Finite Group Databasebeta

← #11773235

Subgroups — #11773235

Order 1152.

942 conjugacy classes of subgroups.

The subgroup lattice has 571 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#157C211yesmaximal, characteristic
2C22×C4×#157C211yesmaximal, characteristic
3C2×#63781C211yesmaximal, characteristic
4C2×#63781C211yesmaximal, characteristic
5C2×#63781C211yesmaximal, characteristic
6C2×#63781C211yesmaximal, characteristic
7C3⋊D3×#95C211yesmaximal, characteristic
8C23×#157C2211yescharacteristic
9C23×#157C2211yescharacteristic
10C23×#157C2211yescharacteristic
11C23×#157C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×C4⋊#157—22no—
16C2×C4⋊#157—22no—
17C2×C4⋊#157C414yescomplemented
18C2×C4×#157—22no—
19C2×C4×#157—22no—
20C2×C4×#157—22no—
21#63781—22no—
22#63781—22no—
23#63781—22no—
24#63781C414yescomplemented
25C32×#95C411yescharacteristic, complemented
26#63658C411yescharacteristic, complemented
27#63658C411yescharacteristic, complemented
28#63658C411yescharacteristic, complemented
29D3×#95—62no—
30C23×C3⋊D3C2311yescharacteristic
31C22×#157—21no—
32C22×#157—21no—
33C22×#157—21no—
34C22×#157—21no—
35C22×#157—21no—
36C22×#157—21no—
37C22×#157—21no—
38C22×#157—21no—
39C22×#157—21no—
40C22×#157—21no—
41C22×#157—21no—
42C22×#157—21no—
43C22×#157—21no—
44C22×#157—21no—
45C22×#157—21no—
46C22×#157—21no—
47C22×#157—21no—
48C22×#157—21no—
49C22×#157—21no—
50C22×#157—21no—
51C22×#157C2×C412yes—
52C22×#157C2×C412yes—
53C22×#157C2×C412yes—
54C22×#157C2×C412yes—
55C22×#157D412yes—
56C22×#157D412yes—
57C22×#157D412yes—
58C22×#157Q812yes—
59C22×C32×C4C2×C411yescharacteristic
60C22×C32×C4C2×C411yescharacteristic
61C22×C32×C4C2×C411yescharacteristic
62C22×C3⋊Dic3C2×C411yescharacteristic
63C22×C3⋊Dic3C2×C411yescharacteristic
64C22×C3⋊Dic3C2×C411yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3—21no—
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—21no—
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—21no—
75C2×C4×C3⋊D3—21no—
76C2×C4×C3⋊D3—21no—
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3—21no—
79C2×C4×C3⋊D3C2×C412yes—
80C2×C4×C3⋊D3C2×C412yes—
81C2×C4×C3⋊D3D412yes—
82C2×C4×C3⋊D3Q812yes—
83C4⋊#157—28no—
84C4×#157—28no—
85#1436—91nomaximal, Sylow
86C22×C4×D3—62no—
87C22×C4×D3—62no—
88C22×C4×D3—62no—
89C3×#95—22no—
90C3⋊#95—62no—
91C3⋊#95—62no—
92C3⋊#95—62no—
93C23×C32C22×C411yescharacteristic
94C22×C3⋊D3C22×C411yescharacteristic
95C22×C3⋊D3C22×C411yescharacteristic
96C22×C3⋊D3C2×D411yescharacteristic
97C22×C3⋊D3C2×D411yescharacteristic
98C22×C3⋊D3C2×D411yescharacteristic
99C22×C3⋊D3C2×D411yescharacteristic
100C22×C3⋊D3C2×Q811yescharacteristic
101C22×C3⋊D3C2×Q811yescharacteristic
102C22×C3⋊D3#4111yescharacteristic
103C22×C3⋊D3#4111yescharacteristic
104C22×C3⋊D3#4111yescharacteristic
105C22×C3⋊D3#4111yescharacteristic
106C22×C3⋊D3#4111yescharacteristic
107C22×C3⋊D3#4111yescharacteristic
108C2×#157—22no—
109C2×#157—22no—
110C2×#157—22no—
111C2×#157—22no—
112C2×#157—22no—
113C2×#157—22no—
114C2×#157—22no—
115C2×#157—22no—
116C2×#157—22no—
117C2×#157—22no—
118C2×#157—22no—
119C2×#157—22no—
120C2×#157—22no—
121C2×#157—22no—
122C2×#157—22no—
123C2×#157—22no—
124C2×#157—22no—
125C2×#157—22no—
126C2×#157—41no—
127C2×#157—41no—
128C2×#157—41no—
129C2×#157—41no—
130C2×#157—41no—
131C2×#157—41no—
132C2×#157—41no—
133C2×#157—41no—
134C2×#157C22⋊C414yes—
135C2×#157C4⋊C414yescomplemented
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4C4212yescomplemented
144C2×C32×C4C4⋊C412yescomplemented
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3C4212yescomplemented
153C2×C3⋊Dic3C4⋊C412yescomplemented
154C4×C3⋊D3—22no—
155C4×C3⋊D3—22no—
156C4×C3⋊D3—22no—
157C4×C3⋊D3—22no—
158C4×C3⋊D3—22no—
159C4×C3⋊D3—22no—
160C4×C3⋊D3—22no—
161C4×C3⋊D3—22no—
162C4×C3⋊D3—41no—
163C4×C3⋊D3—41no—
164C4×C3⋊D3—41no—
165C4×C3⋊D3—41no—
166C22×C4⋊C4—91no—
167C22×C42—91no—
168C2×#95—91no—
169C2×#95—91no—
170C2×#95—91no—
171C2×#95—91no—
172C2×#95—91no—
173C23×D3—62no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×Dic3—62no—
178C22×Dic3—62no—
179C22×Dic3—62no—
180C2×C4×D3—64no—
181C2×C4×D3—64no—
182C2×C4×D3—64no—
183C2×C4×D3—64no—
184C2×C4×D3—64no—
185C2×C4×D3—64no—
186C2×C4×D3—122no—
187C2×C4×D3—122no—
188C2×C4×D3—122no—
189C2×C4×D3—122no—
190C2×C4×D3—122no—
191C2×C4×D3—122no—
192C2×C4×D3—122no—
193C2×C4×D3—122no—
194C2×C4×D3—122no—
195C2×C4×D3—122no—
196C2×C4×D3—122no—
197C2×C4×D3—122no—
198C22×C32C2×C4211yescharacteristic
199C22×C32C2×C4⋊C411yescharacteristic
200C22×C32#11711yescharacteristic
201C22×C32C4×D411yescharacteristic
202C22×C32C4×D411yescharacteristic
203C22×C32C4×D411yescharacteristic
204C22×C32C4×Q811yescharacteristic
205C2×C3⋊D3C2×C22⋊C411yescharacteristic
206C2×C3⋊D3C2×C4⋊C411yescharacteristic
207C2×C3⋊D3#11711yescharacteristic
208C2×C3⋊D3#11711yescharacteristic
209C2×C3⋊D3C4×D411yescharacteristic
210C2×C3⋊D3C4×D411yescharacteristic
211C2×C3⋊D3C4×D411yescharacteristic
212C2×C3⋊D3C4×D411yescharacteristic
213C2×C3⋊D3C4×D411yescharacteristic
214C2×C3⋊D3C4×Q811yescharacteristic
215C2×C3⋊D3C4×Q811yescharacteristic
216C2×C3⋊D3C4×Q811yescharacteristic
217C2×C3⋊D3#12011yescharacteristic
218C2×C3⋊D3#12111yescharacteristic
219C2×C3⋊D3#12111yescharacteristic
220C2×C3⋊D3C22⋊Q811yescharacteristic
221C2×C3⋊D3C22⋊Q811yescharacteristic
222C2×C3⋊D3C22⋊Q811yescharacteristic
223C2×C3⋊D3C22⋊Q811yescharacteristic
224C2×C3⋊D3#12311yescharacteristic
225C2×C3⋊D3#12311yescharacteristic
226C2×C3⋊D3#12311yescharacteristic
227C2×C3⋊D3#12411yescharacteristic
228C2×C3⋊D3#12511yescharacteristic
229C2×C3⋊D3#12511yescharacteristic
230C2×C3⋊D3#12611yescharacteristic
231C2×C3⋊D3#12611yescharacteristic
232C2×C3⋊D3C4⋊Q811yescharacteristic
233#157—24no—
234#157—24no—
235#157—42no—
236#157—42no—
237C32×C4—22no—
238C32×C4—22no—
239C32×C4—41no—
240C3⋊Dic3—22no—
241C3⋊Dic3—22no—
242C3⋊Dic3—41no—
243C23×C4—91no—
244C23×C4—91no—
245C23×C4—91no—
246C23×C4—91no—
247C23×C4—91no—
248C23×C4—91no—
249C23×C4—91no—
250C2×C4⋊C4—94no—
251C2×C4⋊C4—182no—
252C2×C4⋊C4—182no—
253C2×C42—182no—
254C2×C42—182no—
255C2×C42—182no—
256#95—94no—
257#95—91no—
258#95—91no—
259#95—91no—
260#95—182no—
261#95—182no—
262#95—182no—
263#95#15711yescharacteristic, complemented
264C23×C3—22no—
265C22×D3—62no—
266C22×D3—62no—
267C22×D3—62no—
268C22×D3—62no—
269C22×D3—62no—
270C22×D3—62no—
271C22×D3—62no—
272C22×D3—62no—
273C22×D3—62no—
274C22×D3—62no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—62no—
278C22×D3—62no—
279C2×C3×C4—24no—
280C2×C3×C4—24no—
281C2×C3×C4—24no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—64no—
291C2×Dic3—122no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294C2×Dic3—122no—
295C2×Dic3—122no—
296C2×Dic3—122no—
297C4×D3—124no—
298C4×D3—124no—
299C4×D3—124no—
300C4×D3—124no—
301C4×D3—124no—
302C4×D3—124no—
303C4×D3—124no—
304C4×D3—124no—
305C4×D3—124no—
306C4×D3—124no—
307C4×D3—124no—
308C4×D3—124no—
309C2×C32C4×C22⋊C411yescharacteristic
310C2×C32C4×C4⋊C411yescharacteristic
311C2×C32C4×C4⋊C411yescharacteristic
312C2×C32#38511yescharacteristic
313C2×C32#38711yescharacteristic
314C2×C32#38811yescharacteristic
315C2×C32#38911yescharacteristic
316C3⋊D3#38511yescharacteristic
317C3⋊D3#38611yescharacteristic
318C3⋊D3#38711yescharacteristic
319C3⋊D3#38711yescharacteristic
320C3⋊D3#38711yescharacteristic
321C3⋊D3#38811yescharacteristic
322C3⋊D3#38911yescharacteristic
323C3⋊D3#39111yescharacteristic
324C24—91no—
325C22×C4—92no—
326C22×C4—92no—
327C22×C4—92no—
328C22×C4—92no—
329C22×C4—92no—
330C22×C4—92no—
331C22×C4—91no—
332C22×C4—91no—
333C22×C4—92no—
334C22×C4—92no—
335C22×C4—92no—
336C22×C4—92no—
337C22×C4—92no—
338C22×C4—92no—
339C22×C4—91no—
340C22×C4—181no—
341C22×C4—181no—
342C22×C4—181no—
343C22×C4—181no—
344C22×C4—181no—
345C22×C4—181no—
346C22×C4—181no—
347C22×C4—181no—
348C22×C4—181no—
349C22×C4—181no—
350C22×C4—181no—
351C22×C4—181no—
352C22×C4—181no—
353C22×C4—181no—
354C22×C4—181no—
355C22×C4—181no—
356C22×C4—181no—
357C22×C4—181no—
358C22×C4—181no—
359C22×C4—181no—
360C22×C4—181no—
361C22×C4—181no—
362C22×C4—181no—
363C22×C4—181no—
364C22×C4—181no—
365C22×C4—181no—
366C22×C4—181no—
367C22×C4—181no—
368C22×C4—181no—
369C22×C4—181no—
370C22×C4—181no—
371C22×C4—181no—
372C22×C4—181no—
373C22×C4—181no—
374C22×C4C2×#15711yescharacteristic
375C22×C4C2×#15711yescharacteristic
376C22×C4C2×#15711yescharacteristic
377C4⋊C4—188no—
378C42—188no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C2×D3—62no—
387C2×D3—62no—
388C2×D3—62no—
389C2×D3—62no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—62no—
394C2×D3—62no—
395C2×D3—62no—
396C2×D3—62no—
397C2×D3—62no—
398C2×D3—62no—
399C2×D3—62no—
400C2×D3—62no—
401C2×D3—62no—
402C2×D3—62no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—62no—
406C2×D3—62no—
407C2×D3—62no—
408C2×D3—62no—
409C2×D3—62no—
410C2×D3—62no—
411C2×D3—62no—
412C2×D3—62no—
413C2×D3—62no—
414C3×C4—44no—
415C3×C4—44no—
416C3×C4—44no—
417Dic3—124no—
418Dic3—124no—
419Dic3—124no—
420C32#143611yescharacteristic, complemented, Sylow
421C23—91no—
422C23—91no—
423C23—91no—
424C23—91no—
425C23—91no—
426C23—91no—
427C23—91no—
428C23—91no—
429C23—91no—
430C23—91no—
431C23—91no—
432C23—91no—
433C23—91no—
434C23—91no—
435C23C22×#15711yescharacteristic
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—94no—
444C2×C4—94no—
445C2×C4—92no—
446C2×C4—92no—
447C2×C4—182no—
448C2×C4—182no—
449C2×C4—182no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4—182no—
454C2×C4—182no—
455C2×C4—182no—
456C2×C4—182no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4—182no—
461C2×C4—182no—
462C2×C4—182no—
463C2×C4—182no—
464C2×C4—182no—
465C2×C4—182no—
466C2×C4—182no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—182no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4—182no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—361no—
481C2×C4—361no—
482C2×C4—361no—
483C2×C4—361no—
484C2×C4—361no—
485C2×C4—361no—
486C2×C4—361no—
487C2×C4—361no—
488C2×C4—361no—
489C2×C4—361no—
490C2×C4—361no—
491C2×C4—361no—
492C2×C4C4×#15712yescomplemented
493C2×C4C4⋊#15712yescomplemented
494C2×C3—22no—
495C2×C3—22no—
496C2×C3—22no—
497C2×C3—22no—
498C2×C3—22no—
499C2×C3—22no—
500C2×C3—22no—
501D3—62no—
502D3—62no—
503D3—62no—
504D3—62no—
505D3—62no—
506D3—62no—
507D3—62no—
508D3—62no—
509C22—91no—
510C22—91no—
511C22—91no—
512C22—91no—
513C22—91no—
514C22—91no—
515C22—91no—
516C22—91no—
517C22—91no—
518C22—91no—
519C22—91no—
520C22—91no—
521C22—91no—
522C22—91no—
523C22—91no—
524C22—91no—
525C22—91no—
526C22—91no—
527C22—91no—
528C22—91no—
529C22—91no—
530C22—91no—
531C22—91no—
532C22—91no—
533C22—91no—
534C22—91no—
535C22—91no—
536C22—91no—
537C22C2×C4×#15711yescharacteristic
538C22C2×C4⋊#15711yescharacteristic
539C22#6428611yescharacteristic
540C22D4×#15711yescharacteristic
541C22D4×#15711yescharacteristic
542C22D4×#15711yescharacteristic
543C22Q8×#15711yescharacteristic
544C4—22no—
545C4—22no—
546C4—41no—
547C4—184no—
548C4—184no—
549C4—182no—
550C4—182no—
551C4—362no—
552C4—362no—
553C4—361no—
554C3—22no—
555C2—91no—
556C2—91no—
557C2—91no—
558C2—91no—
559C2—91no—
560C2—91no—
561C2—91no—
562C2—91no—
563C2C4×C4⋊#15711yescharacteristic
564C2C22⋊C4×#15711yescharacteristic
565C2#1059374611yescharacteristic
566C2#1059374711yescharacteristic
567C2C4⋊C4×#15711yescharacteristic
568C2#1059375811yescharacteristic
569C2#1059375911yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC32×#95C4
socleC23×C32C22×C4
prime radical, cosocleC23×C3⋊D3C23
hypercenter#95#157
hypocenterC32#1436
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
17. C2×C4⋊#157C4semidirect
24. #63781C4semidirect
25. C32×#95C4semidirect
26. #63658C4semidirect
27. #63658C4semidirect
28. #63658C4semidirect
135. C2×#157C4⋊C4semidirect
143. C2×C32×C4C42semidirect
144. C2×C32×C4C4⋊C4semidirect
152. C2×C3⋊Dic3C42semidirect
153. C2×C3⋊Dic3C4⋊C4semidirect
263. #95#157semidirect
420. C32#1436semidirect
492. C2×C4C4×#157semidirect
493. C2×C4C4⋊#157semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C22×C4×#1572
C2×#637812
C3⋊D3×#952
#14369