Finite Group Databasebeta

← #16953483

Subgroups — #16953483

Order 4352.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762636C211yesmaximal, characteristic, complemented
2C2×#11762610C211yesmaximal, characteristic, complemented
3C2×#11762610C211yesmaximal, characteristic, complemented
4C2×C22⋊#63214C211yesmaximal, characteristic, complemented
5#14528813C211yesmaximal, characteristic, complemented
6#14526875C211yesmaximal, characteristic, complemented
7C2×C17×#466C211yesmaximal, characteristic
8C22×#63214C2211yescharacteristic
9C22×#63214C2211yescharacteristic
10C2×#10587489C2211yescharacteristic
11C2×#10587489C2211yescharacteristic
12#11762669—21no—
13#11762636—22no—
14#11762610—22no—
15#11762610—22no—
16C22⋊#63214—22no—
17#11762572—21no—
18C22×D8×C17C2211yescharacteristic
19C23×C8×C17C2211yescharacteristic
20C2×C17×#121—21no—
21C17×#466—22no—
22C17×#466—22no—
23C2×C17×#107C2211yescharacteristic
24C2×C17×#102—21no—
25C22×D4×C17—21no—
26C22×D4×C17—41no—
27C23×C4×C17D411yescharacteristic
28C2×D8×C17—21no—
29C2×D8×C17—21no—
30C2×D8×C17—21no—
31C2×D8×C17—21no—
32C2×D8×C17—21no—
33C2×D8×C17D412yes—
34C22×C8×C17—21no—
35C22×C8×C17—21no—
36C22×C8×C17—21no—
37C22×C8×C17—21no—
38C22×C8×C17—21no—
39C22×C8×C17—21no—
40C22×C8×C17D411yescharacteristic
41C22×C8×C17C2311yescharacteristic
42C17×#121—24no—
43C17×#121—42no—
44C2×C4⋊C4×C17—21no—
45C2×C22⋊C4×C17—41no—
46C2×C22⋊Dic17—41no—
47C2×C4⋊Dic17—21no—
48C2×C4⋊Dic17—21no—
49C17×#107—21no—
50C17×#107D412yes—
51C17×#102—24no—
52#10587502—41no—
53#10587489—21no—
54#10587489—21no—
55#10587489—21no—
56#10587489—21no—
57C2×#63214—21no—
58C2×#63214—21no—
59C2×#63214—21no—
60C2×#63214—21no—
61C2×#63214—21no—
62C2×#63214D412yescomplemented
63C24×C17—41no—
64C24×C17D811yescharacteristic
65C2×D4×C17—22no—
66C2×D4×C17—44no—
67C2×D4×C17—41no—
68C2×D4×C17—41no—
69C2×D4×C17—41no—
70C2×D4×C17—41no—
71C2×D4×C17—41no—
72C2×D4×C17—82no—
73C2×D4×C17—82no—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—21no—
79C22×C4×C17—21no—
80C22×C4×C17—41no—
81C22×C4×C17D811yescharacteristic
82C22×C4×C17C2×D411yescharacteristic
83C22×Dic17—41no—
84C22×Dic17—41no—
85D8×C17—22no—
86D8×C17—22no—
87D8×C17—41no—
88D8×C17—41no—
89C2×C8×C17—21no—
90C2×C8×C17—21no—
91C2×C8×C17—21no—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C2×C8×C17—41no—
95C2×C8×C17—41no—
96C2×C8×C17C2×D411yescharacteristic
97C2×C8×C17C2×D411yescharacteristic
98C2×C8×C17C2×D411yescharacteristic
99C2×C8×C17#4111yescharacteristic
100C2×C8×C17#4111yescharacteristic
101C2×C8×C17#4111yescharacteristic
102C4⋊C4×C17—22no—
103C4⋊C4×C17—41no—
104C22⋊C4×C17—44no—
105C22⋊Dic17—82no—
106C4⋊Dic17—41no—
107C4⋊Dic17—41no—
108C4⋊Dic17—41no—
109C4⋊Dic17—41no—
110#63214—22no—
111#63214—41no—
112#13381—171nomaximal, Sylow
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—21no—
118C23×C17—21no—
119C23×C17—42no—
120C23×C17—81no—
121C23×C17—81no—
122C23×C17—81no—
123C23×C17—81no—
124C23×C17—81no—
125C23×C17—81no—
126C23×C17SD3212yes—
127C23×C17C2×D811yescharacteristic
128D4×C17—42no—
129D4×C17—42no—
130D4×C17—88no—
131D4×C17—81no—
132D4×C17—81no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—42no—
141C2×C4×C17—81no—
142C2×C4×C17—81no—
143C2×C4×C17#12011yescharacteristic
144C2×C4×C17#12111yescharacteristic
145C2×C4×C17#12311yescharacteristic
146C2×C4×C17#13511yescharacteristic
147C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C17#13711yescharacteristic
149C2×Dic17—81no—
150C2×Dic17—81no—
151C2×Dic17—81no—
152C2×Dic17—81no—
153C2×Dic17—81no—
154C2×Dic17—81no—
155C8×C17—41no—
156C8×C17#12111yescharacteristic
157C8×C17#12111yescharacteristic
158C8×C17#12311yescharacteristic
159C8×C17#12411yescharacteristic
160C2×#466D1711yescharacteristic
161C2×#367—171no—
162C2×#357—171no—
163C2×#357—171no—
164C2×C22⋊C16—171no—
165#1808—171no—
166#1380—171no—
167C22×C17—22no—
168C22×C17—22no—
169C22×C17—22no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—82no—
175C22×C17—82no—
176C22×C17—82no—
177C22×C17—161no—
178C22×C17—161no—
179C22×C17—161no—
180C22×C17—161no—
181C22×C17#44711yescharacteristic
182C22×C17#46611yescharacteristic
183C22×C17#48011yescharacteristic
184C22×C17C2×SD3211yescharacteristic
185C22×C17#50811yescharacteristic
186C22×C17#50911yescharacteristic
187C22×C17#50911yescharacteristic
188C4×C17—41no—
189C4×C17—82no—
190C4×C17#39411yescharacteristic
191C4×C17#45211yescharacteristic
192C4×C17#46811yescharacteristic
193C4×C17#48211yescharacteristic
194Dic17—161no—
195Dic17—161no—
196C22×D8C2×D1711yescharacteristic
197C23×C8C2×D1711yescharacteristic
198C2×#121—21no—
199C22×C16—171no—
200C22×C16—171no—
201#466—22no—
202#466—22no—
203C2×#107—171no—
204C2×#107—171no—
205C2×#107C2×D1711yescharacteristic
206C2×#102—21no—
207#380—341no—
208#367—342no—
209#357—342no—
210#357—342no—
211C22⋊C16—342no—
212#340—341no—
213C2×C17—42no—
214C2×C17—162no—
215C2×C17#203311yescharacteristic
216C2×C17#218611yescharacteristic
217C2×C17#218711yescharacteristic
218C2×C17#221711yescharacteristic
219C2×C17#221811yescharacteristic
220C2×C17#223311yescharacteristic
221C2×C17#223411yescharacteristic
222C22×D4—21no—
223C22×D4—41no—
224C23×C4C22⋊D1711yescharacteristic
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8C22⋊D1712yes—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8C22⋊D1711yescharacteristic
238C22×C8C22×D1711yescharacteristic
239#121—24no—
240#121—42no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—341no—
243C2×C4⋊C4—341no—
244C2×C22⋊C4—41no—
245C2×C22⋊C4—681no—
246C2×C16—172no—
247C2×C16—341no—
248C2×C16—341no—
249C2×C16—341no—
250C2×C16—341no—
251C2×C16—341no—
252#107—21no—
253#107—341no—
254#107—341no—
255#107—341no—
256#107—341no—
257#107C22⋊D1712yes—
258#102—24no—
259#95—681no—
260C17#1338111yescharacteristic, complemented, Sylow
261C24—41no—
262C24#6322811yescharacteristic
263C2×D4—22no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—82no—
271C2×D4—82no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—681no—
280C22×C4—681no—
281C22×C4#6322811yescharacteristic
282C22×C4C2×C22⋊D1711yescharacteristic
283D8—22no—
284D8—22no—
285D8—41no—
286D8—41no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8D4×D1711yescharacteristic
295C2×C8#6325411yescharacteristic
296C2×C8#6325411yescharacteristic
297C2×C8#6325411yescharacteristic
298C2×C8C2×C22⋊D1711yescharacteristic
299C2×C8C2×C22⋊D1711yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—681no—
303C4⋊C4—681no—
304C4⋊C4—681no—
305C4⋊C4—681no—
306C22⋊C4—44no—
307C22⋊C4—1362no—
308C16—342no—
309C16—681no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23#1058749812yes—
324C23C2×#6322811yescharacteristic
325D4—42no—
326D4—42no—
327D4—88no—
328D4—81no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—1361no—
341C2×C4—1361no—
342C2×C4—1361no—
343C2×C4—1361no—
344C2×C4—1361no—
345C2×C4—1361no—
346C2×C4#1058761811yescharacteristic
347C2×C4#1058762111yescharacteristic
348C2×C4#1058762511yescharacteristic
349C2×C4#1058763611yescharacteristic
350C2×C4#1058763711yescharacteristic
351C2×C4#1058763911yescharacteristic
352C8—41no—
353C8#1058762111yescharacteristic
354C8#1058762211yescharacteristic
355C8#1058762411yescharacteristic
356C8#1058762511yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—161no—
368C22—161no—
369C22—161no—
370C22—161no—
371C22#1176294311yescharacteristic
372C22#1176304311yescharacteristic
373C22#1176312011yescharacteristic
374C22C2×#1058749811yescharacteristic
375C22#1176323911yescharacteristic
376C22#1176324411yescharacteristic
377C22#1176324511yescharacteristic
378C4—41no—
379C4—82no—
380C4—2721no—
381C4—2721no—
382C4#1176272311yescharacteristic
383C4#1176297111yescharacteristic
384C4#1176305311yescharacteristic
385C4#1176313011yescharacteristic
386C2—42no—
387C2—162no—
388C2#1452996311yescharacteristic
389C2#1453070711yescharacteristic
390C2#1453071311yescharacteristic
391C2#1453087811yescharacteristic
392C2#1453088511yescharacteristic
393C2#1453096711yescharacteristic
394C2#1453097211yescharacteristic
subgroupG/H
centerC23C2×#63228
commutator, cosocleC22×C8×C17C23
FrattiniC22×C8C22×D17
Fitting, prime radicalC2×C17×#466C2
socleC23×C17C2×D8
hypercenterC2×#466D17
hypocenterC17#13381
LCSG ▷ C22×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#11762636C2semidirect
2. C2×#11762610C2semidirect
3. C2×#11762610C2semidirect
4. C2×C22⋊#63214C2semidirect
5. #14528813C2semidirect
6. #14526875C2semidirect
62. C2×#63214D4semidirect
260. C17#13381semidirect

Maximal subgroups

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

subgroupindex
C2×#117626362
C2×#117626102
C2×C22⋊#632142
#145288132
#145268752
C2×C17×#4662
#1338117