Finite Group Databasebeta

← #16930620

Subgroups — #16930620

Order 4352.

588 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538780C211yesmaximal, characteristic
2#14531248C211yesmaximal, characteristic, complemented
3#14527279C211yesmaximal, characteristic, complemented
4#14527208C211yesmaximal, characteristic, complemented
5#14526685C211yesmaximal, characteristic, complemented
6#14526617C211yesmaximal, characteristic, complemented
7C17×#1962C211yesmaximal, characteristic, complemented
8C2×C4×D68C2211yescharacteristic
9C2×#10587558—21no—
10#11763120—21no—
11#11763086C412yescomplemented
12#11763001C412yescomplemented
13#11762942—21no—
14C4×#63228—22no—
15#11762862C2211yescharacteristic
16#11762862C2211yescharacteristic
17#11762711—21no—
18#11762707—21no—
19#11762700—22no—
20C4×C4⋊Dic17C2211yescharacteristic
21C4×#63227—21no—
22#11762543—22no—
23#11762536—22no—
24C17×#532C2211yescharacteristic
25C17×#423C2211yescharacteristic
26C2×C17×#104—21no—
27C2×C17×#104—21no—
28C43×C17C2211yescharacteristic
29C2×#41×C17—21no—
30C22×D68D411yescharacteristic
31C22×C4×D17—21no—
32C2×M16×C17—21no—
33C17×C4⋊Q8C2×C411yescharacteristic
34C17×#127C2×C411yescharacteristic
35C17×#124—21no—
36C17×#121—21no—
37C17×#121—21no—
38C4×D4×C17—21no—
39C4×D4×C17—21no—
40C2×C42×C17—21no—
41C2×C42×C17—21no—
42C2×C42×C17D411yescharacteristic
43C2×C42×C17D411yescharacteristic
44C2×C42×C17C2311yescharacteristic
45C2×#63228—22no—
46C2×#63227—22no—
47C2×#63227—22no—
48C2×#63227—21no—
49C2×C4⋊Dic17—21no—
50C2×C4⋊Dic17D411yescharacteristic
51C2×#63225—22no—
52C2×C4×Dic17—21no—
53C4×D68—21no—
54C4×D68—21no—
55C4×D68C2×C412yes—
56C4×D68D412yes—
57#10587558—42no—
58#10587558—42no—
59C17×C4⋊C8—21no—
60C17×C4⋊C8—21no—
61C17×#104—42no—
62C17×#104—42no—
63#10587503—22no—
64#10587502—22no—
65#10587502D412yes—
66C22⋊#3622—21no—
67C22⋊#3622—21no—
68#10587480—22no—
69#10587478—22no—
70C4⋊#3622—21no—
71C4⋊#3622C2×C412yes—
72C4×#3622—21no—
73C4×#3622—21no—
74C23×D17—21no—
75#41×C17—41no—
76#41×C17—41no—
77#41×C17—41no—
78#41×C17—41no—
79C2×Q8×C17—21no—
80C2×D4×C17—21no—
81C2×D4×C17—21no—
82C2×D4×C17—21no—
83C2×D4×C17—41no—
84C22×C4×C17—21no—
85C22×C4×C17—21no—
86C22×C4×C17—41no—
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2×D411yescharacteristic
90C22×Dic17—21no—
91C22×Dic17—22no—
92C2×D68—21no—
93C2×D68—42no—
94C2×D68C22⋊C412yes—
95C2×C4×D17—22no—
96C2×C4×D17—22no—
97C2×C4×D17—41no—
98C2×C4×D17—41no—
99C2×C4×D17—41no—
100C2×C4×D17—41no—
101M16×C17—41no—
102M16×C17—41no—
103C2×C8×C17—41no—
104C4⋊C4×C17—21no—
105C4⋊C4×C17—21no—
106C22⋊C4×C17—41no—
107C22⋊C4×C17—41no—
108C42×C17—21no—
109C42×C17—21no—
110C42×C17—21no—
111C42×C17—42no—
112C42×C17—42no—
113C42×C17D812yescomplemented
114C42×C17C22×C411yescharacteristic
115C42×C17C2×D411yescharacteristic
116C42×C17#4111yescharacteristic
117C42×C17#4111yescharacteristic
118#63228—44no—
119#63227—22no—
120#63227—22no—
121#63227—44no—
122#63227—44no—
123C4⋊Dic17—21no—
124C4⋊Dic17—42no—
125C4⋊Dic17C22⋊C412yes—
126#63225—44no—
127C4×Dic17—41no—
128C4×Dic17—41no—
129C2×#3622—22no—
130C2×#3622—41no—
131#9237—171nomaximal, Sylow
132C23×C17—41no—
133C23×C17#12011yescharacteristic
134C22×D17—22no—
135C22×D17—42no—
136C22×D17—42no—
137C22×D17—41no—
138C22×D17—41no—
139Q8×C17—41no—
140Q8×C17—41no—
141D4×C17—42no—
142D4×C17—41no—
143D4×C17—41no—
144D4×C17—81no—
145D4×C17—81no—
146D4×C17—81no—
147C2×C4×C17—22no—
148C2×C4×C17—22no—
149C2×C4×C17—22no—
150C2×C4×C17—41no—
151C2×C4×C17—41no—
152C2×C4×C17—41no—
153C2×C4×C17—41no—
154C2×C4×C17—41no—
155C2×C4×C17—41no—
156C2×C4×C17—81no—
157C2×C4×C17—81no—
158C2×C4×C17C2×C22⋊C411yescharacteristic
159C2×C4×C17C4×D411yescharacteristic
160C2×C4×C17C4×D411yescharacteristic
161C2×C4×C17#12111yescharacteristic
162C2×C4×C17#12111yescharacteristic
163C2×C4×C17#12311yescharacteristic
164C2×C4×C17C2×D811yescharacteristic
165C2×C4×C17#13511yescharacteristic
166C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
168C2×Dic17—22no—
169C2×Dic17—41no—
170C2×Dic17—41no—
171C2×Dic17—42no—
172C2×Dic17—42no—
173C2×Dic17—42no—
174D68—22no—
175D68—22no—
176D68—42no—
177C4×D17—42no—
178C4×D17—42no—
179C4×D17—42no—
180C4×D17—42no—
181C8×C17—81no—
182#3622—42no—
183#3622—81no—
184#3100—171no—
185#2293—171no—
186#1962D1711yescharacteristic, complemented
187#1502—171no—
188#1486—171no—
189#1303—171no—
190#1276—171no—
191C22×C17—21no—
192C22×C17—21no—
193C22×C17—81no—
194C22×C17—81no—
195C22×C17—81no—
196C22×C17#38611yescharacteristic
197C22×C17#44711yescharacteristic
198C22×C17#44911yescharacteristic
199C2×D17—42no—
200C2×D17—42no—
201C2×D17—42no—
202C2×D17—82no—
203C2×D17—82no—
204C4×C17—21no—
205C4×C17—21no—
206C4×C17—21no—
207C4×C17—42no—
208C4×C17—42no—
209C4×C17—81no—
210C4×C17#42112yes—
211C4×C17C4×D811yescharacteristic
212C4×C17#44211yescharacteristic
213C4×C17#45911yescharacteristic
214C4×C17#46311yescharacteristic
215Dic17—42no—
216Dic17—82no—
217#532C2×D1711yescharacteristic
218C2×C4×D4—171no—
219C2×#117—341no—
220#480—341no—
221#474—172no—
222#459—172no—
223#447—341no—
224C4×D8—342no—
225#431—171no—
226#431—171no—
227#423C2×D1711yescharacteristic
228C2×#104—21no—
229C2×#104—21no—
230#390—341no—
231#389—341no—
232#388—342no—
233C4×C4⋊C4—171no—
234C4×C22⋊C4—341no—
235C43C2×D1711yescharacteristic
236#327—342no—
237D4⋊C8—342no—
238C2×C17—21no—
239C2×C17—21no—
240C2×C17—161no—
241C2×C17#187911yescharacteristic
242C2×C17#189711yescharacteristic
243C2×C17#190611yescharacteristic
244D17—82no—
245C2×#41—21no—
246C22×D4—171no—
247C23×C4—341no—
248C2×D8—342no—
249C2×M16—21no—
250C4⋊Q8C4×D1711yescharacteristic
251#127C4×D1711yescharacteristic
252#124—21no—
253#121—21no—
254#121—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—172no—
258C4×D4—172no—
259C4×D4—341no—
260C4×D4—341no—
261#117—682no—
262#117—682no—
263C2×C4⋊C4—171no—
264C2×C4⋊C4—342no—
265C2×C4⋊C4—341no—
266C2×C22⋊C4—341no—
267C2×C22⋊C4—342no—
268C2×C22⋊C4—342no—
269C2×C42—21no—
270C2×C42—21no—
271C2×C42—341no—
272C2×C42C22⋊D1711yescharacteristic
273C2×C42C22⋊D1711yescharacteristic
274C2×C42C22×D1711yescharacteristic
275#107—342no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—172no—
279C4⋊C8—341no—
280#104—42no—
281#104—42no—
282#102—342no—
283#102—342no—
284C22⋊C8—341no—
285C22⋊C8—341no—
286C4×C8—341no—
287C4×C8—341no—
288#95—172no—
289#95—342no—
290C17#923711yescharacteristic, complemented, Sylow
291C24—341no—
292#41—41no—
293#41—41no—
294#41—41no—
295#41—41no—
296C2×Q8—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—41no—
301C2×D4—172no—
302C2×D4—341no—
303C2×D4—682no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—341no—
308C22×C4—342no—
309C22×C4—342no—
310C22×C4—342no—
311C22×C4—681no—
312C22×C4—681no—
313C22×C4—681no—
314C22×C4—681no—
315C22×C4D4×D1711yescharacteristic
316C22×C4D4×D1711yescharacteristic
317C22×C4C2×C22⋊D1711yescharacteristic
318D8—684no—
319M16—41no—
320M16—41no—
321C2×C8—41no—
322C2×C8—342no—
323C2×C8—681no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—172no—
327C4⋊C4—341no—
328C4⋊C4—684no—
329C4⋊C4—682no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—342no—
333C22⋊C4—342no—
334C22⋊C4—684no—
335C22⋊C4—684no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42—42no—
340C42—42no—
341C42—681no—
342C42—681no—
343C42#6322812yescomplemented
344C42C2×C4×D1711yescharacteristic
345C42#6325211yescharacteristic
346C42D4×D1711yescharacteristic
347C42#6325411yescharacteristic
348C23—41no—
349C23—342no—
350C23—682no—
351C23—682no—
352C23—681no—
353C23—681no—
354C23#1058762311yescharacteristic
355Q8—41no—
356Q8—41no—
357D4—42no—
358D4—41no—
359D4—41no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—342no—
364D4—342no—
365D4—682no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—342no—
378C2×C4—681no—
379C2×C4—681no—
380C2×C4—682no—
381C2×C4—682no—
382C2×C4—682no—
383C2×C4—682no—
384C2×C4—682no—
385C2×C4—682no—
386C2×C4—682no—
387C2×C4C22⋊C4×D1711yescharacteristic
388C2×C4#1058756711yescharacteristic
389C2×C4#1058756911yescharacteristic
390C2×C4#1058757011yescharacteristic
391C2×C4C4×C22⋊D1711yescharacteristic
392C2×C4C2×#6322811yescharacteristic
393C2×C4#1058761811yescharacteristic
394C2×C4#1058762411yescharacteristic
395C2×C4#1058763511yescharacteristic
396C2×C4#1058763611yescharacteristic
397C8—81no—
398C8—682no—
399C8—1361no—
400C22—21no—
401C22—21no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—682no—
406C22—682no—
407C22—682no—
408C22—1362no—
409C22—1362no—
410C22#1176268511yescharacteristic
411C22#1176294211yescharacteristic
412C22#1176295211yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—42no—
418C4—81no—
419C4—682no—
420C4—1362no—
421C4#1176282412yes—
422C4C4×#6322811yescharacteristic
423C4#1176291911yescharacteristic
424C4#1176300111yescharacteristic
425C4#1176302111yescharacteristic
426C2—21no—
427C2—21no—
428C2—161no—
429C2—1362no—
430C2#1452913511yescharacteristic
431C2#1452922911yescharacteristic
432C2#1452928811yescharacteristic
subgroupG/H
centerC2×C4#10587624
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1962C2
socleC22×C17#386
prime radical#14538780C2
cosocleC2×C42×C17C23
hypercenter#1962D17
hypocenterC17#9237
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
2. #14531248C2semidirect
3. #14527279C2semidirect
4. #14527208C2semidirect
5. #14526685C2semidirect
6. #14526617C2semidirect
7. C17×#1962C2semidirect
11. #11763086C4semidirect
12. #11763001C4semidirect
113. C42×C17D8semidirect
186. #1962D17semidirect
290. C17#9237semidirect
343. C42#63228semidirect

Maximal subgroups

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

subgroupindex
#145387802
#145312482
#145272792
#145272082
#145266852
#145266172
C17×#19622
#923717