Finite Group Databasebeta

← #14533909

Subgroups — #14533909

Order 2176.

574 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10587565C211yesmaximal, characteristic, complemented
2#11762748C211yesmaximal, characteristic, complemented
3#11762723C211yesmaximal, characteristic, complemented
4#11762723C211yesmaximal, characteristic, complemented
5#11762723C211yesmaximal, characteristic, complemented
6#11762712C211yesmaximal, characteristic, complemented
7#11762704C211yesmaximal, characteristic, complemented
8#11762703C211yesmaximal, characteristic, complemented
9#11762697C211yesmaximal, characteristic, complemented
10#11762689C211yesmaximal, characteristic, complemented
11#11762689C211yesmaximal, characteristic, complemented
12#11762682C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
15C2×C17×#121C211yesmaximal, characteristic
16C22×D4×C17C2211yescharacteristic
17C22×D4×C17C2211yescharacteristic
18C22×D4×C17C2211yescharacteristic
19C23×C4×C17C2211yescharacteristic
20C23×Dic17C2211yescharacteristic
21C17×#121—24no—
22C2×C4⋊C4×C17C2211yescharacteristic
23C2×C22⋊C4×C17C2211yescharacteristic
24C2×C22⋊C4×C17C2211yescharacteristic
25C2×C22⋊Dic17C2211yescharacteristic
26C2×C22⋊Dic17C2211yescharacteristic
27C2×C22⋊Dic17C2211yescharacteristic
28C2×C22⋊Dic17C2211yescharacteristic
29C2×C22⋊Dic17C2211yescharacteristic
30C2×C22⋊Dic17C2211yescharacteristic
31C2×C22⋊Dic17C2211yescharacteristic
32C2×C22⋊Dic17C2211yescharacteristic
33C2×C22⋊Dic17C2211yescharacteristic
34C2×C22⋊Dic17C2211yescharacteristic
35C2×C22⋊Dic17C2211yescharacteristic
36C2×C4⋊Dic17C2211yescharacteristic
37C2×#63225C2211yescharacteristic
38C2×#63225C2211yescharacteristic
39C2×#63225C2211yescharacteristic
40C2×#63225C2211yescharacteristic
41C2×C4×Dic17C2211yescharacteristic
42C2×C4×Dic17C2211yescharacteristic
43C2×C4×Dic17C2211yescharacteristic
44#10587565—24no—
45#10587502C2211yescharacteristic
46#10587502C2211yescharacteristic
47#10587502C2211yescharacteristic
48#10587502C2211yescharacteristic
49#10587502C2211yescharacteristic
50#10587502C2211yescharacteristic
51#10587502C2211yescharacteristic
52#10587502C2211yescharacteristic
53C24×C17C2311yescharacteristic
54C24×C17C2311yescharacteristic
55C24×C17C2311yescharacteristic
56C2×D4×C17—22no—
57C2×D4×C17—22no—
58C2×D4×C17—22no—
59C2×D4×C17—22no—
60C2×D4×C17—22no—
61C2×D4×C17—22no—
62C2×D4×C17—41no—
63C2×D4×C17—41no—
64C2×D4×C17—41no—
65C22×C4×C17—22no—
66C22×C4×C17—22no—
67C22×C4×C17—41no—
68C22×C4×C17C2311yescharacteristic
69C22×C4×C17C2311yescharacteristic
70C22×C4×C17C2311yescharacteristic
71C22×C4×C17C2311yescharacteristic
72C22×Dic17—22no—
73C22×Dic17—41no—
74C22×Dic17—41no—
75C22×Dic17C2311yescharacteristic
76C22×Dic17C2311yescharacteristic
77C22×Dic17C2311yescharacteristic
78C22×Dic17C2311yescharacteristic
79C22×Dic17C2311yescharacteristic
80C22×Dic17C2311yescharacteristic
81C22×Dic17C2311yescharacteristic
82C22×Dic17C2311yescharacteristic
83C4⋊C4×C17—22no—
84C22⋊C4×C17—22no—
85C22⋊C4×C17D414yes—
86C22⋊Dic17—22no—
87C22⋊Dic17—22no—
88C22⋊Dic17—22no—
89C22⋊Dic17—22no—
90C22⋊Dic17—22no—
91C22⋊Dic17—22no—
92C22⋊Dic17—22no—
93C22⋊Dic17—22no—
94C22⋊Dic17—41no—
95C22⋊Dic17—41no—
96C22⋊Dic17—41no—
97C4⋊Dic17—22no—
98#63225—22no—
99#63225—22no—
100#63225—22no—
101#63225—41no—
102C4×Dic17—22no—
103C4×Dic17—41no—
104C4×Dic17—41no—
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—21no—
118C23×C17—21no—
119C23×C17—21no—
120C23×C17—21no—
121C23×C17—21no—
122C23×C17—21no—
123C23×C17—21no—
124C23×C17C2×D412yes—
125C23×C17#4112yes—
126C23×C17C2411yescharacteristic
127D4×C17—44no—
128D4×C17—44no—
129D4×C17—44no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—44no—
140C2×C4×C17C2×D412yes—
141C2×C4×C17C2×D412yes—
142C2×C4×C17#4112yes—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148C2×Dic17—21no—
149C2×Dic17—21no—
150C2×Dic17—21no—
151C2×Dic17—21no—
152C2×Dic17—21no—
153C2×Dic17—21no—
154C2×Dic17—21no—
155C2×Dic17—21no—
156C2×Dic17—21no—
157C2×Dic17—21no—
158C2×Dic17—21no—
159C2×Dic17—21no—
160C2×Dic17—21no—
161C2×Dic17—21no—
162C2×Dic17—21no—
163C2×Dic17—21no—
164C2×Dic17—21no—
165C2×Dic17—44no—
166C2×Dic17#4112yes—
167C2×Dic17#4112yes—
168#2559—171nomaximal, Sylow
169C22×C17—22no—
170C22×C17—22no—
171C22×C17—22no—
172C22×C17—22no—
173C22×C17—22no—
174C22×C17—22no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—41no—
178C22×C17—41no—
179C22×C17—41no—
180C22×C17—41no—
181C22×C17—41no—
182C22×C17—41no—
183C22×C17—41no—
184C22×C17—41no—
185C22×C17—41no—
186C22×C17—41no—
187C22×C17—41no—
188C22×C17—41no—
189C22×C17—41no—
190C22×C17C22×D411yescharacteristic
191C22×C17C2×#4111yescharacteristic
192C22×C17C2×#4111yescharacteristic
193C22×C17C2×#4111yescharacteristic
194C22×C17C2×#4111yescharacteristic
195C22×C17H(5,𝔽2)11yescharacteristic
196C22×C17H(5,𝔽2)11yescharacteristic
197C4×C17—22no—
198C4×C17—22no—
199C4×C17—22no—
200C4×C17—41no—
201Dic17—22no—
202Dic17—22no—
203Dic17—41no—
204Dic17—41no—
205Dic17—41no—
206Dic17—41no—
207Dic17—41no—
208Dic17—41no—
209C2×#126—171no—
210C2×#121D1711yescharacteristic
211#400—171no—
212#394—171no—
213#394—171no—
214#394—171no—
215#390—171no—
216#389—171no—
217#388—171no—
218#388—171no—
219#386—171no—
220#386—171no—
221#385—171no—
222C4×C22⋊C4—171no—
223C4×C22⋊C4—171no—
224C2×C17—42no—
225C2×C17—42no—
226C2×C17—81no—
227C2×C17#52911yescharacteristic
228C2×C17#53211yescharacteristic
229C2×C17#53811yescharacteristic
230C2×C17#54611yescharacteristic
231C2×C17#54611yescharacteristic
232C2×C17#55311yescharacteristic
233C2×C17#55311yescharacteristic
234C22×D4C2×D1711yescharacteristic
235C22×D4C2×D1711yescharacteristic
236C22×D4C2×D1711yescharacteristic
237C23×C4—171no—
238C23×C4C2×D1711yescharacteristic
239#126—344no—
240#121—24no—
241C2×C4⋊C4—171no—
242C2×C4⋊C4—171no—
243C2×C4⋊C4—171no—
244C2×C4⋊C4—171no—
245C2×C4⋊C4—171no—
246C2×C4⋊C4C2×D1711yescharacteristic
247C2×C22⋊C4—171no—
248C2×C22⋊C4—171no—
249C2×C22⋊C4—171no—
250C2×C22⋊C4—171no—
251C2×C22⋊C4—171no—
252C2×C22⋊C4—171no—
253C2×C22⋊C4—171no—
254C2×C22⋊C4—171no—
255C2×C22⋊C4—171no—
256C2×C22⋊C4—171no—
257C2×C22⋊C4—171no—
258C2×C22⋊C4C2×D1711yescharacteristic
259C2×C22⋊C4C2×D1711yescharacteristic
260C2×C42—171no—
261C2×C42—171no—
262C2×C42—171no—
263#95—171no—
264#95—171no—
265#95—171no—
266#95—171no—
267#95—171no—
268#95—171no—
269#95—171no—
270#95—171no—
271C17#255911yescharacteristic, complemented, Sylow
272C24C22×D1711yescharacteristic
273C24C22×D1711yescharacteristic
274C24C22×D1711yescharacteristic
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—171no—
288C22×C4—171no—
289C22×C4—171no—
290C22×C4—171no—
291C22×C4—171no—
292C22×C4—171no—
293C22×C4—171no—
294C22×C4—171no—
295C22×C4—342no—
296C22×C4—681no—
297C22×C4—681no—
298C22×C4C22×D1711yescharacteristic
299C22×C4C22×D1711yescharacteristic
300C22×C4C22×D1711yescharacteristic
301C22×C4C22×D1711yescharacteristic
302C4⋊C4—22no—
303C4⋊C4—342no—
304C4⋊C4—342no—
305C4⋊C4—342no—
306C4⋊C4—342no—
307C4⋊C4—681no—
308C22⋊C4—22no—
309C22⋊C4—342no—
310C22⋊C4—342no—
311C22⋊C4—342no—
312C22⋊C4—342no—
313C22⋊C4—342no—
314C22⋊C4—342no—
315C22⋊C4—342no—
316C22⋊C4—342no—
317C22⋊C4—681no—
318C22⋊C4—681no—
319C22⋊C4—681no—
320C22⋊C4C22⋊D1714yes—
321C42—342no—
322C42—681no—
323C42—681no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23#6325412yes—
344C23C2×C22⋊D1712yes—
345C23C23×D1711yescharacteristic
346D4—44no—
347D4—44no—
348D4—44no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—44no—
359C2×C4—172no—
360C2×C4—172no—
361C2×C4—341no—
362C2×C4—341no—
363C2×C4—341no—
364C2×C4—341no—
365C2×C4—341no—
366C2×C4—341no—
367C2×C4—341no—
368C2×C4—341no—
369C2×C4—341no—
370C2×C4—341no—
371C2×C4—341no—
372C2×C4—341no—
373C2×C4—341no—
374C2×C4—341no—
375C2×C4—341no—
376C2×C4—341no—
377C2×C4—341no—
378C2×C4—341no—
379C2×C4—341no—
380C2×C4—341no—
381C2×C4—341no—
382C2×C4—341no—
383C2×C4—684no—
384C2×C4#6325412yes—
385C2×C4C2×C22⋊D1712yes—
386C2×C4C2×C22⋊D1712yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22C2×#6325411yescharacteristic
409C22C2×#6325411yescharacteristic
410C22#1058769111yescharacteristic
411C22#1058769111yescharacteristic
412C22#41×D1711yescharacteristic
413C22#41×D1711yescharacteristic
414C22C22×C22⋊D1711yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—41no—
419C4—342no—
420C4—342no—
421C4—681no—
422C4—681no—
423C4—681no—
424C4—681no—
425C4—681no—
426C4—681no—
427C2—42no—
428C2—42no—
429C2—81no—
430C2#1176334011yescharacteristic
431C2#1176335511yescharacteristic
432C2#1176339111yescharacteristic
433C2#1176345311yescharacteristic
434C2#1176345311yescharacteristic
435C2#1176350211yescharacteristic
436C2#1176350611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, cosocleC23×C17C24
Fitting, prime radicalC2×C17×#121C2
hypercenterC2×#121D17
hypocenterC17#2559
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10587565C2semidirect
2. #11762748C2semidirect
3. #11762723C2semidirect
4. #11762723C2semidirect
5. #11762723C2semidirect
6. #11762712C2semidirect
7. #11762704C2semidirect
8. #11762703C2semidirect
9. #11762697C2semidirect
10. #11762689C2semidirect
11. #11762689C2semidirect
12. #11762682C2semidirect
13. C22⋊C4×Dic17C2semidirect
14. C4×C22⋊Dic17C2semidirect
271. C17#2559semidirect

Maximal subgroups

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

subgroupindex
C2×#105875652
#117627482
#117627232
#117627122
#117627042
#117627032
#117626972
#117626892
#117626822
C22⋊C4×Dic172
C4×C22⋊Dic172
C2×C17×#1212
#255917