dic9⋊C4C2313yes—
122Dic9⋊C4C2313yes—
123Dic9⋊C4C2311yescharacteristic
124Dic9⋊C4C2316yes—
125Dic9⋊C4C2316yes—
126Dic9⋊C4C2316yes—
127Dic9⋊C4C2313yes—
128C4×Dic9C2313yes—
129C4×Dic9C2313yes—
130C4×Dic9C2316yes—
131C4×Dic9C2313yes—
132C4×Dic9C2313yes—
133C4×Dic9C2313yes—
134C4×Dic9C2316yes—
135#3523—91noSylow
136C22×C3×Q8C2×D311yescharacteristic
137C22×C3×Q8C2×D311yescharacteristic
138C2×D3×Q8—31no—
139C3×C4⋊Q8C2×D313yes—
140C3×C22⋊Q8C2×D313yes—
141C3×C22⋊Q8C2×D313yes—
142C3×C4×Q8C2×D311yescharacteristic
143C3×C4×D4C2×D313yes—
144#946—33no—
145#946—33no—
146Q8×Dic3—33no—
147Q8×Dic3—33no—
148Q8×Dic3—33no—
149Q8×Dic3—33no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153#944—33no—
154#944—33no—
155#939—31no—
156#935—33no—
157C4×#67—33no—
158C4×#67—33no—
159#926—33no—
160#926—33no—
161C2×C4⋊Dic3—33no—
162#924—33no—
163#924—33no—
164C2×C4×Dic3—33no—
165#898—36no—
166#898—33no—
167#892—33no—
168#890—36no—
169#890—33no—
170#889—33no—
171#889—36no—
172#889—36no—
173#888—33no—
174#887—36no—
175#887—33no—
176#886—33no—
177#885—33no—
178#879—36no—
179#879—33no—
180#878—33no—
181#877—36no—
182#872—33no—
183#870—33no—
184C4×Dic6—33no—
185C4×Dic6—33no—
186C23×C9C2411yescharacteristic
187C23×C9C2411yescharacteristic
188C22×D9C2411yescharacteristic
189Q8×C9—26no—
190Q8×C9—26no—
191Q8×C9#4114yes—
192D4×C9—22no—
193C2×C4×C9—26no—
194C2×C4×C9—26no—
195C2×C4×C9C2413yes—
196C2×C4×C9C2413yes—
197C2×C4×C9C2413yes—
198C2×C4×C9C2411yescharacteristic
199C2×C4×C9C2413yes—
200#611—22no—
201#611—22no—
202C2×Dic9—26no—
203C2×Dic9—22no—
204C2×Dic9C2411yescharacteristic
205C2×Dic9C2413yes—
206C2×Dic9C2413yes—
207C2×Dic9C2411yescharacteristic
208C2×Dic9C2413yes—
209C2×Dic9C2413yes—
210C2×Dic9C2411yescharacteristic
211C4×D9—26no—
212Dic18—26no—
213Dic18—26no—
214#557—93no—
215#557—91no—
216#556—93no—
217#552—93no—
218#552—93no—
219D4×Q8—91no—
220D4×Q8—91no—
221D4×Q8D911yescharacteristic, complemented
222#541—93no—
223#541—93no—
224#533—93no—
225#529—93no—
226#519—91no—
227#519—91no—
228C2×C4×Q8—91no—
229C2×C3×Q8—24no—
230C2×C3×Q8—24no—
231C2×C3×Q8C22×D313yes—
232C2×C3×Q8C22×D313yes—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×D4C22×D311yescharacteristic
235C22×C3×C4C22×D313yes—
236C22×C3×C4C22×D313yes—
237C2×#67—31no—
238C2×#67—31no—
239C22×Dic3—33no—
240C22×Dic3—31no—
241D3×Q8—64no—
242C2×C4×D3—33no—
243C2×Dic6—33no—
244C2×Dic6—33no—
245C3×C4⋊C4C22×D313yes—
246C3×C4⋊C4C22×D316yes—
247C3×C4⋊C4C22×D313yes—
248C3×C22⋊C4C22×D313yes—
249C3×C22⋊C4C22×D313yes—
250C3×C42C22×D313yes—
251#217—33no—
252#217—33no—
253#217—31no—
254#217—33no—
255(C2×D3)⋊C4—31no—
256(C2×D3)⋊C4—33no—
257(C2×D3)⋊C4—33no—
258(C2×D3)⋊C4—33no—
259C4⋊Dic3—33no—
260C4⋊Dic3—33no—
261C4⋊Dic3—33no—
262C4⋊Dic3—33no—
263C4⋊Dic3—33no—
264C4⋊Dic3—36no—
265C4⋊Dic3—33no—
266Dic3⋊C4—31no—
267Dic3⋊C4—33no—
268Dic3⋊C4—33no—
269Dic3⋊C4—36no—
270Dic3⋊C4—33no—
271Dic3⋊C4—36no—
272Dic3⋊C4—33no—
273Dic3⋊C4—36no—
274Dic3⋊C4—33no—
275C4×Dic3—36no—
276C4×Dic3—33no—
277C4×Dic3—33no—
278C4×Dic3—33no—
279C4×Dic3—36no—
280C4×Dic3—33no—
281C4×Dic3—33no—
282C22×C9—21no—
283C22×C9—21no—
284C22×C9—21no—
285C22×C9—21no—
286C22×C9—21no—
287C22×C92−1+412yes—
288C22×C9C2511yescharacteristic
289C2×D9—21no—
290C2×D9—21no—
291C2×D9—21no—
292C4×C9—23no—
293C4×C9—23no—
294C4×C9—23no—
295C4×C9—21no—
296C4×C9C2×#4116yes—
297Dic9—23no—
298Dic9—23no—
299Dic9—23no—
300Dic9—23no—
301Dic9—21no—
302Dic9—21no—
303Dic92−1+412yes—
304C22×Q8—91no—
305C22×Q8C2×D911yescharacteristic
306C22×Q8C2×D911yescharacteristic
307C4⋊Q8—93no—
308C4⋊Q8—93no—
309C4⋊Q8—93no—
310C4⋊Q8C2×D913yes—
311#126—93no—
312#126—96no—
313#126—93no—
314#126—96no—
315#125—93no—
316#125—96no—
317#125—96no—
318#125—96no—
319#125—93no—
320#125—93no—
321#124—93no—
322#123—93no—
323#123—93no—
324C22⋊Q8—93no—
325C22⋊Q8—93no—
326C22⋊Q8—93no—
327C22⋊Q8—93no—
328C22⋊Q8—93no—
329C22⋊Q8C2×D913yes—
330C22⋊Q8C2×D913yes—
331#121—91no—
332C4×Q8—91no—
333C4×Q8—93no—
334C4×Q8—91no—
335C4×Q8—93no—
336C4×Q8—93no—
337C4×Q8—91no—
338C4×Q8—93no—
339C4×Q8—93no—
340C4×Q8—96no—
341C4×Q8—93no—
342C4×Q8—93no—
343C4×Q8C2×D911yescharacteristic
344C4×D4—93no—
345C4×D4—93no—
346C4×D4C2×D913yes—
347#117—93no—
348#117—93no—
349#117—93no—
350#117—96no—
351#117—93no—
352C2×C4⋊C4—93no—
353C2×C42—93no—
354C23×C3C23×D311yescharacteristic
355C23×C3C23×D311yescharacteristic
356C22×D3—31no—
357C3×Q8—26no—
358C3×Q8—26no—
359C3×Q8#23714yes—
360C3×D4—22no—
361C2×C3×C4—26no—
362C2×C3×C4—26no—
363C2×C3×C4C23×D313yes—
364C2×C3×C4C23×D313yes—
365C2×C3×C4C23×D313yes—
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D313yes—
368#67—62no—
369#67—62no—
370C2×Dic3—31no—
371C2×Dic3—31no—
372C2×Dic3—33no—
373C2×Dic3—33no—
374C2×Dic3—31no—
375C2×Dic3—33no—
376C2×Dic3—33no—
377C2×Dic3—62no—
378C2×Dic3—66no—
379C4×D3—66no—
380Dic6—66no—
381Dic6—66no—
382C2×C9—22no—
383C2×C9—41no—
384C2×C9C22×#4111yescharacteristic
385C2×C9C2×2−1+411yescharacteristic
386C2×C9C2×2−1+411yescharacteristic
387D9—41no—
388C2×Q8—24no—
389C2×Q8—24no—
390C2×Q8—93no—
391C2×Q8—93no—
392C2×Q8—184no—
393C2×Q8C22×D913yes—
394C2×Q8C22×D913yes—
395C2×Q8C22×D911yescharacteristic
396C2×D4—91no—
397C2×D4—91no—
398C2×D4C22×D911yescharacteristic
399C22×C4—91no—
400C22×C4—93no—
401C22×C4—93no—
402C22×C4C22×D913yes—
403C22×C4C22×D913yes—
404C4⋊C4—93no—
405C4⋊C4—93no—
406C4⋊C4—96no—
407C4⋊C4—93no—
408C4⋊C4—93no—
409C4⋊C4—93no—
410C4⋊C4—93no—
411C4⋊C4—93no—
412C4⋊C4—96no—
413C4⋊C4—96no—
414C4⋊C4—93no—
415C4⋊C4—93no—
416C4⋊C4—91no—
417C4⋊C4—96no—
418C4⋊C4—93no—
419C4⋊C4—93no—
420C4⋊C4C22×D913yes—
421C4⋊C4C22×D913yes—
422C4⋊C4C22×D916yes—
423C22⋊C4—91no—
424C22⋊C4—93no—
425C22⋊C4—93no—
426C22⋊C4—93no—
427C22⋊C4—91no—
428C22⋊C4—93no—
429C22⋊C4—93no—
430C22⋊C4—93no—
431C22⋊C4C22×D913yes—
432C22⋊C4C22×D913yes—
433C42—93no—
434C42—93no—
435C42—93no—
436C42—93no—
437C42—96no—
438C42—96no—
439C42—93no—
440C42C22×D913yes—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3#100712yes—
447C22×C3C24×D311yescharacteristic
448C2×D3—61no—
449C2×D3—61no—
450C2×D3—61no—
451C3×C4—23no—
452C3×C4—23no—
453C3×C4—21no—
454C3×C4—23no—
455C3×C4C2×#23716yes—
456Dic3—32no—
457Dic3—63no—
458Dic3—63no—
459Dic3—63no—
460Dic3—61no—
461Dic3—63no—
462Dic3—61no—
463C9#352311yescharacteristic, complemented, Sylow
464C23—91no—
465C23C23×D911yescharacteristic
466C23C23×D911yescharacteristic
467Q8—26no—
468Q8—26no—
469Q8—186no—
470Q8—186no—
471Q8#369914yes—
472D4—22no—
473D4—182no—
474D4—182no—
475C2×C4—26no—
476C2×C4—26no—
477C2×C4—91no—
478C2×C4—93no—
479C2×C4—91no—
480C2×C4—93no—
481C2×C4—91no—
482C2×C4—93no—
483C2×C4—93no—
484C2×C4—182no—
485C2×C4—186no—
486C2×C4—186no—
487C2×C4C23×D913yes—
488C2×C4C23×D913yes—
489C2×C4C23×D913yes—
490C2×C4C23×D911yescharacteristic
491C2×C4C23×D913yes—
492C2×C3—22no—
493C2×C3—41no—
494C2×C3C22×#23711yescharacteristic
495C2×C3C2×#100711yescharacteristic
496C2×C3D3×2−1+411yescharacteristic
497D3—121no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—181no—
504C22—181no—
505C22—181no—
506C22#6371312yes—
507C22C24×D911yescharacteristic
508C4—23no—
509C4—23no—
510C4—21no—
511C4—23no—
512C4—92no—
513C4—183no—
514C4—183no—
515C4—183no—
516C4—181no—
517C4—181no—
518C4—183no—
519C4C2×#369916yes—
520C3#8675211yescharacteristic
521C2—22no—
522C2—41no—
523C2—361no—
524C2C22×#369911yescharacteristic
525C2C2×#6371311yescharacteristic
526C2D9×2−1+411yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingD4×Q8×C9C2
prime radical#63501C22
hypercenterD4×Q8D9
hypocenterC9#3523
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. D4×Q8×C9C2semidirect
2. Q8×#611C2semidirect
3. Q8×#611C2semidirect
4. #10589914C2semidirect
5. C2×Q8×Dic9C2semidirect
6. #10589833C2semidirect
7. #10589823C2semidirect
8. #10589744C2semidirect
9. #10589743C2semidirect
10. #10589727C2semidirect
11. #10589724C2semidirect
12. #10589674C2semidirect
13. #10589671C2semidirect
14. #10589643C2semidirect
221. D4×Q8D9semidirect
463. C9#3523semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C92
Q8×#6112
#105899142
C2×Q8×Dic92
#105898332
#105898232
#105897442
#105897432
#105897272
#105897242
#105896742
#105896712
#105896432
#105896402
#867523