Finite Group Databasebeta

← #11785518

Subgroups — #11785518

Order 1152.

557 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63815C211yesmaximal, characteristic
2C2×#63649C211yesmaximal, characteristic, complemented
3C3×#5132C211yesmaximal, characteristic
4C2×#63578C211yesmaximal, characteristic, complemented
5#10591076C211yesmaximal, characteristic
6C3×C3⋊#338C211yesmaximal, characteristic, complemented
7#10589159C211yesmaximal, characteristic, complemented
8#70134—31nomaximal
9#68724—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3711C412yes—
18#63815—22no—
19#63815—22no—
20C2×D3×C3⋊C8C412yes—
21#63649—22no—
22C3×#824—21no—
23C3×#823—21no—
24#63578—22no—
25#63560—21no—
26#63558—21no—
27C2×#948—31no—
28C2×#907—31no—
29C3×#413—31no—
30#5237—31no—
31#5132—31no—
32#5132D311yescharacteristic
33C2×#822—31no—
34C2×#822—31no—
35C2×#822—31no—
36C2×#822—31no—
37C2×#822—61no—
38C3×#338—31no—
39C3⋊#338—31no—
40C3⋊#338—31no—
41C3⋊#338D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C2×C3×#67Q812yes—
44C3×#235—21no—
45C3×#235—21no—
46C3×#235—21no—
47C3×#235—21no—
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3C2×C412yes—
50C2×C3×Dic6D411yescharacteristic
51C32×M16—21no—
52C32×M16—21no—
53C2×C32×C8—21no—
54#3748—21no—
55#3748—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
58C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
59C2×C3⋊(C3⋊C8)D412yes—
60C2×C3⋊(C3⋊C8)D412yes—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8C2×C412yes—
70#3711—24no—
71D3×C3⋊C8—24no—
72#1813—91noSylow
73C2×C3×#41—31no—
74C2×#235C2×D311yescharacteristic
75C2×C3×M16—21no—
76C2×C3×M16—31no—
77C2×C3×M16—31no—
78C2×C3×M16—31no—
79C2×C3×M16C2×D311yescharacteristic
80C2×C3×M16C2×D311yescharacteristic
81#948—62no—
82#948—62no—
83C2×#208—32no—
84C2×#208—31no—
85C2×#208—31no—
86C2×#208—61no—
87C2×#208C2×D311yescharacteristic
88C2×#208C2×D311yescharacteristic
89C2×#208C2×D311yescharacteristic
90C22×C3⋊C8—31no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—32no—
93C22×C3⋊C8—61no—
94#907—62no—
95#907—62no—
96C2×ΓL(1,𝔽25)—32no—
97C2×D3×C8—32no—
98C3×#101—61no—
99C3×#100—61no—
100#836—61no—
101#833—61no—
102#824—21no—
103#824—61no—
104#823—21no—
105#823—61no—
106#822—62no—
107#822—62no—
108#822—62no—
109#822—62no—
110#822—64no—
111C23×C32C2×Q811yescharacteristic
112C22×C3×D3C4⋊C412yes—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C3×#67—22no—
120C3×#67—22no—
121C2×C3×Dic3C4⋊C412yes—
122C3×D12—21no—
123C3×D12—21no—
124C3×C4×D3—22no—
125C3×C4×D3—22no—
126C3×Dic6—21no—
127C3×Dic6—21no—
128C32×C8—41no—
129C3⋊(C3⋊C8)—41no—
130C3⋊(C3⋊C8)C22⋊C412yes—
131C3⋊(C3⋊C8)C22⋊C412yes—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135C2×#131—91no—
136C2×#108—91no—
137C2×#108—91no—
138#413—31no—
139#413—91no—
140#338—31no—
141#338—91no—
142C3×#41—61no—
143C3×#41—61no—
144C3×#41—61no—
145C3×#41—61no—
146C2×C3×Q8—31no—
147C2×C3×D4—32no—
148C2×C3×D4—31no—
149C22×C3×C4—21no—
150C22×C3×C4—32no—
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C2×#67Dic612yes—
154#235—21no—
155#235—21no—
156#235—21no—
157#235—21no—
158C2×D12#6711yescharacteristic
159C2×C4×D3C4×D312yes—
160C2×Dic6#6711yescharacteristic
161C3×M16—22no—
162C3×M16—21no—
163C3×M16—21no—
164C3×M16—21no—
165C3×M16—21no—
166C3×M16—41no—
167C3×M16—61no—
168C3×M16—61no—
169C3×M16—61no—
170C3×M16—61no—
171C3×M16—61no—
172C3×M16—61no—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—32no—
176C2×C3×C8—41no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179#208—21no—
180#208—21no—
181#208—21no—
182#208—21no—
183#208—21no—
184#208—21no—
185#208—64no—
186#208—62no—
187#208—61no—
188#208—61no—
189#208—61no—
190#208—61no—
191#208—121no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—31no—
195C2×C3⋊C8—31no—
196C2×C3⋊C8—31no—
197C2×C3⋊C8—31no—
198C2×C3⋊C8—32no—
199C2×C3⋊C8—32no—
200C2×C3⋊C8—32no—
201C2×C3⋊C8—32no—
202C2×C3⋊C8—62no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—64no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210C2×C3⋊C8C4×D312yes—
211ΓL(1,𝔽25)—64no—
212D3×C8—64no—
213C22×C32—41no—
214C22×C32C2×C4⋊C411yescharacteristic
215C22×C32C22⋊Q811yescharacteristic
216C22×C32C22⋊Q811yescharacteristic
217C2×C3×D3—22no—
218C2×C3×D3—42no—
219C32×C4C2×C22⋊C411yescharacteristic
220C32×C4#11711yescharacteristic
221C32×C4#12111yescharacteristic
222C32×C4#12111yescharacteristic
223C3×Dic3—22no—
224C2×#41—31no—
225#131—182no—
226#131—182no—
227C2×M16—31no—
228C2×M16—31no—
229C2×M16—31no—
230C2×M16—92no—
231C2×M16—91no—
232C2×M16D3211yescharacteristic
233C22×C8—92no—
234C22×C8—91no—
235#108—182no—
236#108—182no—
237#101—61no—
238#101—181no—
239#100—61no—
240#100—181no—
241C23×C3—21no—
242C23×C3—32no—
243C23×C3C2×Dic611yescharacteristic
244C23×C3D3×Q811yescharacteristic
245C22×D3Dic3⋊C412yes—
246C3×Q8—61no—
247C3×Q8—61no—
248C3×D4—62no—
249C3×D4—62no—
250C3×D4—61no—
251C3×D4—61no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—32no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4C2×C4×D311yescharacteristic
262C2×C3×C4C2×C4×D311yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273#67—22no—
274#67—22no—
275C2×Dic3Dic3⋊C412yes—
276D12—21no—
277D12—21no—
278C4×D3—22no—
279C4×D3—22no—
280Dic6—21no—
281Dic6—21no—
282C3×C8—42no—
283C3×C8—41no—
284C3×C8—41no—
285C3×C8—62no—
286C3×C8—121no—
287C3×C8—121no—
288C3⋊C8—22no—
289C3⋊C8—32no—
290C3⋊C8—32no—
291C3⋊C8—32no—
292C3⋊C8—32no—
293C3⋊C8—41no—
294C3⋊C8—41no—
295C3⋊C8—62no—
296C3⋊C8—62no—
297C3⋊C8—122no—
298C3⋊C8—121no—
299C3⋊C8—121no—
300C2×C32—21no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32#38011yescharacteristic
304C3×D3—42no—
305#41—61no—
306#41—61no—
307#41—61no—
308#41—61no—
309C2×Q8—31no—
310C2×D4—32no—
311C2×D4—31no—
312C22×C4—32no—
313C22×C4C2×D3211yescharacteristic
314M16—21no—
315M16—21no—
316M16—61no—
317M16—61no—
318M16—61no—
319M16—61no—
320M16—61no—
321M16—61no—
322M16—184no—
323M16—181no—
324M16—181no—
325C2×C8—21no—
326C2×C8—32no—
327C2×C8—61no—
328C2×C8—61no—
329C2×C8—91no—
330C2×C8—91no—
331C2×C8—92no—
332C2×C8—92no—
333C2×C8—184no—
334C2×C8—181no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—42no—
341C22×C3—62no—
342C22×C3—122no—
343C22×C3#87811yescharacteristic
344C22×C3#87811yescharacteristic
345C22×C3D3×C4⋊C411yescharacteristic
346C22×C3#89611yescharacteristic
347C22×C3#89611yescharacteristic
348C22×C3C2×Dic3⋊C411yescharacteristic
349C2×D3—22no—
350C2×D3—42no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—62no—
356C3×C4#87211yescharacteristic
357C3×C4#87711yescharacteristic
358C3×C4D3×C22⋊C411yescharacteristic
359C3×C4D3×C22⋊C411yescharacteristic
360C3×C4#88411yescharacteristic
361C3×C4#88411yescharacteristic
362C3×C4#93911yescharacteristic
363C3×C4#93911yescharacteristic
364Dic3—22no—
365C32#181311yescharacteristic, complemented, Sylow
366C23—32no—
367C23D3×Dic611yescharacteristic
368Q8—61no—
369Q8—61no—
370D4—62no—
371D4—62no—
372D4—61no—
373D4—61no—
374C2×C4—32no—
375C2×C4—62no—
376C2×C4—62no—
377C2×C4#379511yescharacteristic
378C2×C4C4×D3211yescharacteristic
379C2×C4#380211yescharacteristic
380C2×C4#380411yescharacteristic
381C2×C4D3×#6711yescharacteristic
382C2×C4#381111yescharacteristic
383C8—41no—
384C8—62no—
385C8—92no—
386C8—92no—
387C8—121no—
388C8—121no—
389C8—361no—
390C2×C3—22no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3—122no—
401C2×C3#466711yescharacteristic
402C2×C3#494211yescharacteristic
403D3—42no—
404C22—41no—
405C22—62no—
406C22—122no—
407C22D3×Dic3⋊C411yescharacteristic
408C22#6389611yescharacteristic
409C22#6389911yescharacteristic
410C4—62no—
411C4#6387711yescharacteristic
412C4#6388511yescharacteristic
413C4#6392111yescharacteristic
414C4#6397111yescharacteristic
415C3—21no—
416C3#6872411yescharacteristic, complemented
417C3#7013411yescharacteristic, complemented
418C2—21no—
419C2—21no—
420C2—21no—
421C2—122no—
422C2#1059136911yescharacteristic
subgroupG/H
centerC4#63877
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#380
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1813
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63649C2semidirect
4. C2×#63578C2semidirect
6. C3×C3⋊#338C2semidirect
7. #10589159C2semidirect
41. C3⋊#338D3semidirect
365. C32#1813semidirect
416. C3#68724semidirect
417. C3#70134semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
C2×#636492
C3×#51322
C2×#635782
#105910762
C3×C3⋊#3382
#105891592
#701343
#687243