Finite Group Databasebeta

← #11796255

Subgroups — #11796255

Order 1152.

546 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#10595080C211yesmaximal, characteristic
2C2×#63774C211yesmaximal, characteristic, complemented
3C2×#63559C211yesmaximal, characteristic, complemented
4#10590058C212yesmaximal, complemented
5#10590057C212yesmaximal, complemented
6C22×C4⋊(C3⋊D3)C2211yescharacteristic
7C2×#3811C411yescharacteristic, complemented
8C2×C22⋊#157—21no—
9C3×#929—21no—
10C2×C3×#208—21no—
11#63981—21no—
12#63974C411yescharacteristic, complemented
13#63923C411yescharacteristic, complemented
14#63923C2211yescharacteristic
15#63910—21no—
16#63910—21no—
17#63897C411yescharacteristic, complemented
18#63897C2211yescharacteristic
19#63774—21no—
20#63774C2212yes—
21#63559—21no—
22#63559C2212yes—
23#5653—61no—
24C2×#823—61no—
25C23×C3⋊D3C2×C411yescharacteristic
26C23×C3⋊D3D411yescharacteristic
27C22×D32C2×C411yescharacteristic, complemented
28C22×#157—41no—
29C22×C32×C4D411yescharacteristic
30C2×C4⋊(C3⋊D3)—41no—
31C2×C4⋊(C3⋊D3)—41no—
32C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
33C2×C4⋊(C3⋊D3)D411yescharacteristic
34C2×C4⋊(C3⋊D3)D411yescharacteristic
35C2×C4⋊(C3⋊D3)C2311yescharacteristic
36C2×C3×#67—21no—
37#3811—41no—
38#3811—41no—
39C2×#626—21no—
40C2×#626—21no—
41C2×#626—21no—
42C2×#624—21no—
43C2×#624C2×C411yescharacteristic, complemented
44C22⋊#157—22no—
45C22⋊#157—41no—
46C3×#217—21no—
47C3×(C2×D3)⋊C4—21no—
48C3×(C2×D3)⋊C4—21no—
49C3×Dic3⋊C4—21no—
50C3×Dic3⋊C4—21no—
51C3×#208—22no—
52C3×#208—41no—
53C2×C3×C3⋊C8—41no—
54#3722—21no—
55#3722—21no—
56#3722C2×C411yescharacteristic, complemented
57#3722C2×C411yescharacteristic, complemented
58#2121—91nomaximal, Sylow
59C2×D3×D4—61no—
60C22×D12—61no—
61C22×D12—61no—
62C2×C3×M16—61no—
63C3×#123—61no—
64#937—61no—
65#929—21no—
66C2×#208—21no—
67#895—61no—
68#895—61no—
69#894—61no—
70#894—61no—
71#884—61no—
72#884—61no—
73#882—61no—
74#882—61no—
75#882—61no—
76D3×C22⋊C4—61no—
77#823—62no—
78#823—62no—
79C23×C32C22⋊C411yescharacteristic
80C22×C3⋊D3—21no—
81C22×C3⋊D3—21no—
82C22×C3⋊D3—21no—
83C22×C3⋊D3—21no—
84C22×C3⋊D3—81no—
85C22×C3⋊D3—81no—
86C22×C3⋊D3C22⋊C411yescharacteristic
87C22×C3⋊D3C22⋊C411yescharacteristic
88C22×C3⋊D3C22×C411yescharacteristic
89C22×C3⋊D3C2×D411yescharacteristic
90C22×C3×D3—21no—
91C2×D32—41no—
92C2×D32—81no—
93C2×#157—42no—
94C2×#157—82no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C4⋊(C3⋊D3)—41no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C3×#67—41no—
104C3×#67—41no—
105C2×C3×Dic3—21no—
106C2×C3×Dic3—21no—
107C2×C3×Dic3—21no—
108#626—42no—
109#626—81no—
110#626—81no—
111#624—41no—
112#624—81no—
113C3×C3⋊C8—42no—
114#534—91no—
115C2×#100—91no—
116C2×#99—91no—
117#352—92no—
118AΣL(1,𝔽16)—92no—
119C23×D3—61no—
120C23×D3—61no—
121C23×D3—61no—
122C23×D3—61no—
123C23×D3—61no—
124C2×C3×D4—61no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C2×#67—21no—
128C2×#67—61no—
129C2×#67—61no—
130C2×#67—61no—
131D3×D4—122no—
132D3×D4—122no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—61no—
144C2×D12—121no—
145C2×D12—121no—
146C2×D12—121no—
147C2×D12—121no—
148C2×D12—122no—
149C2×D12—122no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C3×M16—62no—
154C3×M16—121no—
155C2×C3×C8—121no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C22⋊C4—61no—
159C3×C22⋊C4—61no—
160C3×C22⋊C4—61no—
161#217—21no—
162(C2×D3)⋊C4—21no—
163(C2×D3)⋊C4—21no—
164(C2×D3)⋊C4—61no—
165(C2×D3)⋊C4—61no—
166(C2×D3)⋊C4—61no—
167(C2×D3)⋊C4—61no—
168(C2×D3)⋊C4—61no—
169(C2×D3)⋊C4—61no—
170Dic3⋊C4—21no—
171Dic3⋊C4—21no—
172#208—22no—
173#208—41no—
174C2×C3⋊C8—41no—
175C22×C32—41no—
176C22×C32#9911yescharacteristic
177C22×C32#9911yescharacteristic
178C22×C32C2×C22⋊C411yescharacteristic
179C2×C3⋊D3—21no—
180C2×C3⋊D3—21no—
181C2×C3⋊D3—21no—
182C2×C3⋊D3—21no—
183C2×C3⋊D3—41no—
184C2×C3⋊D3—41no—
185C2×C3⋊D3—41no—
186C2×C3⋊D3—41no—
187C2×C3⋊D3—42no—
188C2×C3⋊D3—81no—
189C2×C3⋊D3—81no—
190C2×C3⋊D3—81no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C2×C3×D3—41no—
194D32—82no—
195#157—82no—
196C32×C4—21no—
197C32×C4—21no—
198C3×Dic3—41no—
199C3×Dic3—41no—
200C3×Dic3—41no—
201C22×D4—91no—
202C22×D4—91no—
203C2×M16—61no—
204#123—61no—
205#123—91no—
206#123—91no—
207#121—181no—
208#121—181no—
209#120—91no—
210#120—91no—
211#120—181no—
212C2×C22⋊C4—91no—
213C2×C22⋊C4—181no—
214#100—92no—
215#100—181no—
216#99—92no—
217#99—181no—
218C23×C3—21no—
219C23×C3—21no—
220C23×C3—61no—
221C22×D3—21no—
222C22×D3—61no—
223C22×D3—61no—
224C22×D3—61no—
225C22×D3—61no—
226C22×D3—61no—
227C22×D3—61no—
228C22×D3—61no—
229C22×D3—61no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—121no—
233C22×D3—121no—
234C22×D3—121no—
235C22×D3—121no—
236C22×D3—121no—
237C22×D3—121no—
238C22×D3—122no—
239C22×D3—241no—
240C22×D3—241no—
241C22×D3—241no—
242C22×D3—241no—
243C22×D3—241no—
244C22×D3—241no—
245C22×D3—242no—
246C22×D3—242no—
247C3×D4—121no—
248C3×D4—121no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262#67—41no—
263#67—41no—
264#67—122no—
265#67—241no—
266#67—241no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270D12—121no—
271D12—121no—
272D12—121no—
273D12—121no—
274D12—121no—
275D12—121no—
276D12—121no—
277D12—121no—
278D12—122no—
279D12—122no—
280D12—122no—
281D12—122no—
282D12—122no—
283D12—241no—
284D12—241no—
285C4×D3—122no—
286C4×D3—241no—
287C4×D3—241no—
288C3×C8—122no—
289C3⋊C8—42no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32C2×#9911yescharacteristic
294C3⋊D3—41no—
295C3⋊D3—41no—
296C3⋊D3—41no—
297C3⋊D3—41no—
298C3×D3—81no—
299C24—91no—
300C24—91no—
301C24—91no—
302C2×D4—61no—
303C2×D4—91no—
304C2×D4—91no—
305C2×D4—91no—
306C2×D4—91no—
307C2×D4—181no—
308C2×D4—181no—
309C2×D4—181no—
310C2×D4—361no—
311C2×D4—361no—
312C2×D4—361no—
313C2×D4—361no—
314C22×C4—91no—
315C22×C4—181no—
316C22×C4—361no—
317C22×C4GO+(4,𝔽2)11yescharacteristic
318M16—62no—
319M16—121no—
320C2×C8—121no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C22⋊C4—61no—
324C22⋊C4—61no—
325C22⋊C4—61no—
326C22⋊C4—91no—
327C22⋊C4—91no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C22⋊C4—182no—
331C22⋊C4—361no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—42no—
341C22×C3—121no—
342C22×C3—121no—
343C22×C3—121no—
344C2×D3—41no—
345C2×D3—41no—
346C2×D3—41no—
347C2×D3—62no—
348C2×D3—62no—
349C2×D3—121no—
350C2×D3—121no—
351C2×D3—121no—
352C2×D3—121no—
353C2×D3—121no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—121no—
360C2×D3—121no—
361C2×D3—121no—
362C2×D3—121no—
363C2×D3—242no—
364C2×D3—242no—
365C2×D3—241no—
366C2×D3—241no—
367C2×D3—241no—
368C2×D3—241no—
369C2×D3—244no—
370C2×D3—242no—
371C2×D3—242no—
372C2×D3—242no—
373C2×D3—242no—
374C2×D3—242no—
375C2×D3—242no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—121no—
383C3×C4—121no—
384C3×C4—121no—
385Dic3—41no—
386Dic3—41no—
387Dic3—41no—
388C32#212111yescharacteristic, complemented, Sylow
389C23—61no—
390C23—91no—
391C23—91no—
392C23—91no—
393C23—91no—
394C23—181no—
395C23—181no—
396C23—181no—
397C23—181no—
398C23—361no—
399C23—721no—
400C23—721no—
401C23—721no—
402C23D32⋊C411yescharacteristic
403D4—121no—
404D4—121no—
405D4—361no—
406D4—361no—
407D4—361no—
408D4—361no—
409D4—362no—
410D4—721no—
411D4—721no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—361no—
418C2×C4—362no—
419C2×C4—721no—
420C2×C4—722no—
421C2×C4D32⋊C411yescharacteristic
422C2×C4C2×GO+(4,𝔽2)11yescharacteristic
423C8—122no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3—41no—
432C2×C3—41no—
433C2×C3—241no—
434D3—81no—
435D3—122no—
436D3—122no—
437D3—241no—
438D3—241no—
439D3—241no—
440D3—241no—
441D3—241no—
442D3—241no—
443C22—41no—
444C22—121no—
445C22—121no—
446C22—121no—
447C22—181no—
448C22—181no—
449C22—181no—
450C22—181no—
451C22—361no—
452C22—361no—
453C22—361no—
454C22—361no—
455C22—362no—
456C22—721no—
457C22—721no—
458C22—721no—
459C22—722no—
460C22#6373811yescharacteristic
461C22#6373811yescharacteristic
462C22C2×D32⋊C411yescharacteristic
463C4—21no—
464C4—21no—
465C4—121no—
466C4—121no—
467C4—121no—
468C4—722no—
469C3—21no—
470C3—21no—
471C2—21no—
472C2—21no—
473C2—21no—
474C2—241no—
475C2—361no—
476C2—361no—
477C2—361no—
478C2—361no—
479C2C2×#6373811yescharacteristic
subgroupG/H
centerC2C2×#63738
commutatorC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C2×#99
prime radical#10595080C2
cosocleC2×C4⋊(C3⋊D3)C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2121
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63774C2semidirect
3. C2×#63559C2semidirect
4. #10590058C2semidirect
5. #10590057C2semidirect
7. C2×#3811C4semidirect
12. #63974C4semidirect
13. #63923C4semidirect
17. #63897C4semidirect
27. C22×D32C2×C4semidirect
43. C2×#624C2×C4semidirect
56. #3722C2×C4semidirect
57. #3722C2×C4semidirect
388. C32#2121semidirect

Maximal subgroups

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

subgroupindex
#105950802
C2×#637742
C2×#635592
#105900582
#105900572
#21219