Finite Group Databasebeta

← #16937830

Subgroups — #16937830

Order 4352.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14528911C211yesmaximal, characteristic, complemented
2#14528784C211yesmaximal, characteristic, complemented
3#14528784C211yesmaximal, characteristic, complemented
4C2×D4⋊#3622C211yesmaximal, characteristic, complemented
5C2×D4⋊#3622C211yesmaximal, characteristic, complemented
6#14526667C211yesmaximal, characteristic, complemented
7C17×#2537C211yesmaximal, characteristic
8C2×C4⋊#3622C2211yescharacteristic
9C2×C4⋊#3622C2211yescharacteristic
10C2×#10587503—21no—
11C2×#10587503—21no—
12C2×C4×#3622C2211yescharacteristic
13#11762679C2211yescharacteristic
14#11762571—21no—
15#11762571—21no—
16#11762571—22no—
17D4⋊#3622—22no—
18D4⋊#3622—22no—
19C2×C17×#121—21no—
20C2×C17×#121—21no—
21C2×C4×D4×C17C2211yescharacteristic
22C2×C4×D4×C17C2211yescharacteristic
23C17×#394—22no—
24C17×#384C2211yescharacteristic
25C17×#380—21no—
26C17×#380—21no—
27C22×D4×C17—22no—
28C22×D4×C17D411yescharacteristic
29C22×D4×C17D411yescharacteristic
30C23×C4×C17—21no—
31C23×C4×C17—21no—
32C17×#121—42no—
33C17×#121—42no—
34C17×#121—42no—
35C17×#121—42no—
36C4×D4×C17—21no—
37C4×D4×C17—21no—
38C4×D4×C17—21no—
39C4×D4×C17—21no—
40C4×D4×C17—21no—
41C4×D4×C17—21no—
42C4×D4×C17—21no—
43C4×D4×C17—21no—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17D411yescharacteristic
47C2×C4⋊C4×C17D411yescharacteristic
48C2×C4⋊C4×C17D412yes—
49C2×C22⋊C4×C17—22no—
50C2×C22⋊C4×C17—22no—
51C2×C22⋊C4×C17—21no—
52C2×C22⋊C4×C17—21no—
53C2×C42×C17C2311yescharacteristic
54C2×C4⋊Dic17—21no—
55C2×C4⋊Dic17—21no—
56C2×C4⋊Dic17—21no—
57C22×#3622—21no—
58C22×#3622—21no—
59C22×#3622—21no—
60C17×#95—22no—
61#10587503—42no—
62#10587503—42no—
63C4⋊#3622—21no—
64C4⋊#3622—21no—
65C4⋊#3622—21no—
66C4⋊#3622—21no—
67C4×#3622—21no—
68C4×#3622D412yescomplemented
69C24×C17—21no—
70C24×C17—21no—
71C2×D4×C17—21no—
72C2×D4×C17—21no—
73C2×D4×C17—21no—
74C2×D4×C17—21no—
75C2×D4×C17—21no—
76C2×D4×C17—21no—
77C2×D4×C17—21no—
78C2×D4×C17—21no—
79C2×D4×C17—21no—
80C2×D4×C17—21no—
81C2×D4×C17—44no—
82C2×D4×C17—44no—
83C2×D4×C17—82no—
84C2×D4×C17D812yes—
85C2×D4×C17SD1612yes—
86C22×C4×C17—21no—
87C22×C4×C17—21no—
88C22×C4×C17—22no—
89C22×C4×C17—41no—
90C22×C4×C17—41no—
91C22×C4×C17—41no—
92C22×C4×C17—41no—
93C22×C4×C17—41no—
94C22×C4×C17—41no—
95C22×C4×C17—41no—
96C22×C4×C17—41no—
97C22×C4×C17—41no—
98C22×C4×C17—41no—
99C22×C4×C17—41no—
100C22×C4×C17—41no—
101C22×C4×C17C2×D411yescharacteristic
102C22×C4×C17C2×D411yescharacteristic
103C22×C4×C17C2×D411yescharacteristic
104C22×Dic17—41no—
105C4⋊C4×C17—21no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—21no—
108C4⋊C4×C17—21no—
109C4⋊C4×C17—42no—
110C4⋊C4×C17—41no—
111C4⋊C4×C17—41no—
112C4⋊C4×C17—41no—
113C4⋊C4×C17—41no—
114C22⋊C4×C17—44no—
115C22⋊C4×C17—44no—
116C22⋊C4×C17—41no—
117C22⋊C4×C17—41no—
118C22⋊C4×C17—41no—
119C22⋊C4×C17—41no—
120C42×C17C2×D411yescharacteristic
121C42×C17#4111yescharacteristic
122C42×C17#4111yescharacteristic
123C42×C17#4111yescharacteristic
124C4⋊Dic17—42no—
125C4⋊Dic17—41no—
126C4⋊Dic17—41no—
127C4⋊Dic17—41no—
128C4⋊Dic17—41no—
129C2×#3622—22no—
130C2×#3622—41no—
131C2×#3622—41no—
132C2×#3622—41no—
133C2×#3622—41no—
134C2×#3622—41no—
135C2×#3622—41no—
136C2×#3622—41no—
137C2×#3622—41no—
138#10431—171nomaximal, Sylow
139C23×C17—22no—
140C23×C17—22no—
141C23×C17—41no—
142C23×C17—41no—
143C23×C17—41no—
144C23×C17—41no—
145C23×C17—41no—
146C23×C17—41no—
147C23×C17—41no—
148C23×C17—41no—
149C23×C17—41no—
150C23×C17—41no—
151C23×C17—41no—
152C23×C17—41no—
153C23×C17#12011yescharacteristic
154D4×C17—22no—
155D4×C17—22no—
156D4×C17—22no—
157D4×C17—22no—
158D4×C17—41no—
159D4×C17—41no—
160D4×C17—41no—
161D4×C17—41no—
162D4×C17—88no—
163C2×C4×C17—21no—
164C2×C4×C17—21no—
165C2×C4×C17—41no—
166C2×C4×C17—41no—
167C2×C4×C17—41no—
168C2×C4×C17—42no—
169C2×C4×C17—41no—
170C2×C4×C17—41no—
171C2×C4×C17—42no—
172C2×C4×C17—41no—
173C2×C4×C17—42no—
174C2×C4×C17—81no—
175C2×C4×C17—81no—
176C2×C4×C17—81no—
177C2×C4×C17—81no—
178C2×C4×C17—81no—
179C2×C4×C17—81no—
180C2×C4×C17—81no—
181C2×C4×C17—81no—
182C2×C4×C17#12111yescharacteristic
183C2×C4×C17#12111yescharacteristic
184C2×C4×C17#12111yescharacteristic
185C2×C4×C17#12311yescharacteristic
186C2×C4×C17#12311yescharacteristic
187C2×C4×C17#12411yescharacteristic
188C2×C4×C17C2×D811yescharacteristic
189C2×C4×C17C2×SD1611yescharacteristic
190C2×C4×C17#13511yescharacteristic
191C2×C4×C17#13511yescharacteristic
192C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C17#13711yescharacteristic
196C2×Dic17—81no—
197C2×Dic17—81no—
198C2×Dic17—81no—
199#3622—42no—
200#3622—81no—
201#3622—81no—
202#2537D1711yescharacteristic
203#1834—171no—
204#1802—171no—
205#1802—171no—
206C2×D4⋊C8—171no—
207C2×D4⋊C8—171no—
208#1296—171no—
209C22×C17—42no—
210C22×C17—42no—
211C22×C17—42no—
212C22×C17—42no—
213C22×C17—42no—
214C22×C17—42no—
215C22×C17—81no—
216C22×C17—81no—
217C22×C17—81no—
218C22×C17—81no—
219C22×C17—81no—
220C22×C17—81no—
221C22×C17—81no—
222C22×C17—81no—
223C22×C17#39411yescharacteristic
224C22×C17#44711yescharacteristic
225C22×C17#44911yescharacteristic
226C22×C17#45011yescharacteristic
227C22×C17#45211yescharacteristic
228C22×C17#45411yescharacteristic
229C22×C17#45511yescharacteristic
230C4×C17—21no—
231C4×C17—21no—
232C4×C17—82no—
233C4×C17—81no—
234C4×C17—81no—
235C4×C17#46511yescharacteristic
236C4×C17#46611yescharacteristic
237C4×C17#46811yescharacteristic
238C4×C17#46911yescharacteristic
239C4×C17#48011yescharacteristic
240C4×C17#48111yescharacteristic
241C4×C17#48211yescharacteristic
242C4×C17#48211yescharacteristic
243Dic17—161no—
244C2×#121—21no—
245C2×#121—21no—
246C2×C4×D4C2×D1711yescharacteristic
247C2×C4×D4C2×D1711yescharacteristic
248C2×C4⋊C8—171no—
249C2×C4⋊C8—171no—
250C2×#102—341no—
251C2×#102—341no—
252C2×C4×C8—171no—
253#394—22no—
254#384—171no—
255#384C2×D1711yescharacteristic
256#380—21no—
257#380—21no—
258#340—341no—
259#340—341no—
260#340—342no—
261D4⋊C8—342no—
262D4⋊C8—342no—
263C2×C17—82no—
264C2×C17—82no—
265C2×C17#162511yescharacteristic
266C2×C17#163511yescharacteristic
267C2×C17#163911yescharacteristic
268C2×C17#164611yescharacteristic
269C2×C17#203311yescharacteristic
270C2×C17#203411yescharacteristic
271C2×C17#204011yescharacteristic
272C22×D4—22no—
273C22×D4C22⋊D1711yescharacteristic
274C22×D4C22⋊D1711yescharacteristic
275C23×C4—21no—
276C23×C4—21no—
277C22×C8—341no—
278C22×C8—341no—
279C22×C8—341no—
280#121—42no—
281#121—42no—
282#121—42no—
283#121—42no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—341no—
295C2×C4⋊C4—341no—
296C2×C4⋊C4—341no—
297C2×C4⋊C4C22⋊D1711yescharacteristic
298C2×C4⋊C4C22⋊D1711yescharacteristic
299C2×C4⋊C4C22⋊D1712yes—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C42C22×D1711yescharacteristic
305C4⋊C8—341no—
306C4⋊C8—341no—
307C4⋊C8—341no—
308C4⋊C8—341no—
309#102—682no—
310#102—682no—
311C4×C8—172no—
312C4×C8—341no—
313#95—22no—
314C17#1043111yescharacteristic, complemented, Sylow
315C24—21no—
316C24—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—44no—
328C2×D4—44no—
329C2×D4—82no—
330C2×D4#6322812yes—
331C2×D4#6322912yes—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—681no—
348C22×C4C2×C22⋊D1711yescharacteristic
349C22×C4C2×C22⋊D1711yescharacteristic
350C22×C4C2×C22⋊D1711yescharacteristic
351C2×C8—342no—
352C2×C8—681no—
353C2×C8—681no—
354C2×C8—681no—
355C2×C8—681no—
356C2×C8—681no—
357C2×C8—681no—
358C2×C8—681no—
359C2×C8—681no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—42no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—682no—
370C4⋊C4—681no—
371C4⋊C4—681no—
372C4⋊C4—681no—
373C4⋊C4—681no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C42D4×D1711yescharacteristic
381C42#6325411yescharacteristic
382C42#6325411yescharacteristic
383C42#6325411yescharacteristic
384C23—22no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23#1058763911yescharacteristic
399D4—22no—
400D4—22no—
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—41no—
407D4—88no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—1361no—
428C2×C4—1361no—
429C2×C4—1361no—
430C2×C4C2×#6322811yescharacteristic
431C2×C4#1058761811yescharacteristic
432C2×C4#1058761811yescharacteristic
433C2×C4C2×#6322911yescharacteristic
434C2×C4#1058762111yescharacteristic
435C2×C4#1058762111yescharacteristic
436C2×C4#1058762211yescharacteristic
437C2×C4#1058762411yescharacteristic
438C2×C4#1058762511yescharacteristic
439C2×C4#1058762511yescharacteristic
440C2×C4#1058763511yescharacteristic
441C2×C4#1058763611yescharacteristic
442C2×C4#1058763611yescharacteristic
443C2×C4#1058763711yescharacteristic
444C8—682no—
445C8—1361no—
446C8—1361no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#1176272311yescharacteristic
462C22#1176294311yescharacteristic
463C22#1176295411yescharacteristic
464C22#1176296011yescharacteristic
465C22#1176297111yescharacteristic
466C22#1176298211yescharacteristic
467C22#1176298711yescharacteristic
468C4—21no—
469C4—21no—
470C4—81no—
471C4—81no—
472C4—82no—
473C4—2721no—
474C4#1176303611yescharacteristic
475C4#1176304311yescharacteristic
476C4#1176305311yescharacteristic
477C4#1176306011yescharacteristic
478C4#1176312011yescharacteristic
479C4#1176312511yescharacteristic
480C4#1176313011yescharacteristic
481C4#1176313011yescharacteristic
482C2—82no—
483C2—82no—
484C2#1452787311yescharacteristic
485C2#1452793511yescharacteristic
486C2#1452796311yescharacteristic
487C2#1452801211yescharacteristic
488C2#1452996311yescharacteristic
489C2#1452997011yescharacteristic
490C2#1453001011yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
Fitting, prime radicalC17×#2537C2
socleC23×C17#120
hypercenter#2537D17
hypocenterC17#10431
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #14528911C2semidirect
2. #14528784C2semidirect
3. #14528784C2semidirect
4. C2×D4⋊#3622C2semidirect
5. C2×D4⋊#3622C2semidirect
6. #14526667C2semidirect
68. C4×#3622D4semidirect
314. C17#10431semidirect

Maximal subgroups

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

subgroupindex
#145289112
#145287842
C2×D4⋊#36222
#145266672
C17×#25372
#1043117