Finite Group Databasebeta

← #32982171

Subgroups — #32982171

Order 18688.

590 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
1C2×#17988788C211yesmaximal, characteristic
2C2×C8×Dic146C211yesmaximal, characteristic, complemented
3#22610737C211yesmaximal, characteristic
4#22609937C211yesmaximal, characteristic, complemented
5C2×#17988330C211yesmaximal, characteristic
6#22607815C211yesmaximal, characteristic, complemented
7C73×#1277C211yesmaximal, characteristic, complemented
8C22×#11924017—21no—
9C2×#14556588C2211yescharacteristic
10C2×C4×Dic146C2211yescharacteristic
11#17988788—22no—
12#17988788C414yescomplemented
13C8×Dic146—22no—
14C8×Dic146—22no—
15C2×C4⋊#10596831C2211yescharacteristic
16C2×#14556520—21no—
17C2×#14556516—21no—
18C2×#14556513—21no—
19C2×#14556513—21no—
20C2×#14556513—21no—
21C2×C8×Dic73—21no—
22#17988457C2211yescharacteristic
23#17988350—21no—
24#17988330—22no—
25C2×C4⋊C8×C73C2211yescharacteristic
26C2×C4⋊C8×C73C2211yescharacteristic
27C2×C4×C8×C73C2211yescharacteristic
28C22×Dic146D411yescharacteristic
29C22×D292—21no—
30C22×D292—21no—
31C22×D292—21no—
32C2×#11924017—24no—
33C2×#11924017—42no—
34C2×#11924017—42no—
35C22×#10596831—21no—
36#14556588—21no—
37#14556588—21no—
38#14556588—21no—
39#14556588C2×C412yes—
40C4×Dic146—21no—
41C4×Dic146—21no—
42C4×Dic146C2×C412yes—
43C4×Dic146D412yes—
44C2×C4⋊Dic73—21no—
45C2×C4⋊Dic73—21no—
46C2×C4⋊Dic73—21no—
47C2×C4⋊Dic73D411yescharacteristic
48C2×#11924007—21no—
49C2×C4×Dic73—21no—
50C4⋊#10596831—21no—
51C4⋊#10596831D412yes—
52#14556520—24no—
53#14556516—42no—
54#14556513—24no—
55#14556513—42no—
56#14556513—42no—
57C8×Dic73—24no—
58C22×C8×C73—21no—
59C22×C8×C73—21no—
60C22×C8×C73D411yescharacteristic
61C22×C8×C73D411yescharacteristic
62C2×C42×C73C2311yescharacteristic
63C4⋊C8×C73—21no—
64C4⋊C8×C73—21no—
65C4⋊C8×C73—21no—
66C4⋊C8×C73C2×C412yes—
67C4×C8×C73—21no—
68C4×C8×C73—21no—
69C23×D73—41no—
70C2×Dic146—21no—
71C2×Dic146—21no—
72C2×Dic146—21no—
73C2×Dic146C22⋊C412yes—
74C2×Dic146D812yes—
75C2×Dic146SD1612yes—
76C2×D292—22no—
77C2×D292—22no—
78C2×D292—22no—
79C2×D292—41no—
80C2×D292—41no—
81C2×D292—41no—
82C2×D292—41no—
83C2×D292—41no—
84C2×D292—41no—
85C2×D292—41no—
86C2×D292—41no—
87C2×D292—41no—
88C2×D292—41no—
89C2×D292—41no—
90C2×D292—81no—
91C2×D292—81no—
92C22×Dic73—21no—
93C22×Dic73—21no—
94C22×Dic73—41no—
95#11924017—48no—
96C2×#10596831—22no—
97C2×#10596831—41no—
98C2×#10596831—41no—
99C4⋊Dic73—21no—
100C4⋊Dic73—41no—
101C4⋊Dic73—41no—
102C4⋊Dic73—41no—
103C4⋊Dic73—41no—
104C4⋊Dic73—81no—
105C4⋊Dic73C22⋊C412yes—
106#11924007—22no—
107#11924007—22no—
108C4×Dic73—22no—
109C4×Dic73—22no—
110C22×C4×C73C2×D411yescharacteristic
111C22×C4×C73C2×D411yescharacteristic
112C22×C4×C73#4111yescharacteristic
113C2×C8×C73—21no—
114C2×C8×C73—21no—
115C2×C8×C73—22no—
116C2×C8×C73—21no—
117C2×C8×C73—21no—
118C2×C8×C73—21no—
119C2×C8×C73—41no—
120C2×C8×C73—41no—
121C2×C8×C73—41no—
122C2×C8×C73—41no—
123C2×C8×C73—41no—
124C2×C8×C73SD1612yescomplemented
125C42×C73C22×C411yescharacteristic
126C42×C73C2×D411yescharacteristic
127C42×C73C2×D411yescharacteristic
128C42×C73#4111yescharacteristic
129C23×C73#12111yescharacteristic
130C22×D73—42no—
131C22×D73—81no—
132C22×D73—81no—
133C22×D73—81no—
134C22×D73—81no—
135C22×D73—81no—
136C22×D73—81no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73C2×C22⋊C411yescharacteristic
140C2×C4×C73C4×D411yescharacteristic
141C2×C4×C73C4×D411yescharacteristic
142C2×C4×C73#12011yescharacteristic
143C2×C4×C73#12111yescharacteristic
144C2×C4×C73#12311yescharacteristic
145C2×C4×C73C2×D811yescharacteristic
146C2×C4×C73C2×SD1611yescharacteristic
147C2×C4×C73C2×SD1611yescharacteristic
148C2×C4×C73#13511yescharacteristic
149C2×C4×C73#13511yescharacteristic
150C2×C4×C73#13511yescharacteristic
151C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C73#13711yescharacteristic
153C2×Dic73—22no—
154C2×Dic73—22no—
155C2×Dic73—22no—
156C2×Dic73—22no—
157C2×Dic73—41no—
158C2×Dic73—41no—
159C2×Dic73—81no—
160C2×Dic73—81no—
161C2×Dic73—81no—
162D292—42no—
163D292—42no—
164D292—42no—
165D292—42no—
166D292—82no—
167D292—82no—
168D292—81no—
169D292—81no—
170D292—81no—
171D292—81no—
172Dic146—22no—
173Dic146—22no—
174Dic146—22no—
175Dic146#10214yescomplemented
176C8×C73—22no—
177C8×C73—42no—
178C8×C73—41no—
179C8×C73—81no—
180#10596831—42no—
181C22×C73#38611yescharacteristic
182C22×C73#46011yescharacteristic
183C22×C73#46411yescharacteristic
184C22×C73#46511yescharacteristic
185C22×C73#46611yescharacteristic
186C22×C73#47111yescharacteristic
187C22×C73#47211yescharacteristic
188C2×D73—82no—
189C2×D73—82no—
190C2×D73—82no—
191C2×D73—161no—
192C2×D73—161no—
193C2×D73—161no—
194C2×D73—161no—
195C4×C73—21no—
196C4×C73—21no—
197C4×C73C2×#10211yescharacteristic
198C4×C73#41611yescharacteristic
199C4×C73C4×SD1611yescharacteristic
200C4×C73#44011yescharacteristic
201C4×C73#44811yescharacteristic
202C4×C73#44911yescharacteristic
203C4×C73#46511yescharacteristic
204C4×C73#46611yescharacteristic
205Dic73—24no—
206Dic73—42no—
207Dic73—161no—
208#9222—731nomaximal, Sylow
209C2×C73#166611yescharacteristic
210C2×C73#166811yescharacteristic
211C2×C73#167811yescharacteristic
212C2×C73#168211yescharacteristic
213C2×C73#188011yescharacteristic
214C2×C73#189311yescharacteristic
215C2×C73#190711yescharacteristic
216D73—162no—
217C2×#460—731no—
218C2×C8×Q8—731no—
219#1957—731no—
220#1803—731no—
221C2×#331—731no—
222#1296—731no—
223#1277D7311yescharacteristic, complemented
224C73#922211yescharacteristic, complemented, Sylow
225C22×SD16—1461no—
226C2×#127—731no—
227C2×C4×Q8—731no—
228#460—734no—
229#460—1462no—
230C8×Q8—1462no—
231C8×Q8—1462no—
232C2×C4⋊C8—731no—
233C2×C4⋊C8—1461no—
234C2×C4⋊C8C2×D7311yescharacteristic
235C2×C4⋊C8C2×D7311yescharacteristic
236C2×#103—1461no—
237C2×#102—1461no—
238C2×#102—1461no—
239C2×#102—1461no—
240C2×C4×C8—1461no—
241C2×C4×C8C2×D7311yescharacteristic
242#384—731no—
243#340—1461no—
244#331—1462no—
245C22×Q8—731no—
246C22×D4—1461no—
247C22×D4—1461no—
248C22×D4—1461no—
249C2×SD16—2922no—
250C2×SD16—2922no—
251C2×SD16—1464no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—1461no—
255C22×C8D29211yescharacteristic
256C22×C8D29211yescharacteristic
257#127—732no—
258#127—1461no—
259#127—1461no—
260#127—1461no—
261C4×Q8—732no—
262C4×Q8—732no—
263C4×Q8—1461no—
264C4×Q8—1461no—
265C2×C4⋊C4—731no—
266C2×C4⋊C4—1461no—
267C2×C4⋊C4—1461no—
268C2×C4⋊C4—1461no—
269C2×C4⋊C4—1461no—
270C2×C42—1461no—
271C2×C42C22×D7311yescharacteristic
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—732no—
276C4⋊C8—1464no—
277C4⋊C8—1461no—
278C4⋊C8C4×D7312yes—
279#103—2922no—
280#102—2922no—
281#102—2922no—
282#102—1464no—
283C4×C8—21no—
284C4×C8—21no—
285C4×C8—1464no—
286C24—2921no—
287C2×Q8—732no—
288C2×Q8—732no—
289C2×Q8—732no—
290C2×Q8—1461no—
291C2×Q8—1461no—
292C2×Q8—1461no—
293C2×D4—2921no—
294C2×D4—2921no—
295C2×D4—2921no—
296C2×D4—2921no—
297C2×D4—2921no—
298C2×D4—2921no—
299C2×D4—2921no—
300C2×D4—2921no—
301C2×D4—2921no—
302C2×D4—2921no—
303C2×D4—2921no—
304C2×D4—5841no—
305C2×D4—5841no—
306C2×D4—1462no—
307C2×D4—1462no—
308C2×D4—1462no—
309C22×C4—2921no—
310C22×C4—1461no—
311C22×C4—1461no—
312C22×C4D4×D7311yescharacteristic
313C22×C4C2×D29211yescharacteristic
314C22×C4#1192402911yescharacteristic
315SD16—2928no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—22no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—2921no—
328C2×C8—2921no—
329C2×C8—1462no—
330C2×C8#1192401712yescomplemented
331C4⋊C4—2921no—
332C4⋊C4—2921no—
333C4⋊C4—2921no—
334C4⋊C4—2921no—
335C4⋊C4—5841no—
336C4⋊C4—732no—
337C4⋊C4—1462no—
338C4⋊C4—1461no—
339C4⋊C4—1462no—
340C42—1462no—
341C42—1462no—
342C42C2×C4×D7311yescharacteristic
343C42D4×D7311yescharacteristic
344C42D4×D7311yescharacteristic
345C42#1192402811yescharacteristic
346C23—2922no—
347C23—5841no—
348C23—5841no—
349C23—5841no—
350C23—5841no—
351C23—5841no—
352C23—5841no—
353C23#1455656611yescharacteristic
354Q8—734no—
355Q8—1462no—
356Q8—1462no—
357Q8—1462no—
358D4—2922no—
359D4—2922no—
360D4—2922no—
361D4—2922no—
362D4—5842no—
363D4—5842no—
364D4—5841no—
365D4—5841no—
366D4—5841no—
367D4—5841no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—2921no—
371C2×C4—2921no—
372C2×C4—5841no—
373C2×C4—5841no—
374C2×C4—5841no—
375C2×C4—1462no—
376C2×C4—1462no—
377C2×C4—1462no—
378C2×C4—1462no—
379C2×C4C22⋊C4×D7311yescharacteristic
380C2×C4#1455655311yescharacteristic
381C2×C4C4×D29211yescharacteristic
382C2×C4#1455656111yescharacteristic
383C2×C4#1455656411yescharacteristic
384C2×C4#1455657611yescharacteristic
385C2×C4D8×D7311yescharacteristic
386C2×C4SD16×D7311yescharacteristic
387C2×C4C2×#1192401711yescharacteristic
388C2×C4#1455661211yescharacteristic
389C2×C4#1455661311yescharacteristic
390C2×C4#1455661411yescharacteristic
391C2×C4#1455661911yescharacteristic
392C2×C4#1455662411yescharacteristic
393C8—22no—
394C8—41no—
395C8—42no—
396C8—81no—
397C8—2922no—
398C22—5842no—
399C22—5842no—
400C22—5842no—
401C22—11681no—
402C22—11681no—
403C22—11681no—
404C22—11681no—
405C22#1798846511yescharacteristic
406C22#1798878811yescharacteristic
407C22#1798881011yescharacteristic
408C22#1798881711yescharacteristic
409C22#1798882411yescharacteristic
410C22#1798885111yescharacteristic
411C22#1798885811yescharacteristic
412C4—21no—
413C4—21no—
414C4—2922no—
415C4—11681no—
416C4—1464no—
417C4#102×D7311yescharacteristic
418C4#1798858211yescharacteristic
419C4C4×#1192401711yescharacteristic
420C4#1798868911yescharacteristic
421C4#1798872811yescharacteristic
422C4#1798873411yescharacteristic
423C4#1798881911yescharacteristic
424C4#1798882211yescharacteristic
425C2—11682no—
426C2#2260928011yescharacteristic
427C2#2260929211yescharacteristic
428C2#2260934811yescharacteristic
429C2#2260937611yescharacteristic
430C2#2261028511yescharacteristic
431C2#2261035811yescharacteristic
432C2#2261043811yescharacteristic
subgroupG/H
centerC23#14556566
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1277C2
socleC23×C73#121
prime radicalC2×#14556588C22
cosocleC2×C42×C73C23
hypercenter#1277D73
hypocenterC73#9222
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic146C2semidirect
4. #22609937C2semidirect
6. #22607815C2semidirect
7. C73×#1277C2semidirect
12. #17988788C4semidirect
124. C2×C8×C73SD16semidirect
175. Dic146#102semidirect
223. #1277D73semidirect
224. C73#9222semidirect
330. C2×C8#11924017semidirect

Maximal subgroups

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

subgroupindex
C2×#179887882
C2×C8×Dic1462
#226107372
#226099372
C2×#179883302
#226078152
C73×#12772
#922273