Finite Group Databasebeta

← #33069929

Subgroups — #33069929

Order 18688.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620445C211yesmaximal, characteristic, complemented
2#22620093C212yesmaximal
3#22609335C211yesmaximal, characteristic, complemented
4#22609330C211yesmaximal, characteristic, complemented
5#22609325C211yesmaximal, characteristic, complemented
6#22609320C211yesmaximal, characteristic, complemented
7#22609313C212yesmaximal, complemented
8#22609306C212yesmaximal, complemented
9#22608694C211yesmaximal, characteristic, complemented
10#22608639C212yesmaximal, complemented
11C8×#41×C73C211yesmaximal, characteristic
12#17989144C2212yes—
13#17988992C2211yescharacteristic
14#17988992C2211yescharacteristic
15#17988989—21no—
16#17988989—21no—
17#17988985C2212yes—
18#17988928—22no—
19#17988882C2212yes—
20#17988877C2212yes—
21#17988797C2212yes—
22#17988792C2212yes—
23#17988749—22no—
24#17988692—22no—
25#17988687—22no—
26#17988644C2212yes—
27#17988625—21no—
28#17988625—21no—
29#17988340C2211yescharacteristic
30#17988340C2211yescharacteristic
31#17988338C2212yes—
32#17988335C2212yes—
33#17988335C2212yes—
34#17988332C2212yes—
35#17988332C2212yes—
36C4×#41×C73C2211yescharacteristic
37C8×Q8×C73C2211yescharacteristic
38C8×Q8×C73C2211yescharacteristic
39C8×D4×C73—21no—
40C8×D4×C73—21no—
41C8×D4×C73C2211yescharacteristic
42C8×D4×C73C2211yescharacteristic
43#431×C73—21no—
44#431×C73C2211yescharacteristic
45C2×C4×C8×C73—21no—
46C2×C4×C8×C73C2211yescharacteristic
47C2×#11924018—22no—
48C2×#11924016—22no—
49#14556591C2312yes—
50#14556591C2312yes—
51#14556583—22no—
52#14556570—22no—
53#14556570—22no—
54C4×Dic146—22no—
55C4×Dic146—22no—
56#14556550—22no—
57#14556525—21no—
58#14556525—21no—
59#14556525—21no—
60#14556525—21no—
61#14556524—22no—
62#14556523—22no—
63#14556523—22no—
64#14556522—22no—
65C4⋊#10596831C2312yes—
66C4⋊#10596831C2312yes—
67#14556515—22no—
68#14556514—22no—
69#14556514—22no—
70#14556512—22no—
71C22⋊#10596831—22no—
72#14556502—22no—
73C2×#41×C73D411yescharacteristic
74C22×C8×C73—21no—
75C22×C8×C73—21no—
76C22×C8×C73D411yescharacteristic
77C22×C8×C73D411yescharacteristic
78C4×Q8×C73D411yescharacteristic
79C4×Q8×C73C2311yescharacteristic
80C4×D4×C73—21no—
81C4×D4×C73—21no—
82C4×D4×C73D411yescharacteristic
83C4×D4×C73C2311yescharacteristic
84#117×C73—21no—
85#117×C73D411yescharacteristic
86C2×C42×C73—21no—
87C2×C42×C73C2311yescharacteristic
88C4⋊C8×C73—21no—
89C4⋊C8×C73—21no—
90C4⋊C8×C73C2311yescharacteristic
91C4⋊C8×C73C2311yescharacteristic
92C22⋊C8×C73—21no—
93C22⋊C8×C73—21no—
94C22⋊C8×C73—21no—
95C4×C8×C73—21no—
96C4×C8×C73—21no—
97C4×C8×C73—21no—
98C4×C8×C73D411yescharacteristic
99C4×C8×C73D411yescharacteristic
100C4×C8×C73C2311yescharacteristic
101C4×C8×C73C2311yescharacteristic
102C2×Dic146—22no—
103C2×Dic146—22no—
104#11924018—44no—
105#11924016—44no—
106C2×#10596831—22no—
107C2×#10596831—22no—
108C4⋊Dic73—22no—
109C4⋊Dic73—22no—
110C4⋊Dic73—22no—
111C4⋊Dic73—22no—
112#11924007—42no—
113#11924007—42no—
114C22⋊Dic73—42no—
115C4×Dic73—42no—
116#41×C73—22no—
117#41×C73—22no—
118C2×Q8×C73C2×D411yescharacteristic
119C2×D4×C73—21no—
120C2×D4×C73C2×D411yescharacteristic
121C22×C4×C73—21no—
122C22×C4×C73—21no—
123C22×C4×C73—21no—
124C22×C4×C73C2×D411yescharacteristic
125C22×C4×C73C2×D411yescharacteristic
126C22×C4×C73#4111yescharacteristic
127C2×C8×C73—22no—
128C2×C8×C73—22no—
129C2×C8×C73—21no—
130C2×C8×C73—21no—
131C2×C8×C73—42no—
132C2×C8×C73—42no—
133C2×C8×C73C2×D411yescharacteristic
134C2×C8×C73C2×D411yescharacteristic
135C2×C8×C73C2×D411yescharacteristic
136C2×C8×C73C2×D411yescharacteristic
137C4⋊C4×C73—21no—
138C4⋊C4×C73—21no—
139C4⋊C4×C73C2×D411yescharacteristic
140C4⋊C4×C73C2×D411yescharacteristic
141C22⋊C4×C73—21no—
142C22⋊C4×C73—21no—
143C22⋊C4×C73—21no—
144C42×C73—21no—
145C42×C73—21no—
146C42×C73—21no—
147C42×C73C2×D411yescharacteristic
148C42×C73C2×D411yescharacteristic
149C42×C73#4111yescharacteristic
150C42×C73C2411yescharacteristic
151C23×C73—21no—
152C23×C73#12111yescharacteristic
153Q8×C73—21no—
154Q8×C73#13512yes—
155D4×C73—24no—
156D4×C73—21no—
157D4×C73#13512yes—
158C2×C4×C73—24no—
159C2×C4×C73—21no—
160C2×C4×C73—21no—
161C2×C4×C73—21no—
162C2×C4×C73—21no—
163C2×C4×C73—21no—
164C2×C4×C73—21no—
165C2×C4×C73—21no—
166C2×C4×C73—41no—
167C2×C4×C73—42no—
168C2×C4×C73—41no—
169C2×C4×C73—41no—
170C2×C4×C73#12111yescharacteristic
171C2×C4×C73#12111yescharacteristic
172C2×C4×C73#12111yescharacteristic
173C2×C4×C73C22×D411yescharacteristic
174C2×C4×C73C22×D411yescharacteristic
175C2×C4×C73C2×#4111yescharacteristic
176C2×Dic73—42no—
177C2×Dic73—42no—
178Dic146—42no—
179Dic146—42no—
180Dic146—82no—
181C8×C73—21no—
182C8×C73—21no—
183C8×C73—41no—
184C8×C73—41no—
185C8×C73#13712yes—
186C8×C73#13712yes—
187#10596831—42no—
188#10596831—42no—
189C22×C73—21no—
190C22×C73—21no—
191C22×C73—22no—
192C22×C73—21no—
193C22×C73—41no—
194C22×C73—41no—
195C22×C73C2×#12111yescharacteristic
196C4×C73—21no—
197C4×C73—21no—
198C4×C73—22no—
199C4×C73—21no—
200C4×C73—21no—
201C4×C73—41no—
202C4×C73—41no—
203C4×C73C2×#13511yescharacteristic
204C4×C73C2×#13511yescharacteristic
205C4×C73C2×#13711yescharacteristic
206C4×C73C2×#13711yescharacteristic
207Dic73—82no—
208Dic73—82no—
209#19273—731nomaximal, Sylow
210C2×C73—41no—
211C2×C73—42no—
212C2×C73#303911yescharacteristic
213C2×C73#305011yescharacteristic
214C2×C73#306711yescharacteristic
215#3160—731no—
216#3116—732no—
217C8×#41D7311yescharacteristic
218#1676—731no—
219#1675—731no—
220#1674—731no—
221#1673—731no—
222#1672—732no—
223#1671—732no—
224#1568—731no—
225#1554—732no—
226C73#1927311yescharacteristic, complemented, Sylow
227#533—732no—
228C4×#41C2×D7311yescharacteristic
229#500—731no—
230#500—731no—
231#499—1461no—
232#499—1461no—
233#498—732no—
234#485—1462no—
235#477—732no—
236#476—732no—
237#462—732no—
238#461—732no—
239#452—1462no—
240C8×Q8C2×D7311yescharacteristic
241C8×Q8C2×D7311yescharacteristic
242#441—1462no—
243#440—1462no—
244C8×D4—21no—
245C8×D4—21no—
246C8×D4C2×D7311yescharacteristic
247C8×D4C2×D7311yescharacteristic
248#432—732no—
249#431—21no—
250#431C2×D7311yescharacteristic
251#427—1461no—
252#427—1461no—
253C2×C4×C8—21no—
254C2×C4×C8C2×D7311yescharacteristic
255#335—731no—
256#335—731no—
257#334—732no—
258#333—732no—
259#333—732no—
260#332—732no—
261#332—732no—
262C2×#41D29211yescharacteristic
263C2×Q16—1462no—
264C2×SD16—1462no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8C22⋊D7311yescharacteristic
268C22×C8C22⋊D7311yescharacteristic
269C4⋊Q8—732no—
270C4⋊Q8—732no—
271#125—1462no—
272C22⋊Q8—1462no—
273C22⋊Q8—1462no—
274C4×Q8—1462no—
275C4×Q8—1462no—
276C4×Q8D29211yescharacteristic
277C4×Q8C22×D7311yescharacteristic
278C4×D4—21no—
279C4×D4—21no—
280C4×D4D29211yescharacteristic
281C4×D4C22×D7311yescharacteristic
282#117—21no—
283#117—1462no—
284#117D29211yescharacteristic
285C2×C42—21no—
286C2×C42C22×D7311yescharacteristic
287#107—1461no—
288#107—1461no—
289#107—1461no—
290#107—1461no—
291#107—1462no—
292#106—1462no—
293#106—1462no—
294#106—1462no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8—732no—
298C4⋊C8—732no—
299C4⋊C8C22×D7311yescharacteristic
300C4⋊C8C22×D7311yescharacteristic
301#103—1462no—
302#103—1462no—
303#103—1462no—
304#102—1462no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—1462no—
309#97—1462no—
310C4×C8—21no—
311C4×C8—21no—
312C4×C8—21no—
313C4×C8C22⋊D7311yescharacteristic
314C4×C8C22⋊D7311yescharacteristic
315C4×C8C22×D7311yescharacteristic
316C4×C8C22×D7311yescharacteristic
317#41—22no—
318#41—22no—
319C2×Q8—1462no—
320C2×Q8—1462no—
321C2×Q8C2×D29211yescharacteristic
322C2×D4—21no—
323C2×D4C2×D29211yescharacteristic
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4C2×C22⋊D7311yescharacteristic
328C22×C4C2×D29211yescharacteristic
329C22×C4#1192402811yescharacteristic
330Q16—2924no—
331SD16—2924no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—1462no—
339C2×C8—1462no—
340C2×C8C2×C22⋊D7311yescharacteristic
341C2×C8C2×C22⋊D7311yescharacteristic
342C2×C8C2×C22⋊D7311yescharacteristic
343C2×C8C2×C22⋊D7311yescharacteristic
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—2922no—
347C4⋊C4—2922no—
348C4⋊C4—1462no—
349C4⋊C4—1462no—
350C4⋊C4—1462no—
351C4⋊C4—1462no—
352C4⋊C4C2×D29211yescharacteristic
353C4⋊C4C2×D29211yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—2922no—
358C42—21no—
359C42—21no—
360C42—21no—
361C42—2922no—
362C42C2×C22⋊D7311yescharacteristic
363C42C2×D29211yescharacteristic
364C42#1192402811yescharacteristic
365C42C23×D7311yescharacteristic
366C23—21no—
367C23#1455656511yescharacteristic
368Q8—21no—
369Q8—2922no—
370Q8—2922no—
371Q8—5842no—
372Q8#1455661312yes—
373D4—24no—
374D4—21no—
375D4#1455661312yes—
376C2×C4—24no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—2922no—
389C2×C4—2922no—
390C2×C4#1455656511yescharacteristic
391C2×C4#1455656511yescharacteristic
392C2×C4#1455656511yescharacteristic
393C2×C4C22×C22⋊D7311yescharacteristic
394C2×C4C22×D29211yescharacteristic
395C2×C4C2×#1192402811yescharacteristic
396C8—21no—
397C8—21no—
398C8—41no—
399C8—41no—
400C8—2922no—
401C8—2922no—
402C8#1455662112yes—
403C8#1455662112yes—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22C2×#1455656511yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—22no—
416C4—41no—
417C4—41no—
418C4—5842no—
419C4—5842no—
420C4C2×#1455661311yescharacteristic
421C4C2×#1455661311yescharacteristic
422C4C2×#1455662111yescharacteristic
423C4C2×#1455662111yescharacteristic
424C2—41no—
425C2—42no—
426C2#2261941811yescharacteristic
427C2#2261951211yescharacteristic
428C2#2261965111yescharacteristic
subgroupG/H
centerC22C2×#14556565
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC8×#41×C73C2
socleC22×C73C2×#121
prime radicalC2×#41×C73D4
hypercenterC8×#41D73
hypocenterC73#19273
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. #22620445C2semidirect
3. #22609335C2semidirect
4. #22609330C2semidirect
5. #22609325C2semidirect
6. #22609320C2semidirect
7. #22609313C2semidirect
8. #22609306C2semidirect
9. #22608694C2semidirect
10. #22608639C2semidirect
226. C73#19273semidirect

Maximal subgroups

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

subgroupindex
#226204452
#226200932
#226093352
#226093302
#226093252
#226093202
#226093132
#226093062
#226086942
#226086392
C8×#41×C732
#1927373