Finite Group Databasebeta

← #33068730

Subgroups — #33068730

Order 18688.

642 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620510C211yesmaximal, characteristic, complemented
2#22619991C212yesmaximal, complemented
3#22609471C212yesmaximal, complemented
4#22609464C212yesmaximal, complemented
5#22609459C211yesmaximal, characteristic, complemented
6#22609454C211yesmaximal, characteristic, complemented
7#22609415C211yesmaximal, characteristic, complemented
8#22609410C211yesmaximal, characteristic, complemented
9#22608679C211yesmaximal, characteristic, complemented
10#22608591C212yesmaximal, complemented
11C73×#2965C211yesmaximal, characteristic, complemented
12#17989137C2212yes—
13#17988992C2211yescharacteristic
14#17988964C2211yescharacteristic
15#17988934C2212yes—
16#17988911—22no—
17#17988882C2212yes—
18#17988877C2212yes—
19#17988823—21no—
20#17988823—21no—
21#17988787C2212yes—
22#17988782C2212yes—
23#17988732—22no—
24C4×#11924015—22no—
25C4×D584—21no—
26C4×D584—21no—
27C4×#11924013—22no—
28#17988640C2212yes—
29#17988340C2212yes—
30#17988338C2211yescharacteristic
31#17988338C2211yescharacteristic
32#17988335C2212yes—
33#17988335C2212yes—
34#17988330C2212yes—
35#17988330C2212yes—
36C4×#41×C73C2211yescharacteristic
37#446×C73C2211yescharacteristic
38#446×C73C2211yescharacteristic
39#436×C73C2211yescharacteristic
40#436×C73C2211yescharacteristic
41#435×C73—21no—
42#435×C73—21no—
43#431×C73—21no—
44#431×C73C2211yescharacteristic
45C4×M16×C73—21no—
46C2×C4×C8×C73C2211yescharacteristic
47C2×#11924028—22no—
48C2×#11924015—22no—
49C2×D584—21no—
50C2×D584—21no—
51C2×#11924013—22no—
52#14556591C2312yes—
53#14556588C2312yes—
54#14556579—22no—
55#14556565—22no—
56#14556565—22no—
57C4×D292—22no—
58C4×D292—22no—
59#14556525—21no—
60#14556525—21no—
61#14556524—22no—
62#14556522—22no—
63C4⋊#10596831C2312yes—
64C4⋊#10596831C2312yes—
65#14556515—22no—
66#14556513—22no—
67#14556513—22no—
68#14556512—22no—
69#14556511—22no—
70#14556511—22no—
71C22⋊#10596831—22no—
72C4×#10596831—22no—
73C2×#41×C73D411yescharacteristic
74C2×M16×C73—21no—
75C2×M16×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—
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—44no—
110D584—42no—
111D584—42no—
112#11924013—44no—
113C2×#10596831—22no—
114C2×#10596831—22no—
115C4⋊Dic73—22no—
116C4⋊Dic73—22no—
117#11924005—42no—
118#11924005—42no—
119#41×C73—42no—
120C2×Q8×C73C2×D411yescharacteristic
121C2×D4×C73—21no—
122C2×D4×C73C2×D411yescharacteristic
123C22×C4×C73—21no—
124C22×C4×C73—21no—
125C22×C4×C73—21no—
126C22×C4×C73C2×D411yescharacteristic
127C22×C4×C73C2×D411yescharacteristic
128C22×C4×C73#4111yescharacteristic
129M16×C73—42no—
130M16×C73—42no—
131C2×C8×C73—22no—
132C2×C8×C73—21no—
133C2×C8×C73—21no—
134C2×C8×C73—41no—
135C2×C8×C73C2×D411yescharacteristic
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
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—
146C42×C73—21no—
147C42×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—21no—
160C2×C4×C73—21no—
161C2×C4×C73—22no—
162C2×C4×C73—22no—
163C2×C4×C73—21no—
164C2×C4×C73—21no—
165C2×C4×C73—21no—
166C2×C4×C73—42no—
167C2×C4×C73—41no—
168C2×C4×C73—41no—
169C2×C4×C73—42no—
170C2×C4×C73#12111yescharacteristic
171C2×C4×C73#12111yescharacteristic
172C2×C4×C73#12111yescharacteristic
173C2×C4×C73C22×D411yescharacteristic
174C2×C4×C73C22×D411yescharacteristic
175C2×C4×C73C2×#4111yescharacteristic
176C22⋊D73—84no—
177C2×Dic73—42no—
178D292—42no—
179D292—42no—
180D292—42no—
181D292—42no—
182D292—82no—
183C4×D73—84no—
184Dic146—82no—
185C8×C73—21no—
186C8×C73—21no—
187C8×C73—21no—
188C8×C73—41no—
189C8×C73—41no—
190C8×C73#13512yes—
191#10596831—42no—
192#10596831—42no—
193C22×C73—21no—
194C22×C73—21no—
195C22×C73—21no—
196C22×C73—41no—
197C22×C73—41no—
198C22×C73—41no—
199C22×C73C2×#12111yescharacteristic
200C2×D73—82no—
201C2×D73—82no—
202C2×D73—82no—
203C4×C73—21no—
204C4×C73—21no—
205C4×C73—21no—
206C4×C73—41no—
207C4×C73—41no—
208C4×C73—41no—
209C4×C73#47212yes—
210C4×C73C2×#13511yescharacteristic
211C4×C73#57511yescharacteristic
212C4×C73#57512yes—
213Dic73—82no—
214#19160—731nomaximal, Sylow
215C2×C73—41no—
216C2×C73—81no—
217C2×C73#303511yescharacteristic
218C2×C73#305411yescharacteristic
219C2×C73C2×#47211yescharacteristic
220D73—162no—
221#3169—731no—
222#3106—732no—
223#2965D7311yescharacteristic, complemented
224#1698—732no—
225#1697—732no—
226#1696—731no—
227#1695—731no—
228#1688—731no—
229#1687—731no—
230#1564—731no—
231#1543—732no—
232C73#1916011yescharacteristic, complemented, Sylow
233#532—732no—
234C4×#41C2×D7311yescharacteristic
235#500—731no—
236#493—731no—
237#486—732no—
238#482—1462no—
239#477—732no—
240#476—732no—
241#466—1461no—
242#466—1461no—
243#460—732no—
244#459—732no—
245#449—1462no—
246#446C2×D7311yescharacteristic
247#446C2×D7311yescharacteristic
248C4×SD16—1462no—
249C4×D8—1462no—
250C4×D8—1461no—
251C4×D8—1461no—
252#436C2×D7311yescharacteristic
253#436C2×D7311yescharacteristic
254#435—21no—
255#435—21no—
256#431—21no—
257#431—732no—
258#431C2×D7311yescharacteristic
259C4×M16—21no—
260C2×C4×C8C2×D7311yescharacteristic
261#335—732no—
262#334—731no—
263#334—731no—
264#333—732no—
265#333—732no—
266#331—732no—
267#331—732no—
268C2×#41—1462no—
269C2×#41D29211yescharacteristic
270C2×SD16—1462no—
271C2×D8—1462no—
272C2×D8—1461no—
273C2×D8—1461no—
274C2×M16—21no—
275C2×M16—21no—
276C22×C8C22⋊D7311yescharacteristic
277C22×C8C22⋊D7311yescharacteristic
278C4⋊Q8—732no—
279#127—732no—
280#124—1462no—
281#121—1462no—
282#121—1462no—
283C4×Q8D29211yescharacteristic
284C4×Q8C22×D7311yescharacteristic
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—1462no—
288C4×D4—1462no—
289C4×D4D29211yescharacteristic
290C4×D4C22×D7311yescharacteristic
291#117—21no—
292#117D29211yescharacteristic
293C2×C42—21no—
294C2×C42C22×D7311yescharacteristic
295#107—1461no—
296#107—1461no—
297#107—1462no—
298#106—1462no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8—732no—
302C4⋊C8—732no—
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—
314C22⋊C8—1462no—
315#97—21no—
316#97—21no—
317C4×C8—21no—
318C4×C8—1462no—
319C4×C8C22⋊D7311yescharacteristic
320C4×C8C22⋊D7311yescharacteristic
321C4×C8C22×D7311yescharacteristic
322C4×C8C22×D7311yescharacteristic
323#41—42no—
324#41—5844no—
325C2×Q8—1462no—
326C2×Q8C2×D29211yescharacteristic
327C2×D4—21no—
328C2×D4—2922no—
329C2×D4—1462no—
330C2×D4—1462no—
331C2×D4—1462no—
332C2×D4C2×D29211yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—2922no—
337C22×C4C2×C22⋊D7311yescharacteristic
338C22×C4C2×D29211yescharacteristic
339C22×C4#1192402811yescharacteristic
340SD16—2924no—
341D8—2922no—
342D8—2924no—
343D8—2922no—
344M16—42no—
345M16—42no—
346C2×C8—22no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—41no—
350C2×C8—1462no—
351C2×C8—1462no—
352C2×C8C2×C22⋊D7311yescharacteristic
353C2×C8C2×C22⋊D7311yescharacteristic
354C2×C8C2×C22⋊D7311yescharacteristic
355C2×C8C2×C22⋊D7311yescharacteristic
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—1462no—
359C4⋊C4—1462no—
360C4⋊C4C2×D29211yescharacteristic
361C4⋊C4C2×D29211yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—2922no—
366C22⋊C4—2922no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42C2×C22⋊D7311yescharacteristic
371C42C2×D29211yescharacteristic
372C42#1192402811yescharacteristic
373C42C23×D7311yescharacteristic
374C23—21no—
375C23—2922no—
376C23#1455656511yescharacteristic
377Q8—22no—
378Q8—5842no—
379D4—22no—
380D4—42no—
381D4—2922no—
382D4—2922no—
383D4—2922no—
384D4—2922no—
385D4—5842no—
386D4—5844no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—2922no—
399C2×C4—5844no—
400C2×C4#1455656511yescharacteristic
401C2×C4#1455656511yescharacteristic
402C2×C4#1455656511yescharacteristic
403C2×C4C22×C22⋊D7311yescharacteristic
404C2×C4C22×D29211yescharacteristic
405C2×C4C2×#1192402811yescharacteristic
406C8—21no—
407C8—21no—
408C8—21no—
409C8—41no—
410C8—41no—
411C8—2922no—
412C8—2922no—
413C8#1455661112yes—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—5842no—
421C22—5842no—
422C22—5842no—
423C22C2×#1455656511yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—5842no—
431C4#1798885712yes—
432C4C2×#1455661111yescharacteristic
433C4#1798938511yescharacteristic
434C4#1798938712yes—
435C2—41no—
436C2—81no—
437C2—11682no—
438C2#2261938611yescharacteristic
439C2#2261954011yescharacteristic
440C2C2×#1798885711yescharacteristic
subgroupG/H
centerC2×C4#14556565
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC73×#2965C2
socleC22×C73C2×#121
hypercenter#2965D73
hypocenterC73#19160
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
1. #22620510C2semidirect
2. #22619991C2semidirect
3. #22609471C2semidirect
4. #22609464C2semidirect
5. #22609459C2semidirect
6. #22609454C2semidirect
7. #22609415C2semidirect
8. #22609410C2semidirect
9. #22608679C2semidirect
10. #22608591C2semidirect
11. C73×#2965C2semidirect
223. #2965D73semidirect
232. C73#19160semidirect

Maximal subgroups

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

subgroupindex
#226205102
#226199912
#226094712
#226094642
#226094592
#226094542
#226094152
#226094102
#226086792
#226085912
C73×#29652
#1916073