Finite Group Databasebeta

← #16950300

Subgroups — #16950300

Order 4352.

512 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 101 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#14531456C211yesmaximal, characteristic
2C2×#11762599C211yesmaximal, characteristic
3#14528774C211yesmaximal, characteristic
4#14528770C211yesmaximal, characteristic
5#14526903C211yesmaximal, characteristic
6#14526901C211yesmaximal, characteristic
7C2×C17×#352C211yesmaximal, characteristic
8C2×D4×Dic17C2211yescharacteristic
9C22×C4⋊Dic17C411yescharacteristic, complemented
10#11762832—21no—
11C2×#10587504C2211yescharacteristic
12C2×#10587505C2211yescharacteristic
13#11762708—21no—
14#11762702—21no—
15#11762695—21no—
16#11762689C2211yescharacteristic
17#11762684—21no—
18#11762684C411yescharacteristic, complemented
19#11762672C411yescharacteristic, complemented
20#11762667—21no—
21C22⋊C4×Dic17C411yescharacteristic, complemented
22#11762599—22no—
23#11762577—21no—
24#11762575—21no—
25C2×C17×#123C2211yescharacteristic
26C2×C17×#100C2211yescharacteristic
27C2×C17×#99C2211yescharacteristic
28C17×#352—22no—
29C22×D4×C17C2311yescharacteristic
30C23×C4×C17C2×C411yescharacteristic
31C23×Dic17C2×C411yescharacteristic
32C23×Dic17C2×C411yescharacteristic
33C23×Dic17D411yescharacteristic
34C2×M16×C17—21no—
35C17×#123—21no—
36C17×#123—21no—
37C17×#123D412yes—
38C17×#123Q812yes—
39C2×C4⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17C2×C411yescharacteristic
43C2×C22⋊Dic17—21no—
44C2×C22⋊Dic17—21no—
45C2×C22⋊Dic17C2×C411yescharacteristic
46C2×C22⋊Dic17C2×C411yescharacteristic
47C2×C22⋊Dic17D411yescharacteristic
48D4×Dic17—41no—
49D4×Dic17—41no—
50C2×C4⋊Dic17—21no—
51C2×C4⋊Dic17—21no—
52C2×C4⋊Dic17—21no—
53C2×C4⋊Dic17—41no—
54C2×C4⋊Dic17—41no—
55C2×C4⋊Dic17D411yescharacteristic
56C2×#63225—41no—
57C2×C4×Dic17—21no—
58C2×C4×Dic17D411yescharacteristic
59C2×#63223—21no—
60C17×#100—21no—
61C17×#100—21no—
62C17×#99—21no—
63C17×#99—21no—
64#10587505—21no—
65#10587505—21no—
66#10587504—21no—
67#10587504—21no—
68#10587502—21no—
69#10587502—21no—
70#10587502—21no—
71#10587502—21no—
72#10587502—21no—
73#10587502—41no—
74#10587485—41no—
75#10587485—41no—
76C24×C17C22×C411yescharacteristic
77C24×C17C2×D411yescharacteristic
78C2×D4×C17—41no—
79C2×D4×C17—41no—
80C2×D4×C17C2×D411yescharacteristic
81C2×D4×C17C2×Q811yescharacteristic
82C2×D4×C17#4111yescharacteristic
83C2×D4×C17#4111yescharacteristic
84C22×C4×C17—21no—
85C22×C4×C17—21no—
86C22×C4×C17—21no—
87C22×C4×C17—41no—
88C22×C4×C17—41no—
89C22×C4×C17—41no—
90C22×C4×C17C4⋊C412yescomplemented
91C22×C4×C17C2×D411yescharacteristic
92C22×Dic17—21no—
93C22×Dic17—21no—
94C22×Dic17—21no—
95C22×Dic17—21no—
96C22×Dic17—21no—
97C22×Dic17—21no—
98C22×Dic17—41no—
99C22×Dic17—41no—
100C22×Dic17—81no—
101C22×Dic17—81no—
102C22×Dic17—81no—
103C22×Dic17C22⋊C411yescharacteristic
104C22×Dic17C22⋊C411yescharacteristic
105C22×Dic17C22⋊C411yescharacteristic
106C22×Dic17C22⋊C411yescharacteristic
107M16×C17—41no—
108M16×C17—41no—
109C2×C8×C17—41no—
110C4⋊C4×C17—22no—
111C4⋊C4×C17—22no—
112C22⋊C4×C17—21no—
113C22⋊C4×C17—22no—
114C22⋊C4×C17—22no—
115C22⋊C4×C17—41no—
116C22⋊C4×C17—41no—
117C22⋊C4×C17C4⋊C412yescomplemented
118C22⋊Dic17—41no—
119C22⋊Dic17—41no—
120C22⋊Dic17—41no—
121C22⋊Dic17—41no—
122C22⋊Dic17—41no—
123C22⋊Dic17—81no—
124C4⋊Dic17—41no—
125C4⋊Dic17—42no—
126C4⋊Dic17—41no—
127C4⋊Dic17—41no—
128C4⋊Dic17—81no—
129#63225—82no—
130C4×Dic17—21no—
131C4×Dic17—21no—
132C4×Dic17—81no—
133#63223—41no—
134#63223—41no—
135C2×#3622—41no—
136#12796—171nomaximal, Sylow
137C23×C17—21no—
138C23×C17—21no—
139C23×C17—21no—
140C23×C17—21no—
141C23×C17—41no—
142C23×C17—41no—
143C23×C17—41no—
144C23×C17—41no—
145C23×C17C2×C22⋊C411yescharacteristic
146C23×C17C2×C4⋊C411yescharacteristic
147C23×C17#11711yescharacteristic
148C23×C17#12111yescharacteristic
149C23×C17C22⋊Q811yescharacteristic
150D4×C17—41no—
151D4×C17—41no—
152D4×C17—41no—
153D4×C17—41no—
154C2×C4×C17—21no—
155C2×C4×C17—21no—
156C2×C4×C17—22no—
157C2×C4×C17—22no—
158C2×C4×C17—41no—
159C2×C4×C17—42no—
160C2×C4×C17—41no—
161C2×C4×C17—41no—
162C2×C4×C17—41no—
163C2×C4×C17—42no—
164C2×C4×C17—81no—
165C2×C4×C17—81no—
166C2×C4×C17—81no—
167C2×C4×C17#12111yescharacteristic
168C2×C4×C17C22⋊Q811yescharacteristic
169C2×Dic17—21no—
170C2×Dic17—21no—
171C2×Dic17—21no—
172C2×Dic17—41no—
173C2×Dic17—42no—
174C2×Dic17—41no—
175C2×Dic17—41no—
176C2×Dic17—41no—
177C2×Dic17—41no—
178C2×Dic17—41no—
179C2×Dic17—41no—
180C2×Dic17—41no—
181C2×Dic17—41no—
182C2×Dic17—41no—
183C2×Dic17—81no—
184C2×Dic17—81no—
185C2×Dic17—81no—
186C2×Dic17—82no—
187C2×Dic17—81no—
188C2×Dic17—81no—
189C2×Dic17—81no—
190C2×Dic17#9911yescharacteristic
191C2×Dic17#9911yescharacteristic
192C8×C17—81no—
193#3622—81no—
194#2322—171no—
195C2×#352—171no—
196C2×#352D1711yescharacteristic
197#1800—171no—
198#1799—171no—
199#1390—171no—
200#1390—171no—
201C22×C17—21no—
202C22×C17—21no—
203C22×C17—21no—
204C22×C17—21no—
205C22×C17—21no—
206C22×C17—21no—
207C22×C17—41no—
208C22×C17—41no—
209C22×C17—41no—
210C22×C17—41no—
211C22×C17—42no—
212C22×C17—41no—
213C22×C17—41no—
214C22×C17—41no—
215C22×C17—41no—
216C22×C17—81no—
217C22×C17#38011yescharacteristic
218C22×C17C2×#9911yescharacteristic
219C22×C17#41011yescharacteristic
220C4×C17—21no—
221C4×C17—21no—
222C4×C17—42no—
223C4×C17—42no—
224C4×C17—161no—
225Dic17—21no—
226Dic17—21no—
227Dic17—41no—
228Dic17—41no—
229Dic17—41no—
230Dic17—81no—
231Dic17—81no—
232Dic17—161no—
233C2×#123C2×D1711yescharacteristic
234C2×C4×D4—171no—
235C22×C4⋊C4—171no—
236#423—341no—
237C2×#100—171no—
238C2×#100C2×D1711yescharacteristic
239C2×#99—171no—
240C2×#99C2×D1711yescharacteristic
241#389—341no—
242#388—341no—
243#387—341no—
244#386—171no—
245#385—171no—
246#385—341no—
247#381—171no—
248#380—341no—
249C4×C22⋊C4—171no—
250#352—22no—
251#352—342no—
252#343—341no—
253#342—341no—
254C2×C17—21no—
255C2×C17—21no—
256C2×C17—41no—
257C2×C17—41no—
258C2×C17—41no—
259C2×C17—41no—
260C2×C17#179911yescharacteristic
261C2×C17#212111yescharacteristic
262C2×C17#212311yescharacteristic
263C22×D4C22×D1711yescharacteristic
264C23×C4—171no—
265C23×C4—171no—
266C23×C4—171no—
267C23×C4C4×D1711yescharacteristic
268C2×M16—21no—
269C2×M16—341no—
270#123—21no—
271#123—21no—
272#123Dic3412yes—
273#123C22⋊D1712yes—
274C4×D4—681no—
275C4×D4—681no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—171no—
278C2×C4⋊C4—341no—
279C2×C4⋊C4—341no—
280C2×C4⋊C4—341no—
281C2×C4⋊C4—681no—
282C2×C4⋊C4—681no—
283C2×C4⋊C4—681no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—171no—
287C2×C22⋊C4—171no—
288C2×C22⋊C4—171no—
289C2×C22⋊C4—341no—
290C2×C22⋊C4—341no—
291C2×C22⋊C4C4×D1711yescharacteristic
292C2×C42—171no—
293C2×C42—341no—
294C4⋊C8—681no—
295C4⋊C8—681no—
296#100—21no—
297#100—21no—
298#100—341no—
299#100—341no—
300#99—21no—
301#99—21no—
302#99—341no—
303#99—341no—
304#95—341no—
305#95—341no—
306#95—341no—
307#95—341no—
308#95—341no—
309#95—681no—
310C17#1279611yescharacteristic, complemented, Sylow
311C24C2×C4×D1711yescharacteristic
312C24D4×D1711yescharacteristic
313C2×D4—41no—
314C2×D4—41no—
315C2×D4C2×Dic3411yescharacteristic
316C2×D4#6325411yescharacteristic
317C2×D4#6325411yescharacteristic
318C2×D4C2×C22⋊D1711yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—171no—
326C22×C4—171no—
327C22×C4—171no—
328C22×C4—171no—
329C22×C4—341no—
330C22×C4—341no—
331C22×C4—341no—
332C22×C4—341no—
333C22×C4—341no—
334C22×C4—341no—
335C22×C4—681no—
336C22×C4—681no—
337C22×C4—1361no—
338C22×C4—1361no—
339C22×C4—1361no—
340C22×C4#6322512yescomplemented
341C22×C4D4×D1711yescharacteristic
342M16—41no—
343M16—41no—
344M16—681no—
345M16—681no—
346C2×C8—41no—
347C2×C8—681no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—681no—
351C4⋊C4—681no—
352C4⋊C4—681no—
353C4⋊C4—682no—
354C4⋊C4—1361no—
355C4⋊C4—1362no—
356C22⋊C4—21no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—681no—
362C22⋊C4—681no—
363C22⋊C4—681no—
364C22⋊C4—681no—
365C22⋊C4—681no—
366C22⋊C4—1361no—
367C22⋊C4#6322512yescomplemented
368C42—341no—
369C42—341no—
370C42—1361no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23#1058756311yescharacteristic
380C23#1058756411yescharacteristic
381C23C22⋊C4×D1711yescharacteristic
382C23C2×#6322511yescharacteristic
383C23#1058762511yescharacteristic
384D4—41no—
385D4—41no—
386D4—41no—
387D4—41no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—171no—
402C2×C4—171no—
403C2×C4—341no—
404C2×C4—341no—
405C2×C4—341no—
406C2×C4—681no—
407C2×C4—682no—
408C2×C4—681no—
409C2×C4—681no—
410C2×C4—681no—
411C2×C4—681no—
412C2×C4—681no—
413C2×C4—681no—
414C2×C4—681no—
415C2×C4—681no—
416C2×C4—681no—
417C2×C4—1361no—
418C2×C4—1361no—
419C2×C4—1361no—
420C2×C4—1361no—
421C2×C4—1361no—
422C2×C4—1361no—
423C2×C4—1362no—
424C2×C4#1058756411yescharacteristic
425C2×C4#1058762511yescharacteristic
426C8—81no—
427C8—1361no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—81no—
444C22#1176266711yescharacteristic
445C22#99×D1711yescharacteristic
446C22#1176278111yescharacteristic
447C4—21no—
448C4—21no—
449C4—42no—
450C4—42no—
451C4—161no—
452C4—2721no—
453C4—341no—
454C4—341no—
455C4—681no—
456C4—681no—
457C4—681no—
458C4—1361no—
459C4—1361no—
460C2—21no—
461C2—21no—
462C2—41no—
463C2—41no—
464C2—41no—
465C2—41no—
466C2#1452877011yescharacteristic
467C2#1453042911yescharacteristic
468C2#1453043611yescharacteristic
subgroupG/H
centerC22#99×D17
commutatorC24×C17C22×C4
FrattiniC22×D4C22×D17
FittingC2×C17×#352C2
socleC22×C17C2×#99
prime radical, cosocleC22×D4×C17C23
hypercenterC2×#352D17
hypocenterC17#12796
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
9. C22×C4⋊Dic17C4semidirect
18. #11762684C4semidirect
19. #11762672C4semidirect
21. C22⋊C4×Dic17C4semidirect
90. C22×C4×C17C4⋊C4semidirect
117. C22⋊C4×C17C4⋊C4semidirect
310. C17#12796semidirect
340. C22×C4#63225semidirect
367. C22⋊C4#63225semidirect

Maximal subgroups

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

subgroupindex
#145314562
C2×#117625992
#145287742
#145287702
#145269032
#145269012
C2×C17×#3522
#1279617