Finite Group Databasebeta

← #33069431

Subgroups — #33069431

Order 18688.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22621257C212yesmaximal, complemented
2#22620510C211yesmaximal, characteristic, complemented
3#22609459C211yesmaximal, characteristic, complemented
4#22609454C211yesmaximal, characteristic, complemented
5#22609415C211yesmaximal, characteristic, complemented
6#22609410C211yesmaximal, characteristic, complemented
7#22609347C212yesmaximal, complemented
8#22609340C212yesmaximal, complemented
9C2×#17988338C211yesmaximal, characteristic, complemented
10#22608627C212yesmaximal, complemented
11C73×#2966C211yesmaximal, characteristic, complemented
12#17989137C2212yes—
13#17988992C2211yescharacteristic
14#17988964C2211yescharacteristic
15#17988934C2212yes—
16#17988884—22no—
17#17988882C2212yes—
18#17988877C2212yes—
19#17988823—21no—
20#17988823—21no—
21#17988821—22no—
22#17988818—22no—
23#17988799—22no—
24#17988787C2212yes—
25#17988782C2212yes—
26C4×D584—21no—
27C4×D584—21no—
28C2×C4⋊#10596831C2212yes—
29#17988338C2211yescharacteristic
30#17988338C2211yescharacteristic
31#17988338C2212yes—
32#17988335C2212yes—
33#17988335C2212yes—
34#17988330C2212yes—
35#17988330C2212yes—
36#529×C73C2211yescharacteristic
37#446×C73C2211yescharacteristic
38C8×Q8×C73C2211yescharacteristic
39#436×C73C2211yescharacteristic
40#435×C73—21no—
41C8×D4×C73—21no—
42C8×D4×C73C2211yescharacteristic
43#433×C73—21no—
44#432×C73C2211yescharacteristic
45#405×C73—21no—
46C2×C4×C8×C73C2211yescharacteristic
47C2×#11924028—22no—
48C2×#11924015—22no—
49C2×D584—21no—
50C2×D584—21no—
51C2×#11924013—22no—
52C22×#10596831—22no—
53#14556591C2312yes—
54#14556588C2312yes—
55#14556579—22no—
56#14556565—22no—
57#14556565—22no—
58C4×D292—22no—
59C4×D292—22no—
60#14556525—21no—
61#14556525—21no—
62#14556524—22no—
63#14556522—22no—
64C4⋊#10596831—22no—
65C4⋊#10596831C2312yes—
66C4⋊#10596831C2312yes—
67#14556515—22no—
68#14556513—22no—
69#14556513—22no—
70#14556512—22no—
71#14556511—22no—
72#14556511—22no—
73C2×M16×C73—21no—
74C22×C8×C73—21no—
75C22×C8×C73D411yescharacteristic
76C22×C8×C73D411yescharacteristic
77#126×C73—21no—
78#125×C73D411yescharacteristic
79#124×C73D411yescharacteristic
80#123×C73—21no—
81C22⋊Q8×C73D411yescharacteristic
82#121×C73D411yescharacteristic
83C4×Q8×C73C2311yescharacteristic
84C4×D4×C73—21no—
85C4×D4×C73C2311yescharacteristic
86#117×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—
95#97×C73—21no—
96#97×C73—21no—
97C4×C8×C73—21no—
98C4×C8×C73D411yescharacteristic
99C4×C8×C73D411yescharacteristic
100C4×C8×C73C2311yescharacteristic
101C4×C8×C73C2311yescharacteristic
102#11924028—84no—
103C2×Dic146—22no—
104C2×D292—22no—
105C2×D292—22no—
106C2×D292—22no—
107C2×C22⋊D73—42no—
108C2×C4×D73—42no—
109#11924015—82no—
110D584—42no—
111D584—42no—
112#11924013—82no—
113C2×#10596831—22no—
114C2×#10596831—22no—
115C2×#10596831—82no—
116C4⋊Dic73—22no—
117C4⋊Dic73—22no—
118#11924005—42no—
119#11924005—42no—
120C2×Q8×C73C2×D411yescharacteristic
121C2×D4×C73—21no—
122C2×D4×C73C2×D411yescharacteristic
123C22×C4×C73—21no—
124C22×C4×C73C2×D411yescharacteristic
125C22×C4×C73C2×D411yescharacteristic
126C22×C4×C73#4111yescharacteristic
127M16×C73—42no—
128C2×C8×C73—22no—
129C2×C8×C73—21no—
130C2×C8×C73—21no—
131C2×C8×C73—41no—
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×C73—21no—
140C4⋊C4×C73—21no—
141C4⋊C4×C73C2×D411yescharacteristic
142C4⋊C4×C73C2×D411yescharacteristic
143C22⋊C4×C73—21no—
144C22⋊C4×C73—21no—
145C22⋊C4×C73—21no—
146C22⋊C4×C73—21no—
147C22⋊C4×C73—21no—
148C42×C73—21no—
149C42×C73C2×D411yescharacteristic
150C42×C73C2×D411yescharacteristic
151C42×C73#4111yescharacteristic
152C42×C73C2411yescharacteristic
153C23×C73—21no—
154C23×C73#12111yescharacteristic
155C22×D73—42no—
156Q8×C73—22no—
157D4×C73—22no—
158D4×C73—42no—
159C2×C4×C73—22no—
160C2×C4×C73—21no—
161C2×C4×C73—21no—
162C2×C4×C73—22no—
163C2×C4×C73—21no—
164C2×C4×C73—21no—
165C2×C4×C73—21no—
166C2×C4×C73—41no—
167C2×C4×C73—41no—
168C2×C4×C73#12111yescharacteristic
169C2×C4×C73#12111yescharacteristic
170C2×C4×C73#12111yescharacteristic
171C2×C4×C73C22×D411yescharacteristic
172C2×C4×C73C22×D411yescharacteristic
173C2×C4×C73C2×#4111yescharacteristic
174C22⋊D73—84no—
175C2×Dic73—42no—
176D292—42no—
177D292—42no—
178D292—42no—
179D292—42no—
180D292—82no—
181C4×D73—84no—
182Dic146—82no—
183C8×C73—21no—
184C8×C73—21no—
185C8×C73—21no—
186C8×C73—41no—
187C8×C73—41no—
188C8×C73#13512yes—
189#10596831—42no—
190#10596831—42no—
191C22×C73—21no—
192C22×C73—21no—
193C22×C73—41no—
194C22×C73—41no—
195C22×C73—41no—
196C22×C73#47212yes—
197C22×C73C2×#12111yescharacteristic
198C2×D73—82no—
199C2×D73—82no—
200C2×D73—82no—
201C4×C73—21no—
202C4×C73—21no—
203C4×C73—21no—
204C4×C73—21no—
205C4×C73—41no—
206C4×C73—41no—
207C4×C73—41no—
208C4×C73C2×#13511yescharacteristic
209C4×C73#57511yescharacteristic
210C4×C73#57712yes—
211Dic73—82no—
212#19227—731nomaximal, Sylow
213C2×C73—22no—
214C2×C73—81no—
215C2×C73#303511yescharacteristic
216C2×C73#306011yescharacteristic
217C2×C73C2×#47211yescharacteristic
218D73—162no—
219#3247—732no—
220#3169—731no—
221#2966D7311yescharacteristic, complemented
222#1696—731no—
223#1695—731no—
224#1688—731no—
225#1687—731no—
226#1678—732no—
227#1677—732no—
228C2×#334—731no—
229#1551—732no—
230C73#1922711yescharacteristic, complemented, Sylow
231#532—732no—
232#529C2×D7311yescharacteristic
233#500—731no—
234#493—731no—
235#486—732no—
236#478—1462no—
237#477—732no—
238#476—732no—
239#466—1461no—
240#466—1461no—
241#466—1462no—
242#465—1462no—
243#463—1462no—
244#460—732no—
245#459—732no—
246#446C2×D7311yescharacteristic
247C8×Q8C2×D7311yescharacteristic
248C4×D8—1461no—
249C4×D8—1461no—
250#436C2×D7311yescharacteristic
251#435—21no—
252C8×D4—21no—
253C8×D4C2×D7311yescharacteristic
254#433—21no—
255#432C2×D7311yescharacteristic
256C2×C4⋊C8—732no—
257#405—21no—
258C2×C4×C8C2×D7311yescharacteristic
259#334—732no—
260#334—731no—
261#334—731no—
262#333—732no—
263#333—732no—
264#331—732no—
265#331—732no—
266C2×#41—1462no—
267C2×SD16—1462no—
268C2×D8—1462no—
269C2×D8—1461no—
270C2×D8—1461no—
271C2×M16—21no—
272C22×C8—21no—
273C22×C8—1462no—
274C22×C8C22⋊D7311yescharacteristic
275C22×C8C22⋊D7311yescharacteristic
276C4⋊Q8—732no—
277#127—732no—
278#126—21no—
279#125D29211yescharacteristic
280#124—1462no—
281#124D29211yescharacteristic
282#123—21no—
283C22⋊Q8D29211yescharacteristic
284#121—1462no—
285#121—1462no—
286#121D29211yescharacteristic
287C4×Q8C22×D7311yescharacteristic
288C4×D4—21no—
289C4×D4—1462no—
290C4×D4—1462no—
291C4×D4C22×D7311yescharacteristic
292#117—21no—
293C2×C42C22×D7311yescharacteristic
294#107—1461no—
295#107—1461no—
296#107—1462no—
297#106—1462no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300C4⋊C8—732no—
301C4⋊C8—732no—
302C4⋊C8—1462no—
303C4⋊C8C22×D7311yescharacteristic
304C4⋊C8C22×D7311yescharacteristic
305#103—1462no—
306#102—1462no—
307#102—1462no—
308#102—1462no—
309#102—1462no—
310#102—1462no—
311C22⋊C8—21no—
312C22⋊C8—21no—
313C22⋊C8—21no—
314#97—21no—
315#97—21no—
316C4×C8—21no—
317C4×C8C22⋊D7311yescharacteristic
318C4×C8C22⋊D7311yescharacteristic
319C4×C8C22×D7311yescharacteristic
320C4×C8C22×D7311yescharacteristic
321#41—5844no—
322C2×Q8—1462no—
323C2×Q8C2×D29211yescharacteristic
324C2×D4—21no—
325C2×D4—2922no—
326C2×D4—1462no—
327C2×D4—1462no—
328C2×D4—1462no—
329C2×D4C2×D29211yescharacteristic
330C22×C4—21no—
331C22×C4—2922no—
332C22×C4C2×C22⋊D7311yescharacteristic
333C22×C4C2×D29211yescharacteristic
334C22×C4#1192402811yescharacteristic
335SD16—5842no—
336D8—2922no—
337D8—2922no—
338D8—5842no—
339M16—42no—
340C2×C8—22no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—41no—
344C2×C8—42no—
345C2×C8—5842no—
346C2×C8—1462no—
347C2×C8—1462no—
348C2×C8C2×C22⋊D7311yescharacteristic
349C2×C8C2×C22⋊D7311yescharacteristic
350C2×C8C2×C22⋊D7311yescharacteristic
351C2×C8C2×C22⋊D7311yescharacteristic
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—1462no—
357C4⋊C4—1462no—
358C4⋊C4C2×D29211yescharacteristic
359C4⋊C4C2×D29211yescharacteristic
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—2922no—
366C22⋊C4—2922no—
367C42—21no—
368C42C2×C22⋊D7311yescharacteristic
369C42C2×D29211yescharacteristic
370C42#1192402811yescharacteristic
371C42C23×D7311yescharacteristic
372C23—21no—
373C23—2922no—
374C23#1455656511yescharacteristic
375Q8—22no—
376Q8—5842no—
377D4—22no—
378D4—42no—
379D4—2922no—
380D4—2922no—
381D4—2922no—
382D4—2922no—
383D4—5842no—
384D4—5844no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—2922no—
395C2×C4—5844no—
396C2×C4#1455656511yescharacteristic
397C2×C4#1455656511yescharacteristic
398C2×C4#1455656511yescharacteristic
399C2×C4C22×C22⋊D7311yescharacteristic
400C2×C4C22×D29211yescharacteristic
401C2×C4C2×#1192402811yescharacteristic
402C8—21no—
403C8—21no—
404C8—21no—
405C8—41no—
406C8—41no—
407C8—2922no—
408C8—2922no—
409C8#1455661112yes—
410C22—21no—
411C22—21no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—5842no—
416C22—5842no—
417C22—5842no—
418C22#1798885712yes—
419C22C2×#1455656511yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—5842no—
428C4C2×#1455661111yescharacteristic
429C4#1798938511yescharacteristic
430C4#1798939912yes—
431C2—22no—
432C2—81no—
433C2—11682no—
434C2#2261938611yescharacteristic
435C2#2261959311yescharacteristic
436C2C2×#1798885711yescharacteristic
subgroupG/H
centerC22C2×#14556565
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC73×#2966C2
socleC22×C73C2×#121
hypercenter#2966D73
hypocenterC73#19227
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #22621257C2semidirect
2. #22620510C2semidirect
3. #22609459C2semidirect
4. #22609454C2semidirect
5. #22609415C2semidirect
6. #22609410C2semidirect
7. #22609347C2semidirect
8. #22609340C2semidirect
9. C2×#17988338C2semidirect
10. #22608627C2semidirect
11. C73×#2966C2semidirect
221. #2966D73semidirect
230. C73#19227semidirect

Maximal subgroups

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

subgroupindex
#226212572
#226205102
#226094592
#226094542
#226094152
#226094102
#226093472
#226093402
C2×#179883382
#226086272
C73×#29662
#1922773