Finite Group Databasebeta

← #11794532

Subgroups — #11794532

Order 1152.

633 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63645C211yesmaximal, characteristic, complemented
2C2×C3×#821C211yesmaximal, characteristic
3C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
4#10591318C211yesmaximal, characteristic
5#10591212C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7#10589164C211yesmaximal, characteristic, complemented
8#70484—31nomaximal
9#70180—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3724—21no—
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63645—22no—
21C3×#821—22no—
22C3×Dic3⋊C8—22no—
23#63579—21no—
24#63563—22no—
25C2×C3×C4⋊C8—31no—
26C2×C3×#102—31no—
27#5221—31no—
28C2×#832—31no—
29C2×#821—31no—
30C2×#821D311yescharacteristic
31C2×#818—31no—
32C2×#818—31no—
33C2×#818—61no—
34C2×Dic3⋊C8D311yescharacteristic, complemented
35#4972—31no—
36#4939—31no—
37#4928—31no—
38#4551—31no—
39#4529—31no—
40C23×C3×D3—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3D411yescharacteristic
46C22×C3×Dic3D411yescharacteristic
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12Q812yes—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8D412yes—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)D412yes—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3724—42no—
68(C2×D3)⋊Dic3—42no—
69(C2×D3)⋊Dic3—42no—
70#2067—91noSylow
71C22×C3×D4—31no—
72C22×D12C2×D311yescharacteristic
73C22×C3×C8—21no—
74C22×C3×C8—31no—
75C22×C3×C8C2×D311yescharacteristic
76C22×C3×C8C2×D311yescharacteristic
77C2×C3×C4⋊C4—31no—
78C2×C3×C42—31no—
79C2×#217—61no—
80C2×#217—61no—
81C2×(C2×D3)⋊C4—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—61no—
88C2×C4⋊Dic3—61no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4—61no—
92C2×C4×Dic3C2×D311yescharacteristic
93C22×C3⋊C8C2×D311yescharacteristic
94C3×C4⋊C8—62no—
95C3×#102—62no—
96#832—62no—
97C3⋊#95—61no—
98C3⋊#95—61no—
99#821—22no—
100#821—62no—
101#818—62no—
102#818—62no—
103#818—64no—
104Dic3⋊C8—22no—
105C23×C32C2×D411yescharacteristic
106C22×C3×D3—22no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C22×C3×D3—41no—
110C22×C3×D3—41no—
111C22×C3×D3—41no—
112C22×C3×D3—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×Q811yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3D812yes—
134C3×D12—22no—
135C3×D12—22no—
136C3×D12—41no—
137C3×D12—41no—
138C32×C8—22no—
139C3×C3⋊C8—41no—
140C2×#107—91no—
141C2×C4⋊C8—31no—
142C2×#102—31no—
143C2×#102—91no—
144#390—91no—
145#389—91no—
146#340—91no—
147C24×C3—61no—
148C23×D3—21no—
149C2×C3×D4—32no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—121no—
167C22×Dic3—121no—
168C22×Dic3D1211yescharacteristic
169C22×Dic3D1211yescharacteristic
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12Dic612yes—
176C2×C3×C8—22no—
177C2×C3×C8—22no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—22no—
183C2×C3×C8—61no—
184C2×C3×C8—61no—
185C2×C3×C8—61no—
186C2×C3×C8#6712yes—
187C2×C3×C8#6712yes—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C42—61no—
191C3×C42—61no—
192#217—122no—
193#217—122no—
194(C2×D3)⋊C4—122no—
195(C2×D3)⋊C4—122no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—32no—
199C4⋊Dic3—32no—
200C4⋊Dic3—62no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—62no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—121no—
209C4⋊Dic3—121no—
210Dic3⋊C4—122no—
211Dic3⋊C4—122no—
212C4×Dic3—21no—
213C4×Dic3—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C22×C32#12111yescharacteristic
218C22×C32#12111yescharacteristic
219C22×C32C22⋊Q811yescharacteristic
220C22×C32C2×D811yescharacteristic
221C22×C32#13511yescharacteristic
222C22×C32AGL(1,ℤ/8)11yescharacteristic
223C22×C32#13711yescharacteristic
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—81no—
228C2×C3×D3—81no—
229C2×C3×D3—81no—
230C2×C3×D3—81no—
231C32×C4#12111yescharacteristic
232C32×C4C22⋊Q811yescharacteristic
233C32×C4C22⋊Q811yescharacteristic
234C32×C4#12611yescharacteristic
235C3⋊Dic3—42no—
236C3⋊Dic3—81no—
237C3×Dic3—22no—
238C3×Dic3—41no—
239C3×Dic3—81no—
240C22×D4—31no—
241C22×C8—31no—
242C22×C8D3211yescharacteristic
243C2×C4⋊C4—31no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—181no—
247C2×C22⋊C4—181no—
248C2×C22⋊C4—181no—
249C2×C42—31no—
250#107—182no—
251C4⋊C8—62no—
252#102—62no—
253#102—182no—
254#95—181no—
255C23×C3—21no—
256C23×C3—62no—
257C23×C3—121no—
258C23×C3—121no—
259C23×C3—121no—
260C23×C3—121no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3C2×D1211yescharacteristic
264C23×C3D3×D411yescharacteristic
265C22×D3—22no—
266C22×D3—41no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3—41no—
270C22×D3—41no—
271C22×D3—41no—
272C3×D4—62no—
273C3×D4—62no—
274C3×D4—121no—
275C3×D4—121no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—32no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4C2×Dic611yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4#23711yescharacteristic
297C2×C3×C4#23711yescharacteristic
298C2×C3×C4#23711yescharacteristic
299C2×C3×C4D3×Q811yescharacteristic
300C2×C3×C4#23911yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×Dic3—21no—
304C2×Dic3—21no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—122no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—122no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—241no—
326C2×Dic3—241no—
327C2×Dic3—241no—
328C2×Dic3—241no—
329C2×Dic3D2412yes—
330D12—22no—
331D12—22no—
332D12—41no—
333D12—41no—
334C3×C8—24no—
335C3×C8—22no—
336C3×C8—22no—
337C3×C8—121no—
338C3⋊C8—41no—
339C2×C32#39611yescharacteristic
340C2×C32#45911yescharacteristic
341C2×C32#46411yescharacteristic
342C2×C32#46611yescharacteristic
343C2×C32#46811yescharacteristic
344C2×C32#47411yescharacteristic
345C2×C32#47811yescharacteristic
346C3×D3—82no—
347C24—61no—
348C2×D4—32no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4—61no—
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—61no—
357C22×C4—181no—
358C22×C4—181no—
359C22×C4C2×D3211yescharacteristic
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—61no—
363C2×C8—61no—
364C2×C8—61no—
365C2×C8#62512yes—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—92no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C4⋊C4—181no—
372C4⋊C4—362no—
373C22⋊C4—362no—
374C22⋊C4—362no—
375C42—61no—
376C42—61no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—122no—
385C22×C3—122no—
386C22×C3—122no—
387C22×C3—241no—
388C22×C3—241no—
389C22×C3—241no—
390C22×C3—241no—
391C22×C3#87811yescharacteristic
392C22×C3#88411yescharacteristic
393C22×C3#89511yescharacteristic
394C22×C3#89711yescharacteristic
395C22×C3C2×D2411yescharacteristic
396C22×C3#90411yescharacteristic
397C22×C3#90811yescharacteristic
398C22×C3#90911yescharacteristic
399C22×C3D3×D811yescharacteristic
400C22×C3#91211yescharacteristic
401C22×C3#91411yescharacteristic
402C22×C3#91511yescharacteristic
403C22×C3#93011yescharacteristic
404C22×C3#93811yescharacteristic
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—42no—
408C2×D3—81no—
409C2×D3—81no—
410C2×D3—81no—
411C2×D3—81no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—62no—
417C3×C4—121no—
418C3×C4—241no—
419C3×C4#87811yescharacteristic
420C3×C4#87911yescharacteristic
421C3×C4#89611yescharacteristic
422C3×C4#89811yescharacteristic
423C3×C4#92411yescharacteristic
424C3×C4#93911yescharacteristic
425C3×C4#93911yescharacteristic
426C3×C4#94611yescharacteristic
427Dic3—22no—
428Dic3—41no—
429Dic3—81no—
430Dic3—122no—
431Dic3—122no—
432Dic3—242no—
433Dic3—242no—
434Dic3—241no—
435Dic3—241no—
436C32#206711yescharacteristic, complemented, Sylow
437C23—62no—
438C23—121no—
439C23—121no—
440C23—121no—
441C23—121no—
442C23—121no—
443C23—121no—
444C23D3×D1211yescharacteristic
445D4—62no—
446D4—62no—
447D4—121no—
448D4—121no—
449C2×C4—32no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—182no—
459C2×C4—361no—
460C2×C4—361no—
461C2×C4—361no—
462C2×C4—361no—
463C2×C4—361no—
464C2×C4D3×Dic611yescharacteristic
465C2×C4#379511yescharacteristic
466C2×C4#379911yescharacteristic
467C2×C4#380511yescharacteristic
468C2×C4C2×#62511yescharacteristic
469C2×C4#381111yescharacteristic
470C8—22no—
471C8—121no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—242no—
480C2×C3#475911yescharacteristic
481C2×C3#476611yescharacteristic
482C2×C3#476711yescharacteristic
483C2×C3#478611yescharacteristic
484C2×C3#484311yescharacteristic
485C2×C3#484511yescharacteristic
486C2×C3#484611yescharacteristic
487C2×C3#484711yescharacteristic
488C2×C3#494811yescharacteristic
489C2×C3#499411yescharacteristic
490C2×C3#511511yescharacteristic
491C2×C3#513411yescharacteristic
492C2×C3#515711yescharacteristic
493C2×C3#517411yescharacteristic
494D3—82no—
495C22—122no—
496C22—122no—
497C22—122no—
498C22—241no—
499C22—241no—
500C22—241no—
501C22—241no—
502C22D3×D2411yescharacteristic
503C22#6379411yescharacteristic
504C22#6380011yescharacteristic
505C22#6380711yescharacteristic
506C22#6389311yescharacteristic
507C22#6390811yescharacteristic
508C22#6391011yescharacteristic
509C4—62no—
510C4—121no—
511C4—241no—
512C4—362no—
513C4—721no—
514C4#6385611yescharacteristic
515C4#6386111yescharacteristic
516C4#6389611yescharacteristic
517C4#6398011yescharacteristic
518C3—21no—
519C3#7018011yescharacteristic, complemented
520C3#7048411yescharacteristic, complemented
521C2—242no—
522C2#1059076211yescharacteristic
523C2#1059076511yescharacteristic
524C2#1059076711yescharacteristic
525C2#1059083111yescharacteristic
526C2#1059083311yescharacteristic
527C2#1059086111yescharacteristic
528C2#1059131911yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#2067
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
1. C2×#63645C2semidirect
3. C2×C3×Dic3⋊C8C2semidirect
5. #10591212C2semidirect
7. #10589164C2semidirect
34. C2×Dic3⋊C8D3semidirect
436. C32#2067semidirect
519. C3#70180semidirect
520. C3#70484semidirect

Maximal subgroups

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

subgroupindex
C2×#636452
C2×C3×#8212
C2×C3×Dic3⋊C82
#105913182
#105912122
C2×#635632
#105891642
#704843
#701803