Finite Group Databasebeta

← #11789674

Subgroups — #11789674

Order 1152.

565 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63659C211yesmaximal, characteristic
2C2×C3×#833C211yesmaximal, characteristic
3C3×#5215C211yesmaximal, characteristic
4#10591131C211yesmaximal, characteristic, complemented
5#10591057C211yesmaximal, characteristic, complemented
6#10589168C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#70318—31nomaximal
9#70072—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63659—21no—
18#63659—21no—
19C3×#833C414yescomplemented
20C3×#832—21no—
21C3×#832—21no—
22#63575—21no—
23#63573—21no—
24#63554—21no—
25Dic3×C3⋊C8—21no—
26C3×#418—31no—
27C2×C3×#100—31no—
28C2×#833D311yescharacteristic
29#5215D311yescharacteristic
30C2×#832—31no—
31C2×#832—31no—
32C2×#832—61no—
33#5122—31no—
34#5121—31no—
35#4997—31no—
36#4995—31no—
37#4558—31no—
38#4558—31no—
39#4554—31no—
40#4554—31no—
41C24×C32—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4C2×C412yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)D411yescharacteristic
55C2×C3⋊(C3⋊C8)D411yescharacteristic
56C3×#217—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4×Dic3—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208—21no—
64C3×#208C2×C412yes—
65C3×#208C2×C412yes—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#1931—91noSylow
70C22×C3×D4—21no—
71C22×C3×D4C2×D311yescharacteristic
72C22×C3×D4C2×D311yescharacteristic
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C3×#117—31no—
77#926C2×D311yescharacteristic
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—61no—
81C2×#208C2×D311yescharacteristic
82C2×#208C2×D311yescharacteristic
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8—31no—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—61no—
87C3×#102—61no—
88C3×#102—61no—
89C3×#100—34no—
90#833Dic314yescomplemented
91#832—21no—
92#832—21no—
93#832—61no—
94#832—61no—
95#832—61no—
96#832—61no—
97#832—62no—
98#832—62no—
99#818—61no—
100#817—61no—
101#815—61no—
102C8×Dic3—61no—
103#808—61no—
104#807—61no—
105#803—61no—
106C4×C3⋊C8—61no—
107C23×C32—22no—
108C23×C32—41no—
109C23×C32—41no—
110C23×C32—81no—
111C23×C32—81no—
112C23×C32#4111yescharacteristic
113C32×D4—22no—
114C32×D4—22no—
115C32×D4—41no—
116C32×D4—41no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—81no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C3⋊(C3⋊C8)—21no—
128C3⋊(C3⋊C8)—21no—
129C3×C3⋊C8—22no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—41no—
132#428—91no—
133#418—31no—
134C2×#102—91no—
135C2×#100—31no—
136#405—91no—
137#343—91no—
138#341—91no—
139C24×C3—21no—
140C24×C3—21no—
141C24×C3—41no—
142C2×C3×D4—22no—
143C2×C3×D4—22no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—22no—
155C2×C3×D4—41no—
156C2×C3×D4—41no—
157C2×C3×D4—41no—
158C2×C3×D4C4×D312yes—
159C2×C3×D4C2×Dic312yes—
160C22×C3×C4—21no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—121no—
166C3×M16—32no—
167C3×M16—32no—
168C3×M16—61no—
169C3×M16—61no—
170C3×M16—61no—
171C3×M16—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—31no—
177C3×C22⋊C4—61no—
178C3×C42—61no—
179#217—21no—
180C4⋊Dic3—62no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—121no—
186C4⋊Dic3#6711yescharacteristic
187C4⋊Dic3#6711yescharacteristic
188C4×Dic3—21no—
189#208—21no—
190#208—21no—
191#208—21no—
192#208—21no—
193#208C2×Dic312yes—
194#208C2×Dic312yes—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—31no—
199C2×C3⋊C8—31no—
200C2×C3⋊C8—31no—
201C2×C3⋊C8—31no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—121no—
209C2×C3⋊C8—121no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—42no—
213C22×C32—82no—
214C22×C32—82no—
215C22×C32—81no—
216C22×C32—81no—
217C22×C32#11711yescharacteristic
218C22×C32#12111yescharacteristic
219C22×C32#12611yescharacteristic
220C32×C4C4×D411yescharacteristic
221C32×C4C4×D411yescharacteristic
222C32×C4#12311yescharacteristic
223C32×C4#12411yescharacteristic
224C3⋊Dic3—81no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C22×D4D3211yescharacteristic
228C2×M16—31no—
229C2×M16—31no—
230C2×M16—31no—
231C22×C8—91no—
232#117—31no—
233C2×C4⋊C4—91no—
234#107—181no—
235#106—181no—
236#102—61no—
237#102—61no—
238#102—181no—
239#102—181no—
240#100—34no—
241#97—181no—
242C4×C8—181no—
243C23×C3—22no—
244C23×C3—22no—
245C23×C3—21no—
246C23×C3—42no—
247C23×C3—42no—
248C23×C3—42no—
249C23×C3—41no—
250C23×C3—41no—
251C23×C3—41no—
252C23×C3—41no—
253C23×C3—81no—
254C23×C3—81no—
255C23×C3—81no—
256C23×C3—81no—
257C23×C3—82no—
258C23×C3—82no—
259C23×C3#23511yescharacteristic
260C23×C3#23711yescharacteristic
261C3×D4—24no—
262C3×D4—22no—
263C3×D4—22no—
264C3×D4—22no—
265C3×D4—22no—
266C3×D4—42no—
267C3×D4—42no—
268C3×D4—42no—
269C3×D4—41no—
270C3×D4—41no—
271C3×D4—41no—
272C3×D4—41no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4#23511yescharacteristic
283C2×C3×C4#23511yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4#23711yescharacteristic
289C2×C3×C4#23711yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4C22×Dic311yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—122no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—242no—
299C2×Dic3—241no—
300C2×Dic3—241no—
301C3×C8—62no—
302C3×C8—62no—
303C3×C8—121no—
304C3⋊C8—22no—
305C3⋊C8—22no—
306C3⋊C8—41no—
307C3⋊C8—61no—
308C3⋊C8—61no—
309C3⋊C8—61no—
310C3⋊C8—61no—
311C3⋊C8—121no—
312C3⋊C8—121no—
313C2×C32—21no—
314C2×C32—21no—
315C2×C32—82no—
316C2×C32#38811yescharacteristic
317C2×C32#47111yescharacteristic
318C2×C32#47211yescharacteristic
319C24—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4D3×Dic312yes—
326C22×C4—181no—
327C22×C4C2×D3211yescharacteristic
328M16—32no—
329M16—32no—
330M16—61no—
331M16—61no—
332M16—61no—
333M16—61no—
334C2×C8—61no—
335C2×C8—61no—
336C2×C8—61no—
337C2×C8—91no—
338C2×C8—91no—
339C2×C8—181no—
340C2×C8—181no—
341C4⋊C4—31no—
342C4⋊C4—31no—
343C4⋊C4—181no—
344C4⋊C4—181no—
345C22⋊C4—61no—
346C42—61no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—44no—
357C22×C3—42no—
358C22×C3—42no—
359C22×C3—82no—
360C22×C3—82no—
361C22×C3—84no—
362C22×C3—84no—
363C22×C3—82no—
364C22×C3—82no—
365C22×C3—82no—
366C22×C3—82no—
367C22×C3—81no—
368C22×C3—81no—
369C22×C3—81no—
370C22×C3—81no—
371C22×C3#87711yescharacteristic
372C22×C3#87911yescharacteristic
373C22×C3#87911yescharacteristic
374C22×C3#88411yescharacteristic
375C22×C3#92611yescharacteristic
376C22×C3#93911yescharacteristic
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—121no—
382C3×C4—121no—
383C3×C4#67⋊C411yescharacteristic
384C3×C4#88311yescharacteristic
385C3×C4#88311yescharacteristic
386C3×C4#88511yescharacteristic
387C3×C4C4×#6711yescharacteristic
388C3×C4D4×Dic311yescharacteristic
389C3×C4D4×Dic311yescharacteristic
390C3×C4#93611yescharacteristic
391Dic3—41no—
392Dic3—41no—
393Dic3—242no—
394Dic3—241no—
395Dic3—241no—
396C32#193111yescharacteristic, complemented, Sylow
397C23—22no—
398C23—41no—
399C23—41no—
400C23—81no—
401C23—81no—
402C23#380411yescharacteristic
403D4—22no—
404D4—22no—
405D4—41no—
406D4—41no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—361no—
410C2×C4—721no—
411C2×C4C2×D3×Dic311yescharacteristic
412C2×C4#380411yescharacteristic
413C2×C4#380411yescharacteristic
414C2×C4#380511yescharacteristic
415C2×C4D3×#6711yescharacteristic
416C2×C4#381111yescharacteristic
417C8—62no—
418C8—62no—
419C8—121no—
420C8—181no—
421C8—181no—
422C2×C3—22no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—84no—
432C2×C3—82no—
433C2×C3—82no—
434C2×C3#474811yescharacteristic
435C2×C3#474911yescharacteristic
436C2×C3#494511yescharacteristic
437C2×C3#495111yescharacteristic
438C2×C3#519911yescharacteristic
439C2×C3#520011yescharacteristic
440C22—21no—
441C22—21no—
442C22—42no—
443C22—82no—
444C22—82no—
445C22—81no—
446C22—81no—
447C22#6395511yescharacteristic
448C22#6395611yescharacteristic
449C22#6397111yescharacteristic
450C4—121no—
451C4—121no—
452C4—721no—
453C4#6395911yescharacteristic
454C4Dic3×#6711yescharacteristic
455C4#67⋊Dic311yescharacteristic
456C4#6397511yescharacteristic
457C3—21no—
458C3#7007211yescharacteristic, complemented
459C3#7031811yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—82no—
463C2#1059150711yescharacteristic
464C2#1059150811yescharacteristic
465C2#1059170211yescharacteristic
subgroupG/H
centerC22#63971
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#121
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1931
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591131C2semidirect
5. #10591057C2semidirect
6. #10589168C2semidirect
7. #10589165C2semidirect
19. C3×#833C4semidirect
90. #833Dic3semidirect
396. C32#1931semidirect
458. C3#70072semidirect
459. C3#70318semidirect

Maximal subgroups

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

subgroupindex
C2×#636592
C2×C3×#8332
C3×#52152
#105911312
#105910572
#105891682
#105891652
#703183
#700723