Finite Group Databasebeta

← #11773375

Subgroups — #11773375

Order 1152.

982 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C2×#63883C211yesmaximal, characteristic
3C2×#63781C211yesmaximal, characteristic
4C2×#63737C212yesmaximal
5C2×#63737C212yesmaximal
6C23×#157C2212yes—
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#624C2211yescharacteristic
9C22×#624C2212yes—
10C22×#624C2211yescharacteristic
11C2×C3×C4⋊Dic3—21no—
12C2×C3×Dic3⋊C4—21no—
13C2×#3724—21no—
14C2×Dic3⋊Dic3—21no—
15#63900—24no—
16#63883—22no—
17#63883C414yescomplemented
18#63781—22no—
19#63737—24no—
20#63737—24no—
21C2×D3×C4⋊C4—61no—
22C2×D3×C4⋊C4—61no—
23C23×C3⋊D3C2311yescharacteristic
24C22×#157—22no—
25C22×#157—22no—
26C22×#157—22no—
27C22×#157—22no—
28C22×#157—22no—
29C22×#157—22no—
30C22×#157Q814yes—
31C22×C32×C4D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3C2×C412yes—
36C2×C4×C3⋊D3D412yes—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39C22×C3×Dic3—22no—
40C2×#624—21no—
41C2×#624—21no—
42C2×#624—21no—
43C2×#624—22no—
44C2×#624—22no—
45C2×#624—22no—
46C2×#624—22no—
47C2×#624—22no—
48C2×#624—22no—
49C2×#624—21no—
50C2×#624—22no—
51C2×#624C2×C412yes—
52C2×#624C2×C412yes—
53C2×#624D414yes—
54C2×#624D412yes—
55C2×#624Q812yes—
56C3×C4⋊Dic3—24no—
57C3×Dic3⋊C4—24no—
58#3724—24no—
59Dic3⋊Dic3—24no—
60#1441—91nomaximal, Sylow
61C22×C4×D3—61no—
62C22×C4×D3—61no—
63C22×C4×D3—61no—
64C22×C4×D3—62no—
65C22×C4×D3—61no—
66C2×C3×C4⋊C4—61no—
67C2×C3×C4⋊C4—61no—
68C2×C4⋊Dic3—21no—
69C2×C4⋊Dic3—61no—
70C2×Dic3⋊C4—21no—
71C2×Dic3⋊C4—61no—
72C2×Dic3⋊C4—62no—
73D3×C4⋊C4—64no—
74D3×C4⋊C4—64no—
75D3×C4⋊C4—68no—
76C23×C32C2×D411yescharacteristic
77C22×C3⋊D3C22×C411yescharacteristic
78C22×C3⋊D3C2×D411yescharacteristic
79C22×C3⋊D3C2×D412yes—
80C22×C3⋊D3C2×D411yescharacteristic
81C22×C3⋊D3C2×Q811yescharacteristic
82C22×C3⋊D3C2×Q812yes—
83C22×C3⋊D3#4111yescharacteristic
84C22×C3⋊D3#4111yescharacteristic
85C22×C3⋊D3#4112yes—
86C22×C3⋊D3#4112yes—
87C2×#157—24no—
88C2×#157—24no—
89C2×#157—24no—
90C2×#157—42no—
91C2×#157—42no—
92C2×#157—42no—
93C2×#157—42no—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4C22⋊C412yes—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3C22⋊C412yes—
100C4×C3⋊D3—24no—
101C4×C3⋊D3—24no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—22no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3—42no—
109C2×C3×Dic3—41no—
110C2×C3×Dic3—42no—
111#624—22no—
112#624—22no—
113#624—22no—
114#624—24no—
115#624—24no—
116#624—24no—
117#624—42no—
118#624—42no—
119#624—42no—
120#624C4⋊C414yescomplemented
121C22×C4⋊C4—91no—
122C22×C4⋊C4—91no—
123C2×#95—91no—
124C2×#95—92no—
125C2×#95—92no—
126C23×D3—61no—
127C23×D3—61no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—61no—
131C22×C3×C4—61no—
132C22×C3×C4—62no—
133C22×Dic3—21no—
134C22×Dic3—21no—
135C22×Dic3—22no—
136C22×Dic3—61no—
137C22×Dic3—61no—
138C2×C4×D3—62no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—62no—
144C2×C4×D3—64no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—64no—
151C2×C4×D3—64no—
152C2×C4×D3—62no—
153C2×C4×D3—64no—
154C2×C4×D3—122no—
155C2×C4×D3—122no—
156C2×C4×D3—122no—
157C2×C4×D3—122no—
158C2×C4×D3—122no—
159C2×C4×D3—122no—
160C2×C4×D3—122no—
161C2×C4×D3—122no—
162C3×C4⋊C4—64no—
163C3×C4⋊C4—64no—
164C4⋊Dic3—24no—
165C4⋊Dic3—64no—
166Dic3⋊C4—24no—
167Dic3⋊C4—64no—
168Dic3⋊C4—68no—
169C22×C32C2×C22⋊C411yescharacteristic
170C22×C32#12011yescharacteristic
171C22×C32#12111yescharacteristic
172C22×C32C22⋊Q811yescharacteristic
173C22×C32#12311yescharacteristic
174C22×C32#12411yescharacteristic
175C22×C32C4⋊Q811yescharacteristic
176C2×C3⋊D3C2×C4⋊C411yescharacteristic
177C2×C3⋊D3#11711yescharacteristic
178C2×C3⋊D3C4×D412yes—
179C2×C3⋊D3C4×Q812yes—
180C2×C3⋊D3#12112yes—
181C2×C3⋊D3#12111yescharacteristic
182C2×C3⋊D3#12112yes—
183C2×C3⋊D3C22⋊Q812yes—
184C2×C3⋊D3C22⋊Q812yes—
185C2×C3⋊D3C22⋊Q812yes—
186C2×C3⋊D3C22⋊Q811yescharacteristic
187C2×C3⋊D3#12312yes—
188C2×C3⋊D3#12512yes—
189C2×C3⋊D3#12512yes—
190C2×C3⋊D3#12612yes—
191C2×C3⋊D3C4⋊Q812yes—
192#157—44no—
193C32×C4—22no—
194C3⋊Dic3—22no—
195C3×Dic3—24no—
196C3×Dic3—42no—
197C3×Dic3—44no—
198C23×C4—91no—
199C23×C4—92no—
200C23×C4—91no—
201C23×C4—91no—
202C23×C4—92no—
203C2×C4⋊C4—61no—
204C2×C4⋊C4—61no—
205C2×C4⋊C4—94no—
206C2×C4⋊C4—184no—
207C2×C4⋊C4—182no—
208C2×C4⋊C4—181no—
209C2×C4⋊C4—181no—
210#95—182no—
211#95—184no—
212#95—184no—
213C23×C3—21no—
214C23×C3—21no—
215C22×D3—61no—
216C22×D3—61no—
217C22×D3—61no—
218C22×D3—62no—
219C22×D3—61no—
220C22×D3—61no—
221C22×D3—61no—
222C22×D3—62no—
223C22×D3—61no—
224C22×D3—61no—
225C22×D3—62no—
226C22×D3—62no—
227C22×D3—61no—
228C22×D3—61no—
229C22×D3—62no—
230C22×D3—62no—
231C22×D3—61no—
232C22×D3—62no—
233C22×D3—61no—
234C22×D3—62no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—62no—
242C2×C3×C4—62no—
243C2×C3×C4—62no—
244C2×C3×C4—62no—
245C2×C3×C4—64no—
246C2×C3×C4—122no—
247C2×C3×C4—122no—
248C2×C3×C4—121no—
249C2×C3×C4—121no—
250C2×Dic3—22no—
251C2×Dic3—22no—
252C2×Dic3—22no—
253C2×Dic3—22no—
254C2×Dic3—24no—
255C2×Dic3—42no—
256C2×Dic3—42no—
257C2×Dic3—41no—
258C2×Dic3—41no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—121no—
264C2×Dic3—121no—
265C4×D3—64no—
266C4×D3—64no—
267C4×D3—64no—
268C4×D3—64no—
269C4×D3—68no—
270C4×D3—68no—
271C4×D3—124no—
272C4×D3—124no—
273C4×D3—124no—
274C4×D3—124no—
275C4×D3—124no—
276C4×D3—124no—
277C4×D3—124no—
278C4×D3—124no—
279C2×C32#38011yescharacteristic
280C2×C32#38611yescharacteristic
281C2×C32#39111yescharacteristic
282C2×C32#39411yescharacteristic
283C2×C32#39511yescharacteristic
284C2×C32#39811yescharacteristic
285C2×C32#40011yescharacteristic
286C3⋊D3#38712yes—
287C3⋊D3#38912yes—
288C3⋊D3#39612yes—
289C3⋊D3#39812yes—
290C24—91no—
291C22×C4—61no—
292C22×C4—61no—
293C22×C4—62no—
294C22×C4—92no—
295C22×C4—92no—
296C22×C4—92no—
297C22×C4—94no—
298C22×C4—92no—
299C22×C4—91no—
300C22×C4—92no—
301C22×C4—92no—
302C22×C4—94no—
303C22×C4—182no—
304C22×C4—182no—
305C22×C4—181no—
306C22×C4—181no—
307C22×C4—181no—
308C22×C4—181no—
309C22×C4—182no—
310C22×C4—182no—
311C22×C4—182no—
312C22×C4—182no—
313C22×C4—182no—
314C22×C4—182no—
315C22×C4—182no—
316C22×C4—182no—
317C22×C4—182no—
318C22×C4—182no—
319C22×C4—182no—
320C22×C4—182no—
321C22×C4—182no—
322C22×C4GO+(4,𝔽2)11yescharacteristic
323C4⋊C4—64no—
324C4⋊C4—64no—
325C4⋊C4—184no—
326C4⋊C4—184no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C2×D3—61no—
342C2×D3—61no—
343C2×D3—62no—
344C2×D3—61no—
345C2×D3—62no—
346C2×D3—61no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—61no—
352C2×D3—61no—
353C2×D3—62no—
354C2×D3—62no—
355C2×D3—62no—
356C2×D3—61no—
357C2×D3—62no—
358C2×D3—62no—
359C2×D3—62no—
360C2×D3—62no—
361C2×D3—61no—
362C2×D3—62no—
363C2×D3—62no—
364C2×D3—62no—
365C2×D3—62no—
366C2×D3—62no—
367C2×D3—62no—
368C2×D3—62no—
369C2×D3—62no—
370C2×D3—62no—
371C2×D3—62no—
372C2×D3—62no—
373C3×C4—24no—
374C3×C4—42no—
375C3×C4—64no—
376C3×C4—124no—
377C3×C4—122no—
378Dic3—24no—
379Dic3—44no—
380Dic3—42no—
381Dic3—64no—
382Dic3—122no—
383C32#144111yescharacteristic, complemented, Sylow
384C23—91no—
385C23—91no—
386C23—92no—
387C23—92no—
388C23—91no—
389C23—91no—
390C23—91no—
391C23—91no—
392C23—92no—
393C23—92no—
394C23C2×GO+(4,𝔽2)11yescharacteristic
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—64no—
402C2×C4—94no—
403C2×C4—92no—
404C2×C4—122no—
405C2×C4—122no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—184no—
409C2×C4—184no—
410C2×C4—182no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C4—184no—
414C2×C4—184no—
415C2×C4—184no—
416C2×C4—181no—
417C2×C4—181no—
418C2×C4—184no—
419C2×C4—184no—
420C2×C4—184no—
421C2×C4—362no—
422C2×C4—362no—
423C2×C4—362no—
424C2×C4—362no—
425C2×C4—362no—
426C2×C4—362no—
427C2×C4—362no—
428C2×C4D32⋊C412yes—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443D3—62no—
444D3—62no—
445D3—62no—
446D3—62no—
447D3—62no—
448D3—62no—
449D3—62no—
450D3—62no—
451C22—92no—
452C22—92no—
453C22—92no—
454C22—92no—
455C22—92no—
456C22—92no—
457C22—92no—
458C22—92no—
459C22—91no—
460C22—91no—
461C22—91no—
462C22—91no—
463C22—92no—
464C22—92no—
465C22—92no—
466C22—92no—
467C22D32⋊Q811yescharacteristic
468C22#6422111yescharacteristic
469C22#6422211yescharacteristic
470C22#6423011yescharacteristic
471C22C2×D32⋊C411yescharacteristic
472C22#6423311yescharacteristic
473C22#6424111yescharacteristic
474C4—22no—
475C4—64no—
476C4—124no—
477C4—122no—
478C4—182no—
479C4—364no—
480C3—21no—
481C3—21no—
482C2—92no—
483C2—92no—
484C2—92no—
485C2—92no—
486C2#1059333911yescharacteristic
487C2#1059334211yescharacteristic
488C2#1059334311yescharacteristic
489C2#1059340111yescharacteristic
490C2#1059340311yescharacteristic
491C2#1059341111yescharacteristic
492C2#1059351411yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC22×C3⋊D3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1441
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
17. #63883C4semidirect
120. #624C4⋊C4semidirect
383. C32#1441semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#638832
C2×#637812
C2×#637372
#14419