Finite Group Databasebeta

← #16935546

Subgroups — #16935546

Order 4352.

790 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763157C211yesmaximal, characteristic, complemented
2#14533730C211yesmaximal, characteristic
3#14529708C211yesmaximal, characteristic, complemented
4C2×#11762552C211yesmaximal, characteristic, complemented
5C2×D4⋊#3622C211yesmaximal, characteristic, complemented
6#14526623C211yesmaximal, characteristic, complemented
7C2×C17×#474C211yesmaximal, characteristic, complemented
8C2×#10587560C2211yescharacteristic
9C2×#10587626—21no—
10C2×#10587616—22no—
11#11763157—22no—
12#11763157—22no—
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587506—22no—
15C2×#10587480—22no—
16C2×C4×#3622C2211yescharacteristic
17#11762718—22no—
18#11762710—21no—
19C4×C4⋊Dic17C2211yescharacteristic
20#11762552—22no—
21D4⋊#3622—22no—
22C2×C17×C4⋊Q8C2211yescharacteristic
23C2×C4×D4×C17C2211yescharacteristic
24C17×#474—22no—
25C17×#474—22no—
26C2×C17×#107—21no—
27C2×C17×C4⋊C8C2211yescharacteristic
28C2×C17×#102—21no—
29C22×Q8×C17—21no—
30C22×D4×C17D411yescharacteristic
31C23×C4×C17—21no—
32C22×C22⋊D17—24no—
33C22×D68—21no—
34C22×D68—21no—
35C22×D68D412yes—
36C22×C8×C17—21no—
37C17×C4⋊Q8—21no—
38C17×C4⋊Q8—21no—
39C17×C4⋊Q8—21no—
40C17×C4⋊Q8D412yescomplemented
41C4×D4×C17—21no—
42C4×D4×C17—21no—
43C4×D4×C17—21no—
44C4×D4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17D411yescharacteristic
48C2×C22⋊C4×C17—21no—
49C2×C42×C17C2311yescharacteristic
50#10587626—42no—
51#10587626—42no—
52#10587616—44no—
53#10587616—44no—
54C2×#63227—24no—
55C2×C4⋊Dic17D412yes—
56C2×C4×Dic17—21no—
57C22×#3622—21no—
58C22×#3622—21no—
59#10587560—21no—
60#10587560—21no—
61#10587560—21no—
62#10587560—21no—
63C17×#107—24no—
64C17×C4⋊C8—21no—
65C17×C4⋊C8D412yescomplemented
66C17×#102—24no—
67#10587506—44no—
68#10587502—21no—
69#10587480—28no—
70C4⋊#3622—21no—
71C4⋊#3622—21no—
72C4×#3622—21no—
73C4×#3622D412yescomplemented
74C24×C17—21no—
75C23×D17—22no—
76C2×Q8×C17—22no—
77C2×Q8×C17—41no—
78C2×Q8×C17—42no—
79C2×Q8×C17—42no—
80C2×D4×C17—21no—
81C2×D4×C17—21no—
82C2×D4×C17—21no—
83C2×D4×C17—21no—
84C2×D4×C17—21no—
85C2×D4×C17SD1612yes—
86C22×C4×C17—21no—
87C22×C4×C17—41no—
88C22×C4×C17—41no—
89C22×C4×C17—41no—
90C22×C4×C17—42no—
91C22×C4×C17—42no—
92C22×C4×C17C2×D411yescharacteristic
93C22×C4×C17C2×D411yescharacteristic
94C22×C4×C17C2×D411yescharacteristic
95C2×C22⋊D17—48no—
96C2×C22⋊D17—48no—
97C2×C22⋊D17—84no—
98C22×Dic17—22no—
99C2×D68—22no—
100C2×D68—22no—
101C2×D68—44no—
102C2×D68—41no—
103C2×D68—41no—
104C2×D68—41no—
105C2×D68—41no—
106C2×D68—42no—
107C2×D68—41no—
108C2×D68—41no—
109C2×D68—42no—
110C2×D68—41no—
111C2×D68—41no—
112C2×C8×C17—22no—
113C2×C8×C17—41no—
114C2×C8×C17—41no—
115C4⋊C4×C17—22no—
116C4⋊C4×C17—22no—
117C4⋊C4×C17—21no—
118C4⋊C4×C17—21no—
119C4⋊C4×C17—41no—
120C4⋊C4×C17—41no—
121C22⋊C4×C17—41no—
122C22⋊C4×C17—41no—
123C42×C17C2×D411yescharacteristic
124C42×C17C2×D411yescharacteristic
125C42×C17C2×D411yescharacteristic
126C42×C17#4111yescharacteristic
127#63227—48no—
128C4⋊Dic17—22no—
129C4⋊Dic17D814yes—
130C4×Dic17—41no—
131C4×Dic17—41no—
132C2×#3622—22no—
133C2×#3622—42no—
134C2×#3622—41no—
135C2×#3622—42no—
136#10070—171nomaximal, Sylow
137C23×C17—22no—
138C23×C17—41no—
139C23×C17—42no—
140C23×C17—41no—
141C23×C17—42no—
142C23×C17#12011yescharacteristic
143C22×D17—42no—
144C22×D17—44no—
145C22×D17—42no—
146C22×D17—42no—
147C22×D17—44no—
148Q8×C17—44no—
149Q8×C17—81no—
150Q8×C17—81no—
151D4×C17—22no—
152D4×C17—22no—
153D4×C17—41no—
154D4×C17—41no—
155C2×C4×C17—22no—
156C2×C4×C17—41no—
157C2×C4×C17—42no—
158C2×C4×C17—42no—
159C2×C4×C17—82no—
160C2×C4×C17—82no—
161C2×C4×C17—81no—
162C2×C4×C17—81no—
163C2×C4×C17#12011yescharacteristic
164C2×C4×C17#12011yescharacteristic
165C2×C4×C17#12111yescharacteristic
166C2×C4×C17#12111yescharacteristic
167C2×C4×C17#12111yescharacteristic
168C2×C4×C17#12711yescharacteristic
169C2×C4×C17C2×D812yes—
170C2×C4×C17C2×SD1611yescharacteristic
171C2×C4×C17#13511yescharacteristic
172C2×C4×C17AGL(1,ℤ/8)12yes—
173C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C17#13711yescharacteristic
175C22⋊D17—816no—
176C2×Dic17—24no—
177C2×Dic17—42no—
178C2×Dic17—42no—
179D68—44no—
180D68—82no—
181D68—81no—
182D68—81no—
183D68—82no—
184D68—81no—
185D68—81no—
186D68—81no—
187D68—81no—
188C8×C17—42no—
189#3622—42no—
190#3622—81no—
191C2×#486—171no—
192C2×#474D1711yescharacteristic, complemented
193#2541—171no—
194#1981—171no—
195C2×#331—171no—
196C2×D4⋊C8—171no—
197#1279—171no—
198C22×C17—44no—
199C22×C17—42no—
200C22×C17—82no—
201C22×C17—81no—
202C22×C17—81no—
203C22×C17#39211yescharacteristic
204C22×C17#44712yes—
205C22×C17#45011yescharacteristic
206C22×C17#45211yescharacteristic
207C22×C17#45512yes—
208C2×D17—84no—
209C2×D17—84no—
210C2×D17—82no—
211C2×D17—82no—
212C2×D17—82no—
213C4×C17—21no—
214C4×C17—21no—
215C4×C17—81no—
216C4×C17—82no—
217C4×C17#44811yescharacteristic
218C4×C17#44911yescharacteristic
219C4×C17#45912yes—
220C4×C17#46511yescharacteristic
221C4×C17#46811yescharacteristic
222C4×C17#49311yescharacteristic
223C4×C17#49611yescharacteristic
224Dic17—44no—
225C2×C4⋊Q8C2×D1711yescharacteristic
226C2×#127—171no—
227C2×#127—341no—
228C2×#121—342no—
229C2×C4×D4C2×D1711yescharacteristic
230#486—342no—
231#486—342no—
232#474—22no—
233#474—22no—
234C2×#107—21no—
235C2×C4⋊C8—171no—
236C2×C4⋊C8C2×D1711yescharacteristic
237C2×#103—342no—
238C2×#102—21no—
239C2×#102—342no—
240C2×C4×C8—171no—
241#392—342no—
242#390—341no—
243C4×C4⋊C4—171no—
244#331—342no—
245D4⋊C8—342no—
246C2×C17—82no—
247C2×C17#163912yes—
248C2×C17#164112yes—
249C2×C17#200011yescharacteristic
250C2×C17#200411yescharacteristic
251C2×C17#201111yescharacteristic
252D17—162no—
253C22×Q8—21no—
254C22×D4—172no—
255C22×D4—344no—
256C22×D4—341no—
257C22×D4—341no—
258C22×D4C22⋊D1711yescharacteristic
259C23×C4—21no—
260C22×C8—21no—
261C22×C8—341no—
262C22×C8—341no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8C22⋊D1712yescomplemented
267#127—341no—
268#127—341no—
269#127—341no—
270#127—341no—
271#127—682no—
272#127—682no—
273#121—684no—
274#121—684no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—172no—
282C2×C4⋊C4C22⋊D1711yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—344no—
285C2×C42—341no—
286C2×C42C22×D1711yescharacteristic
287#107—24no—
288C4⋊C8—21no—
289C4⋊C8—341no—
290C4⋊C8—341no—
291C4⋊C8C22⋊D1712yescomplemented
292#103—684no—
293#102—24no—
294#102—348no—
295C4×C8—172no—
296C4×C8—341no—
297#95—341no—
298C17#1007011yescharacteristic, complemented, Sylow
299C24—21no—
300C24—342no—
301C2×Q8—22no—
302C2×Q8—41no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—342no—
311C2×D4—342no—
312C2×D4—684no—
313C2×D4—688no—
314C2×D4—688no—
315C2×D4—682no—
316C2×D4—682no—
317C2×D4—681no—
318C2×D4—681no—
319C2×D4—681no—
320C2×D4—681no—
321C2×D4—681no—
322C2×D4—681no—
323C2×D4—681no—
324C2×D4—681no—
325C2×D4—1364no—
326C2×D4#6323012yes—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—342no—
334C22×C4D4×D1711yescharacteristic
335C22×C4D4×D1711yescharacteristic
336C22×C4C2×C22⋊D1711yescharacteristic
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—342no—
341C2×C8—682no—
342C2×C8—682no—
343C2×C8—681no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—174no—
351C4⋊C4—342no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—688no—
355C42—681no—
356C42—681no—
357C42D4×D1711yescharacteristic
358C42#6325411yescharacteristic
359C42C2×C22⋊D1711yescharacteristic
360C42C2×C22⋊D1711yescharacteristic
361C23—22no—
362C23—41no—
363C23—41no—
364C23—42no—
365C23—42no—
366C23—682no—
367C23—682no—
368C23—682no—
369C23—684no—
370C23—684no—
371C23#1058762311yescharacteristic
372Q8—44no—
373Q8—81no—
374Q8—81no—
375D4—22no—
376D4—22no—
377D4—41no—
378D4—41no—
379D4—684no—
380D4—1362no—
381D4—13616no—
382D4—1361no—
383D4—1361no—
384D4—1362no—
385D4—1361no—
386D4—1361no—
387D4—1361no—
388D4—1361no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—344no—
398C2×C4—682no—
399C2×C4—682no—
400C2×C4D8×D1712yes—
401C2×C4#1058759712yes—
402C2×C4#1058762311yescharacteristic
403C2×C4#1058762411yescharacteristic
404C2×C4#1058762511yescharacteristic
405C2×C4#1058762511yescharacteristic
406C2×C4#1058762611yescharacteristic
407C2×C4C2×#6323011yescharacteristic
408C2×C4#1058762811yescharacteristic
409C2×C4#1058763511yescharacteristic
410C2×C4#1058763611yescharacteristic
411C2×C4#1058763911yescharacteristic
412C8—42no—
413C8—682no—
414C8—1361no—
415C22—44no—
416C22—42no—
417C22—81no—
418C22—81no—
419C22—82no—
420C22—1362no—
421C22—1362no—
422C22—1364no—
423C22—1364no—
424C22—1362no—
425C22#1176271711yescharacteristic
426C22#1176294112yes—
427C22#1176295911yescharacteristic
428C22#1176296911yescharacteristic
429C22#1176298512yes—
430C4—21no—
431C4—21no—
432C4—81no—
433C4—82no—
434C4—684no—
435C4#1176294811yescharacteristic
436C4#1176295411yescharacteristic
437C4#1176300212yes—
438C4#1176304011yescharacteristic
439C4#1176305711yescharacteristic
440C4#1176318411yescharacteristic
441C4#1176319711yescharacteristic
442C2—82no—
443C2—2722no—
444C2#1452796212yes—
445C2#1452797612yes—
446C2#1452978511yescharacteristic
447C2#1452981011yescharacteristic
448C2#1452985311yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×#474C2
socleC23×C17#120
prime radical#14533730C2
hypercenterC2×#474D17
hypocenterC17#10070
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#11763157C2semidirect
3. #14529708C2semidirect
4. C2×#11762552C2semidirect
5. C2×D4⋊#3622C2semidirect
6. #14526623C2semidirect
7. C2×C17×#474C2semidirect
40. C17×C4⋊Q8D4semidirect
65. C17×C4⋊C8D4semidirect
73. C4×#3622D4semidirect
192. C2×#474D17semidirect
266. C4⋊Q8C22⋊D17semidirect
291. C4⋊C8C22⋊D17semidirect
298. C17#10070semidirect

Maximal subgroups

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

subgroupindex
C2×#117631572
#145337302
#145297082
C2×#117625522
C2×D4⋊#36222
#145266232
C2×C17×#4742
#1007017