Finite Group Databasebeta

← #11794353

Subgroups — #11794353

Order 1152.

557 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63636C211yesmaximal, characteristic
2C3×#4964C211yesmaximal, characteristic, complemented
3C2×#63578C211yesmaximal, characteristic, complemented
4#10591117C211yesmaximal, characteristic, complemented
5#10591096C211yesmaximal, characteristic
6C2×#63559C211yesmaximal, characteristic
7C3×#4530C211yesmaximal, characteristic, complemented
8#70676—31nomaximal
9#68996—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63636—22no—
18C3×#808—21no—
19C3×#807—21no—
20#63578—22no—
21Dic3⋊(C3⋊C8)—22no—
22#63564—21no—
23#63564—21no—
24#63559—22no—
25C3×#428—31no—
26#5131—31no—
27C2×#823—31no—
28C2×#823—31no—
29C2×#822—31no—
30C2×#822—31no—
31#5119—31no—
32#5001—31no—
33#4999—31no—
34C2×#809—31no—
35C2×#809—31no—
36C2×#809—61no—
37#4964D311yescharacteristic, complemented
38C3×#343—31no—
39#4530D311yescharacteristic, complemented
40C23×C3⋊D3—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)Q812yes—
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)D412yes—
54C3×#217—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4×Dic3—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208D412yes—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#2063—91noSylow
68C22×D12—31no—
69C22×D12—31no—
70C22×D12—61no—
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C3×#117—31no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C4⋊C4C2×D311yescharacteristic
78#926C2×D311yescharacteristic
79C2×#208C2×D311yescharacteristic
80C2×#208C2×D311yescharacteristic
81C2×#208C2×D311yescharacteristic
82C22×C3⋊C8—31no—
83C22×C3⋊C8—31no—
84C22×C3⋊C8—61no—
85C3×#107—61no—
86C3×#106—61no—
87#823—62no—
88#823—62no—
89#822—62no—
90#822—62no—
91#821—61no—
92#821—61no—
93Dic3⋊C8—62no—
94#809—61no—
95#809—61no—
96#809—62no—
97#809—62no—
98#809—64no—
99#808—21no—
100#807—21no—
101C4⋊(C3⋊C8)—62no—
102C23×C32#4111yescharacteristic
103C22×C3⋊D3—22no—
104C22×C3⋊D3—41no—
105C22×C3⋊D3—41no—
106C22×C3⋊D3—81no—
107C22×C3⋊D3—81no—
108C2×C32×C4—41no—
109C2×C32×C4—81no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×Q811yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C4⋊(C3⋊D3)—22no—
117C4⋊(C3⋊D3)—22no—
118C4⋊(C3⋊D3)—41no—
119C4⋊(C3⋊D3)—41no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C3⋊(C3⋊C8)—22no—
123C3×C3⋊C8—22no—
124C3×C3⋊C8—41no—
125C3×C3⋊C8—41no—
126C2×#108—91no—
127#428—31no—
128#424—91no—
129#418—91no—
130C2×#102—91no—
131C2×#100—91no—
132#343—31no—
133C23×D3—61no—
134C23×D3—61no—
135C23×D3—121no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—41no—
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C2×D12—32no—
143C2×D12—32no—
144C2×D12—62no—
145C2×D12—62no—
146C2×D12—62no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—121no—
158C2×D12—121no—
159C2×D12—121no—
160C3×M16—32no—
161C3×M16—61no—
162C3×M16—61no—
163C3×M16—61no—
164C3×M16—61no—
165C3×M16—61no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—41no—
177C3×C22⋊C4—61no—
178C3×C42—61no—
179#217—21no—
180C4⋊Dic3#6711yescharacteristic
181C4⋊Dic3#6711yescharacteristic
182C4×Dic3—21no—
183#208—21no—
184#208—21no—
185#208—21no—
186#208—21no—
187#208—21no—
188#208D1212yes—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—32no—
193C2×C3⋊C8—32no—
194C2×C3⋊C8—62no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—121no—
200C2×C3⋊C8—121no—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32#12111yescharacteristic
204C22×C32C22⋊Q811yescharacteristic
205C22×C32#12611yescharacteristic
206C2×C3⋊D3—42no—
207C2×C3⋊D3—82no—
208C2×C3⋊D3—81no—
209C2×C3⋊D3—81no—
210C2×C3⋊D3—82no—
211C32×C4—81no—
212C32×C4#12111yescharacteristic
213C32×C4#12111yescharacteristic
214C32×C4C22⋊Q811yescharacteristic
215C32×C4C22⋊Q811yescharacteristic
216C3×Dic3—41no—
217C3×Dic3—41no—
218C22×D4—91no—
219C2×M16—31no—
220C2×M16—31no—
221C2×M16—31no—
222C22×C8—91no—
223#117—31no—
224C2×C4⋊C4D3211yescharacteristic
225#108—182no—
226#107—61no—
227#106—61no—
228C4⋊C8—182no—
229#102—182no—
230#102—181no—
231#102—181no—
232#100—182no—
233C23×C3—21no—
234C23×C3#23511yescharacteristic
235C23×C3#23711yescharacteristic
236C22×D3—62no—
237C22×D3—62no—
238C22×D3—122no—
239C22×D3—122no—
240C22×D3—122no—
241C22×D3—121no—
242C22×D3—121no—
243C22×D3—121no—
244C22×D3—121no—
245C22×D3—242no—
246C22×D3—242no—
247C22×D3—241no—
248C22×D3—241no—
249C22×D3—241no—
250C22×D3—241no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—42no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—82no—
263C2×C3×C4—81no—
264C2×C3×C4—81no—
265C2×C3×C4C2×D1211yescharacteristic
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4#23511yescharacteristic
268C2×C3×C4#23511yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×Q811yescharacteristic
274C2×C3×C4D3×Q811yescharacteristic
275C2×C3×C4#23911yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277C2×Dic3—21no—
278C2×Dic3—21no—
279D12—64no—
280D12—62no—
281D12—62no—
282D12—62no—
283D12—62no—
284D12—122no—
285D12—122no—
286D12—122no—
287D12—121no—
288D12—121no—
289D12—121no—
290D12—121no—
291C3×C8—62no—
292C3×C8—121no—
293C3×C8—121no—
294C3⋊C8—22no—
295C3⋊C8—41no—
296C3⋊C8—41no—
297C3⋊C8—62no—
298C3⋊C8—62no—
299C3⋊C8—122no—
300C2×C32—21no—
301C2×C32—21no—
302C2×C32#39611yescharacteristic
303C2×C32#47111yescharacteristic
304C2×C32#47211yescharacteristic
305C3⋊D3—82no—
306C24—181no—
307C2×D4—92no—
308C2×D4—181no—
309C2×D4—181no—
310C2×D4—181no—
311C2×D4—181no—
312C2×D4—181no—
313C22×C4—21no—
314C22×C4C2×D3211yescharacteristic
315M16—32no—
316M16—61no—
317M16—61no—
318M16—61no—
319M16—61no—
320M16—61no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—61no—
324C2×C8—92no—
325C2×C8—181no—
326C2×C8—181no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—31no—
330C4⋊C4—31no—
331C22⋊C4—61no—
332C42—61no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3#87611yescharacteristic
343C22×C3#88411yescharacteristic
344C22×C3#89611yescharacteristic
345C22×C3#89711yescharacteristic
346C22×C3#89811yescharacteristic
347C22×C3#93911yescharacteristic
348C2×D3—124no—
349C2×D3—122no—
350C2×D3—122no—
351C2×D3—244no—
352C2×D3—244no—
353C2×D3—242no—
354C2×D3—242no—
355C2×D3—242no—
356C2×D3—242no—
357C2×D3—241no—
358C2×D3—241no—
359C2×D3—241no—
360C2×D3—241no—
361C2×D3—242no—
362C2×D3—242no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—82no—
368C3×C4—81no—
369C3×C4—81no—
370C3×C4—121no—
371C3×C4—121no—
372C3×C4#88411yescharacteristic
373C3×C4#88411yescharacteristic
374C3×C4#89511yescharacteristic
375C3×C4#89611yescharacteristic
376C3×C4#89611yescharacteristic
377C3×C4#89611yescharacteristic
378C3×C4#93011yescharacteristic
379C3×C4#94611yescharacteristic
380Dic3—41no—
381Dic3—41no—
382C32#206311yescharacteristic, complemented, Sylow
383C23—182no—
384C23—361no—
385C23—361no—
386C23—721no—
387C23—721no—
388C23#380411yescharacteristic
389D4—182no—
390D4—182no—
391D4—361no—
392D4—361no—
393C2×C4—41no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—81no—
397C2×C4#379711yescharacteristic
398C2×C4#379811yescharacteristic
399C2×C4#379911yescharacteristic
400C2×C4D3×D1211yescharacteristic
401C2×C4D3×#6711yescharacteristic
402C2×C4#381111yescharacteristic
403C8—62no—
404C8—121no—
405C8—121no—
406C8—182no—
407C2×C3—22no—
408C2×C3—22no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3#467611yescharacteristic
417C2×C3#474911yescharacteristic
418C2×C3#475411yescharacteristic
419C2×C3#499411yescharacteristic
420C2×C3#519911yescharacteristic
421C2×C3#520311yescharacteristic
422D3—244no—
423D3—242no—
424D3—242no—
425C22—21no—
426C22—21no—
427C22—362no—
428C22—722no—
429C22—722no—
430C22—721no—
431C22—721no—
432C22#6386811yescharacteristic
433C22#6389511yescharacteristic
434C22#6397111yescharacteristic
435C4—81no—
436C4—121no—
437C4—121no—
438C4#6386511yescharacteristic
439C4#6388811yescharacteristic
440C4#6390611yescharacteristic
441C4#6391011yescharacteristic
442C3—21no—
443C3#6899611yescharacteristic, complemented
444C3#7067611yescharacteristic, complemented
445C2—21no—
446C2—21no—
447C2—722no—
448C2#1059134711yescharacteristic
449C2#1059150811yescharacteristic
450C2#1059164311yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2063
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4964C2semidirect
3. C2×#63578C2semidirect
4. #10591117C2semidirect
7. C3×#4530C2semidirect
37. #4964D3semidirect
39. #4530D3semidirect
382. C32#2063semidirect
443. C3#68996semidirect
444. C3#70676semidirect

Maximal subgroups

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

subgroupindex
C2×#636362
C3×#49642
C2×#635782
#105911172
#105910962
C2×#635592
C3×#45302
#706763
#689963