Finite Group Databasebeta

← #16938121

Subgroups — #16938121

Order 4352.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763004C211yesmaximal, characteristic
2#14529589C211yesmaximal, characteristic, complemented
3#14529579C211yesmaximal, characteristic, complemented
4C2×#11762559C211yesmaximal, characteristic, complemented
5C2×#11762552C211yesmaximal, characteristic, complemented
6#14526667C211yesmaximal, characteristic, complemented
7C17×#1802C211yesmaximal, characteristic, complemented
8C22×#63228—21no—
9C2×#10587560C2211yescharacteristic
10#11763004—22no—
11#11763004—22no—
12C2×C4⋊#3622C2211yescharacteristic
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587480—21no—
15C2×#10587480—21no—
16C2×#10587480—21no—
17C2×C22⋊#3622—21no—
18C2×C22⋊#3622—21no—
19C2×C4×#3622C2211yescharacteristic
20#11762559—22no—
21#11762552—22no—
22C2×C4×D4×C17C2211yescharacteristic
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C17×#102—21no—
25C17×#384C2211yescharacteristic
26C17×#340—21no—
27C22×D4×C17D411yescharacteristic
28C23×C4×C17—21no—
29C22×D68—21no—
30C22×D68—21no—
31C22×D68—21no—
32C22×C8×C17—21no—
33C4×D4×C17—21no—
34C4×D4×C17—21no—
35C4×D4×C17—21no—
36C4×D4×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17—21no—
40C2×C4⋊C4×C17D411yescharacteristic
41C2×C22⋊C4×C17—21no—
42C2×C42×C17C2311yescharacteristic
43C2×#63228—24no—
44C2×#63228—42no—
45C2×#63228—42no—
46C22×#3622—21no—
47C22×#3622—21no—
48C22×#3622D411yescharacteristic
49C22×#3622D411yescharacteristic
50#10587560—21no—
51#10587560—21no—
52#10587560—21no—
53#10587560D412yes—
54C17×C4⋊C8—21no—
55C17×C4⋊C8—21no—
56C17×#102—42no—
57C22⋊#3622—42no—
58C22⋊#3622—42no—
59#10587480—24no—
60#10587480—42no—
61#10587480—42no—
62C4⋊#3622—21no—
63C4⋊#3622—21no—
64C4⋊#3622—21no—
65C4⋊#3622D412yes—
66C4×#3622—21no—
67C4×#3622—21no—
68C24×C17—21no—
69C23×D17—41no—
70C2×D4×C17—21no—
71C2×D4×C17—21no—
72C2×D4×C17—21no—
73C2×D4×C17—21no—
74C2×D4×C17—21no—
75C2×D4×C17SD1612yes—
76C22×C4×C17—21no—
77C22×C4×C17—41no—
78C22×C4×C17—41no—
79C22×C4×C17—41no—
80C22×C4×C17—41no—
81C22×C4×C17—41no—
82C22×C4×C17—41no—
83C22×C4×C17—41no—
84C22×C4×C17C2×D411yescharacteristic
85C22×C4×C17C2×D411yescharacteristic
86C22×C4×C17#4111yescharacteristic
87C2×D68—22no—
88C2×D68—22no—
89C2×D68—22no—
90C2×D68—41no—
91C2×D68—41no—
92C2×D68—41no—
93C2×D68—41no—
94C2×D68—41no—
95C2×D68—41no—
96C2×D68—41no—
97C2×D68—41no—
98C2×D68—41no—
99C2×D68—41no—
100C2×D68—41no—
101C2×D68—81no—
102C2×D68—81no—
103C2×C8×C17—41no—
104C2×C8×C17—41no—
105C2×C8×C17—41no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—21no—
108C4⋊C4×C17—41no—
109C4⋊C4×C17—41no—
110C4⋊C4×C17—41no—
111C4⋊C4×C17—41no—
112C4⋊C4×C17—81no—
113C22⋊C4×C17—41no—
114C22⋊C4×C17—41no—
115C42×C17C2×D411yescharacteristic
116C42×C17C2×D411yescharacteristic
117C42×C17#4111yescharacteristic
118C42×C17#4111yescharacteristic
119#63228—48no—
120C2×#3622—21no—
121C2×#3622—21no—
122C2×#3622—22no—
123C2×#3622—21no—
124C2×#3622—21no—
125C2×#3622—21no—
126C2×#3622—41no—
127C2×#3622—41no—
128C2×#3622—41no—
129C2×#3622—41no—
130C2×#3622—41no—
131C2×#3622D812yescomplemented
132#10473—171nomaximal, Sylow
133C23×C17—22no—
134C23×C17—41no—
135C23×C17—41no—
136C23×C17—41no—
137C23×C17—41no—
138C23×C17—41no—
139C23×C17—41no—
140C23×C17#12111yescharacteristic
141C22×D17—42no—
142C22×D17—81no—
143C22×D17—81no—
144C22×D17—81no—
145C22×D17—81no—
146C22×D17—81no—
147C22×D17—81no—
148D4×C17—22no—
149D4×C17—22no—
150D4×C17—41no—
151D4×C17—41no—
152C2×C4×C17—21no—
153C2×C4×C17—21no—
154C2×C4×C17—41no—
155C2×C4×C17—41no—
156C2×C4×C17—41no—
157C2×C4×C17—81no—
158C2×C4×C17—81no—
159C2×C4×C17—81no—
160C2×C4×C17—81no—
161C2×C4×C17—81no—
162C2×C4×C17—81no—
163C2×C4×C17—81no—
164C2×C4×C17#12011yescharacteristic
165C2×C4×C17#12111yescharacteristic
166C2×C4×C17#12111yescharacteristic
167C2×C4×C17#12311yescharacteristic
168C2×C4×C17#12311yescharacteristic
169C2×C4×C17#12411yescharacteristic
170C2×C4×C17C2×D811yescharacteristic
171C2×C4×C17C2×SD1611yescharacteristic
172C2×C4×C17#13511yescharacteristic
173C2×C4×C17#13511yescharacteristic
174C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
178D68—42no—
179D68—42no—
180D68—42no—
181D68—42no—
182D68—82no—
183D68—82no—
184D68—81no—
185D68—81no—
186D68—81no—
187D68—81no—
188C8×C17—81no—
189#3622—22no—
190#3622—42no—
191#3622—41no—
192#3622—81no—
193C2×#459—171no—
194#1957—171no—
195#1954—171no—
196#1802D1711yescharacteristic, complemented
197C2×#334—171no—
198C2×#331—171no—
199#1296—171no—
200C22×C17—42no—
201C22×C17—42no—
202C22×C17—42no—
203C22×C17—81no—
204C22×C17—81no—
205C22×C17—81no—
206C22×C17—81no—
207C22×C17#39411yescharacteristic
208C22×C17#45911yescharacteristic
209C22×C17#46311yescharacteristic
210C22×C17#46511yescharacteristic
211C22×C17#46911yescharacteristic
212C22×C17#47111yescharacteristic
213C22×C17#47211yescharacteristic
214C2×D17—82no—
215C2×D17—82no—
216C2×D17—82no—
217C2×D17—161no—
218C2×D17—161no—
219C2×D17—161no—
220C2×D17—161no—
221C4×C17—21no—
222C4×C17—21no—
223C4×C17—81no—
224C4×C17—161no—
225C4×C17#44911yescharacteristic
226C4×C17#45011yescharacteristic
227C4×C17#45911yescharacteristic
228C4×C17#46311yescharacteristic
229C4×C17#46611yescharacteristic
230C4×C17#46911yescharacteristic
231C4×C17#48111yescharacteristic
232C4×C17#48211yescharacteristic
233C22×D8—341no—
234C2×#127—171no—
235C2×C4×D4C2×D1711yescharacteristic
236#459—342no—
237#459—342no—
238C2×C4⋊C8—171no—
239C2×C4⋊C8—171no—
240C2×C4⋊C8C2×D1711yescharacteristic
241C2×#102—21no—
242C2×#102—341no—
243C2×#102—341no—
244C2×#102—341no—
245C2×C22⋊C8—341no—
246C2×C22⋊C8—341no—
247C2×C4×C8—171no—
248#384C2×D1711yescharacteristic
249#340—21no—
250#334—342no—
251#331—342no—
252C2×C17—82no—
253C2×C17#166511yescharacteristic
254C2×C17#167711yescharacteristic
255C2×C17#168711yescharacteristic
256C2×C17#170111yescharacteristic
257C2×C17#203411yescharacteristic
258C2×C17#205111yescharacteristic
259C2×C17#205411yescharacteristic
260D17—162no—
261C22×D4—341no—
262C22×D4—341no—
263C22×D4—341no—
264C22×D4C22⋊D1711yescharacteristic
265C23×C4—21no—
266C2×D8—344no—
267C2×D8—682no—
268C2×D8—682no—
269C22×C8—21no—
270C22×C8—171no—
271C22×C8—171no—
272C22×C8—341no—
273C22×C8—341no—
274#127—172no—
275#127—341no—
276#127—341no—
277#127—341no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4C22⋊D1711yescharacteristic
286C2×C22⋊C4—21no—
287C2×C42C22×D1711yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—172no—
291C4⋊C8—341no—
292C4⋊C8—341no—
293C4⋊C8—341no—
294#102—42no—
295#102—344no—
296#102—682no—
297#102—682no—
298C22⋊C8—682no—
299C22⋊C8—682no—
300C4×C8—341no—
301C4×C8—341no—
302C17#1047311yescharacteristic, complemented, Sylow
303C24—21no—
304C24—681no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—342no—
311C2×D4—342no—
312C2×D4—342no—
313C2×D4—681no—
314C2×D4—681no—
315C2×D4—681no—
316C2×D4—681no—
317C2×D4—681no—
318C2×D4—681no—
319C2×D4—681no—
320C2×D4—681no—
321C2×D4—681no—
322C2×D4—681no—
323C2×D4—681no—
324C2×D4—1361no—
325C2×D4—1361no—
326C2×D4#6323012yes—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4D4×D1711yescharacteristic
336C22×C4#6325411yescharacteristic
337C22×C4C2×C22⋊D1711yescharacteristic
338D8—688no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—172no—
343C2×C8—341no—
344C2×C8—341no—
345C2×C8—341no—
346C2×C8—341no—
347C2×C8—341no—
348C2×C8—342no—
349C2×C8—681no—
350C2×C8—681no—
351C2×C8—681no—
352C2×C8—681no—
353C2×C8—681no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—81no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42#6325211yescharacteristic
364C42#6325211yescharacteristic
365C42D4×D1711yescharacteristic
366C42D4×D1711yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—682no—
375C23—1361no—
376C23—1361no—
377C23—1361no—
378C23—1361no—
379C23—1361no—
380C23—1361no—
381C23#1058762511yescharacteristic
382D4—22no—
383D4—22no—
384D4—41no—
385D4—41no—
386D4—682no—
387D4—682no—
388D4—682no—
389D4—682no—
390D4—1362no—
391D4—1362no—
392D4—1361no—
393D4—1361no—
394D4—1361no—
395D4—1361no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4#1058756911yescharacteristic
409C2×C4#1058757011yescharacteristic
410C2×C4#1058757011yescharacteristic
411C2×C4#1058757111yescharacteristic
412C2×C4D8×D1711yescharacteristic
413C2×C4#1058759711yescharacteristic
414C2×C4#1058760011yescharacteristic
415C2×C4#1058760211yescharacteristic
416C2×C4#1058761511yescharacteristic
417C2×C4#1058761811yescharacteristic
418C2×C4#1058762311yescharacteristic
419C2×C4C2×#6323011yescharacteristic
420C2×C4#1058763511yescharacteristic
421C2×C4#1058763611yescharacteristic
422C8—81no—
423C8—342no—
424C8—682no—
425C8—681no—
426C8—1361no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—2721no—
435C22—2721no—
436C22—2721no—
437C22—2721no—
438C22—1362no—
439C22—1362no—
440C22—1362no—
441C22#1176272411yescharacteristic
442C22#1176300211yescharacteristic
443C22#1176302611yescharacteristic
444C22#1176304011yescharacteristic
445C22#1176306011yescharacteristic
446C22#1176307411yescharacteristic
447C22#1176307711yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—161no—
452C4#1176295211yescharacteristic
453C4#1176295911yescharacteristic
454C4#1176300311yescharacteristic
455C4#1176302311yescharacteristic
456C4#1176304411yescharacteristic
457C4#1176306111yescharacteristic
458C4#1176312711yescharacteristic
459C4#1176313311yescharacteristic
460C2—82no—
461C2—2722no—
462C2#1452812711yescharacteristic
463C2#1452819511yescharacteristic
464C2#1452826111yescharacteristic
465C2#1452834711yescharacteristic
466C2#1452997311yescharacteristic
467C2#1453007411yescharacteristic
468C2#1453009311yescharacteristic
subgroupG/H
centerC23#10587625
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1802C2
socleC23×C17#121
prime radicalC2×#11763004C2
hypercenter#1802D17
hypocenterC17#10473
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. #14529589C2semidirect
3. #14529579C2semidirect
4. C2×#11762559C2semidirect
5. C2×#11762552C2semidirect
6. #14526667C2semidirect
7. C17×#1802C2semidirect
131. C2×#3622D8semidirect
196. #1802D17semidirect
302. C17#10473semidirect

Maximal subgroups

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

subgroupindex
C2×#117630042
#145295892
#145295792
C2×#117625592
C2×#117625522
#145266672
C17×#18022
#1047317