Finite Group Databasebeta

← #11793947

Subgroups — #11793947

Order 1152.

653 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64151C211yesmaximal, characteristic
2C2×C3×#836C211yesmaximal, characteristic, complemented
3C2×C3×#835C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591106C211yesmaximal, characteristic
6#10591073C211yesmaximal, characteristic
7#10589167C211yesmaximal, characteristic, complemented
8#70264—31nomaximal
9#70126—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C2×#3756—21no—
13#64151—22no—
14#64151—22no—
15C2×#3755—21no—
16C2×#3748C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#836—22no—
22C3×#835—22no—
23#63577—22no—
24#63567—21no—
25#63564—21no—
26#63557—22no—
27C2×#942—31no—
28C2×#942—31no—
29C2×#942—61no—
30C2×C3×#103—31no—
31C2×C3×#101—31no—
32C2×#836D311yescharacteristic, complemented
33C2×#835D311yescharacteristic, complemented
34#5133—31no—
35#5129—31no—
36C2×#822—31no—
37#5110—31no—
38C2×#819—31no—
39#4966—31no—
40#4554—31no—
41#4530—31no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8D412yes—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×#638—21no—
51#3828—21no—
52#3828—21no—
53#3828—21no—
54#3828—21no—
55C2×C4⋊(C3⋊D3)D411yescharacteristic
56C2×C4×C3⋊D3—21no—
57C2×#634D411yescharacteristic
58C22×C3×Dic3—21no—
59#3756—24no—
60#3755—24no—
61#3748—21no—
62#3748D412yes—
63C2×C3⋊(C3⋊C8)—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8D412yes—
75#2052—91noSylow
76C22×C3×Q8—21no—
77C22×C3×Q8C2×D311yescharacteristic
78C22×C3×Q8C2×D311yescharacteristic
79C2×#235—31no—
80C2×#235—31no—
81C2×#235—61no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C22×C3×C8—31no—
85C2×C3×C4⋊C4—31no—
86C2×#216—61no—
87C2×#216—61no—
88C2×#216—62no—
89#942—62no—
90#942—62no—
91#942—64no—
92#942—64no—
93#942—62no—
94#942—62no—
95C2×#215—61no—
96C2×#215—61no—
97C2×#215—62no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×#208—31no—
100C2×#208—31no—
101C2×#208—61no—
102C2×#208C2×D311yescharacteristic
103C2×#208C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105C3×#103—62no—
106C3×#101—62no—
107#836—22no—
108#835—22no—
109#822—62no—
110#821—61no—
111(C2×D3)⋊C8—62no—
112(C2×D3)⋊C8—62no—
113#819—62no—
114#816—61no—
115#810—61no—
116#809—61no—
117C23×C32#4111yescharacteristic
118C22×C3⋊D3—21no—
119C32×Q8—22no—
120C32×Q8—22no—
121C32×Q8—41no—
122C32×Q8—41no—
123C2×C32×C4—22no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132#638—41no—
133#638—41no—
134C2×C3⋊Dic3—21no—
135C4⋊(C3⋊D3)—21no—
136C4⋊(C3⋊D3)—21no—
137C4×C3⋊D3—41no—
138C4×C3⋊D3—41no—
139#634—21no—
140#634—21no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—81no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C3×C3⋊C8—41no—
147C2×#137—91no—
148C2×#108—91no—
149#417—91no—
150C2×#103—31no—
151C2×#101—31no—
152#408—91no—
153#343—91no—
154C2×C3×Q8—21no—
155C2×C3×Q8—21no—
156C2×C3×Q8—22no—
157C2×C3×Q8—22no—
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—21no—
162C2×C3×Q8—21no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—21no—
166C2×C3×Q8—22no—
167C2×C3×Q8—41no—
168C2×C3×Q8—41no—
169C2×C3×Q8—41no—
170C2×C3×Q8D1212yes—
171C2×C3×Q8#6712yes—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—41no—
176C22×C3×C4—61no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C2×#67—61no—
180C2×#67—61no—
181C2×#67—121no—
182C22×Dic3—21no—
183#235—62no—
184#235—62no—
185#235—61no—
186#235—61no—
187#235—61no—
188#235—61no—
189#235—61no—
190#235—61no—
191#235—61no—
192#235—61no—
193#235—121no—
194#235—121no—
195C2×D12—31no—
196C2×D12—31no—
197C2×D12—61no—
198C2×C4×D3—61no—
199C2×C4×D3—61no—
200C2×C4×D3—121no—
201C2×Dic6—31no—
202C2×Dic6—31no—
203C2×Dic6—61no—
204C3×M16—61no—
205C3×M16—61no—
206C3×M16—61no—
207C3×M16—61no—
208C2×C3×C8—32no—
209C2×C3×C8—61no—
210C2×C3×C8—61no—
211C2×C3×C8—61no—
212C2×C3×C8—61no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215#216—68no—
216#216—64no—
217#216—64no—
218#215—68no—
219#215—64no—
220#215—64no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223#208—21no—
224#208—21no—
225#208—21no—
226#208—21no—
227#208—32no—
228#208—32no—
229#208—62no—
230#208—62no—
231#208—61no—
232#208—61no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8#6712yes—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32#12111yescharacteristic
244C22×C32#12311yescharacteristic
245C22×C32#12411yescharacteristic
246C2×C3⋊D3—41no—
247C2×C3⋊D3—41no—
248C2×C3⋊D3—41no—
249C32×C4—42no—
250C32×C4#12011yescharacteristic
251C32×C4#12111yescharacteristic
252C32×C4#12111yescharacteristic
253C32×C4#12311yescharacteristic
254C3⋊Dic3—41no—
255C3×Dic3—81no—
256C2×#41—91no—
257C22×Q8D3211yescharacteristic
258#137—182no—
259#137—182no—
260C2×Q16—181no—
261C2×SD16—181no—
262C2×M16—31no—
263C2×M16—31no—
264C2×M16—91no—
265C22×C8—31no—
266C2×C4⋊C4—31no—
267#108—182no—
268#103—62no—
269#103—181no—
270#102—181no—
271#101—62no—
272C22⋊C8—182no—
273C23×C3—21no—
274C23×C3#23511yescharacteristic
275C23×C3#23711yescharacteristic
276C22×D3—61no—
277C22×D3—61no—
278C22×D3—121no—
279C3×Q8—24no—
280C3×Q8—22no—
281C3×Q8—22no—
282C3×Q8—22no—
283C3×Q8—22no—
284C3×Q8—42no—
285C3×Q8—42no—
286C3×Q8—42no—
287C3×Q8—41no—
288C3×Q8—41no—
289C3×Q8—41no—
290C3×Q8—41no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—121no—
307C2×C3×C4—241no—
308C2×C3×C4C2×D1211yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4#23511yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4#23711yescharacteristic
317C2×C3×C4#23711yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320#67—122no—
321#67—122no—
322#67—121no—
323#67—121no—
324#67—121no—
325#67—121no—
326C2×Dic3—41no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—81no—
330C2×Dic3—121no—
331D12—62no—
332D12—61no—
333D12—61no—
334D12—61no—
335D12—61no—
336D12—121no—
337C4×D3—122no—
338C4×D3—122no—
339C4×D3—121no—
340C4×D3—121no—
341C4×D3—121no—
342C4×D3—121no—
343Dic6—62no—
344Dic6—61no—
345Dic6—61no—
346Dic6—61no—
347Dic6—61no—
348Dic6—121no—
349C3×C8—62no—
350C3×C8—121no—
351C3×C8—121no—
352C3⋊C8—22no—
353C3⋊C8—41no—
354C3⋊C8—41no—
355C3⋊C8—64no—
356C3⋊C8—62no—
357C3⋊C8—62no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32#39411yescharacteristic
361C2×C32#47111yescharacteristic
362C2×C32#47311yescharacteristic
363C3⋊D3—81no—
364#41—181no—
365#41—181no—
366#41—181no—
367#41—181no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—91no—
374C2×Q8#62612yes—
375C2×D4—91no—
376C2×D4—181no—
377C22×C4—21no—
378C22×C4—61no—
379C22×C4—181no—
380C22×C4C2×D3211yescharacteristic
381Q16—184no—
382SD16—184no—
383M16—61no—
384M16—61no—
385M16—61no—
386M16—61no—
387M16—92no—
388M16—181no—
389C2×C8—32no—
390C2×C8—61no—
391C2×C8—61no—
392C2×C8—61no—
393C2×C8—61no—
394C2×C8—181no—
395C4⋊C4—61no—
396C4⋊C4—61no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3#88411yescharacteristic
407C22×C3#88511yescharacteristic
408C22×C3#88511yescharacteristic
409C22×C3#88611yescharacteristic
410C22×C3#92911yescharacteristic
411C22×C3#93811yescharacteristic
412C2×D3—122no—
413C2×D3—121no—
414C2×D3—121no—
415C2×D3—121no—
416C2×D3—121no—
417C2×D3—121no—
418C2×D3—121no—
419C2×D3—241no—
420C2×D3—241no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—44no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4—241no—
429C3×C4#88211yescharacteristic
430C3×C4#88311yescharacteristic
431C3×C4#88311yescharacteristic
432C3×C4#88411yescharacteristic
433C3×C4#93011yescharacteristic
434C3×C4#93711yescharacteristic
435C3×C4#93911yescharacteristic
436C3×C4#93911yescharacteristic
437Dic3—81no—
438Dic3—122no—
439Dic3—121no—
440Dic3—121no—
441C32#205211yescharacteristic, complemented, Sylow
442C23—181no—
443C23#380411yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—41no—
447Q8—41no—
448Q8—181no—
449Q8—181no—
450D4—181no—
451D4—181no—
452D4—361no—
453D4—361no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—121no—
458C2×C4—181no—
459C2×C4—241no—
460C2×C4—361no—
461C2×C4—361no—
462C2×C4#380411yescharacteristic
463C2×C4#380411yescharacteristic
464C2×C4C2×#62611yescharacteristic
465C2×C4D3×#6711yescharacteristic
466C2×C4#381111yescharacteristic
467C2×C4#381111yescharacteristic
468C8—62no—
469C8—121no—
470C8—121no—
471C8—182no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—41no—
480C2×C3—41no—
481C2×C3#475411yescharacteristic
482C2×C3#475511yescharacteristic
483C2×C3#495911yescharacteristic
484C2×C3#496111yescharacteristic
485C2×C3#517711yescharacteristic
486C2×C3#519211yescharacteristic
487D3—242no—
488D3—241no—
489D3—241no—
490C22—21no—
491C22—21no—
492C22—361no—
493C22—361no—
494C22—361no—
495C22#6395311yescharacteristic
496C22#6395811yescharacteristic
497C22#6396611yescharacteristic
498C4—42no—
499C4—241no—
500C4—361no—
501C4#6397111yescharacteristic
502C4#6397511yescharacteristic
503C4#6397811yescharacteristic
504C4#6398111yescharacteristic
505C3—21no—
506C3#7012611yescharacteristic, complemented
507C3#7026411yescharacteristic, complemented
508C2—21no—
509C2—21no—
510C2—721no—
511C2#1059154211yescharacteristic
512C2#1059154311yescharacteristic
513C2#1059171211yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#121
prime radicalC2×#3828C22
hypercenterC22×Q8D32
hypocenterC32#2052
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#836C2semidirect
3. C2×C3×#835C2semidirect
4. C2×#63577C2semidirect
7. #10589167C2semidirect
32. C2×#836D3semidirect
33. C2×#835D3semidirect
441. C32#2052semidirect
506. C3#70126semidirect
507. C3#70264semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
C2×C3×#8362
C2×C3×#8352
C2×#635772
#105911062
#105910732
#105891672
#702643
#701263