Finite Group Databasebeta

← #16930729

Subgroups — #16930729

Order 4352.

612 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#14529624C211yesmaximal, characteristic, complemented
3#14527453C211yesmaximal, characteristic, complemented
4#14527209C211yesmaximal, characteristic, complemented
5#14526658C211yesmaximal, characteristic, complemented
6#14526635C211yesmaximal, characteristic, complemented
7D4×M16×C17C211yesmaximal, characteristic, complemented
8C22×#63228C412yes—
9C2×#10587560C2211yescharacteristic
10#11763004—21no—
11#11763004—21no—
12#11763004—21no—
13#11763004—21no—
14#11762862C2211yescharacteristic
15#11762833C2211yescharacteristic
16C2×C4⋊#3622C2211yescharacteristic
17C2×#10587480C412yes—
18C2×#10587494—21no—
19C2×#10587494—21no—
20#11762552—22no—
21D4⋊#3622—21no—
22D4⋊#3622—21no—
23C22×M16×C17—21no—
24C2×C4×D4×C17C2211yescharacteristic
25C17×#436—21no—
26C17×#435—22no—
27C8×D4×C17—21no—
28C17×#423C2211yescharacteristic
29C17×#407—21no—
30C4×M16×C17C2211yescharacteristic
31C22×D4×C17C2×C411yescharacteristic
32C23×C4×C17—21no—
33C22×D68—21no—
34C22×D68—21no—
35C22×D68C2×C412yes—
36C2×M16×C17—22no—
37C2×M16×C17—21no—
38C2×M16×C17—42no—
39C2×M16×C17—42no—
40C2×M16×C17D411yescharacteristic
41C2×M16×C17D411yescharacteristic
42C22×C8×C17—22no—
43C4×D4×C17—21no—
44C4×D4×C17—21no—
45C4×D4×C17D411yescharacteristic
46C4×D4×C17D411yescharacteristic
47C4×D4×C17D411yescharacteristic
48C4×D4×C17D411yescharacteristic
49C2×C4⋊C4×C17C2×C411yescharacteristic
50C2×C22⋊C4×C17—21no—
51C2×C42×C17C2311yescharacteristic
52C2×#63228—22no—
53C2×#63228—22no—
54C2×#63228—44no—
55C2×#63223—21no—
56C22×#3622C2×C412yes—
57#10587560—21no—
58#10587560—21no—
59#10587560—21no—
60#10587560—21no—
61C17×C4⋊C8—21no—
62C17×C4⋊C8D412yes—
63C17×C22⋊C8—22no—
64C17×C22⋊C8—22no—
65C17×#97—21no—
66C4×C8×C17—21no—
67C22⋊#3622—21no—
68#10587494—42no—
69#10587494—42no—
70#10587480—22no—
71#10587480—22no—
72C4⋊#3622—21no—
73C4⋊#3622—21no—
74C4⋊#3622—21no—
75C4⋊#3622—21no—
76C4⋊#3622—21no—
77C4×#3622—21no—
78C24×C17—21no—
79C23×D17—22no—
80C2×D4×C17—22no—
81C2×D4×C17—21no—
82C2×D4×C17—41no—
83C2×D4×C17C22⋊C411yescharacteristic
84C2×D4×C17C22⋊C411yescharacteristic
85C22×C4×C17—21no—
86C22×C4×C17—21no—
87C22×C4×C17—21no—
88C22×C4×C17—21no—
89C22×C4×C17—21no—
90C22×C4×C17—41no—
91C22×C4×C17—41no—
92C22×C4×C17—41no—
93C22×C4×C17—41no—
94C22×C4×C17C22×C411yescharacteristic
95C22×C4×C17C2×D411yescharacteristic
96C22×C4×C17#4111yescharacteristic
97C2×D68—22no—
98C2×D68—22no—
99C2×D68—42no—
100C2×D68—42no—
101C2×D68—41no—
102C2×D68—41no—
103C2×D68—41no—
104C2×D68—41no—
105C2×D68—41no—
106C2×D68—41no—
107C2×D68—41no—
108C2×D68—41no—
109C2×D68—82no—
110M16×C17—21no—
111M16×C17—21no—
112M16×C17—21no—
113M16×C17—44no—
114M16×C17—41no—
115M16×C17—41no—
116M16×C17D812yescomplemented
117C2×C8×C17—21no—
118C2×C8×C17—22no—
119C2×C8×C17—21no—
120C2×C8×C17—44no—
121C4⋊C4×C17—21no—
122C4⋊C4×C17C22⋊C411yescharacteristic
123C4⋊C4×C17C22⋊C411yescharacteristic
124C22⋊C4×C17—21no—
125C22⋊C4×C17—21no—
126C22⋊C4×C17—21no—
127C22⋊C4×C17—21no—
128C42×C17C2×D411yescharacteristic
129C42×C17C2×D411yescharacteristic
130C42×C17C2×D411yescharacteristic
131C42×C17#4111yescharacteristic
132#63228—44no—
133#63228—44no—
134#63223—41no—
135#63223—41no—
136C2×#3622—22no—
137C2×#3622—42no—
138C2×#3622—41no—
139C2×#3622—41no—
140#9253—171nomaximal, Sylow
141C23×C17—21no—
142C23×C17—21no—
143C23×C17—42no—
144C23×C17—41no—
145C23×C17—41no—
146C23×C17—81no—
147C23×C17C4×D411yescharacteristic
148C22×D17—42no—
149C22×D17—42no—
150C22×D17—42no—
151C22×D17—82no—
152C22×D17—82no—
153D4×C17—21no—
154D4×C17—21no—
155D4×C17—21no—
156D4×C17—42no—
157D4×C17#10012yescomplemented
158C2×C4×C17—21no—
159C2×C4×C17—21no—
160C2×C4×C17—21no—
161C2×C4×C17—21no—
162C2×C4×C17—41no—
163C2×C4×C17—41no—
164C2×C4×C17—41no—
165C2×C4×C17—41no—
166C2×C4×C17—41no—
167C2×C4×C17—41no—
168C2×C4×C17—41no—
169C2×C4×C17—41no—
170C2×C4×C17—41no—
171C2×C4×C17—41no—
172C2×C4×C17—41no—
173C2×C4×C17C2×C22⋊C411yescharacteristic
174C2×C4×C17C4×D411yescharacteristic
175C2×C4×C17#12011yescharacteristic
176C2×C4×C17#12111yescharacteristic
177C2×C4×C17#12111yescharacteristic
178C2×C4×C17#12311yescharacteristic
179C2×C4×C17C2×D811yescharacteristic
180C2×C4×C17#13511yescharacteristic
181C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
183D68—42no—
184D68—42no—
185D68—82no—
186D68—82no—
187D68—82no—
188D68—81no—
189D68—81no—
190D68—81no—
191D68—81no—
192C8×C17—22no—
193C8×C17—42no—
194C8×C17—41no—
195#3622—42no—
196#3622—81no—
197#3622—81no—
198C2×#459—171no—
199D4×M16D1711yescharacteristic, complemented
200#1965—171no—
201#1545—171no—
202#1486—171no—
203#1292—171no—
204#1283—171no—
205C22×C17—21no—
206C22×C17—21no—
207C22×C17—22no—
208C22×C17—41no—
209C22×C17—41no—
210C22×C17—41no—
211C22×C17—41no—
212C22×C17—41no—
213C22×C17—82no—
214C22×C17—82no—
215C22×C17#38611yescharacteristic
216C22×C17C4×D811yescharacteristic
217C22×C17#44211yescharacteristic
218C2×D17—82no—
219C2×D17—82no—
220C2×D17—82no—
221C2×D17—162no—
222C2×D17—162no—
223C4×C17—21no—
224C4×C17—21no—
225C4×C17—21no—
226C4×C17—41no—
227C4×C17—41no—
228C4×C17C2×#10011yescharacteristic
229C4×C17#41311yescharacteristic
230C4×C17#44711yescharacteristic
231C4×C17#44911yescharacteristic
232C4×C17#45911yescharacteristic
233C4×C17#46311yescharacteristic
234C22×D8—172no—
235C22×M16—21no—
236C2×#127—171no—
237C2×C4×D4C2×D1711yescharacteristic
238#459—341no—
239#459—341no—
240#459—341no—
241#459—341no—
242#436—21no—
243#435—22no—
244C8×D4—21no—
245#431—171no—
246#423—171no—
247#423C2×D1711yescharacteristic
248C2×C4⋊C8—171no—
249C2×#102—172no—
250C2×#100—341no—
251C2×#100—341no—
252#407—21no—
253C4×M16C2×D1711yescharacteristic
254#331—342no—
255D4⋊C8—341no—
256D4⋊C8—341no—
257C2×C17—21no—
258C2×C17—21no—
259C2×C17—42no—
260C2×C17—81no—
261C2×C17#187911yescharacteristic
262C2×C17#190011yescharacteristic
263C2×C17#190311yescharacteristic
264D17—162no—
265C22×D4—172no—
266C22×D4—341no—
267C22×D4—341no—
268C22×D4C4×D1711yescharacteristic
269C23×C4—21no—
270C2×D8—342no—
271C2×D8—342no—
272C2×D8—684no—
273C2×M16—22no—
274C2×M16—21no—
275C2×M16—42no—
276C2×M16—42no—
277C2×M16—341no—
278C2×M16C22⋊D1711yescharacteristic
279C2×M16C22⋊D1711yescharacteristic
280C22×C8—22no—
281C22×C8—172no—
282#127—341no—
283#127—341no—
284#127—341no—
285#127—341no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4D6811yescharacteristic
289C4×D4D6811yescharacteristic
290C4×D4C22⋊D1711yescharacteristic
291C4×D4C22⋊D1711yescharacteristic
292C2×C4⋊C4C4×D1711yescharacteristic
293C2×C22⋊C4—21no—
294C2×C42C22×D1711yescharacteristic
295C4⋊C8—21no—
296C4⋊C8—341no—
297C4⋊C8—341no—
298C4⋊C8—341no—
299C4⋊C8—341no—
300C4⋊C8—341no—
301C4⋊C8C22⋊D1712yes—
302#102—342no—
303#102—342no—
304#100—682no—
305#100—682no—
306C22⋊C8—22no—
307C22⋊C8—22no—
308C22⋊C8—341no—
309#97—21no—
310C4×C8—21no—
311C4×C8—341no—
312C17#925311yescharacteristic, complemented, Sylow
313C24—21no—
314C24—342no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—342no—
319C2×D4—342no—
320C2×D4—682no—
321C2×D4—682no—
322C2×D4—681no—
323C2×D4—681no—
324C2×D4—681no—
325C2×D4—681no—
326C2×D4—681no—
327C2×D4—681no—
328C2×D4—681no—
329C2×D4—681no—
330C2×D4—1362no—
331C2×D4#6322711yescharacteristic
332C2×D4#6322711yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4C2×C4×D1711yescharacteristic
343C22×C4#6325211yescharacteristic
344C22×C4C2×C22⋊D1711yescharacteristic
345D8—684no—
346D8—684no—
347M16—21no—
348M16—21no—
349M16—21no—
350M16—44no—
351M16—41no—
352M16—41no—
353M16—681no—
354M16—681no—
355M16#6322812yescomplemented
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—44no—
360C2×C8—342no—
361C2×C8—682no—
362C2×C8—681no—
363C2×C8—681no—
364C4⋊C4—21no—
365C4⋊C4#6322711yescharacteristic
366C4⋊C4#6322711yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C42C2×D6811yescharacteristic
372C42#6325211yescharacteristic
373C42C2×C22⋊D1711yescharacteristic
374C42C2×C22⋊D1711yescharacteristic
375C23—21no—
376C23—21no—
377C23—42no—
378C23—41no—
379C23—41no—
380C23—81no—
381C23—682no—
382C23—682no—
383C23—682no—
384C23—1362no—
385C23—1362no—
386C23C4×C22⋊D1711yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4—682no—
392D4—682no—
393D4—1362no—
394D4—1362no—
395D4—1362no—
396D4—1361no—
397D4—1361no—
398D4—1361no—
399D4—1361no—
400D4#1058749412yescomplemented
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4C2×#6322711yescharacteristic
417C2×C4C4×C22⋊D1711yescharacteristic
418C2×C4#1058761511yescharacteristic
419C2×C4#1058761611yescharacteristic
420C2×C4#1058761611yescharacteristic
421C2×C4C2×#6322811yescharacteristic
422C2×C4#1058761811yescharacteristic
423C2×C4#1058763511yescharacteristic
424C2×C4#1058763611yescharacteristic
425C2×C4#1058763911yescharacteristic
426C8—22no—
427C8—41no—
428C8—42no—
429C8—682no—
430C8—1361no—
431C8—1361no—
432C22—21no—
433C22—21no—
434C22—22no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—82no—
441C22—82no—
442C22—2722no—
443C22—2722no—
444C22—1362no—
445C22—1362no—
446C22—1362no—
447C22#1176268811yescharacteristic
448C22C4×#6322811yescharacteristic
449C22#1176291911yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—41no—
454C4—41no—
455C4C2×#1058749411yescharacteristic
456C4#1176279111yescharacteristic
457C4#1176294311yescharacteristic
458C4#1176295411yescharacteristic
459C4#1176300411yescharacteristic
460C4#1176302411yescharacteristic
461C2—21no—
462C2—21no—
463C2—42no—
464C2—81no—
465C2—2722no—
466C2#1452913211yescharacteristic
467C2#1452924711yescharacteristic
468C2#1452926411yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingD4×M16×C17C2
socleC22×C17#386
prime radicalC2×#11763004C2
cosocleC2×C42×C17C23
hypercenterD4×M16D17
hypocenterC17#9253
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. #14529624C2semidirect
3. #14527453C2semidirect
4. #14527209C2semidirect
5. #14526658C2semidirect
6. #14526635C2semidirect
7. D4×M16×C17C2semidirect
116. M16×C17D8semidirect
157. D4×C17#100semidirect
199. D4×M16D17semidirect
312. C17#9253semidirect
355. M16#63228semidirect
400. D4#10587494semidirect

Maximal subgroups

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

subgroupindex
C2×#117630042
#145296242
#145274532
#145272092
#145266582
#145266352
D4×M16×C172
#925317