Finite Group Databasebeta

← #17954496

Subgroups — #17954496

Order 4352.

736 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763825C211yesmaximal, characteristic, complemented
2#14544674C211yesmaximal, characteristic, complemented
3C2×#11763652C212yesmaximal
4#14543622C212yesmaximal, complemented
5C2×#11762702C211yesmaximal, characteristic
6#11763825—24no—
7C2×C4⋊#3624—21no—
8C2×C22⋊#3624C2212yes—
9C2×C22⋊#3624C2212yes—
10C2×C4×#3624—21no—
11#11763675—21no—
12#11763675—21no—
13#11763652—24no—
14C22×C4⋊Dic17C411yescharacteristic
15C22×C22⋊Dic17C411yescharacteristic
16C22×C22⋊Dic17C2211yescharacteristic
17C22×C4×Dic17C2211yescharacteristic
18#11762702—21no—
19#11762702—21no—
20#11762702—21no—
21#11762702—21no—
22C2×#10587502C411yescharacteristic
23C2×#10587502C2211yescharacteristic
24C22×C22⋊C4×C17C411yescharacteristic
25C25×C17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C23×C4×C17C2×C411yescharacteristic
28C23×Dic17C2×C411yescharacteristic
29C23×Dic17C2×C411yescharacteristic
30C23×Dic17C2×C411yescharacteristic
31C23×Dic17C2311yescharacteristic
32C22×#3624—22no—
33C22×#3624—22no—
34C2×C22⋊C4×C17—21no—
35C2×C22⋊C4×C17—21no—
36C2×C22⋊C4×C17—22no—
37C2×C22⋊C4×C17C814yescomplemented
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40C2×C22⋊Dic17—21no—
41C2×C22⋊Dic17—21no—
42C2×C22⋊Dic17—22no—
43C2×C22⋊Dic17—22no—
44C2×C22⋊Dic17—42no—
45C2×C4⋊Dic17—21no—
46C2×C4⋊Dic17—21no—
47C2×C4⋊Dic17—42no—
48C2×C4×Dic17—22no—
49C2×C4×Dic17—22no—
50C2×C4×Dic17D411yescharacteristic
51C2×C4×Dic17D411yescharacteristic
52C2×C4×Dic17D411yescharacteristic
53C2×C4×Dic17D411yescharacteristic
54C22⋊#3624—22no—
55C22⋊#3624—22no—
56C22⋊#3624—22no—
57C22⋊#3624D414yes—
58C4⋊#3624—24no—
59C4×#3624—24no—
60#10587502—21no—
61#10587502—21no—
62#10587502—21no—
63#10587502—21no—
64C24×C17—21no—
65C24×C17—21no—
66C24×C17—22no—
67C24×C17—22no—
68C24×C17—41no—
69C24×C17—41no—
70C24×C17—41no—
71C24×C17—41no—
72C24×C17C2×C812yes—
73C24×C17C22×C411yescharacteristic
74C22×C4×C17—22no—
75C22×C4×C17—22no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—41no—
79C22×C4×C17—41no—
80C22×C4×C17C22⋊C411yescharacteristic
81C22×C4×C17C22⋊C411yescharacteristic
82C22×C4×C17C2×C812yes—
83C22×C4×C17C2×C812yes—
84C22×C4×C17M1612yes—
85C22×Dic17—22no—
86C22×Dic17—22no—
87C22×Dic17—21no—
88C22×Dic17—21no—
89C22×Dic17—22no—
90C22×Dic17—22no—
91C22×Dic17—41no—
92C22×Dic17—41no—
93C22×Dic17—41no—
94C22×Dic17—41no—
95C22×Dic17—41no—
96C22×Dic17—41no—
97C22×Dic17—41no—
98C22×Dic17C22⋊C411yescharacteristic
99C22×Dic17C22⋊C411yescharacteristic
100C22×Dic17C2×D411yescharacteristic
101C22×Dic17C2×D411yescharacteristic
102C22×Dic17C2×D412yes—
103C22×Dic17#4112yes—
104C2×#3624—24no—
105C2×#3624—42no—
106C2×#3624—42no—
107C2×#3624—42no—
108C2×#3624—42no—
109C2×#3624—42no—
110C22⋊C4×C17—24no—
111C22⋊C4×C17—24no—
112C22⋊Dic17—42no—
113C22⋊Dic17—42no—
114C22⋊Dic17—41no—
115C22⋊Dic17—42no—
116C22⋊Dic17—41no—
117C4⋊Dic17—42no—
118C4⋊Dic17—42no—
119C4×Dic17—21no—
120C4×Dic17—21no—
121C4×Dic17—22no—
122C4×Dic17—22no—
123C4×Dic17—21no—
124C4×Dic17—21no—
125#9080—171nomaximal, Sylow
126C23×C17—21no—
127C23×C17—21no—
128C23×C17—21no—
129C23×C17—21no—
130C23×C17—22no—
131C23×C17—24no—
132C23×C17—42no—
133C23×C17—42no—
134C23×C17—42no—
135C23×C17—42no—
136C23×C17—41no—
137C23×C17—41no—
138C23×C17—41no—
139C23×C17—41no—
140C23×C17—41no—
141C23×C17—41no—
142C23×C17—42no—
143C23×C17—82no—
144C23×C17—82no—
145C23×C17—82no—
146C23×C17—82no—
147C23×C17C2×C22⋊C411yescharacteristic
148C23×C17C4×D412yes—
149C23×C17C22×C811yescharacteristic
150C23×C17C2×M1611yescharacteristic
151C23×C17#13112yes—
152C2×C4×C17—21no—
153C2×C4×C17—21no—
154C2×C4×C17—21no—
155C2×C4×C17—21no—
156C2×C4×C17—24no—
157C2×C4×C17—24no—
158C2×C4×C17—22no—
159C2×C4×C17—42no—
160C2×C4×C17—41no—
161C2×C4×C17—41no—
162C2×C4×C17—42no—
163C2×C4×C17C22⋊C812yes—
164C2×C4×C17C22⋊C812yes—
165C2×Dic17—21no—
166C2×Dic17—21no—
167C2×Dic17—21no—
168C2×Dic17—21no—
169C2×Dic17—21no—
170C2×Dic17—21no—
171C2×Dic17—21no—
172C2×Dic17—21no—
173C2×Dic17—21no—
174C2×Dic17—42no—
175C2×Dic17—42no—
176C2×Dic17—44no—
177C2×Dic17—41no—
178C2×Dic17—41no—
179C2×Dic17—41no—
180C2×Dic17—41no—
181C2×Dic17—41no—
182C2×Dic17—41no—
183C2×Dic17—82no—
184C2×Dic17—82no—
185C2×Dic17#10012yes—
186C2×Dic17#12011yescharacteristic
187C2×Dic17#12112yes—
188C2×Dic17#12311yescharacteristic
189#3624—44no—
190#3624—82no—
191C2×#431—171no—
192C2×#388—171no—
193#1817—171no—
194C2×#323—172no—
195#1280—172no—
196C22×C17—22no—
197C22×C17—22no—
198C22×C17—21no—
199C22×C17—21no—
200C22×C17—21no—
201C22×C17—21no—
202C22×C17—22no—
203C22×C17—22no—
204C22×C17—42no—
205C22×C17—42no—
206C22×C17—42no—
207C22×C17—84no—
208C22×C17—84no—
209C22×C17—81no—
210C22×C17—81no—
211C22×C17—81no—
212C22×C17—81no—
213C22×C17#38611yescharacteristic
214C22×C17C2×C22⋊C811yescharacteristic
215C22×C17#40811yescharacteristic
216C22×C17#41011yescharacteristic
217C22×C17#41011yescharacteristic
218C22×C17C2×#10011yescharacteristic
219C22×C17#41311yescharacteristic
220C22×C17C8×D412yes—
221C22×C17#43512yes—
222C4×C17—22no—
223C4×C17—22no—
224C4×C17—42no—
225Dic17—21no—
226Dic17—22no—
227Dic17—21no—
228Dic17—22no—
229Dic17—41no—
230Dic17—81no—
231Dic17—81no—
232C22×C4⋊C4—171no—
233C22×C22⋊C4—171no—
234C22×C22⋊C4—171no—
235C22×C22⋊C4#59511yescharacteristic
236C22×C42—171no—
237#431—344no—
238C2×C4⋊C8—341no—
239C2×C22⋊C8—172no—
240C2×C22⋊C8—172no—
241C2×C4×C8—341no—
242#388—341no—
243#388—341no—
244#388—341no—
245#388—341no—
246C2×#95—171no—
247C2×#95—171no—
248#336—341no—
249#336—341no—
250#323—344no—
251C2×C17—22no—
252C2×C17—22no—
253C2×C17—82no—
254C2×C17#145811yescharacteristic
255C2×C17#146011yescharacteristic
256C2×C17#146911yescharacteristic
257C2×C17#147311yescharacteristic
258C2×C17#186911yescharacteristic
259C2×C17#189911yescharacteristic
260C2×C17#190011yescharacteristic
261C25C2×#59511yescharacteristic
262C23×C4—171no—
263C23×C4—171no—
264C23×C4—171no—
265C23×C4—171no—
266C23×C4C2×#59511yescharacteristic
267C23×C4C2×#59511yescharacteristic
268C22×C8—342no—
269C22×C8—342no—
270C2×C4⋊C4—341no—
271C2×C4⋊C4—341no—
272C2×C4⋊C4—682no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—342no—
277C2×C22⋊C4—341no—
278C2×C22⋊C4—341no—
279C2×C22⋊C4—341no—
280C2×C22⋊C4—341no—
281C2×C22⋊C4—342no—
282C2×C22⋊C4—682no—
283C2×C22⋊C4#362414yescomplemented
284C2×C42—171no—
285C2×C42—171no—
286C2×C42—171no—
287C2×C42—171no—
288C2×C42—342no—
289C2×C42—342no—
290C4⋊C8—344no—
291C22⋊C8—174no—
292C22⋊C8—342no—
293C22⋊C8—342no—
294C22⋊C8—342no—
295C4×C8—344no—
296#95—341no—
297#95—341no—
298#95—341no—
299#95—341no—
300C17#908011yescharacteristic, complemented, Sylow
301C24—21no—
302C24—21no—
303C24—22no—
304C24—22no—
305C24—41no—
306C24—41no—
307C24—41no—
308C24—41no—
309C24C2×#362412yes—
310C24C22×#59511yescharacteristic
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—171no—
318C22×C4—171no—
319C22×C4—171no—
320C22×C4—172no—
321C22×C4—172no—
322C22×C4—171no—
323C22×C4—342no—
324C22×C4—342no—
325C22×C4—341no—
326C22×C4—341no—
327C22×C4—342no—
328C22×C4—342no—
329C22×C4—681no—
330C22×C4—681no—
331C22×C4—681no—
332C22×C4—681no—
333C22×C4—681no—
334C22×C4—681no—
335C22×C4—681no—
336C22×C4C2×#362412yes—
337C22×C4C2×#362412yes—
338C22×C4#6324712yes—
339C22×C4C22⋊#59511yescharacteristic
340C22×C4C22⋊#59511yescharacteristic
341C2×C8—344no—
342C2×C8—682no—
343C2×C8—682no—
344C2×C8—682no—
345C2×C8—682no—
346C2×C8—682no—
347C4⋊C4—682no—
348C4⋊C4—682no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—681no—
352C22⋊C4—682no—
353C22⋊C4—681no—
354C22⋊C4—682no—
355C22⋊C4—682no—
356C42—341no—
357C42—341no—
358C42—342no—
359C42—342no—
360C42—341no—
361C42—341no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—22no—
367C23—24no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—42no—
379C23—82no—
380C23—82no—
381C23—82no—
382C23—82no—
383C23#1058767812yes—
384C23D4×#59512yes—
385C23C22×#362411yescharacteristic
386C23C2×#6324711yescharacteristic
387C23C2×C22⋊#59511yescharacteristic
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—171no—
400C2×C4—172no—
401C2×C4—171no—
402C2×C4—172no—
403C2×C4—341no—
404C2×C4—341no—
405C2×C4—341no—
406C2×C4—341no—
407C2×C4—341no—
408C2×C4—341no—
409C2×C4—341no—
410C2×C4—341no—
411C2×C4—341no—
412C2×C4—682no—
413C2×C4—682no—
414C2×C4—684no—
415C2×C4—681no—
416C2×C4—681no—
417C2×C4—681no—
418C2×C4—681no—
419C2×C4—681no—
420C2×C4—681no—
421C2×C4—1362no—
422C2×C4—1362no—
423C2×C4C22⋊#362412yes—
424C2×C4C22⋊#362412yes—
425C8—684no—
426C8—1362no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—84no—
439C22—84no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22#1176375711yescharacteristic
445C22C2×C22⋊#362411yescharacteristic
446C22#1176378211yescharacteristic
447C22#1176378811yescharacteristic
448C22#1176378911yescharacteristic
449C22D17⋊#10011yescharacteristic
450C22#1176379511yescharacteristic
451C22D4×#362412yes—
452C22#1176384012yes—
453C4—22no—
454C4—22no—
455C4—42no—
456C4—341no—
457C4—342no—
458C4—341no—
459C4—342no—
460C4—681no—
461C4—1361no—
462C4—1361no—
463C2—22no—
464C2—22no—
465C2—82no—
466C2#1454401511yescharacteristic
467C2#1454402411yescharacteristic
468C2#1454405311yescharacteristic
469C2#1454406611yescharacteristic
470C2#1454475711yescharacteristic
471C2#1454480711yescharacteristic
472C2#1454481011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC25×C17C2×C4
cosocleC23×Dic17C23
hypercenterC22×C22⋊C4#595
hypocenterC17#9080
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11763825C2semidirect
2. #14544674C2semidirect
4. #14543622C2semidirect
37. C2×C22⋊C4×C17C8semidirect
283. C2×C22⋊C4#3624semidirect
300. C17#9080semidirect

Maximal subgroups

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

subgroupindex
C2×#117638252
#145446742
C2×#117636522
#145436222
C2×#117627022
#908017