Finite Group Databasebeta

← #16935408

Subgroups — #16935408

Order 4352.

702 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763157C211yesmaximal, characteristic, complemented
2C2×#11763004C211yesmaximal, characteristic
3#14529711C211yesmaximal, characteristic, complemented
4C2×#11762555C211yesmaximal, characteristic, complemented
5C2×D4⋊#3622C211yesmaximal, characteristic, complemented
6#14526625C211yesmaximal, characteristic, complemented
7C17×#2547C211yesmaximal, characteristic, complemented
8C22×#63228—21no—
9C2×#10587560C2211yescharacteristic
10#11763157—22no—
11#11763157—22no—
12#11763004—22no—
13#11763004—22no—
14C2×C4⋊#3622C2211yescharacteristic
15C2×C4⋊#3622C2211yescharacteristic
16C2×#10587480—22no—
17C2×#10587480—21no—
18C2×#10587480—22no—
19C2×C4×#3622C2211yescharacteristic
20#11762555—22no—
21D4⋊#3622—22no—
22C2×C17×C4⋊Q8C2211yescharacteristic
23C2×C17×#124—21no—
24C2×C4×D4×C17C2211yescharacteristic
25C17×#397—22no—
26C17×#391—21no—
27C17×#380—22no—
28C4×C4⋊C4×C17C2211yescharacteristic
29C22×Q8×C17—21no—
30C22×D4×C17D411yescharacteristic
31C23×C4×C17—21no—
32C22×D68—21no—
33C22×D68—21no—
34C22×D68—21no—
35C17×C4⋊Q8—21no—
36C17×C4⋊Q8—21no—
37C17×C4⋊Q8—21no—
38C17×C4⋊Q8—21no—
39C17×#124—42no—
40C17×#124—42no—
41C4×D4×C17—21no—
42C4×D4×C17—21no—
43C4×D4×C17—21no—
44C4×D4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17D411yescharacteristic
47C2×C4⋊C4×C17D412yes—
48C2×C4⋊C4×C17D412yes—
49C2×C22⋊C4×C17—24no—
50C2×C22⋊C4×C17—21no—
51C2×C42×C17—21no—
52C2×C42×C17C2311yescharacteristic
53C2×#63228—24no—
54C2×#63228—42no—
55C2×#63228—42no—
56C22×#3622—21no—
57C22×#3622—21no—
58C22×#3622—21no—
59#10587560—21no—
60#10587560—21no—
61#10587560—21no—
62#10587560D412yes—
63C17×#95—24no—
64C17×#95—21no—
65#10587480—24no—
66#10587480—28no—
67#10587480—44no—
68C4⋊#3622—21no—
69C4⋊#3622—21no—
70C4⋊#3622—21no—
71C4⋊#3622D412yes—
72C4×#3622—21no—
73C4×#3622D412yes—
74C24×C17—21no—
75C23×D17—41no—
76C2×Q8×C17—41no—
77C2×Q8×C17—41no—
78C2×Q8×C17—41no—
79C2×Q8×C17—41no—
80C2×Q8×C17—41no—
81C2×Q8×C17—41no—
82C2×D4×C17—21no—
83C2×D4×C17—21no—
84C2×D4×C17—21no—
85C2×D4×C17—21no—
86C2×D4×C17—21no—
87C2×D4×C17D812yes—
88C22×C4×C17—21no—
89C22×C4×C17—22no—
90C22×C4×C17—22no—
91C22×C4×C17—41no—
92C22×C4×C17—41no—
93C22×C4×C17—42no—
94C22×C4×C17—42no—
95C22×C4×C17C2×D411yescharacteristic
96C22×C4×C17C2×D411yescharacteristic
97C22×C4×C17C2×D411yescharacteristic
98C2×D68—22no—
99C2×D68—22no—
100C2×D68—22no—
101C2×D68—44no—
102C2×D68—41no—
103C2×D68—41no—
104C2×D68—42no—
105C2×D68—41no—
106C2×D68—42no—
107C2×D68—41no—
108C2×D68—41no—
109C2×D68—41no—
110C2×D68—41no—
111C4⋊C4×C17—22no—
112C4⋊C4×C17—21no—
113C4⋊C4×C17—22no—
114C4⋊C4×C17—21no—
115C4⋊C4×C17—22no—
116C4⋊C4×C17—22no—
117C4⋊C4×C17—41no—
118C4⋊C4×C17—41no—
119C22⋊C4×C17—48no—
120C22⋊C4×C17—41no—
121C22⋊C4×C17—41no—
122C42×C17—41no—
123C42×C17—41no—
124C42×C17C2×D411yescharacteristic
125C42×C17C2×D411yescharacteristic
126C42×C17C2×D411yescharacteristic
127C42×C17#4111yescharacteristic
128#63228—48no—
129C2×#3622—22no—
130C2×#3622—22no—
131C2×#3622—42no—
132C2×#3622—41no—
133C2×#3622—41no—
134C2×#3622—41no—
135C2×#3622—42no—
136#10050—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—81no—
145C22×D17—81no—
146C22×D17—82no—
147C22×D17—82no—
148Q8×C17—81no—
149Q8×C17—81no—
150Q8×C17—81no—
151Q8×C17—81no—
152D4×C17—22no—
153D4×C17—22no—
154D4×C17—41no—
155D4×C17—41no—
156C2×C4×C17—22no—
157C2×C4×C17—41no—
158C2×C4×C17—42no—
159C2×C4×C17—42no—
160C2×C4×C17—42no—
161C2×C4×C17—42no—
162C2×C4×C17—42no—
163C2×C4×C17—42no—
164C2×C4×C17—42no—
165C2×C4×C17—82no—
166C2×C4×C17—81no—
167C2×C4×C17—81no—
168C2×C4×C17#12011yescharacteristic
169C2×C4×C17#12011yescharacteristic
170C2×C4×C17#12111yescharacteristic
171C2×C4×C17#12111yescharacteristic
172C2×C4×C17#12111yescharacteristic
173C2×C4×C17#12711yescharacteristic
174C2×C4×C17C2×D811yescharacteristic
175C2×C4×C17#13511yescharacteristic
176C2×C4×C17#13512yes—
177C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C17AGL(1,ℤ/8)12yes—
180D68—44no—
181D68—42no—
182D68—42no—
183D68—44no—
184D68—82no—
185D68—81no—
186D68—81no—
187D68—81no—
188D68—81no—
189#3622—42no—
190#3622—42no—
191#3622—81no—
192C2×#486—171no—
193C2×#459—171no—
194#2547D1711yescharacteristic, complemented
195#1982—171no—
196C2×#332—171no—
197C2×D4⋊C8—171no—
198#1279—171no—
199C22×C17—44no—
200C22×C17—42no—
201C22×C17—82no—
202C22×C17—81no—
203C22×C17—81no—
204C22×C17#39211yescharacteristic
205C22×C17#44711yescharacteristic
206C22×C17#44912yes—
207C22×C17#44911yescharacteristic
208C22×C17#45412yes—
209C2×D17—82no—
210C2×D17—82no—
211C2×D17—82no—
212C2×D17—162no—
213C2×D17—162no—
214C4×C17—21no—
215C4×C17—21no—
216C4×C17—82no—
217C4×C17—82no—
218C4×C17—81no—
219C4×C17#44711yescharacteristic
220C4×C17#44911yescharacteristic
221C4×C17#46312yes—
222C4×C17#46611yescharacteristic
223C4×C17#46911yescharacteristic
224C4×C17#49511yescharacteristic
225C4×C17#49611yescharacteristic
226C22×D8—341no—
227C2×C4⋊Q8C2×D1711yescharacteristic
228C2×#127—171no—
229C2×#124—21no—
230C2×C4×D4C2×D1711yescharacteristic
231#486—342no—
232#486—342no—
233#459—342no—
234#459—342no—
235C2×C4⋊C8—171no—
236C2×C4⋊C8—171no—
237C2×#102—342no—
238C2×#102—341no—
239C2×#102—342no—
240C2×C4×C8—171no—
241#397—22no—
242#391—21no—
243#380—22no—
244C4×C4⋊C4C2×D1711yescharacteristic
245#332—342no—
246D4⋊C8—342no—
247C2×C17—82no—
248C2×C17#162512yes—
249C2×C17#162812yes—
250C2×C17#199911yescharacteristic
251C2×C17#200311yescharacteristic
252C2×C17#201211yescharacteristic
253D17—162no—
254C22×Q8—21no—
255C22×D4—341no—
256C22×D4—341no—
257C22×D4—341no—
258C22×D4C22⋊D1711yescharacteristic
259C23×C4—21no—
260C2×D8—344no—
261C2×D8—682no—
262C2×D8—682no—
263C22×C8—341no—
264C22×C8—341no—
265C22×C8—341no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270#127—172no—
271#127—341no—
272#127—341no—
273#127—341no—
274#124—42no—
275#124—42no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4C22⋊D1711yescharacteristic
282C2×C4⋊C4C22⋊D1712yes—
283C2×C4⋊C4C22⋊D1712yes—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—21no—
286C2×C42—21no—
287C2×C42C22×D1711yescharacteristic
288C4⋊C8—172no—
289C4⋊C8—341no—
290C4⋊C8—341no—
291C4⋊C8—341no—
292#102—344no—
293#102—348no—
294#102—684no—
295C4×C8—172no—
296C4×C8—341no—
297#95—24no—
298#95—21no—
299C17#1005011yescharacteristic, complemented, Sylow
300C24—21no—
301C24—681no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—342no—
314C2×D4—342no—
315C2×D4—342no—
316C2×D4—684no—
317C2×D4—681no—
318C2×D4—681no—
319C2×D4—681no—
320C2×D4—681no—
321C2×D4—681no—
322C2×D4—682no—
323C2×D4—681no—
324C2×D4—681no—
325C2×D4—682no—
326C2×D4#6322812yes—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4C2×C22⋊D1711yescharacteristic
335C22×C4C2×C22⋊D1711yescharacteristic
336C22×C4C2×C22⋊D1711yescharacteristic
337D8—688no—
338C2×C8—342no—
339C2×C8—342no—
340C2×C8—682no—
341C2×C8—681no—
342C2×C8—681no—
343C2×C8—681no—
344C2×C8—682no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C22⋊C4—48no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C42—41no—
357C42—41no—
358C42D4×D1711yescharacteristic
359C42D4×D1711yescharacteristic
360C42D4×D1711yescharacteristic
361C42#6325411yescharacteristic
362C23—22no—
363C23—42no—
364C23—41no—
365C23—41no—
366C23—42no—
367C23—682no—
368C23—1362no—
369C23—1361no—
370C23—1362no—
371C23—1361no—
372C23#1058763911yescharacteristic
373Q8—81no—
374Q8—81no—
375Q8—81no—
376Q8—81no—
377D4—22no—
378D4—22no—
379D4—41no—
380D4—41no—
381D4—684no—
382D4—682no—
383D4—684no—
384D4—682no—
385D4—1362no—
386D4—1361no—
387D4—1361no—
388D4—1361no—
389D4—1361no—
390C2×C4—22no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—82no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4C2×#6322811yescharacteristic
403C2×C4#1058761811yescharacteristic
404C2×C4#1058762311yescharacteristic
405C2×C4#1058762311yescharacteristic
406C2×C4#1058762411yescharacteristic
407C2×C4#1058762511yescharacteristic
408C2×C4#1058762511yescharacteristic
409C2×C4#1058762611yescharacteristic
410C2×C4#1058763512yes—
411C2×C4#1058763511yescharacteristic
412C2×C4#1058763611yescharacteristic
413C2×C4#1058763612yes—
414C8—682no—
415C8—682no—
416C8—1361no—
417C22—44no—
418C22—42no—
419C22—81no—
420C22—81no—
421C22—82no—
422C22—2722no—
423C22—2722no—
424C22—1362no—
425C22—1362no—
426C22—1362no—
427C22#1176271711yescharacteristic
428C22#1176294311yescharacteristic
429C22#1176295412yes—
430C22#1176295411yescharacteristic
431C22#1176298212yes—
432C4—21no—
433C4—21no—
434C4—81no—
435C4—82no—
436C4—82no—
437C4#1176294211yescharacteristic
438C4#1176295211yescharacteristic
439C4#1176302112yes—
440C4#1176304311yescharacteristic
441C4#1176306011yescharacteristic
442C4#1176319111yescharacteristic
443C4#1176319911yescharacteristic
444C2—82no—
445C2—2722no—
446C2#1452787312yes—
447C2#1452789412yes—
448C2#1452978011yescharacteristic
449C2#1452980411yescharacteristic
450C2#1452986111yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2547C2
socleC23×C17#120
prime radicalC2×#11763004C2
hypercenter#2547D17
hypocenterC17#10050
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2547

Complements

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

NH ≅ G/Ntype
1. C2×#11763157C2semidirect
3. #14529711C2semidirect
4. C2×#11762555C2semidirect
5. C2×D4⋊#3622C2semidirect
6. #14526625C2semidirect
7. C17×#2547C2semidirect
194. #2547D17semidirect
299. C17#10050semidirect

Maximal subgroups

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

subgroupindex
C2×#117631572
C2×#117630042
#145297112
C2×#117625552
C2×D4⋊#36222
#145266252
C17×#25472
#1005017