Finite Group Databasebeta

← #11789668

Subgroups — #11789668

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×#63648C211yesmaximal, characteristic
2C3×#5101C211yesmaximal, characteristic, complemented
3#10591131C211yesmaximal, characteristic, complemented
4#10591096C211yesmaximal, characteristic
5C2×#63559C211yesmaximal, characteristic
6C3×#4552C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#69892—31nomaximal
9#68931—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63648—21no—
18#63648—21no—
19C3×#815—21no—
20C3×C8×Dic3—21no—
21#63575—21no—
22#63573—21no—
23#63564—21no—
24#63564—21no—
25#63559C414yescomplemented
26C3×#405—31no—
27#5131—31no—
28C2×#823—31no—
29C2×#823—31no—
30#5121—31no—
31C2×#821—31no—
32C2×#821—31no—
33C2×#821—61no—
34#5101D311yescharacteristic, complemented
35#5001—31no—
36#4995—31no—
37C3×#341—31no—
38#4554—31no—
39#4554—31no—
40#4552D311yescharacteristic, complemented
41C23×C3⋊D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—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)—21no—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D411yescharacteristic
53C2×C32×C8D411yescharacteristic
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
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×D12—31no—
71C22×D12—31no—
72C22×D12—61no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C22×C3×C8—21no—
77C22×C3×C8C2×D311yescharacteristic
78C22×C3×C8C2×D311yescharacteristic
79C3×#117—31no—
80#926C2×D311yescharacteristic
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C2×#208C2×D311yescharacteristic
87C3×#97—61no—
88C3×C4×C8—61no—
89#823—34no—
90#823—34no—
91#821—62no—
92#821—62no—
93#821—61no—
94#821—61no—
95#821—61no—
96#821—61no—
97#821—61no—
98#821—61no—
99#818—61no—
100#817—61no—
101#815—21no—
102C8×Dic3—21no—
103#809—61no—
104#809—61no—
105#808—61no—
106#807—61no—
107C23×C32#4111yescharacteristic
108C22×C3⋊D3—22no—
109C22×C3⋊D3—41no—
110C22×C3⋊D3—41no—
111C22×C3⋊D3—81no—
112C22×C3⋊D3—81no—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3—81no—
121C4⋊(C3⋊D3)—22no—
122C4⋊(C3⋊D3)—22no—
123C4⋊(C3⋊D3)—41no—
124C4⋊(C3⋊D3)—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C32×C8—21no—
128C32×C8—21no—
129C3×C3⋊C8—22no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—41no—
132#428—91no—
133#418—91no—
134C2×#102—91no—
135C2×#100—91no—
136#405—31no—
137#343—91no—
138#341—31no—
139C23×D3—61no—
140C23×D3—61no—
141C23×D3—121no—
142C22×C3×C4—21no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×Dic3—61no—
146C22×Dic3—61no—
147C22×Dic3—121no—
148C2×D12—32no—
149C2×D12—32no—
150C2×D12—62no—
151C2×D12—62no—
152C2×D12—62no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—61no—
159C2×D12—61no—
160C2×D12—61no—
161C2×D12—61no—
162C2×D12—61no—
163C2×D12—121no—
164C2×D12—121no—
165C2×D12—121no—
166C3×M16—32no—
167C3×M16—32no—
168C3×M16—61no—
169C3×M16—61no—
170C3×M16—61no—
171C3×M16—61no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—41no—
179C2×C3×C8—41no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8D1211yescharacteristic
184C2×C3×C8D1211yescharacteristic
185C2×C3×C8#6711yescharacteristic
186C2×C3×C8#6711yescharacteristic
187C3×C4⋊C4—31no—
188C3×C4⋊C4—31no—
189C3×C22⋊C4—61no—
190C3×C42—61no—
191#217—21no—
192C4⋊Dic3—62no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—121no—
198C4⋊Dic3D1211yescharacteristic
199C4⋊Dic3D1211yescharacteristic
200C4×Dic3—21no—
201#208—21no—
202#208—21no—
203#208—21no—
204#208—21no—
205#208C4×D312yes—
206#208C4×D312yes—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#11711yescharacteristic
213C22×C32#12111yescharacteristic
214C22×C32#12611yescharacteristic
215C2×C3⋊D3—42no—
216C2×C3⋊D3—82no—
217C2×C3⋊D3—81no—
218C2×C3⋊D3—81no—
219C2×C3⋊D3—82no—
220C32×C4C4×D411yescharacteristic
221C32×C4C4×D411yescharacteristic
222C32×C4#12311yescharacteristic
223C32×C4#12411yescharacteristic
224C3⋊Dic3—81no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C22×D4—91no—
228C2×M16—31no—
229C2×M16—31no—
230C2×M16—31no—
231C22×C8D3211yescharacteristic
232#117—31no—
233C2×C4⋊C4—91no—
234#107—181no—
235#106—181no—
236#102—181no—
237#102—181no—
238#102—181no—
239#102—181no—
240#100—94no—
241#97—61no—
242C4×C8—61no—
243C23×C3—21no—
244C23×C3#23511yescharacteristic
245C23×C3#23911yescharacteristic
246C22×D3—62no—
247C22×D3—62no—
248C22×D3—122no—
249C22×D3—122no—
250C22×D3—122no—
251C22×D3—121no—
252C22×D3—121no—
253C22×D3—121no—
254C22×D3—121no—
255C22×D3—242no—
256C22×D3—242no—
257C22×D3—241no—
258C22×D3—241no—
259C22×D3—241no—
260C22×D3—241no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4C2×D1211yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4#23511yescharacteristic
275C2×C3×C4#23511yescharacteristic
276C2×C3×C4#23511yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4#23711yescharacteristic
279C2×C3×C4#23711yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—122no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286C2×Dic3—242no—
287C2×Dic3—241no—
288C2×Dic3—241no—
289D12—64no—
290D12—62no—
291D12—62no—
292D12—62no—
293D12—62no—
294D12—122no—
295D12—122no—
296D12—122no—
297D12—121no—
298D12—121no—
299D12—121no—
300D12—121no—
301C3×C8—21no—
302C3×C8—21no—
303C3×C8—21no—
304C3×C8—21no—
305C3×C8—41no—
306C3×C8—41no—
307C3×C8—62no—
308C3×C8—62no—
309C3×C8—121no—
310C3⋊C8—22no—
311C3⋊C8—22no—
312C3⋊C8—41no—
313C2×C32—21no—
314C2×C32—21no—
315C2×C32#38811yescharacteristic
316C2×C32#47111yescharacteristic
317C2×C32#47211yescharacteristic
318C3⋊D3—82no—
319C24—181no—
320C2×D4—92no—
321C2×D4—181no—
322C2×D4—181no—
323C2×D4—181no—
324C2×D4—181no—
325C2×D4—181no—
326C22×C4—181no—
327C22×C4C2×D3211yescharacteristic
328M16—32no—
329M16—32no—
330M16—61no—
331M16—61no—
332M16—61no—
333M16—61no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—61no—
337C2×C8—61no—
338C2×C8—61no—
339C2×C8#62611yescharacteristic
340C2×C8#62611yescharacteristic
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#87211yescharacteristic
357C22×C3#87611yescharacteristic
358C22×C3#89211yescharacteristic
359C22×C3#89511yescharacteristic
360C22×C3#89811yescharacteristic
361C22×C3#93011yescharacteristic
362C2×D3—124no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—244no—
366C2×D3—244no—
367C2×D3—242no—
368C2×D3—242no—
369C2×D3—242no—
370C2×D3—242no—
371C2×D3—241no—
372C2×D3—241no—
373C2×D3—241no—
374C2×D3—241no—
375C2×D3—242no—
376C2×D3—242no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—121no—
382C3×C4—121no—
383C3×C4C4×D1211yescharacteristic
384C3×C4C4×D1211yescharacteristic
385C3×C4#87511yescharacteristic
386C3×C4#67⋊C411yescharacteristic
387C3×C4#88511yescharacteristic
388C3×C4#88611yescharacteristic
389C3×C4C4×#6711yescharacteristic
390C3×C4#92911yescharacteristic
391Dic3—41no—
392Dic3—41no—
393Dic3—242no—
394Dic3—241no—
395Dic3—241no—
396C32#193111yescharacteristic, complemented, Sylow
397C23—182no—
398C23—361no—
399C23—361no—
400C23—721no—
401C23—721no—
402C23#379911yescharacteristic
403D4—182no—
404D4—182no—
405D4—361no—
406D4—361no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—361no—
410C2×C4—721no—
411C2×C4#379811yescharacteristic
412C2×C4C4×D3211yescharacteristic
413C2×C4D3×D1211yescharacteristic
414C2×C4#380411yescharacteristic
415C2×C4#380411yescharacteristic
416C2×C4C2×#62611yescharacteristic
417C8—21no—
418C8—21no—
419C8—62no—
420C8—62no—
421C8—121no—
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#467011yescharacteristic
432C2×C3#489711yescharacteristic
433C2×C3#489811yescharacteristic
434C2×C3#494011yescharacteristic
435C2×C3#514111yescharacteristic
436C2×C3#514211yescharacteristic
437D3—244no—
438D3—242no—
439D3—242no—
440C22—21no—
441C22—21no—
442C22—362no—
443C22—722no—
444C22—722no—
445C22—721no—
446C22—721no—
447C22#6383611yescharacteristic
448C22#6386811yescharacteristic
449C22#6390911yescharacteristic
450C4—121no—
451C4—121no—
452C4—721no—
453C4#6385211yescharacteristic
454C4#6388011yescharacteristic
455C4C4×#62611yescharacteristic
456C4#6396611yescharacteristic
457C3—21no—
458C3#6893111yescharacteristic, complemented
459C3#6989211yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—722no—
463C2#1059092711yescharacteristic
464C2#1059093111yescharacteristic
465C2#1059119411yescharacteristic
subgroupG/H
centerC22#63909
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32#121
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1931
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C3×#5101C2semidirect
3. #10591131C2semidirect
6. C3×#4552C2semidirect
7. #10589168C2semidirect
25. #63559C4semidirect
34. #5101D3semidirect
40. #4552D3semidirect
396. C32#1931semidirect
458. C3#68931semidirect
459. C3#69892semidirect

Maximal subgroups

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

subgroupindex
C2×#636482
C3×#51012
#105911312
#105910962
C2×#635592
C3×#45522
#105891682
#698923
#689313