Finite Group Databasebeta

← #17981656

Subgroups — #17981656

Order 4352.

682 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 123 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#14545924C212yesmaximal
2C2×#11763895C212yesmaximal
3#14545793C212yesmaximal
4C2×C4⋊C4×#595C211yesmaximal, characteristic
5C2×C4⋊#3633—22no—
6C2×C22⋊#3633C2214yes—
7(C2×#3633)⋊C4—22no—
8#11763895—24no—
9C22×C4⋊#595C2211yescharacteristic
10C22×C4×#595C411yescharacteristic
11C22×C4×#595C411yescharacteristic
12C22×C4×#595C2211yescharacteristic
13C4⋊C4×#595—22no—
14C4⋊C4×#595—22no—
15C2×(C2×#595)⋊C4C411yescharacteristic
16C2×(C2×#595)⋊C4C2211yescharacteristic
17C2×C4⋊C4×D17C411yescharacteristic
18C23×#595C2×C411yescharacteristic
19C23×#595C2×C411yescharacteristic
20C23×#595C2×C411yescharacteristic
21C23×#595C2311yescharacteristic
22C22×#3633—24no—
23C22×C4×D17C2×C411yescharacteristic
24C22×C4×D17C2×C411yescharacteristic
25C22×C4×D17C2×C411yescharacteristic
26C2×C4⋊#595—22no—
27C2×C4⋊#595—22no—
28C2×C4⋊#595D412yes—
29C2×C4⋊#595Q812yes—
30C2×C4×#595—21no—
31C2×C4×#595—21no—
32C2×C4×#595—22no—
33C2×C4×#595—22no—
34C2×C4×#595—21no—
35C2×C4×#595—21no—
36C2×C4×#595—42no—
37C2×C4×#595—42no—
38C2×C4×#595D412yes—
39C2×C4×#595D412yes—
40C22⋊#3633—24no—
41C22⋊#3633—24no—
42C4⋊#3633—44no—
43C2×C4⋊C4×C17C811yescharacteristic, complemented
44C2×C4⋊Dic17C811yescharacteristic, complemented
45C2×#63225C811yescharacteristic, complemented
46C2×#63225C811yescharacteristic, complemented
47C4⋊C4×D17—22no—
48C4⋊C4×D17—22no—
49(C2×#595)⋊C4—22no—
50(C2×#595)⋊C4—22no—
51C23×D17C22×C411yescharacteristic
52C22×#595—21no—
53C22×#595—21no—
54C22×#595—22no—
55C22×#595—22no—
56C22×#595—21no—
57C22×#595—21no—
58C22×#595—21no—
59C22×#595—21no—
60C22×#595—41no—
61C22×#595—41no—
62C22×#595—41no—
63C22×#595—41no—
64C22×#595—41no—
65C22×#595—41no—
66C22×#595C22⋊C411yescharacteristic
67C22×#595C22⋊C411yescharacteristic
68C22×#595C4⋊C412yes—
69C22×#595M1612yes—
70C22×#595C2×D412yes—
71C22×#595C2×D411yescharacteristic
72C22×#595C2×Q811yescharacteristic
73C22×#595#4112yes—
74C2×#3633—44no—
75C2×#3633—44no—
76C2×#3633—44no—
77C22×C4×C17C2×C811yescharacteristic
78C22×C4×C17C2×C811yescharacteristic
79C22×C4×C17C2×C811yescharacteristic
80C22×Dic17C2×C811yescharacteristic
81C22×Dic17C2×C811yescharacteristic
82C22×Dic17C2×C811yescharacteristic
83C2×C4×D17—21no—
84C2×C4×D17—21no—
85C2×C4×D17—21no—
86C2×C4×D17—21no—
87C2×C4×D17—21no—
88C2×C4×D17—21no—
89C2×C4×D17—41no—
90C2×C4×D17—41no—
91C2×C4×D17—41no—
92C2×C4×D17—41no—
93C2×C4×D17C22⋊C412yes—
94C2×C4×D17C4⋊C412yes—
95C2×C4×D17M1612yes—
96C2×C4×D17M1612yes—
97C4⋊#595—24no—
98C4⋊#595—24no—
99C4×#595—24no—
100C4×#595—24no—
101C4×#595—24no—
102C4×#595—42no—
103C4×#595—42no—
104C4×#595—42no—
105C4⋊C4×C17—22no—
106C4⋊Dic17—22no—
107#63225—22no—
108#63225—22no—
109#8560—171nomaximal, Sylow
110C23×C17C22×C811yescharacteristic
111C22×D17—21no—
112C22×D17—21no—
113C22×D17—21no—
114C22×D17—21no—
115C22×D17C2×C22⋊C411yescharacteristic
116C22×D17C2×C4⋊C411yescharacteristic
117C22×D17#11711yescharacteristic
118C22×D17C2×M1611yescharacteristic
119C22×D17C2×M1611yescharacteristic
120C22×D17C2×M1611yescharacteristic
121C2×#595—24no—
122C2×#595—24no—
123C2×#595—21no—
124C2×#595—21no—
125C2×#595—22no—
126C2×#595—21no—
127C2×#595—22no—
128C2×#595—21no—
129C2×#595—22no—
130C2×#595—22no—
131C2×#595—41no—
132C2×#595—41no—
133C2×#595—42no—
134C2×#595—42no—
135C2×#595—42no—
136C2×#595—41no—
137C2×#595—41no—
138C2×#595—41no—
139C2×#595—41no—
140C2×#595—42no—
141C2×#595—42no—
142C2×#595#9912yes—
143C2×#595#10112yes—
144C2×#595#12112yes—
145C2×#595C22⋊Q812yes—
146#3633—84no—
147C2×C4×C17—21no—
148C2×C4×C17—21no—
149C2×C4×C17—21no—
150C2×C4×C17—41no—
151C2×C4×C17—41no—
152C2×C4×C17C22⋊C812yes—
153C2×C4×C17C4⋊C812yescomplemented
154C2×Dic17—21no—
155C2×Dic17—21no—
156C2×Dic17—21no—
157C2×Dic17—41no—
158C2×Dic17—41no—
159C2×Dic17C22⋊C812yes—
160C2×Dic17C4⋊C812yescomplemented
161C4×D17—22no—
162C4×D17—22no—
163C4×D17—22no—
164C4×D17—22no—
165C4×D17—22no—
166C4×D17—22no—
167C4×D17—42no—
168C4×D17—42no—
169C4×D17—41no—
170C4×D17—41no—
171C2×C4×C4⋊C4—171no—
172#1797—172no—
173C2×#324—172no—
174#1280—172no—
175C22×C17—21no—
176C22×C17—21no—
177C22×C17C2×C22⋊C811yescharacteristic
178C22×C17C2×C4⋊C811yescharacteristic
179C22×C17#43111yescharacteristic
180C2×D17—21no—
181C2×D17—21no—
182C2×D17—21no—
183C2×D17—21no—
184C2×D17—21no—
185C2×D17—21no—
186C2×D17—21no—
187C2×D17—21no—
188C2×D17—21no—
189C2×D17—21no—
190C2×D17#38011yescharacteristic
191C2×D17#40711yescharacteristic
192C2×D17C2×#9911yescharacteristic
193C2×D17#41011yescharacteristic
194C2×D17C2×#10111yescharacteristic
195C2×D17#41311yescharacteristic
196C2×D17#42311yescharacteristic
197C2×D17#43211yescharacteristic
198#595—22no—
199#595—22no—
200#595—22no—
201#595—22no—
202#595—42no—
203#595—42no—
204C4×C17—22no—
205C4×C17—22no—
206C4×C17—41no—
207Dic17—22no—
208Dic17—22no—
209Dic17—41no—
210C22×C4⋊C4—171no—
211C22×C4⋊C4—171no—
212C22×C42—171no—
213C22×C42—171no—
214C22×C42—171no—
215C2×C4⋊C8—342no—
216C2×C22⋊C8—174no—
217C4×C4⋊C4—342no—
218C4×C4⋊C4—342no—
219C2×#95—171no—
220C2×#95—171no—
221#336—342no—
222#324—344no—
223C2×C17—21no—
224C2×C17—21no—
225C2×C17#145911yescharacteristic
226C2×C17#146111yescharacteristic
227C2×C17#179711yescharacteristic
228D17—21no—
229D17—21no—
230D17#146311yescharacteristic
231D17#146411yescharacteristic
232D17#179911yescharacteristic
233D17#180111yescharacteristic
234C23×C4—171no—
235C23×C4—171no—
236C23×C4—171no—
237C23×C4—171no—
238C23×C4—171no—
239C23×C4—171no—
240C23×C4—171no—
241C22×C8—344no—
242C2×C4⋊C4—172no—
243C2×C4⋊C4—172no—
244C2×C4⋊C4—171no—
245C2×C4⋊C4—171no—
246C2×C4⋊C4—171no—
247C2×C4⋊C4—342no—
248C2×C4⋊C4—342no—
249C2×C4⋊C4—342no—
250C2×C4⋊C4—342no—
251C2×C4⋊C4#363311yescharacteristic, complemented
252C2×C42—172no—
253C2×C42—172no—
254C2×C42—341no—
255C2×C42—341no—
256C2×C42—342no—
257C2×C42—342no—
258C2×C42—341no—
259C2×C42—341no—
260C2×C42—682no—
261C2×C42—682no—
262C4⋊C8—684no—
263C22⋊C8—344no—
264C22⋊C8—344no—
265#95—342no—
266#95—342no—
267C17#856011yescharacteristic, complemented, Sylow
268C24—171no—
269C22×C4—171no—
270C22×C4—171no—
271C22×C4—172no—
272C22×C4—171no—
273C22×C4—171no—
274C22×C4—171no—
275C22×C4—172no—
276C22×C4—171no—
277C22×C4—172no—
278C22×C4—172no—
279C22×C4—172no—
280C22×C4—172no—
281C22×C4—172no—
282C22×C4—172no—
283C22×C4—171no—
284C22×C4—341no—
285C22×C4—341no—
286C22×C4—341no—
287C22×C4—341no—
288C22×C4—341no—
289C22×C4—341no—
290C22×C4—342no—
291C22×C4—342no—
292C22×C4—341no—
293C22×C4—341no—
294C22×C4—341no—
295C22×C4—341no—
296C22×C4—341no—
297C22×C4—341no—
298C22×C4—681no—
299C22×C4—681no—
300C22×C4—681no—
301C22×C4—681no—
302C22×C4—681no—
303C22×C4—681no—
304C22×C4—681no—
305C22×C4—681no—
306C22×C4—681no—
307C22×C4—681no—
308C22×C4C2×#363311yescharacteristic
309C22×C4C2×#363311yescharacteristic
310C22×C4C2×#363311yescharacteristic
311C2×C8—684no—
312C2×C8—684no—
313C2×C8—684no—
314C4⋊C4—22no—
315C4⋊C4—342no—
316C4⋊C4—342no—
317C4⋊C4—344no—
318C4⋊C4—344no—
319C4⋊C4—342no—
320C42—344no—
321C42—344no—
322C42—344no—
323C42—682no—
324C42—682no—
325C42—682no—
326C23—171no—
327C23—171no—
328C23—171no—
329C23—171no—
330C23—171no—
331C23—171no—
332C23—341no—
333C23—341no—
334C23—341no—
335C23—341no—
336C23C22×#363311yescharacteristic
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—172no—
343C2×C4—172no—
344C2×C4—172no—
345C2×C4—172no—
346C2×C4—172no—
347C2×C4—172no—
348C2×C4—342no—
349C2×C4—342no—
350C2×C4—342no—
351C2×C4—342no—
352C2×C4—342no—
353C2×C4—342no—
354C2×C4—341no—
355C2×C4—341no—
356C2×C4—342no—
357C2×C4—341no—
358C2×C4—342no—
359C2×C4—341no—
360C2×C4—344no—
361C2×C4—344no—
362C2×C4—341no—
363C2×C4—341no—
364C2×C4—342no—
365C2×C4—342no—
366C2×C4—341no—
367C2×C4—682no—
368C2×C4—681no—
369C2×C4—681no—
370C2×C4—682no—
371C2×C4—681no—
372C2×C4—681no—
373C2×C4—682no—
374C2×C4—681no—
375C2×C4—681no—
376C2×C4—681no—
377C2×C4—681no—
378C2×C4—681no—
379C2×C4—682no—
380C2×C4—682no—
381C2×C4—681no—
382C2×C4—682no—
383C2×C4—682no—
384C2×C4C4⋊#363312yescomplemented
385C2×C4C22⋊#363312yes—
386C8—1364no—
387C22—21no—
388C22—21no—
389C22—171no—
390C22—171no—
391C22—171no—
392C22—171no—
393C22—171no—
394C22—171no—
395C22—171no—
396C22—171no—
397C22—341no—
398C22—341no—
399C22—341no—
400C22—341no—
401C22—341no—
402C22—341no—
403C22—341no—
404C22—341no—
405C22—341no—
406C22—341no—
407C22C2×C22⋊#363311yescharacteristic
408C22C2×C4⋊#363311yescharacteristic
409C22#1176392211yescharacteristic
410C4—22no—
411C4—22no—
412C4—41no—
413C4—342no—
414C4—342no—
415C4—342no—
416C4—342no—
417C4—342no—
418C4—342no—
419C4—682no—
420C4—682no—
421C4—681no—
422C2—21no—
423C2—21no—
424C2—171no—
425C2—171no—
426C2—171no—
427C2—171no—
428C2—341no—
429C2—341no—
430C2#1454589711yescharacteristic
431C2#1454589911yescharacteristic
432C2#1454592411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3633
commutatorC23×C17C22×C8
FrattiniC23C22×#3633
FittingC2×C4⋊C4×C17C8
socleC22×C17C2×C22⋊C8
prime radicalC23×D17C22×C4
cosocleC23×#595C23
hypercenterC2×C4⋊C4#3633
hypocenterC17#8560
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
43. C2×C4⋊C4×C17C8semidirect
44. C2×C4⋊Dic17C8semidirect
45. C2×#63225C8semidirect
46. C2×#63225C8semidirect
153. C2×C4×C17C4⋊C8semidirect
160. C2×Dic17C4⋊C8semidirect
251. C2×C4⋊C4#3633semidirect
267. C17#8560semidirect
384. C2×C4C4⋊#3633semidirect

Maximal subgroups

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

subgroupindex
#145459242
C2×#117638952
#145457932
C2×C4⋊C4×#5952
#856017