Finite Group Databasebeta

← #33240632

Subgroups — #33240632

Order 18688.

546 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620445C211yesmaximal, characteristic, complemented
2C4×#14556613C211yesmaximal, characteristic
3#22612096C212yesmaximal, complemented
4#22612089C212yesmaximal, complemented
5#22612084C211yesmaximal, characteristic, complemented
6#22612079C211yesmaximal, characteristic, complemented
7#22612074C211yesmaximal, characteristic, complemented
8#22612069C211yesmaximal, characteristic, complemented
9#22611715C212yesmaximal, complemented
10#22611639C212yesmaximal
11C2×C4⋊C16×C73C211yesmaximal, characteristic, complemented
12C2×#14556613C2211yescharacteristic
13#17989144—21no—
14C4×#11924028—21no—
15#17988992C2211yescharacteristic
16#17988992C2211yescharacteristic
17#17988989—21no—
18#17988989C2212yes—
19#17988985—21no—
20C4×Dic292C2211yescharacteristic
21C4×Dic292C2211yescharacteristic
22C4×#11924017—21no—
23C4×#11924017—21no—
24C4×D584C2211yescharacteristic
25C4×D584C2211yescharacteristic
26#17988625—21no—
27#17988625C2211yescharacteristic
28#17988625C2212yes—
29#17988584—21no—
30#17988415C2212yes—
31#17988415C2212yes—
32#17988413C2212yes—
33#17988413C2212yes—
34#17988392C2212yes—
35#17988392C2212yes—
36#17988389C2212yes—
37#17988389C2212yes—
38C22×C16×C73C2212yes—
39C2×C4×C8×C73C2211yescharacteristic
40C4⋊C16×C73C2211yescharacteristic
41C4⋊C16×C73C2211yescharacteristic
42C4⋊C16×C73C2212yes—
43C2×#11924028—21no—
44#14556613—22no—
45#14556613Q814yescomplemented
46C2×Dic292C2311yescharacteristic
47C2×#11924017—21no—
48C2×D584C2311yescharacteristic
49#14556591—21no—
50#14556591—21no—
51#14556583—22no—
52#14556570—41no—
53#14556570—41no—
54C4×Dic146—21no—
55C4×Dic146—21no—
56C4×Dic146—41no—
57C4×Dic146—41no—
58C4×D292—21no—
59C4×D292—21no—
60C4×C22⋊D73—41no—
61C4×C22⋊D73—41no—
62#14556550—22no—
63#14556550—21no—
64#14556548—41no—
65C42×D73—41no—
66#14556525—21no—
67#14556525—21no—
68#14556525C2312yes—
69#14556525C2312yes—
70#14556525C2311yescharacteristic
71#14556525C2311yescharacteristic
72#14556523—22no—
73#14556523—21no—
74#14556523—22no—
75#14556516—21no—
76#14556516—21no—
77#14556513—21no—
78#14556513—21no—
79C22×C8×C73D411yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C2×C42×C73D411yescharacteristic
82C2×C16×C73—24no—
83C2×C16×C73C2312yes—
84C2×C16×C73C2312yes—
85C4×C8×C73D411yescharacteristic
86C4×C8×C73D411yescharacteristic
87C4×C8×C73C2311yescharacteristic
88C4×C8×C73C2311yescharacteristic
89#11924028—24no—
90#11924028—42no—
91C2×Dic146—21no—
92C2×Dic146—41no—
93C2×Dic146—41no—
94C2×D292—21no—
95C2×C22⋊D73—41no—
96C2×C4×D73—41no—
97C2×C4×D73—41no—
98C2×C4×D73—41no—
99Dic292—21no—
100Dic292C2×Q812yes—
101#11924017—24no—
102D584—21no—
103D584C2×Q812yes—
104C4⋊Dic73—21no—
105C4⋊Dic73—21no—
106C4⋊Dic73—22no—
107C4⋊Dic73—22no—
108C4⋊Dic73—41no—
109C4⋊Dic73—41no—
110#11924007—41no—
111#11924007—41no—
112#11924007—42no—
113#11924007—42no—
114C22⋊Dic73—41no—
115C22⋊Dic73—42no—
116#11924005—41no—
117#11924005—41no—
118C4×Dic73—41no—
119C4×Dic73—41no—
120C4×Dic73—41no—
121C4×Dic73—42no—
122C22×C4×C73D811yescharacteristic
123C22×C4×C73D811yescharacteristic
124C22×C4×C73C2×D411yescharacteristic
125C2×C8×C73—22no—
126C2×C8×C73C2×D411yescharacteristic
127C2×C8×C73C2×D411yescharacteristic
128C2×C8×C73C2×D411yescharacteristic
129C2×C8×C73C2×Q812yes—
130C2×C8×C73#4112yes—
131C2×C8×C73C2411yescharacteristic
132C42×C73D811yescharacteristic
133C42×C73D811yescharacteristic
134C42×C73C2×D411yescharacteristic
135C42×C73C2×D411yescharacteristic
136C16×C73—22no—
137C16×C73—22no—
138C23×C73C2×D811yescharacteristic
139C22×D73—41no—
140C2×C4×C73—22no—
141C2×C4×C73—41no—
142C2×C4×C73C22⋊Q812yes—
143C2×C4×C73C2×D811yescharacteristic
144C2×C4×C73C2×D811yescharacteristic
145C2×C4×C73C2×D811yescharacteristic
146C2×C4×C73C2×D811yescharacteristic
147C2×C4×C73C2×D811yescharacteristic
148C2×C4×C73#13712yes—
149C2×C4×C73C22×D411yescharacteristic
150C22⋊D73—44no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—42no—
155C2×Dic73—42no—
156D292—22no—
157D292—41no—
158C4×D73—44no—
159C4×D73—82no—
160C4×D73—82no—
161Dic146—22no—
162Dic146—41no—
163Dic146—82no—
164Dic146—82no—
165C8×C73—21no—
166C8×C73—21no—
167C8×C73C22⋊Q812yes—
168C8×C73C22×Q811yescharacteristic
169C8×C73C2×#4111yescharacteristic
170C22×C73—21no—
171C22×C73—21no—
172C22×C73#47412yes—
173C22×C73C22×D811yescharacteristic
174C2×D73—42no—
175C2×D73—81no—
176C2×D73—81no—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—21no—
180C4×C73#47412yes—
181C4×C73#50812yes—
182C4×C73C2×C22⋊Q811yescharacteristic
183C4×C73C2×#13711yescharacteristic
184Dic73—42no—
185Dic73—82no—
186Dic73—81no—
187Dic73—82no—
188Dic73—81no—
189#33626—731nomaximal, Sylow
190C2×C73—22no—
191C2×C73C2×#47411yescharacteristic
192C2×C73C2×#50811yescharacteristic
193C2×C73#341411yescharacteristic
194D73—82no—
195#3160—731no—
196C4×#135—731no—
197#2229—732no—
198#2228—732no—
199#2227—731no—
200#2226—731no—
201#2225—731no—
202#2224—731no—
203#2158—732no—
204C2×C4⋊C16D7311yescharacteristic, complemented
205#2138—732no—
206C73#3362611yescharacteristic, complemented, Sylow
207C2×#135—731no—
208#533—1461no—
209C4×#41—1461no—
210C22×C16C2×D7312yes—
211#500—731no—
212#500—731no—
213#499—732no—
214#499—1461no—
215#498—1461no—
216C4×Q16—731no—
217C4×Q16—731no—
218C4×SD16—1461no—
219C4×SD16—1461no—
220C4×D8—731no—
221C4×D8—731no—
222#427—732no—
223#427—731no—
224#427—1461no—
225#416—1461no—
226C2×C4×C8C2×D7311yescharacteristic
227#367—732no—
228#367—732no—
229#366—732no—
230#366—732no—
231C4⋊C16C2×D7311yescharacteristic
232C4⋊C16C2×D7311yescharacteristic
233C4⋊C16C2×D7312yes—
234#358—732no—
235#358—732no—
236#357—732no—
237#357—732no—
238C2×#41—1461no—
239#135—734no—
240#135—1462no—
241C2×Q16—731no—
242C2×SD16—1461no—
243C2×D8—731no—
244C22×C8D29211yescharacteristic
245C22×C8C22×D7311yescharacteristic
246C4⋊Q8—1461no—
247C4⋊Q8—1461no—
248#125—1462no—
249C22⋊Q8—2921no—
250C22⋊Q8—2921no—
251C4×Q8—2921no—
252C4×Q8—2921no—
253C4×Q8—1461no—
254C4×Q8—1461no—
255C4×D4—2921no—
256C4×D4—2921no—
257C4×D4—1461no—
258C4×D4—1461no—
259#117—2921no—
260#117—1461no—
261#117—1462no—
262C2×C42—2921no—
263C2×C42D29211yescharacteristic
264C2×C16—24no—
265C2×C16C22×D7312yes—
266C2×C16C22×D7312yes—
267#107—732no—
268#107—732no—
269#107—731no—
270#107—731no—
271#107—1461no—
272#107—1461no—
273#106—1461no—
274#106—1462no—
275#106—1462no—
276#103—1461no—
277#103—1461no—
278#102—1461no—
279#102—1461no—
280C4×C8D29211yescharacteristic
281C4×C8D29211yescharacteristic
282C4×C8C22×D7311yescharacteristic
283C4×C8C22×D7311yescharacteristic
284#41—2922no—
285#41—1464no—
286C2×Q8—2921no—
287C2×Q8—2921no—
288C2×Q8—1461no—
289C2×D4—2921no—
290C2×D4—1461no—
291C22×C4—2921no—
292C22×C4—2921no—
293C22×C4—2921no—
294C22×C4D58411yescharacteristic
295C22×C4D58411yescharacteristic
296C22×C4C2×D29211yescharacteristic
297Q16—732no—
298Q16—1461no—
299SD16—1464no—
300D8—732no—
301D8—1461no—
302C2×C8—22no—
303C2×C8C2×D29211yescharacteristic
304C2×C8C2×D29211yescharacteristic
305C2×C8C2×D29211yescharacteristic
306C2×C8Q8×D7312yes—
307C2×C8#1192402712yes—
308C2×C8C23×D7311yescharacteristic
309C4⋊C4—2921no—
310C4⋊C4—2921no—
311C4⋊C4—2922no—
312C4⋊C4—2922no—
313C4⋊C4—2921no—
314C4⋊C4—2921no—
315C4⋊C4—1461no—
316C4⋊C4—1461no—
317C4⋊C4—1462no—
318C4⋊C4—1462no—
319C22⋊C4—2921no—
320C22⋊C4—2922no—
321C22⋊C4—2921no—
322C22⋊C4—2921no—
323C42—2921no—
324C42—2921no—
325C42—2921no—
326C42—2922no—
327C42D58411yescharacteristic
328C42D58411yescharacteristic
329C42C2×D29211yescharacteristic
330C42C2×D29211yescharacteristic
331C16—22no—
332C16—22no—
333C23—2921no—
334C23C2×D58411yescharacteristic
335Q8—2921no—
336Q8—5842no—
337Q8—5842no—
338Q8—1462no—
339D4—2924no—
340D4—2921no—
341D4—1462no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—2921no—
345C2×C4—2924no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—2922no—
349C2×C4—2922no—
350C2×C4—5842no—
351C2×C4—5842no—
352C2×C4#1455657112yes—
353C2×C4C2×D58411yescharacteristic
354C2×C4C2×D58411yescharacteristic
355C2×C4C2×D58411yescharacteristic
356C2×C4C2×D58411yescharacteristic
357C2×C4C2×D58411yescharacteristic
358C2×C4#1455662412yes—
359C2×C4C22×D29211yescharacteristic
360C8—21no—
361C8—21no—
362C8#1455657112yes—
363C8C2×Q8×D7311yescharacteristic
364C8C2×#1192402711yescharacteristic
365C22—21no—
366C22—21no—
367C22—2922no—
368C22—5841no—
369C22—5841no—
370C22#1798886812yes—
371C22C22×D58411yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—2922no—
376C4—5841no—
377C4—5842no—
378C4—5841no—
379C4—5842no—
380C4#1798886812yes—
381C4#1798901912yes—
382C4C2×#1455657111yescharacteristic
383C4C2×#1455662411yescharacteristic
384C2—22no—
385C2—5842no—
386C2C2×#1798886811yescharacteristic
387C2C2×#1798901911yescharacteristic
388C2#2262306711yescharacteristic
subgroupG/H
centerC2×C4C2×D584
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC2×C4⋊C16×C73C2
socleC22×C73C22×D8
prime radicalC2×#14556613C22
hypercenterC2×C4⋊C16D73
hypocenterC73#33626
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
1. #22620445C2semidirect
3. #22612096C2semidirect
4. #22612089C2semidirect
5. #22612084C2semidirect
6. #22612079C2semidirect
7. #22612074C2semidirect
8. #22612069C2semidirect
9. #22611715C2semidirect
11. C2×C4⋊C16×C73C2semidirect
45. #14556613Q8semidirect
204. C2×C4⋊C16D73semidirect
206. C73#33626semidirect

Maximal subgroups

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

subgroupindex
#226204452
C4×#145566132
#226120962
#226120892
#226120842
#226120792
#226120742
#226120692
#226117152
#226116392
C2×C4⋊C16×C732
#3362673