Finite Group Databasebeta

← #16937697

Subgroups — #16937697

Order 4352.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533783C211yesmaximal, characteristic
2#14529590C211yesmaximal, characteristic
3#14529548C211yesmaximal, characteristic, complemented
4#14528789C211yesmaximal, characteristic, complemented
5C2×#11762552C211yesmaximal, characteristic
6#14526624C211yesmaximal, characteristic, complemented
7C2×C17×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10587560C2211yescharacteristic
9C2×#10587633—21no—
10C2×#10587488—21no—
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587506—21no—
13C2×#10587492—22no—
14#11762726—22no—
15#11762711—21no—
16#11762711—21no—
17#11762710—21no—
18#11762679C2211yescharacteristic
19C4×C4⋊Dic17C2211yescharacteristic
20#11762572—21no—
21#11762571—21no—
22#11762552—22no—
23C2×C4×Q8×C17C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C17C2211yescharacteristic
26C17×Q8⋊C8—22no—
27C22×Q8×C17D411yescharacteristic
28C22×D68—21no—
29C22×D68—21no—
30C22×D68D412yes—
31C22×C8×C17—21no—
32C22×C8×C17—21no—
33C4×Q8×C17—21no—
34C4×Q8×C17—21no—
35C4×Q8×C17—21no—
36C4×Q8×C17—21no—
37C2×C4⋊C4×C17—21no—
38C2×C4⋊C4×C17D411yescharacteristic
39C2×C42×C17—21no—
40C2×C42×C17C2311yescharacteristic
41#10587633—42no—
42#10587633—42no—
43C2×#63227—22no—
44C2×#63227—22no—
45C2×#63227—22no—
46C2×#63227—22no—
47C2×C4⋊Dic17—21no—
48C2×C4⋊Dic17—21no—
49C2×C4⋊Dic17—21no—
50C2×C4⋊Dic17D411yescharacteristic
51C2×C4⋊Dic17D411yescharacteristic
52C2×C4×Dic17—21no—
53C22×#3622—21no—
54#10587560—21no—
55#10587560—21no—
56#10587560—21no—
57#10587560—21no—
58C17×C4⋊C8—21no—
59C17×C4⋊C8D412yes—
60C4×C8×C17—21no—
61C4×C8×C17—21no—
62#10587506—42no—
63#10587502—21no—
64#10587492—44no—
65#10587488—42no—
66C4⋊#3622—21no—
67C4⋊#3622—21no—
68C23×D17—22no—
69C2×Q8×C17—21no—
70C2×Q8×C17—21no—
71C2×Q8×C17—21no—
72C2×Q8×C17—21no—
73C2×Q8×C17—21no—
74C2×Q8×C17SD1612yes—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C22×Dic17—21no—
81C22×Dic17—21no—
82C22×Dic17—41no—
83C2×D68—22no—
84C2×D68—22no—
85C2×D68—42no—
86C2×D68—42no—
87C2×D68—41no—
88C2×D68—41no—
89C2×D68—41no—
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×C8×C17—22no—
100C2×C8×C17—22no—
101C2×C8×C17—41no—
102C2×C8×C17—41no—
103C2×C8×C17—41no—
104C2×C8×C17—41no—
105C4⋊C4×C17—21no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—41no—
108C4⋊C4×C17—41no—
109C42×C17—41no—
110C42×C17—41no—
111C42×C17C2×D411yescharacteristic
112C42×C17#4111yescharacteristic
113C42×C17#4111yescharacteristic
114C42×C17#4111yescharacteristic
115#63227—44no—
116#63227—44no—
117#63227—82no—
118#63227—82no—
119C4⋊Dic17—21no—
120C4⋊Dic17—21no—
121C4⋊Dic17—21no—
122C4⋊Dic17—21no—
123C4⋊Dic17—42no—
124C4⋊Dic17—41no—
125C4⋊Dic17—41no—
126C4⋊Dic17—41no—
127C4⋊Dic17—41no—
128C4×Dic17—41no—
129C4×Dic17—41no—
130C2×#3622—41no—
131C2×#3622—41no—
132C2×#3622—41no—
133#10410—171nomaximal, Sylow
134C23×C17#12011yescharacteristic
135C22×D17—42no—
136C22×D17—42no—
137C22×D17—42no—
138C22×D17—42no—
139C22×D17—42no—
140C22×D17—42no—
141C22×D17—42no—
142Q8×C17—22no—
143Q8×C17—22no—
144Q8×C17—41no—
145Q8×C17—41no—
146C2×C4×C17—21no—
147C2×C4×C17—21no—
148C2×C4×C17—22no—
149C2×C4×C17—41no—
150C2×C4×C17—41no—
151C2×C4×C17—41no—
152C2×C4×C17—41no—
153C2×C4×C17—41no—
154C2×C4×C17#12111yescharacteristic
155C2×C4×C17#12111yescharacteristic
156C2×C4×C17#12111yescharacteristic
157C2×C4×C17#12311yescharacteristic
158C2×C4×C17#12311yescharacteristic
159C2×C4×C17#12411yescharacteristic
160C2×C4×C17C2×SD1611yescharacteristic
161C2×C4×C17#13511yescharacteristic
162C2×C4×C17#13511yescharacteristic
163C2×C4×C17#13511yescharacteristic
164C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C17#13711yescharacteristic
168C2×Dic17—41no—
169C2×Dic17—41no—
170C2×Dic17—41no—
171C2×Dic17—41no—
172C2×Dic17—41no—
173C2×Dic17—41no—
174C2×Dic17—81no—
175C2×Dic17—81no—
176C2×Dic17—81no—
177D68—44no—
178D68—82no—
179D68—81no—
180D68—81no—
181D68—81no—
182D68—81no—
183D68—81no—
184D68—81no—
185D68—81no—
186D68—81no—
187C8×C17—42no—
188C8×C17—42no—
189#3622—81no—
190#2548—171no—
191#1957—171no—
192#1948—171no—
193#1803—171no—
194C2×#331—171no—
195C2×Q8⋊C8D1711yescharacteristic, complemented
196#1279—171no—
197C22×C17#39411yescharacteristic
198C22×C17#44911yescharacteristic
199C22×C17#44911yescharacteristic
200C22×C17#45011yescharacteristic
201C22×C17#45211yescharacteristic
202C22×C17#45311yescharacteristic
203C22×C17#45511yescharacteristic
204C2×D17—82no—
205C2×D17—82no—
206C2×D17—82no—
207C2×D17—82no—
208C2×D17—82no—
209C2×D17—82no—
210C2×D17—82no—
211C4×C17—21no—
212C4×C17—21no—
213C4×C17—42no—
214C4×C17—81no—
215C4×C17#46311yescharacteristic
216C4×C17#46411yescharacteristic
217C4×C17#46511yescharacteristic
218C4×C17#46911yescharacteristic
219C4×C17#48111yescharacteristic
220C4×C17#48211yescharacteristic
221C4×C17#48811yescharacteristic
222C4×C17#48911yescharacteristic
223Dic17—81no—
224Dic17—81no—
225Dic17—161no—
226C2×#127—171no—
227C2×#124—341no—
228C2×C4×Q8C2×D1711yescharacteristic
229C2×#106—341no—
230C2×C4⋊C8—171no—
231C2×C4⋊C8C2×D1711yescharacteristic
232C2×#103—341no—
233C2×#102—342no—
234C2×C4×C8C2×D1711yescharacteristic
235#394—342no—
236#390—341no—
237#390—341no—
238#390—341no—
239#384—171no—
240C4×C4⋊C4—171no—
241#340—341no—
242#340—341no—
243#331—342no—
244Q8⋊C8—22no—
245C2×C17#162011yescharacteristic
246C2×C17#163111yescharacteristic
247C2×C17#164011yescharacteristic
248C2×C17#164211yescharacteristic
249C2×C17#203411yescharacteristic
250C2×C17#203711yescharacteristic
251C2×C17#204211yescharacteristic
252D17—162no—
253C22×Q8D6811yescharacteristic
254C22×D4—172no—
255C22×D4—341no—
256C22×D4—341no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—341no—
260#127—341no—
261#127—341no—
262#127—341no—
263#127—341no—
264#124—682no—
265#124—682no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—171no—
272C2×C4⋊C4—171no—
273C2×C4⋊C4—341no—
274C2×C4⋊C4—341no—
275C2×C4⋊C4—341no—
276C2×C4⋊C4D6811yescharacteristic
277C2×C22⋊C4—342no—
278C2×C22⋊C4—342no—
279C2×C22⋊C4—342no—
280C2×C22⋊C4—342no—
281C2×C42—21no—
282C2×C42—341no—
283C2×C42C22×D1711yescharacteristic
284#106—682no—
285C4⋊C8—21no—
286C4⋊C8—341no—
287C4⋊C8—341no—
288C4⋊C8C22⋊D1712yes—
289#103—682no—
290#102—684no—
291C4×C8—21no—
292C4×C8—21no—
293#95—341no—
294C17#1041011yescharacteristic, complemented, Sylow
295C24—342no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8#6321912yes—
302C2×D4—342no—
303C2×D4—342no—
304C2×D4—682no—
305C2×D4—682no—
306C2×D4—681no—
307C2×D4—681no—
308C2×D4—681no—
309C2×D4—681no—
310C2×D4—681no—
311C2×D4—681no—
312C2×D4—681no—
313C2×D4—681no—
314C2×D4—681no—
315C2×D4—681no—
316C2×D4—681no—
317C2×D4—681no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—341no—
321C22×C4—341no—
322C22×C4—681no—
323C22×C4C2×D6811yescharacteristic
324C22×C4D4×D1711yescharacteristic
325C22×C4D4×D1711yescharacteristic
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—681no—
333C2×C8—681no—
334C2×C8—681no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—341no—
340C4⋊C4—341no—
341C4⋊C4—341no—
342C4⋊C4—341no—
343C4⋊C4—682no—
344C4⋊C4—681no—
345C4⋊C4—681no—
346C4⋊C4—681no—
347C4⋊C4—681no—
348C22⋊C4—684no—
349C22⋊C4—684no—
350C22⋊C4—1362no—
351C22⋊C4—1362no—
352C42—41no—
353C42—41no—
354C42—681no—
355C42—681no—
356C42#6325211yescharacteristic
357C42#6325411yescharacteristic
358C42#6325411yescharacteristic
359C42C2×C22⋊D1711yescharacteristic
360C23—682no—
361C23—682no—
362C23—682no—
363C23—682no—
364C23—682no—
365C23—682no—
366C23—682no—
367C23#1058756811yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372D4—684no—
373D4—1362no—
374D4—1361no—
375D4—1361no—
376D4—1361no—
377D4—1361no—
378D4—1361no—
379D4—1361no—
380D4—1361no—
381D4—1361no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—681no—
391C2×C4—681no—
392C2×C4—681no—
393C2×C4—681no—
394C2×C4—681no—
395C2×C4—681no—
396C2×C4—1361no—
397C2×C4—1361no—
398C2×C4—1361no—
399C2×C4#1058756911yescharacteristic
400C2×C4#1058757111yescharacteristic
401C2×C4#1058757211yescharacteristic
402C2×C4C2×#6321911yescharacteristic
403C2×C4#1058759011yescharacteristic
404C2×C4#1058759411yescharacteristic
405C2×C4#1058759411yescharacteristic
406C2×C4#1058760011yescharacteristic
407C2×C4#1058760211yescharacteristic
408C2×C4#1058760411yescharacteristic
409C2×C4#1058760511yescharacteristic
410C2×C4#1058761611yescharacteristic
411C2×C4#1058762411yescharacteristic
412C2×C4#1058762511yescharacteristic
413C8—42no—
414C8—42no—
415C8—1361no—
416C22—1362no—
417C22—1362no—
418C22—1362no—
419C22—1362no—
420C22—1362no—
421C22—1362no—
422C22—1362no—
423C22#1176272511yescharacteristic
424C22#1176295611yescharacteristic
425C22#1176295711yescharacteristic
426C22#1176296211yescharacteristic
427C22#1176297411yescharacteristic
428C22#1176297811yescharacteristic
429C22#1176298811yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—2721no—
435C4—1361no—
436C4—1361no—
437C4#1176302611yescharacteristic
438C4#1176303311yescharacteristic
439C4#1176303811yescharacteristic
440C4#1176306211yescharacteristic
441C4#1176312811yescharacteristic
442C4#1176313411yescharacteristic
443C4#1176316511yescharacteristic
444C4#1176317011yescharacteristic
445C2—2722no—
446C2#1452784511yescharacteristic
447C2#1452791311yescharacteristic
448C2#1452797211yescharacteristic
449C2#1452798711yescharacteristic
450C2#1452997411yescharacteristic
451C2#1452999311yescharacteristic
452C2#1453002211yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC2×C17×Q8⋊C8C2
socleC23×C17#120
prime radicalC2×#10587560C22
hypercenterC2×Q8⋊C8D17
hypocenterC17#10410
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #14529548C2semidirect
4. #14528789C2semidirect
6. #14526624C2semidirect
7. C2×C17×Q8⋊C8C2semidirect
195. C2×Q8⋊C8D17semidirect
294. C17#10410semidirect

Maximal subgroups

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

subgroupindex
#145337832
#145295902
#145295482
#145287892
C2×#117625522
#145266242
C2×C17×Q8⋊C82
#1041017