Finite Group Databasebeta

← #17949950

Subgroups — #17949950

Order 4352.

584 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544676C211yesmaximal, characteristic, complemented
2#14544639C211yesmaximal, characteristic, complemented
3#14543602C212yesmaximal, complemented
4#14543601C212yesmaximal, complemented
5C4×#10587581C211yesmaximal, characteristic
6C2×C4⋊#3624—21no—
7C2×#10587543—21no—
8C2×#10587543—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587581C411yescharacteristic
13C2×C4×D68—21no—
14C2×C4×D68C411yescharacteristic
15C2×C42×D17C2211yescharacteristic
16#11762710C2211yescharacteristic
17#11762708C2211yescharacteristic
18#11762701—21no—
19#11762687—21no—
20#11762666C411yescharacteristic
21C4×#63227—21no—
22C4×C4⋊C4×C17C411yescharacteristic
23C22×D68—21no—
24C22×D68C2×C411yescharacteristic
25C22×C4×D17—21no—
26C22×C4×D17C2×C411yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×C4×D17D411yescharacteristic
29C22×#3624—22no—
30C22×#3624—22no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C42×C17—21no—
34C2×C42×C17C2×C411yescharacteristic
35C2×#63227—21no—
36C2×#63227—21no—
37C2×#63227—21no—
38C2×#63227—21no—
39C2×#63227—21no—
40C2×C4⋊Dic17—21no—
41C2×C4⋊Dic17C2×C411yescharacteristic
42C2×C4×Dic17D411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44C2×C4×Dic17C2311yescharacteristic
45#10587581—22no—
46#10587581—22no—
47C4×D68—42no—
48C4×D68—42no—
49C4×D68—42no—
50C42×D17—42no—
51#10587543—42no—
52#10587543—42no—
53C4⋊#3624—42no—
54C17×#95—21no—
55#10587502—21no—
56#10587502—21no—
57C23×D17—21no—
58C23×D17C22⋊C411yescharacteristic
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22×C411yescharacteristic
64C22×Dic17—21no—
65C22×Dic17C22⋊C411yescharacteristic
66C22×Dic17C2×D411yescharacteristic
67C22×Dic17C2×D411yescharacteristic
68C2×D68—24no—
69C2×D68—21no—
70C2×D68—41no—
71C2×D68—41no—
72C2×D68—42no—
73C2×D68—42no—
74C2×D68M1612yes—
75C2×C4×D17—22no—
76C2×C4×D17—21no—
77C2×C4×D17—21no—
78C2×C4×D17—22no—
79C2×C4×D17—41no—
80C2×C4×D17—41no—
81C2×C4×D17—41no—
82C2×C4×D17—41no—
83C2×C4×D17—41no—
84C2×C4×D17—42no—
85C2×C4×D17—42no—
86C2×C4×D17—42no—
87C2×C4×D17D812yes—
88C2×C4×D17SD1612yes—
89C2×#3624—42no—
90C2×#3624—42no—
91C2×#3624—42no—
92C2×#3624—42no—
93C2×#3624—42no—
94C2×#3624—42no—
95C4⋊C4×C17—21no—
96C4⋊C4×C17—41no—
97C4⋊C4×C17M1612yes—
98C42×C17—22no—
99C42×C17—42no—
100#63227—24no—
101#63227—42no—
102#63227—42no—
103#63227—41no—
104#63227—41no—
105#63227—42no—
106C4⋊Dic17—41no—
107C4⋊Dic17—41no—
108C4⋊Dic17—41no—
109C4×Dic17—22no—
110C4×Dic17—41no—
111C4×Dic17—41no—
112#7647—171nomaximal, Sylow
113C23×C17C2×C22⋊C411yescharacteristic
114C22×D17—21no—
115C22×D17—21no—
116C22×D17—21no—
117C22×D17—21no—
118C22×D17—21no—
119C22×D17—21no—
120C22×D17—22no—
121C22×D17—41no—
122C22×D17—41no—
123C22×D17—41no—
124C22×D17—41no—
125C22×D17—41no—
126C22×D17—41no—
127C22×D17#10212yes—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—22no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17#9912yes—
141C2×C4×C17#10212yes—
142C2×C4×C17C2×M1611yescharacteristic
143C2×C4×C17C2×M1611yescharacteristic
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148C2×Dic17—21no—
149C2×Dic17—21no—
150C2×Dic17—21no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17C2×D811yescharacteristic
155C2×Dic17C2×SD1611yescharacteristic
156C2×Dic17#13512yes—
157D68—42no—
158D68—42no—
159D68—48no—
160C4×D17—42no—
161C4×D17—42no—
162C4×D17—44no—
163C4×D17—42no—
164C4×D17—42no—
165C4×D17—84no—
166#3624—82no—
167#3624—82no—
168C4×#121—171no—
169#1817—171no—
170#1797—171no—
171#1271—172no—
172#1270—172no—
173C22×C17#40711yescharacteristic
174C22×C17C2×#9911yescharacteristic
175C22×C17#41311yescharacteristic
176C22×C17C2×#10211yescharacteristic
177C22×C17#41611yescharacteristic
178C22×C17#42111yescharacteristic
179C22×C17#42111yescharacteristic
180C2×D17—22no—
181C2×D17—22no—
182C2×D17—22no—
183C2×D17—41no—
184C2×D17—41no—
185C2×D17—41no—
186C2×D17—41no—
187C2×D17—42no—
188C2×D17—42no—
189C2×D17—42no—
190C2×D17—81no—
191C2×D17—81no—
192C2×D17—81no—
193C2×D17—81no—
194C4×C17—21no—
195C4×C17—21no—
196C4×C17—22no—
197C4×C17—22no—
198C4×C17—42no—
199C4×C17—81no—
200Dic17—22no—
201Dic17—21no—
202Dic17—21no—
203Dic17—41no—
204Dic17—81no—
205C2×#121—171no—
206C2×C4×D4—171no—
207C2×C4×D4—341no—
208C22×C42—171no—
209C2×C4⋊C8—341no—
210C2×C22⋊C8—341no—
211C2×C22⋊C8—341no—
212#390—171no—
213#389—171no—
214#388—341no—
215#386—341no—
216#380—171no—
217C4×C4⋊C4#59511yescharacteristic
218C4×C22⋊C4—341no—
219#336—172no—
220#336—172no—
221#336—341no—
222C2×C17#146511yescharacteristic
223C2×C17#148611yescharacteristic
224C2×C17#148811yescharacteristic
225C2×C17#151611yescharacteristic
226C2×C17#151911yescharacteristic
227C2×C17#153511yescharacteristic
228C2×C17#154011yescharacteristic
229D17—42no—
230D17—82no—
231C22×D4—171no—
232C22×D4—341no—
233C23×C4—171no—
234C23×C4—171no—
235C23×C4—171no—
236C23×C4—341no—
237C22×C8—342no—
238C22×C8—342no—
239#121—342no—
240#121—342no—
241C4×D4—682no—
242C4×D4—682no—
243C4×D4—682no—
244C2×C4⋊C4—171no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4C2×#59511yescharacteristic
247C2×C4⋊C4C2×#59511yescharacteristic
248C2×C22⋊C4—341no—
249C2×C22⋊C4—341no—
250C2×C22⋊C4—341no—
251C2×C22⋊C4—341no—
252C2×C22⋊C4—341no—
253C2×C42—21no—
254C2×C42—171no—
255C2×C42—171no—
256C2×C42—171no—
257C2×C42—682no—
258C2×C42C2×#59511yescharacteristic
259C4⋊C8—682no—
260C22⋊C8—682no—
261C22⋊C8—682no—
262#95—21no—
263#95—341no—
264#95—341no—
265C17#764711yescharacteristic, complemented, Sylow
266C24—171no—
267C24—341no—
268C2×D4—172no—
269C2×D4—344no—
270C2×D4—341no—
271C2×D4—681no—
272C2×D4—681no—
273C2×D4—682no—
274C2×D4—682no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—171no—
278C22×C4—171no—
279C22×C4—172no—
280C22×C4—172no—
281C22×C4—171no—
282C22×C4—342no—
283C22×C4—341no—
284C22×C4—341no—
285C22×C4—342no—
286C22×C4—341no—
287C22×C4—681no—
288C22×C4—681no—
289C22×C4—681no—
290C22×C4—681no—
291C22×C4—681no—
292C22×C4—682no—
293C22×C4—682no—
294C22×C4—682no—
295C22×C4C22⋊#59511yescharacteristic
296C22×C4C22⋊#59511yescharacteristic
297C22×C4C22×#59511yescharacteristic
298C2×C8—682no—
299C2×C8—682no—
300C2×C8—682no—
301C2×C8—682no—
302C2×C8—682no—
303C2×C8—682no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—681no—
307C4⋊C4—681no—
308C4⋊C4—681no—
309C4⋊C4#6324312yes—
310C22⋊C4—344no—
311C22⋊C4—681no—
312C22⋊C4—681no—
313C22⋊C4—682no—
314C22⋊C4—682no—
315C22⋊C4—682no—
316C42—22no—
317C42—42no—
318C42—342no—
319C42—681no—
320C42—681no—
321C23—172no—
322C23—341no—
323C23—341no—
324C23—341no—
325C23—341no—
326C23—341no—
327C23—341no—
328C23—342no—
329C23—681no—
330C23—681no—
331C23—681no—
332C23—681no—
333C23—681no—
334C23—681no—
335C23C2×C22⋊#59511yescharacteristic
336D4—682no—
337D4—682no—
338D4—688no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—171no—
352C2×C4—171no—
353C2×C4—172no—
354C2×C4—341no—
355C2×C4—341no—
356C2×C4—341no—
357C2×C4—341no—
358C2×C4—341no—
359C2×C4—341no—
360C2×C4—341no—
361C2×C4—682no—
362C2×C4—682no—
363C2×C4—684no—
364C2×C4—682no—
365C2×C4—682no—
366C2×C4—681no—
367C2×C4—681no—
368C2×C4—681no—
369C2×C4—1364no—
370C2×C4#1058753912yes—
371C2×C4#1058754712yes—
372C2×C4C2×#6324311yescharacteristic
373C2×C4D17⋊M1611yescharacteristic
374C8—1362no—
375C8—1362no—
376C22—342no—
377C22—342no—
378C22—342no—
379C22—681no—
380C22—681no—
381C22—681no—
382C22—681no—
383C22—682no—
384C22—682no—
385C22—682no—
386C22—1361no—
387C22—1361no—
388C22—1361no—
389C22—1361no—
390C22#1176378011yescharacteristic
391C22C2×#1058753911yescharacteristic
392C22#1176379511yescharacteristic
393C22C2×#1058754711yescharacteristic
394C22#1176379911yescharacteristic
395C22#1176380611yescharacteristic
396C22#1176380811yescharacteristic
397C4—22no—
398C4—22no—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—81no—
403C4—342no—
404C4—341no—
405C4—341no—
406C4—681no—
407C4—1361no—
408C2—682no—
409C2—1362no—
410C2#1454404111yescharacteristic
411C2#1454411011yescharacteristic
412C2#1454411811yescharacteristic
413C2#1454421211yescharacteristic
414C2#1454422111yescharacteristic
415C2#1454427011yescharacteristic
416C2#1454428111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587581C4
cosocleC2×C4×Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#7647
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14544676C2semidirect
2. #14544639C2semidirect
3. #14543602C2semidirect
4. #14543601C2semidirect
265. C17#7647semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145446392
#145436022
#145436012
C4×#105875812
#764717