Finite Group Databasebeta

← #11897622

Subgroups — #11897622

Order 1152.

510 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic18C211yesmaximal, characteristic, complemented
2#10589641C211yesmaximal, characteristic
3C9×#440C211yesmaximal, characteristic
4#10588844C211yesmaximal, characteristic
5SD16×Dic9C211yesmaximal, characteristic
6#10588704C211yesmaximal, characteristic, complemented
7#10588690C211yesmaximal, characteristic
8#10588556C211yesmaximal, characteristic, complemented
9#10588554C211yesmaximal, characteristic, complemented
10#10588479C211yesmaximal, characteristic, complemented
11#10588473C211yesmaximal, characteristic, complemented
12#10588441C211yesmaximal, characteristic
13#10588439C211yesmaximal, characteristic
14#10588382C211yesmaximal, characteristic, complemented
15#10588381C211yesmaximal, characteristic, complemented
16#79759—31nomaximal
17C2×C9×SD16C2211yescharacteristic
18C4×Q8×C9C2211yescharacteristic
19C4×D4×C9C2211yescharacteristic
20Q8×Dic9C2211yescharacteristic
21Q8×Dic9C2211yescharacteristic
22D4×Dic9C2211yescharacteristic
23D4×Dic9C2211yescharacteristic
24#63486—21no—
25C2×Dic9⋊C4—21no—
26#63452C2211yescharacteristic
27#63450—21no—
28#63450—21no—
29#63450C2211yescharacteristic
30#63450C2211yescharacteristic
31#63450C2211yescharacteristic
32#63440—21no—
33#63440—21no—
34#63432C2211yescharacteristic
35#63431—21no—
36#63431C2211yescharacteristic
37C4×Dic18—21no—
38C4×Dic18C2211yescharacteristic
39C9×#107C2211yescharacteristic
40C9×#103C2211yescharacteristic
41C9×#102C2211yescharacteristic
42C9×#97C2211yescharacteristic
43#63395C2211yescharacteristic
44#63395C2211yescharacteristic
45#63392C2211yescharacteristic
46#63392C2211yescharacteristic
47#63378C2211yescharacteristic
48#63378C2211yescharacteristic
49#63377C2211yescharacteristic
50#63377C2211yescharacteristic
51#63375C2211yescharacteristic
52Dic9⋊C8C2211yescharacteristic
53Dic9⋊C8C2211yescharacteristic
54C8×Dic9C2211yescharacteristic
55#63367C2211yescharacteristic
56#63366C2211yescharacteristic
57#63366C2211yescharacteristic
58#63366C2211yescharacteristic
59C4⋊(C9⋊C8)C2211yescharacteristic
60Q8×Dic6—31no—
61#5539—31no—
62C3×#440D311yescharacteristic
63#5164—31no—
64Dic3×SD16—31no—
65#5022—31no—
66#5007—31no—
67#4876—31no—
68#4874—31no—
69#4799—31no—
70#4793—31no—
71#4761—31no—
72#4759—31no—
73#4702—31no—
74#4701—31no—
75C2×Q8×C9C2311yescharacteristic
76C2×D4×C9C2311yescharacteristic
77C22×C4×C9—21no—
78C22×Dic9—21no—
79C22×Dic9—21no—
80C2×Dic18—21no—
81C2×Dic18—21no—
82C2×Dic18—21no—
83C2×Dic18—21no—
84C2×Dic18D411yescharacteristic
85C9×SD16Q814yescomplemented
86C2×C8×C9C2311yescharacteristic
87C2×C8×C9C2311yescharacteristic
88C9×C4⋊C4—21no—
89C9×C4⋊C4C2311yescharacteristic
90C9×C4⋊C4C2311yescharacteristic
91C9×C22⋊C4—21no—
92C42×C9—21no—
93C42×C9C2311yescharacteristic
94#3676—21no—
95#3676—21no—
96C4⋊Dic9—21no—
97C4⋊Dic9—21no—
98C4⋊Dic9—21no—
99C4⋊Dic9—21no—
100C4⋊Dic9D411yescharacteristic
101C4⋊Dic9C2311yescharacteristic
102C4⋊Dic9C2311yescharacteristic
103C4⋊Dic9C2311yescharacteristic
104C4⋊Dic9C2311yescharacteristic
105Dic9⋊C4—21no—
106Dic9⋊C4—21no—
107Dic9⋊C4—21no—
108Dic9⋊C4—21no—
109Dic9⋊C4—21no—
110Dic9⋊C4—21no—
111Dic9⋊C4D411yescharacteristic
112Dic9⋊C4D411yescharacteristic
113C4×Dic9—21no—
114C4×Dic9—21no—
115C4×Dic9C2311yescharacteristic
116C4×Dic9C2311yescharacteristic
117C2×C9⋊C8C2311yescharacteristic
118C2×C9⋊C8C2311yescharacteristic
119#3385—91noSylow
120C2×C3×SD16C2×D311yescharacteristic
121C3×C4×Q8C2×D311yescharacteristic
122C3×C4×D4C2×D311yescharacteristic
123Q8×Dic3—31no—
124Q8×Dic3—31no—
125D4×Dic3—31no—
126D4×Dic3—31no—
127#924—61no—
128C2×Dic3⋊C4—61no—
129#890—31no—
130#888—31no—
131#888—31no—
132#888—31no—
133#888—61no—
134#888—61no—
135#878—61no—
136#878—61no—
137#870—31no—
138#869—31no—
139#869—61no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×#107C2×D311yescharacteristic
143C3×#103C2×D311yescharacteristic
144C3×#102C2×D311yescharacteristic
145C3×#97C2×D311yescharacteristic
146#835—31no—
147#835—31no—
148#832—31no—
149#832—31no—
150#818—31no—
151#818—31no—
152#817—31no—
153#817—31no—
154#815—31no—
155Dic3⋊C8—31no—
156Dic3⋊C8—31no—
157C8×Dic3—31no—
158#808—31no—
159#807—31no—
160#807—31no—
161#807—31no—
162C4⋊(C3⋊C8)—31no—
163C23×C9—21no—
164Q8×C9—21no—
165Q8×C9C2×Q812yes—
166D4×C9—21no—
167D4×C9C2×Q812yes—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—81no—
172C2×C4×C9C2×D411yescharacteristic
173C2×C4×C9C2×D411yescharacteristic
174C2×C4×C9C2411yescharacteristic
175C2×Dic9—21no—
176C2×Dic9—21no—
177C2×Dic9—21no—
178C2×Dic9—21no—
179C2×Dic9—42no—
180C2×Dic9—81no—
181C2×Dic9C2×D411yescharacteristic
182C2×Dic9C2×D411yescharacteristic
183C2×Dic9C2×D411yescharacteristic
184C2×Dic9C2×D411yescharacteristic
185Dic18—22no—
186Dic18—81no—
187Dic18—81no—
188Dic18—81no—
189Dic18—81no—
190C8×C9—21no—
191C8×C9C2×Q812yes—
192C9⋊C8—21no—
193C9⋊C8—21no—
194Q82—91no—
195#554—91no—
196#501—91no—
197#501—91no—
198#500—91no—
199#479—91no—
200#479—91no—
201#477—91no—
202#476—91no—
203#474—91no—
204#474—91no—
205#446—91no—
206#440—91no—
207#440D911yescharacteristic
208C4×SD16—91no—
209C2×C3×Q8C22×D311yescharacteristic
210C2×C3×D4C22×D311yescharacteristic
211C22×C3×C4—21no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C2×Dic6—31no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C3×SD16Dic614yes—
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C3×C4⋊C4—21no—
223C3×C4⋊C4C22×D311yescharacteristic
224C3×C4⋊C4C22×D311yescharacteristic
225C3×C22⋊C4—21no—
226C3×C42—21no—
227C3×C42C22×D311yescharacteristic
228#217—61no—
229#217—61no—
230C4⋊Dic3—31no—
231C4⋊Dic3—31no—
232C4⋊Dic3—31no—
233C4⋊Dic3—31no—
234C4⋊Dic3—31no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239Dic3⋊C4—31no—
240Dic3⋊C4—31no—
241Dic3⋊C4—61no—
242Dic3⋊C4—61no—
243Dic3⋊C4—61no—
244Dic3⋊C4—61no—
245Dic3⋊C4—61no—
246Dic3⋊C4—61no—
247C4×Dic3—31no—
248C4×Dic3—31no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C2×C3⋊C8—31no—
252C2×C3⋊C8—31no—
253C22×C9—22no—
254C22×C9—41no—
255C22×C9—41no—
256C22×C9C22×D411yescharacteristic
257C4×C9—22no—
258C4×C9—21no—
259C4×C9—21no—
260C4×C9—41no—
261C4×C9—41no—
262C4×C9C22×Q811yescharacteristic
263C4×C92−1+411yescharacteristic
264Dic9—21no—
265Dic9—21no—
266Dic9—21no—
267Dic9—41no—
268Dic9—41no—
269Dic9—41no—
270Dic9—41no—
271Dic9#13712yes—
272C2×SD16C2×D911yescharacteristic
273C4⋊Q8—91no—
274C4⋊Q8—91no—
275C4⋊Q8—91no—
276C4⋊Q8—91no—
277C4⋊Q8—181no—
278C4⋊Q8—181no—
279C4⋊Q8—181no—
280#125—91no—
281#125—91no—
282C22⋊Q8—181no—
283C22⋊Q8—181no—
284C22⋊Q8—181no—
285C4×Q8—91no—
286C4×Q8—91no—
287C4×Q8—91no—
288C4×Q8—181no—
289C4×Q8C2×D911yescharacteristic
290C4×D4—91no—
291C4×D4—91no—
292C4×D4C2×D911yescharacteristic
293C2×C4⋊C4—181no—
294#107—91no—
295#107—91no—
296#107—91no—
297#107—91no—
298#107—91no—
299#107C2×D911yescharacteristic
300#106—91no—
301#106—91no—
302#106—91no—
303C4⋊C8—91no—
304C4⋊C8—91no—
305C4⋊C8—91no—
306#103—91no—
307#103—91no—
308#103C2×D911yescharacteristic
309#102—91no—
310#102—91no—
311#102C2×D911yescharacteristic
312#97—91no—
313#97C2×D911yescharacteristic
314C4×C8—91no—
315C23×C3—21no—
316C3×Q8—21no—
317C3×Q8C2×Dic612yes—
318C3×D4—21no—
319C3×D4C2×Dic612yes—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—81no—
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327C2×Dic3—31no—
328C2×Dic3—31no—
329C2×Dic3—31no—
330C2×Dic3—31no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—122no—
336C2×Dic3—241no—
337Dic6—62no—
338Dic6—241no—
339Dic6—241no—
340Dic6—241no—
341Dic6—241no—
342C3×C8—21no—
343C3×C8C2×Dic612yes—
344C3⋊C8—61no—
345C3⋊C8—61no—
346C2×C9—42no—
347C2×C9D4×Q811yescharacteristic
348C2×C9C2×#13711yescharacteristic
349C2×C9#57611yescharacteristic
350C2×Q8—91no—
351C2×Q8—181no—
352C2×Q8—181no—
353C2×Q8—181no—
354C2×Q8—181no—
355C2×Q8C22×D911yescharacteristic
356C2×D4C22×D911yescharacteristic
357C22×C4—21no—
358C22×C4—181no—
359C22×C4—181no—
360SD16Dic1814yescomplemented
361C2×C8—91no—
362C2×C8—91no—
363C2×C8C22×D911yescharacteristic
364C2×C8C22×D911yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—91no—
367C4⋊C4—91no—
368C4⋊C4—91no—
369C4⋊C4—91no—
370C4⋊C4—91no—
371C4⋊C4—91no—
372C4⋊C4—91no—
373C4⋊C4—181no—
374C4⋊C4—181no—
375C4⋊C4—181no—
376C4⋊C4—181no—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C4⋊C4—181no—
380C4⋊C4—181no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C4⋊C4C22×D911yescharacteristic
384C4⋊C4C22×D911yescharacteristic
385C22⋊C4—21no—
386C22⋊C4—181no—
387C22⋊C4—181no—
388C42—21no—
389C42—91no—
390C42—91no—
391C42—181no—
392C42—181no—
393C42C22×D911yescharacteristic
394C22×C3—22no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3C2×D3×D411yescharacteristic
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—22no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4C22×Dic611yescharacteristic
404C3×C4#101011yescharacteristic
405Dic3—32no—
406Dic3—61no—
407Dic3—61no—
408Dic3—61no—
409Dic3—121no—
410Dic3—121no—
411Dic3—121no—
412Dic3—121no—
413C9#338511yescharacteristic, complemented, Sylow
414C23—21no—
415Q8—21no—
416Q8—182no—
417Q8—721no—
418Q8—721no—
419Q8—721no—
420Q8—721no—
421Q8C2×Dic1812yes—
422D4—21no—
423D4C2×Dic1812yes—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—81no—
428C2×C4—91no—
429C2×C4—91no—
430C2×C4—91no—
431C2×C4—91no—
432C2×C4—181no—
433C2×C4—181no—
434C2×C4—181no—
435C2×C4—181no—
436C2×C4—362no—
437C2×C4—721no—
438C2×C4D4×D911yescharacteristic
439C2×C4D4×D911yescharacteristic
440C2×C4C23×D911yescharacteristic
441C8—21no—
442C8—181no—
443C8—181no—
444C8C2×Dic1812yes—
445C2×C3—42no—
446C2×C3D4×Dic611yescharacteristic
447C2×C3#577411yescharacteristic
448C2×C3D3×#13711yescharacteristic
449C22—22no—
450C22—41no—
451C22—41no—
452C22C2×D4×D911yescharacteristic
453C4—21no—
454C4—21no—
455C4—22no—
456C4—41no—
457C4—41no—
458C4—92no—
459C4—181no—
460C4—181no—
461C4—181no—
462C4—361no—
463C4—361no—
464C4—361no—
465C4—361no—
466C4C22×Dic1811yescharacteristic
467C4#6371611yescharacteristic
468C3#7975911yescharacteristic
469C2—42no—
470C2D4×Dic1811yescharacteristic
471C2#1058987611yescharacteristic
472C2D9×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#440C2
socleC22×C3C2×D3×D4
prime radicalC2×C3×D4C22×D3
hypercenter#440D9
hypocenterC9#3385
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. Q8×Dic18C2semidirect
6. #10588704C2semidirect
8. #10588556C2semidirect
9. #10588554C2semidirect
10. #10588479C2semidirect
11. #10588473C2semidirect
14. #10588382C2semidirect
15. #10588381C2semidirect
85. C9×SD16Q8semidirect
360. SD16Dic18semidirect
413. C9#3385semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic182
#105896412
C9×#4402
#105888442
SD16×Dic92
#105887042
#105886902
#105885562
#105885542
#105884792
#105884732
#105884412
#105884392
#105883822
#105883812
#797593