Finite Group Databasebeta

← #11897629

Subgroups — #11897629

Order 1152.

1020 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
1#10596161C211yesmaximal, characteristic
2Q8×#634C211yesmaximal, characteristic, complemented
3C32×#479C211yesmaximal, characteristic, complemented
4#10592763C211yesmaximal, characteristic, complemented
5#10592725C211yesmaximal, characteristic
6#10592589C211yesmaximal, characteristic
7#10592573C211yesmaximal, characteristic, complemented
8#10592569C211yesmaximal, characteristic
9#10592555C211yesmaximal, characteristic, complemented
10#10592545C211yesmaximal, characteristic
11#10592527C211yesmaximal, characteristic, complemented
12#10592516C211yesmaximal, characteristic
13#10592495C211yesmaximal, characteristic, complemented
14#10592492C211yesmaximal, characteristic, complemented
15#10592487C211yesmaximal, characteristic
16#81223—34nomaximal
17C32×#125C2211yescharacteristic
18C32×C4×Q8C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22#64106—21no—
23#64105—21no—
24#64105—21no—
25#64102C2211yescharacteristic
26#64102C2211yescharacteristic
27C4⋊C4×C3⋊D3—21no—
28#64099C2211yescharacteristic
29#64097—21no—
30#64097—21no—
31#64097C2211yescharacteristic
32#64097C2211yescharacteristic
33#64097C2211yescharacteristic
34C4×C4⋊(C3⋊D3)C2211yescharacteristic
35#64078—21no—
36#64078C2211yescharacteristic
37C4×#634—21no—
38C4×#634C2211yescharacteristic
39C32×#107C2211yescharacteristic
40C32×#106C2211yescharacteristic
41C32×C4⋊C8C2211yescharacteristic
42C32×#103C2211yescharacteristic
43C32×#103C2211yescharacteristic
44#63662C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63645C2211yescharacteristic
48#63645C2211yescharacteristic
49#63642C2211yescharacteristic
50#63641C2211yescharacteristic
51#63641C2211yescharacteristic
52C8×C3⋊Dic3C2211yescharacteristic
53#63636C2211yescharacteristic
54#63635C2211yescharacteristic
55#63635C2211yescharacteristic
56#63634C2211yescharacteristic
57#63634C2211yescharacteristic
58#63634C2211yescharacteristic
59#63630C2211yescharacteristic
60#5690—34no—
61Q8×Dic6—34no—
62C3×#479D314yescomplemented
63#5064—34no—
64#5026—34no—
65#4890—34no—
66#4874—34no—
67#4870—34no—
68#4856—34no—
69#4846—34no—
70#4828—34no—
71#4817—34no—
72#4796—34no—
73#4793—34no—
74#4788—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C4⋊(C3⋊D3)C2311yescharacteristic
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3—21no—
79C2×C4×C3⋊D3—21no—
80C2×#634—21no—
81C2×#634—21no—
82C2×#634—21no—
83C2×#634—21no—
84C2×#634D411yescharacteristic
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C4⋊C4—21no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4—21no—
90C32×C4⋊C4C2311yescharacteristic
91C32×C4⋊C4C2311yescharacteristic
92C32×C4⋊C4C2311yescharacteristic
93C32×C42—21no—
94C32×C42C2311yescharacteristic
95#3755Q814yescomplemented
96#3752—21no—
97#3752—21no—
98#3752—21no—
99C4⋊(C3⋊Dic3)—21no—
100C4⋊(C3⋊Dic3)—21no—
101C4⋊(C3⋊Dic3)—21no—
102C4⋊(C3⋊Dic3)—21no—
103C4⋊(C3⋊Dic3)D411yescharacteristic
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108#3750—21no—
109#3750—21no—
110#3750—21no—
111#3750D411yescharacteristic
112#3750D411yescharacteristic
113C4×C3⋊Dic3—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3C2311yescharacteristic
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3385—91noSylow
120C3×#125C2×D314yes—
121C3×C4×Q8C2×D314yes—
122Q8×Dic3—34no—
123Q8×Dic3—34no—
124C2×#215—34no—
125#897—64no—
126#896—64no—
127#896—64no—
128#893—34no—
129#893—34no—
130D3×C4⋊C4—64no—
131#890—34no—
132#888—34no—
133#888—34no—
134#888—34no—
135#888—64no—
136#888—64no—
137C4×D12—34no—
138#869—34no—
139#869—64no—
140C4×Dic6—34no—
141C4×Dic6—64no—
142C3×#107C2×D314yes—
143C3×#106C2×D314yes—
144C3×C4⋊C8C2×D314yes—
145C3×#103C2×D314yes—
146C3×#103C2×D314yes—
147#835—34no—
148#821—34no—
149#821—34no—
150#818—34no—
151#818—34no—
152#815—34no—
153Dic3⋊C8—34no—
154Dic3⋊C8—34no—
155C8×Dic3—34no—
156#809—34no—
157#808—34no—
158#808—34no—
159#807—34no—
160#807—34no—
161#807—34no—
162#803—34no—
163C22×C3⋊D3—21no—
164C32×Q8—21no—
165C32×Q8C2×Q812yes—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3C2×D411yescharacteristic
177C2×C3⋊Dic3C2×D411yescharacteristic
178C2×C3⋊Dic3C2×D411yescharacteristic
179C2×C3⋊Dic3C2×D411yescharacteristic
180C4⋊(C3⋊D3)—21no—
181C4⋊(C3⋊D3)C2×Q812yes—
182C4×C3⋊D3—42no—
183C4×C3⋊D3—81no—
184C4×C3⋊D3—81no—
185#634—22no—
186#634—81no—
187#634—81no—
188#634—81no—
189#634—81no—
190C32×C8—21no—
191C32×C8—21no—
192C3⋊(C3⋊C8)—21no—
193C3⋊(C3⋊C8)C2×Q812yes—
194Q82—91no—
195#554—91no—
196#501—91no—
197#501—91no—
198#500—91no—
199#479—91no—
200#479C3⋊D311yescharacteristic, complemented
201#477—91no—
202#476—91no—
203#474—91no—
204#474—91no—
205#446—91no—
206#440—91no—
207#440—91no—
208C4×SD16—91no—
209C2×C3×Q8C22×D314yes—
210C2×D12—34no—
211C2×C4×D3—64no—
212C2×C4×D3—64no—
213C2×C4×D3—64no—
214C2×Dic6—34no—
215C2×Dic6—64no—
216C2×Dic6—64no—
217C2×Dic6—64no—
218C2×Dic6—64no—
219C2×C3×C8C22×D314yes—
220C2×C3×C8C22×D314yes—
221C3×C4⋊C4—24no—
222C3×C4⋊C4—24no—
223C3×C4⋊C4—24no—
224C3×C4⋊C4C22×D314yes—
225C3×C4⋊C4C22×D314yes—
226C3×C4⋊C4C22×D314yes—
227C3×C42—24no—
228C3×C42C22×D314yes—
229#215—316no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232(C2×D3)⋊C4—64no—
233C4⋊Dic3—34no—
234C4⋊Dic3—34no—
235C4⋊Dic3—34no—
236C4⋊Dic3—34no—
237C4⋊Dic3—64no—
238C4⋊Dic3—64no—
239C4⋊Dic3—64no—
240C4⋊Dic3—64no—
241Dic3⋊C4—34no—
242Dic3⋊C4—34no—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247C4×Dic3—34no—
248C4×Dic3—34no—
249C4×Dic3—64no—
250C4×Dic3—64no—
251C2×C3⋊C8—34no—
252C2×C3⋊C8—34no—
253C22×C32C22×D411yescharacteristic
254C2×C3⋊D3—22no—
255C2×C3⋊D3—41no—
256C2×C3⋊D3—41no—
257C32×C4—22no—
258C32×C4—21no—
259C32×C4—21no—
260C32×C4—41no—
261C32×C4—41no—
262C32×C4—41no—
263C32×C4C22×Q811yescharacteristic
264C32×C42−1+411yescharacteristic
265C3⋊Dic3—21no—
266C3⋊Dic3—21no—
267C3⋊Dic3—21no—
268C3⋊Dic3—41no—
269C3⋊Dic3—41no—
270C3⋊Dic3—41no—
271C3⋊Dic3#13712yes—
272C2×SD16—91no—
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#125C2×C3⋊D311yescharacteristic
282C22⋊Q8—181no—
283C22⋊Q8—181no—
284C22⋊Q8—181no—
285C4×Q8—91no—
286C4×Q8—91no—
287C4×Q8—91no—
288C4×Q8—181no—
289C4×Q8C2×C3⋊D311yescharacteristic
290C4×D4—91no—
291C4×D4—91no—
292C4×D4—91no—
293C2×C4⋊C4—181no—
294#107—91no—
295#107—91no—
296#107—91no—
297#107—91no—
298#107—91no—
299#107C2×C3⋊D311yescharacteristic
300#106—91no—
301#106—91no—
302#106C2×C3⋊D311yescharacteristic
303C4⋊C8—91no—
304C4⋊C8—91no—
305C4⋊C8C2×C3⋊D311yescharacteristic
306#103—91no—
307#103C2×C3⋊D311yescharacteristic
308#103C2×C3⋊D311yescharacteristic
309#102—91no—
310#102—91no—
311#102—91no—
312#97—91no—
313#97—91no—
314C4×C8—91no—
315C22×D3—64no—
316C3×Q8—24no—
317C3×Q8D3×Q818yes—
318C2×C3×C4—24no—
319C2×C3×C4—24no—
320C2×C3×C4—24no—
321C2×C3×C4—24no—
322C2×C3×C4D3×D414yes—
323C2×C3×C4D3×D414yes—
324C2×C3×C4C23×D314yes—
325C2×Dic3—34no—
326C2×Dic3—34no—
327C2×Dic3—34no—
328C2×Dic3—34no—
329C2×Dic3—64no—
330C2×Dic3—64no—
331C2×Dic3—64no—
332D12—38no—
333D12—64no—
334C4×D3—128no—
335C4×D3—244no—
336C4×D3—244no—
337Dic6—68no—
338Dic6—244no—
339Dic6—244no—
340Dic6—244no—
341Dic6—244no—
342C3×C8—24no—
343C3×C8—24no—
344C3⋊C8—38no—
345C3⋊C8—64no—
346C2×C32D4×Q811yescharacteristic
347C2×C32C2×#13711yescharacteristic
348C2×C32#57611yescharacteristic
349C3⋊D3—42no—
350C2×Q8—91no—
351C2×Q8—181no—
352C2×Q8—181no—
353C2×Q8—181no—
354C2×Q8—181no—
355C2×Q8C22×C3⋊D311yescharacteristic
356C2×D4—91no—
357C22×C4—181no—
358C22×C4—181no—
359C22×C4—181no—
360SD16—94no—
361C2×C8—91no—
362C2×C8—91no—
363C2×C8C22×C3⋊D311yescharacteristic
364C2×C8C22×C3⋊D311yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—91no—
369C4⋊C4—91no—
370C4⋊C4—91no—
371C4⋊C4—91no—
372C4⋊C4—91no—
373C4⋊C4—91no—
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⋊C4C22×C3⋊D311yescharacteristic
383C4⋊C4C22×C3⋊D311yescharacteristic
384C4⋊C4C22×C3⋊D311yescharacteristic
385C22⋊C4—181no—
386C22⋊C4—181no—
387C22⋊C4—181no—
388C42—21no—
389C42—91no—
390C42—91no—
391C42—181no—
392C42—181no—
393C42C22×C3⋊D311yescharacteristic
394C22×C3C2×D3×D414yes—
395C2×D3—68no—
396C2×D3—124no—
397C2×D3—124no—
398C3×C4—28no—
399C3×C4—24no—
400C3×C4—24no—
401C3×C4—44no—
402C3×C4—44no—
403C3×C4—44no—
404C3×C4C2×D3×Q814yes—
405C3×C4#101014yes—
406Dic3—38no—
407Dic3—64no—
408Dic3—64no—
409Dic3—64no—
410Dic3—124no—
411Dic3—124no—
412Dic3—124no—
413C32#338511yescharacteristic, complemented, Sylow
414C23—181no—
415Q8—21no—
416Q8—182no—
417Q8—721no—
418Q8—721no—
419Q8—721no—
420Q8—721no—
421Q8Q8×C3⋊D312yes—
422D4—92no—
423D4—181no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—91no—
429C2×C4—91no—
430C2×C4—91no—
431C2×C4—91no—
432C2×C4—181no—
433C2×C4—181no—
434C2×C4—181no—
435C2×C4—362no—
436C2×C4—721no—
437C2×C4—721no—
438C2×C4D4×C3⋊D311yescharacteristic
439C2×C4D4×C3⋊D311yescharacteristic
440C2×C4C23×C3⋊D311yescharacteristic
441C8—21no—
442C8—21no—
443C8—92no—
444C8—181no—
445C2×C3#563214yes—
446C2×C3#576914yes—
447C2×C3D3×#13714yes—
448D3—128no—
449C22—182no—
450C22—361no—
451C22—361no—
452C22C2×D4×C3⋊D311yescharacteristic
453C4—22no—
454C4—21no—
455C4—21no—
456C4—41no—
457C4—41no—
458C4—41no—
459C4—92no—
460C4—181no—
461C4—181no—
462C4—181no—
463C4—361no—
464C4—361no—
465C4—361no—
466C4C2×Q8×C3⋊D311yescharacteristic
467C4#6436711yescharacteristic
468C3#8122314yescomplemented
469C2—362no—
470C2#1059610311yescharacteristic
471C2#1059624011yescharacteristic
472C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#479C2
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenter#479C3⋊D3
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. Q8×#634C2semidirect
3. C32×#479C2semidirect
4. #10592763C2semidirect
7. #10592573C2semidirect
9. #10592555C2semidirect
11. #10592527C2semidirect
13. #10592495C2semidirect
14. #10592492C2semidirect
62. C3×#479D3semidirect
95. #3755Q8semidirect
200. #479C3⋊D3semidirect
413. C32#3385semidirect
468. C3#81223semidirect

Maximal subgroups

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

subgroupindex
#105961612
Q8×#6342
C32×#4792
#105927632
#105927252
#105925892
#105925732
#105925692
#105925552
#105925452
#105925272
#105925162
#105924952
#105924922
#105924872
#812233