Finite Group Databasebeta

← #11795436

Subgroups — #11795436

Order 1152.

639 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#821C211yesmaximal, characteristic
2C2×C3×#818C211yesmaximal, characteristic, complemented
3#10591359C211yesmaximal, characteristic, complemented
4#10591323C211yesmaximal, characteristic
5C2×#63576C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7#10589416C211yesmaximal, characteristic, complemented
8#70641—31nomaximal
9#70183—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×#3724—22no—
18C2×(C2×D3)⋊Dic3—22no—
19C3×#821—22no—
20C3×#818—22no—
21#63576—22no—
22#63562—22no—
23C2×C3×#107—31no—
24C2×C3×#102—31no—
25#5221—31no—
26C2×#832—31no—
27C2×#821D311yescharacteristic
28C2×#818D311yescharacteristic, complemented
29#4988—31no—
30#4975—31no—
31#4975—31no—
32C2×#809—31no—
33C2×#807—31no—
34C2×#807—31no—
35#4550—31no—
36#4550—31no—
37#4550—61no—
38C23×C3×D3—21no—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3D412yes—
41C22×C3×Dic3—21no—
42C22×C3×Dic3—21no—
43C22×C3×Dic3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12Q812yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)D412yes—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64#3724—44no—
65(C2×D3)⋊Dic3—44no—
66#2093—91noSylow
67C22×C3×D4—31no—
68C22×D12C2×D311yescharacteristic
69C22×C3×C8—21no—
70C22×C3×C8C2×D311yescharacteristic
71C22×C3×C8C2×D311yescharacteristic
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—31no—
75C2×#217—62no—
76C2×(C2×D3)⋊C4—62no—
77C2×C4⋊Dic3C2×D311yescharacteristic
78C2×C4⋊Dic3C2×D311yescharacteristic
79C2×C4⋊Dic3C2×D311yescharacteristic
80C2×Dic3⋊C4—62no—
81C2×Dic3⋊C4—62no—
82C2×C4×Dic3—31no—
83C2×C4×Dic3—31no—
84C2×C4×Dic3—61no—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—31no—
87C22×C3⋊C8—61no—
88C3×#107—62no—
89C3×#102—62no—
90#832—62no—
91#821—22no—
92#818—22no—
93#809—62no—
94#807—62no—
95#807—62no—
96C23×C32C2×D411yescharacteristic
97C22×C3×D3—22no—
98C22×C3×D3—41no—
99C22×C3×D3—41no—
100C22×C3×D3—42no—
101C22×C3×D3—42no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×Q811yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3D814yes—
111C2×C3×Dic3—41no—
112C2×C3×Dic3—41no—
113C2×C3×Dic3—41no—
114C2×C3×Dic3—42no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—42no—
117C3×D12—22no—
118C3×D12—22no—
119C3×D12—41no—
120C3×D12—41no—
121C32×C8—22no—
122C3⋊(C3⋊C8)—22no—
123C2×#107—31no—
124C2×#107—91no—
125C2×#102—31no—
126C2×#102—91no—
127#390—91no—
128#384—91no—
129#336—91no—
130C24×C3—61no—
131C23×D3—21no—
132C2×C3×D4—32no—
133C2×C3×D4—61no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C22×C3×C4—21no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C22×C3×C4—61no—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C22×Dic3—21no—
145C22×Dic3—21no—
146C22×Dic3—21no—
147C22×Dic3—32no—
148C22×Dic3—32no—
149C22×Dic3—62no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12Dic612yes—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—22no—
161C2×C3×C8—41no—
162C2×C3×C8—41no—
163C2×C3×C8#6712yes—
164C2×C3×C8#6712yes—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171#217—124no—
172(C2×D3)⋊C4—124no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179Dic3⋊C4—124no—
180Dic3⋊C4—124no—
181C4×Dic3—61no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—61no—
185C4×Dic3—121no—
186C4×Dic3—121no—
187C2×C3⋊C8—32no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—62no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—121no—
195C2×C3⋊C8—121no—
196C22×C32C22⋊Q811yescharacteristic
197C22×C32#12311yescharacteristic
198C22×C32#12711yescharacteristic
199C22×C32C2×D812yes—
200C22×C32#13712yes—
201C2×C3×D3—42no—
202C2×C3×D3—44no—
203C2×C3×D3—82no—
204C2×C3×D3—81no—
205C2×C3×D3—81no—
206C32×C4C22⋊Q811yescharacteristic
207C32×C4C22⋊Q811yescharacteristic
208C32×C4#12311yescharacteristic
209C32×C4#12311yescharacteristic
210C3⋊Dic3—24no—
211C3×Dic3—81no—
212C3×Dic3—81no—
213C3×Dic3—81no—
214C22×D4—31no—
215C22×C8—91no—
216C22×C8D3211yescharacteristic
217C2×C4⋊C4—31no—
218C2×C4⋊C4—31no—
219C2×C4⋊C4—31no—
220C2×C4⋊C4—182no—
221C2×C22⋊C4—182no—
222C2×C42—91no—
223#107—62no—
224#107—182no—
225#102—62no—
226#102—182no—
227C23×C3—21no—
228C23×C3—62no—
229C23×C3—121no—
230C23×C3—122no—
231C23×C3—122no—
232C23×C3—121no—
233C23×C3D3×D411yescharacteristic
234C23×C3D3×D411yescharacteristic
235C22×D3—22no—
236C22×D3—41no—
237C22×D3—42no—
238C22×D3—42no—
239C22×D3—41no—
240C3×D4—62no—
241C3×D4—62no—
242C3×D4—121no—
243C3×D4—121no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—122no—
251C2×C3×C4—122no—
252C2×C3×C4—122no—
253C2×C3×C4—121no—
254C2×C3×C4—121no—
255C2×C3×C4—121no—
256C2×C3×C4C2×Dic611yescharacteristic
257C2×C3×C4#23511yescharacteristic
258C2×C3×C4#23511yescharacteristic
259C2×C3×C4#23511yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4#23711yescharacteristic
263C2×C3×C4#23711yescharacteristic
264C2×C3×C4D3×Q811yescharacteristic
265C2×C3×C4#23911yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×Dic3—34no—
269C2×Dic3—34no—
270C2×Dic3—42no—
271C2×Dic3—42no—
272C2×Dic3—42no—
273C2×Dic3—41no—
274C2×Dic3—41no—
275C2×Dic3—41no—
276C2×Dic3—64no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—122no—
282C2×Dic3—122no—
283D12—22no—
284D12—22no—
285D12—41no—
286D12—41no—
287C3×C8—22no—
288C3×C8—22no—
289C3×C8—42no—
290C3⋊C8—62no—
291C3⋊C8—62no—
292C3⋊C8—122no—
293C2×C32#39911yescharacteristic
294C2×C32#47412yes—
295C2×C32#48012yes—
296C2×C32#49311yescharacteristic
297C2×C32#49711yescharacteristic
298C3×D3—82no—
299C24—61no—
300C2×D4—32no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—61no—
304C2×D4—61no—
305C2×D4—61no—
306C22×C4—61no—
307C22×C4—61no—
308C22×C4—61no—
309C22×C4—92no—
310C22×C4C2×D3211yescharacteristic
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—92no—
314C2×C8—181no—
315C2×C8—181no—
316C2×C8#62512yes—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4—364no—
324C22⋊C4—364no—
325C42—181no—
326C42—181no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—124no—
333C22×C3—122no—
334C22×C3—242no—
335C22×C3—241no—
336C22×C3—241no—
337C22×C3#87811yescharacteristic
338C22×C3#88311yescharacteristic
339C22×C3#89411yescharacteristic
340C22×C3#89611yescharacteristic
341C22×C3D3×D812yes—
342C22×C3D3×D812yes—
343C22×C3#91512yes—
344C22×C3#91812yes—
345C22×C3#94011yescharacteristic
346C22×C3#94011yescharacteristic
347C2×D3—42no—
348C2×D3—44no—
349C2×D3—81no—
350C2×D3—81no—
351C2×D3—82no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—241no—
357C3×C4—241no—
358C3×C4—241no—
359C3×C4#87811yescharacteristic
360C3×C4#88311yescharacteristic
361C3×C4#89411yescharacteristic
362C3×C4#89611yescharacteristic
363C3×C4#92411yescharacteristic
364C3×C4#92911yescharacteristic
365C3×C4#93511yescharacteristic
366C3×C4#94611yescharacteristic
367Dic3—64no—
368Dic3—64no—
369Dic3—81no—
370Dic3—81no—
371Dic3—81no—
372Dic3—124no—
373C32#209311yescharacteristic, complemented, Sylow
374C23—62no—
375C23—122no—
376C23—122no—
377C23—121no—
378C23—121no—
379C23#380211yescharacteristic
380D4—62no—
381D4—62no—
382D4—121no—
383D4—121no—
384C2×C4—94no—
385C2×C4—122no—
386C2×C4—122no—
387C2×C4—122no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4—121no—
391C2×C4—182no—
392C2×C4—182no—
393C2×C4D3×Dic611yescharacteristic
394C2×C4#379911yescharacteristic
395C2×C4#380211yescharacteristic
396C2×C4#380411yescharacteristic
397C2×C4#380411yescharacteristic
398C2×C4C2×#62511yescharacteristic
399C8—22no—
400C8—182no—
401C2×C3—22no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—22no—
406C2×C3—242no—
407C2×C3#475912yes—
408C2×C3#477412yes—
409C2×C3#488212yes—
410C2×C3#489012yes—
411C2×C3#494911yescharacteristic
412C2×C3#499311yescharacteristic
413C2×C3#515111yescharacteristic
414C2×C3#515111yescharacteristic
415C2×C3#516711yescharacteristic
416C2×C3#519011yescharacteristic
417D3—82no—
418C22—124no—
419C22—122no—
420C22—241no—
421C22—241no—
422C22—242no—
423C22#6379712yes—
424C22#6381112yes—
425C22#6385411yescharacteristic
426C22#6389911yescharacteristic
427C22#6391411yescharacteristic
428C4—184no—
429C4—241no—
430C4—241no—
431C4—241no—
432C4#6385411yescharacteristic
433C4#6385611yescharacteristic
434C4#6389911yescharacteristic
435C4#6396111yescharacteristic
436C3—21no—
437C3#7018311yescharacteristic, complemented
438C3#7064111yescharacteristic, complemented
439C2—242no—
440C2#1059065012yes—
441C2#1059077812yes—
442C2#1059087011yescharacteristic
443C2#1059088611yescharacteristic
444C2#1059132411yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#2093
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#818C2semidirect
3. #10591359C2semidirect
5. C2×#63576C2semidirect
7. #10589416C2semidirect
28. C2×#818D3semidirect
373. C32#2093semidirect
437. C3#70183semidirect
438. C3#70641semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8212
C2×C3×#8182
#105913592
#105913232
C2×#635762
C2×#635622
#105894162
#706413
#701833