Finite Group Databasebeta

← #11773373

Subgroups — #11773373

Order 1152.

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

normal subgroups only

This group has 938 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
1C22×C4⋊#157C211yesmaximal, characteristic
2C2×#63883C211yesmaximal, characteristic
3C2×#63737C212yesmaximal
4C2×#63737C212yesmaximal
5#10591370C211yesmaximal, characteristic
6C23×#157C2212yes—
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#624C2211yescharacteristic
9C22×#624C2212yes—
10C22×#624C2211yescharacteristic
11C2×C4⋊#157—22no—
12C2×C4⋊#157—24no—
13C2×C3×Dic3⋊C4—21no—
14C2×Dic3⋊Dic3—21no—
15#63883—22no—
16#63883C414yescomplemented
17#63737—24no—
18#63737—24no—
19C3×C3⋊#95—21no—
20#63579—21no—
21C2×D3×C4⋊C4—61no—
22D3×#95—61no—
23C23×C3⋊D3C2311yescharacteristic
24C22×#157—22no—
25C22×#157—22no—
26C22×#157—22no—
27C22×#157—22no—
28C22×#157—22no—
29C22×#157—22no—
30C22×#157D414yes—
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×#624D412yes—
54C2×#624Q814yes—
55C2×#624Q812yes—
56C4⋊#157—28no—
57C3×Dic3⋊C4—24no—
58Dic3⋊Dic3—24no—
59#1441—91nomaximal, Sylow
60C22×C4×D3—61no—
61C22×C4×D3—62no—
62C22×C4×D3—61no—
63C22×C4×D3—61no—
64C22×C4×D3—61no—
65C2×C3×C4⋊C4—61no—
66C2×C4⋊Dic3—61no—
67C2×Dic3⋊C4—21no—
68C2×Dic3⋊C4—61no—
69D3×C4⋊C4—64no—
70D3×C4⋊C4—64no—
71C3×#95—61no—
72C3⋊#95—21no—
73C3⋊#95—62no—
74C23×C32C2×D411yescharacteristic
75C22×C3⋊D3C22×C411yescharacteristic
76C22×C3⋊D3C2×D411yescharacteristic
77C22×C3⋊D3C2×D412yes—
78C22×C3⋊D3C2×D411yescharacteristic
79C22×C3⋊D3C2×Q811yescharacteristic
80C22×C3⋊D3C2×Q812yes—
81C22×C3⋊D3#4111yescharacteristic
82C22×C3⋊D3#4111yescharacteristic
83C22×C3⋊D3#4112yes—
84C22×C3⋊D3#4112yes—
85C2×#157—24no—
86C2×#157—24no—
87C2×#157—24no—
88C2×#157—42no—
89C2×#157—42no—
90C2×#157—42no—
91C2×#157—42no—
92C2×C32×C4—22no—
93C2×C32×C4C22⋊C412yes—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3C22⋊C412yes—
96C4×C3⋊D3—24no—
97C4×C3⋊D3—22no—
98C4×C3⋊D3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—42no—
105C2×C3×Dic3—42no—
106C2×C3×Dic3—42no—
107#624—22no—
108#624—22no—
109#624—22no—
110#624—24no—
111#624—24no—
112#624—24no—
113#624—41no—
114#624—42no—
115#624—41no—
116#624—42no—
117#624C4⋊C414yescomplemented
118C22×C4⋊C4—91no—
119C22×C4⋊C4—91no—
120C2×#95—91no—
121C2×#95—92no—
122C2×#95—92no—
123C23×D3—61no—
124C23×D3—61no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—61no—
128C22×C3×C4—62no—
129C22×C3×C4—61no—
130C22×Dic3—21no—
131C22×Dic3—22no—
132C22×Dic3—21no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—62no—
139C2×C4×D3—64no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×C4×D3—64no—
149C2×C4×D3—122no—
150C2×C4×D3—122no—
151C2×C4×D3—122no—
152C2×C4×D3—122no—
153C2×C4×D3—122no—
154C2×C4×D3—122no—
155C2×C4×D3—122no—
156C2×C4×D3—122no—
157C2×C4×D3—122no—
158C2×C4×D3—122no—
159C3×C4⋊C4—64no—
160C4⋊Dic3—64no—
161Dic3⋊C4—24no—
162Dic3⋊C4—64no—
163C22×C32C2×C22⋊C411yescharacteristic
164C22×C32#12111yescharacteristic
165C22×C32#12112yes—
166C22×C32C22⋊Q811yescharacteristic
167C22×C32C22⋊Q812yes—
168C2×C3⋊D3C2×C4⋊C411yescharacteristic
169C2×C3⋊D3#11711yescharacteristic
170C2×C3⋊D3C4×D412yes—
171C2×C3⋊D3C4×Q812yes—
172C2×C3⋊D3#12011yescharacteristic
173C2×C3⋊D3#12112yes—
174C2×C3⋊D3#12111yescharacteristic
175C2×C3⋊D3C22⋊Q812yes—
176C2×C3⋊D3C22⋊Q812yes—
177C2×C3⋊D3C22⋊Q811yescharacteristic
178C2×C3⋊D3#12312yes—
179C2×C3⋊D3#12311yescharacteristic
180C2×C3⋊D3#12411yescharacteristic
181C2×C3⋊D3#12512yes—
182C2×C3⋊D3#12512yes—
183C2×C3⋊D3#12612yes—
184C2×C3⋊D3C4⋊Q812yes—
185C2×C3⋊D3C4⋊Q811yescharacteristic
186#157—44no—
187C32×C4—22no—
188C3⋊Dic3—22no—
189C3×Dic3—24no—
190C3×Dic3—42no—
191C3×Dic3—44no—
192C23×C4—91no—
193C23×C4—91no—
194C23×C4—92no—
195C23×C4—91no—
196C23×C4—92no—
197C2×C4⋊C4—61no—
198C2×C4⋊C4—94no—
199C2×C4⋊C4—182no—
200C2×C4⋊C4—181no—
201C2×C4⋊C4—182no—
202C2×C4⋊C4—184no—
203#95—61no—
204#95—181no—
205#95—184no—
206#95—184no—
207C23×C3—21no—
208C23×C3—21no—
209C22×D3—61no—
210C22×D3—61no—
211C22×D3—61no—
212C22×D3—61no—
213C22×D3—61no—
214C22×D3—61no—
215C22×D3—62no—
216C22×D3—62no—
217C22×D3—61no—
218C22×D3—62no—
219C22×D3—61no—
220C22×D3—62no—
221C22×D3—61no—
222C22×D3—62no—
223C22×D3—61no—
224C22×D3—61no—
225C22×D3—62no—
226C22×D3—62no—
227C22×D3—61no—
228C22×D3—62no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—62no—
234C2×C3×C4—62no—
235C2×C3×C4—62no—
236C2×C3×C4—62no—
237C2×C3×C4—64no—
238C2×C3×C4—122no—
239C2×C3×C4—122no—
240C2×C3×C4—122no—
241C2×Dic3—22no—
242C2×Dic3—22no—
243C2×Dic3—22no—
244C2×Dic3—22no—
245C2×Dic3—24no—
246C2×Dic3—42no—
247C2×Dic3—42no—
248C2×Dic3—42no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—122no—
252C2×Dic3—122no—
253C4×D3—64no—
254C4×D3—64no—
255C4×D3—64no—
256C4×D3—64no—
257C4×D3—124no—
258C4×D3—124no—
259C4×D3—124no—
260C4×D3—122no—
261C4×D3—122no—
262C4×D3—124no—
263C4×D3—122no—
264C4×D3—124no—
265C4×D3—122no—
266C4×D3—122no—
267C4×D3—122no—
268C4×D3—124no—
269C4×D3—124no—
270C2×C32#38011yescharacteristic
271C2×C32#38611yescharacteristic
272C2×C32#39111yescharacteristic
273C2×C32#39612yes—
274C2×C32#39812yes—
275C3⋊D3#38712yes—
276C3⋊D3#38912yes—
277C3⋊D3#39411yescharacteristic
278C3⋊D3#39511yescharacteristic
279C3⋊D3#39811yescharacteristic
280C3⋊D3#40011yescharacteristic
281C24—91no—
282C22×C4—61no—
283C22×C4—62no—
284C22×C4—61no—
285C22×C4—92no—
286C22×C4—92no—
287C22×C4—92no—
288C22×C4—92no—
289C22×C4—94no—
290C22×C4—91no—
291C22×C4—92no—
292C22×C4—92no—
293C22×C4—94no—
294C22×C4—182no—
295C22×C4—182no—
296C22×C4—181no—
297C22×C4—181no—
298C22×C4—181no—
299C22×C4—181no—
300C22×C4—182no—
301C22×C4—182no—
302C22×C4—182no—
303C22×C4—182no—
304C22×C4—182no—
305C22×C4—182no—
306C22×C4—182no—
307C22×C4—182no—
308C22×C4—182no—
309C22×C4—182no—
310C22×C4—182no—
311C22×C4—182no—
312C22×C4—182no—
313C22×C4GO+(4,𝔽2)11yescharacteristic
314C4⋊C4—64no—
315C4⋊C4—184no—
316C4⋊C4—188no—
317C22×C3—21no—
318C22×C3—22no—
319C22×C3—21no—
320C22×C3—22no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—22no—
326C22×C3—22no—
327C2×D3—61no—
328C2×D3—61no—
329C2×D3—61no—
330C2×D3—61no—
331C2×D3—62no—
332C2×D3—61no—
333C2×D3—61no—
334C2×D3—62no—
335C2×D3—61no—
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—62no—
339C2×D3—61no—
340C2×D3—62no—
341C2×D3—61no—
342C2×D3—61no—
343C2×D3—62no—
344C2×D3—62no—
345C2×D3—61no—
346C2×D3—62no—
347C2×D3—61no—
348C2×D3—62no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—62no—
352C2×D3—61no—
353C2×D3—61no—
354C2×D3—62no—
355C2×D3—62no—
356C2×D3—62no—
357C2×D3—62no—
358C2×D3—62no—
359C2×D3—62no—
360C2×D3—62no—
361C2×D3—61no—
362C2×D3—61no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4—64no—
366C3×C4—124no—
367C3×C4—122no—
368Dic3—24no—
369Dic3—44no—
370Dic3—42no—
371Dic3—122no—
372Dic3—122no—
373C32#144111yescharacteristic, complemented, Sylow
374C23—91no—
375C23—92no—
376C23—91no—
377C23—92no—
378C23—91no—
379C23—91no—
380C23—91no—
381C23—91no—
382C23—92no—
383C23—92no—
384C23C2×GO+(4,𝔽2)11yescharacteristic
385C2×C4—22no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—64no—
390C2×C4—62no—
391C2×C4—94no—
392C2×C4—92no—
393C2×C4—122no—
394C2×C4—122no—
395C2×C4—122no—
396C2×C4—182no—
397C2×C4—184no—
398C2×C4—182no—
399C2×C4—182no—
400C2×C4—182no—
401C2×C4—182no—
402C2×C4—184no—
403C2×C4—184no—
404C2×C4—184no—
405C2×C4—182no—
406C2×C4—184no—
407C2×C4—184no—
408C2×C4—184no—
409C2×C4—362no—
410C2×C4—362no—
411C2×C4—361no—
412C2×C4—361no—
413C2×C4—362no—
414C2×C4—362no—
415C2×C4—362no—
416C2×C4—362no—
417C2×C4D32⋊C412yes—
418C2×C3—22no—
419C2×C3—22no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—22no—
425C2×C3—22no—
426C2×C3—21no—
427C2×C3—21no—
428D3—62no—
429D3—62no—
430D3—62no—
431D3—62no—
432D3—61no—
433D3—61no—
434D3—61no—
435D3—61no—
436D3—61no—
437D3—61no—
438D3—61no—
439D3—61no—
440C22—92no—
441C22—92no—
442C22—92no—
443C22—92no—
444C22—91no—
445C22—91no—
446C22—92no—
447C22—91no—
448C22—91no—
449C22—91no—
450C22—91no—
451C22—92no—
452C22—92no—
453C22—92no—
454C22—92no—
455C22—91no—
456C22—92no—
457C22—91no—
458C22D32⋊Q811yescharacteristic
459C22D32⋊Q812yes—
460C22#6423011yescharacteristic
461C22C2×D32⋊C411yescharacteristic
462C22#6424212yes—
463C4—22no—
464C4—64no—
465C4—124no—
466C4—122no—
467C4—182no—
468C4—364no—
469C3—21no—
470C3—21no—
471C2—91no—
472C2—92no—
473C2—91no—
474C2—92no—
475C2—91no—
476C2—91no—
477C2#1059334012yes—
478C2#1059334111yescharacteristic
479C2#1059340311yescharacteristic
480C2#1059340612yes—
481C2#1059351511yescharacteristic
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
16. #63883C4semidirect
117. #624C4⋊C4semidirect
373. C32#1441semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C2×#638832
C2×#637372
#105913702
#14419