Finite Group Databasebeta

← #32980819

Subgroups — #32980819

Order 18688.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988789C211yesmaximal, characteristic
2#22612882C211yesmaximal, characteristic
3#22610884C211yesmaximal, characteristic, complemented
4C2×#17988316C211yesmaximal, characteristic
5#22607814C211yesmaximal, characteristic, complemented
6#22607771C211yesmaximal, characteristic, complemented
7C73×#1990C211yesmaximal, characteristic, complemented
8C22×#11924015—21no—
9C2×C4×D292C2211yescharacteristic
10C2×#14556549—21no—
11#17988789—22no—
12#17988789C414yescomplemented
13C2×C4⋊#10596831C2211yescharacteristic
14C2×C4⋊#10596831C2211yescharacteristic
15C2×#14556515—21no—
16#17988488—21no—
17#17988477—22no—
18#17988444—21no—
19C4⋊C4×Dic73—21no—
20C4×C4⋊Dic73C2211yescharacteristic
21#17988349—21no—
22#17988349—21no—
23#17988316—22no—
24C2×C4⋊Q8×C73C2211yescharacteristic
25C2×C4×C8×C73C2211yescharacteristic
26#384×C73C2211yescharacteristic
27#340×C73—22no—
28C22×D292D411yescharacteristic
29C22×C4×D73—21no—
30C2×#11924015—24no—
31C2×#11924015—42no—
32C2×#11924015—42no—
33C22×#10596831—21no—
34C22×#10596831—21no—
35C4×D292—21no—
36C4×D292—21no—
37C4×D292C2×C412yes—
38C4×D292D412yes—
39#14556549—42no—
40#14556549—42no—
41C2×C4⋊Dic73D411yescharacteristic
42C2×C4⋊Dic73D411yescharacteristic
43C2×C4⋊Dic73D411yescharacteristic
44C2×#11924005—22no—
45C2×#11924005—22no—
46C2×#11924005—21no—
47C2×C4×Dic73—22no—
48C2×C4×Dic73—21no—
49C4⋊#10596831—21no—
50C4⋊#10596831—21no—
51C4⋊#10596831—21no—
52C4⋊#10596831C2×C412yes—
53#14556515—24no—
54#14556498—22no—
55#14556498—21no—
56C22×Q8×C73—21no—
57C22×C8×C73—21no—
58C4⋊Q8×C73—21no—
59C4⋊Q8×C73—21no—
60C4⋊Q8×C73—21no—
61C4⋊Q8×C73C2×C412yes—
62C2×C4⋊C4×C73—21no—
63C2×C4⋊C4×C73—21no—
64C2×C4⋊C4×C73—21no—
65C2×C4⋊C4×C73—21no—
66C2×C4⋊C4×C73D412yes—
67C2×C42×C73C2311yescharacteristic
68C4×C8×C73—21no—
69C4×C8×C73—21no—
70C23×D73—21no—
71C2×D292—21no—
72C2×D292—21no—
73C2×D292—21no—
74C2×D292—21no—
75C2×D292—21no—
76C2×D292C22⋊C412yes—
77C22×Dic73—21no—
78C22×Dic73—21no—
79C22×Dic73—21no—
80C2×C4×D73—22no—
81C2×C4×D73—22no—
82C2×C4×D73—41no—
83C2×C4×D73—41no—
84C2×C4×D73—41no—
85C2×C4×D73—41no—
86#11924015—48no—
87C2×#10596831—22no—
88C2×#10596831—41no—
89C2×#10596831—41no—
90C2×#10596831—41no—
91C2×#10596831—41no—
92C2×#10596831—41no—
93C4⋊Dic73—21no—
94C4⋊Dic73—21no—
95C4⋊Dic73—21no—
96C4⋊Dic73—21no—
97C4⋊Dic73C22⋊C412yes—
98C4⋊Dic73SD1612yescomplemented
99#11924005—22no—
100#11924005—22no—
101#11924005—44no—
102#11924005—82no—
103C4×Dic73—44no—
104C4×Dic73—41no—
105C4×Dic73—41no—
106C2×Q8×C73—22no—
107C2×Q8×C73—41no—
108C2×Q8×C73—41no—
109C2×Q8×C73—41no—
110C2×Q8×C73—41no—
111C2×Q8×C73—41no—
112C22×C4×C73—22no—
113C22×C4×C73—41no—
114C22×C4×C73C2×D411yescharacteristic
115C22×C4×C73C2×D411yescharacteristic
116C22×C4×C73C2×D411yescharacteristic
117C2×C8×C73—22no—
118C2×C8×C73—41no—
119C2×C8×C73—41no—
120C4⋊C4×C73—22no—
121C4⋊C4×C73—22no—
122C4⋊C4×C73—42no—
123C4⋊C4×C73—41no—
124C4⋊C4×C73—41no—
125C4⋊C4×C73—41no—
126C4⋊C4×C73—41no—
127C4⋊C4×C73—41no—
128C4⋊C4×C73—41no—
129C42×C73C22×C411yescharacteristic
130C42×C73C2×D411yescharacteristic
131C42×C73#4111yescharacteristic
132C42×C73#4111yescharacteristic
133C23×C73#12011yescharacteristic
134C22×D73—22no—
135C22×D73—41no—
136C22×D73—41no—
137C22×D73—41no—
138C22×D73—41no—
139C22×D73—41no—
140C22×D73—41no—
141Q8×C73—42no—
142Q8×C73—42no—
143Q8×C73—81no—
144Q8×C73—81no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—42no—
148C2×C4×C73—42no—
149C2×C4×C73—42no—
150C2×C4×C73—42no—
151C2×C4×C73—81no—
152C2×C4×C73—81no—
153C2×C4×C73C2×C22⋊C411yescharacteristic
154C2×C4×C73C4×D411yescharacteristic
155C2×C4×C73C4×D411yescharacteristic
156C2×C4×C73#12111yescharacteristic
157C2×C4×C73#12111yescharacteristic
158C2×C4×C73#12311yescharacteristic
159C2×C4×C73C2×SD1611yescharacteristic
160C2×C4×C73#13511yescharacteristic
161C2×C4×C73#13511yescharacteristic
162C2×C4×C73#13511yescharacteristic
163C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C73#13711yescharacteristic
167C2×Dic73—22no—
168C2×Dic73—22no—
169C2×Dic73—41no—
170C2×Dic73—41no—
171C2×Dic73—41no—
172C2×Dic73—41no—
173C2×Dic73—41no—
174C2×Dic73—41no—
175C2×Dic73—41no—
176D292—22no—
177D292—22no—
178D292—41no—
179D292—41no—
180C4×D73—42no—
181C4×D73—42no—
182C4×D73—42no—
183C4×D73—42no—
184C8×C73—42no—
185#10596831—42no—
186#10596831—81no—
187C22×C73#38611yescharacteristic
188C22×C73#44911yescharacteristic
189C22×C73#44911yescharacteristic
190C22×C73#45011yescharacteristic
191C22×C73#45211yescharacteristic
192C22×C73#45511yescharacteristic
193C22×C73#45611yescharacteristic
194C2×D73—42no—
195C2×D73—42no—
196C2×D73—42no—
197C2×D73—81no—
198C2×D73—81no—
199C2×D73—81no—
200C2×D73—81no—
201C4×C73—21no—
202C4×C73—21no—
203C4×C73—82no—
204C4×C73—82no—
205C4×C73#41611yescharacteristic
206C4×C73#41811yescharacteristic
207C4×C73C4×SD1611yescharacteristic
208C4×C73#44011yescharacteristic
209C4×C73#46111yescharacteristic
210C4×C73#46311yescharacteristic
211C4×C73#48211yescharacteristic
212C4×C73#48211yescharacteristic
213Dic73—42no—
214Dic73—42no—
215Dic73—81no—
216#8988—731nomaximal, Sylow
217C2×C73#164211yescharacteristic
218C2×C73#164611yescharacteristic
219C2×C73#165011yescharacteristic
220C2×C73#165411yescharacteristic
221C2×C73#187511yescharacteristic
222C2×C73#187711yescharacteristic
223C2×C73#188211yescharacteristic
224D73—82no—
225C2×#461—731no—
226#2354—731no—
227#1990D7311yescharacteristic, complemented
228#1988—731no—
229C2×D4⋊C8—731no—
230#1296—731no—
231#1279—731no—
232C73#898811yescharacteristic, complemented, Sylow
233C22×SD16—1461no—
234C2×C4⋊Q8C2×D7311yescharacteristic
235C2×C4×D4—731no—
236C2×#117—1461no—
237#461—734no—
238#461—1462no—
239C2×C4⋊C8—731no—
240C2×C4⋊C8—731no—
241C2×#103—1461no—
242C2×C4×C8C2×D7311yescharacteristic
243#390—1461no—
244#388—1462no—
245#384C2×D7311yescharacteristic
246#380—1461no—
247C4×C4⋊C4—731no—
248C4×C4⋊C4—1461no—
249#340—22no—
250#340—1461no—
251#340—1461no—
252D4⋊C8—1462no—
253C22×Q8—21no—
254C22×D4—731no—
255C23×C4—1461no—
256C2×SD16—2922no—
257C2×SD16—2922no—
258C2×SD16—1464no—
259C22×C8—21no—
260C22×C8—1461no—
261C22×C8—1461no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8C4×D7312yes—
266C4×D4—732no—
267C4×D4—732no—
268C4×D4—1461no—
269C4×D4—1461no—
270#117—2922no—
271#117—2922no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—731no—
277C2×C4⋊C4—731no—
278C2×C4⋊C4—731no—
279C2×C4⋊C4C22⋊D7312yes—
280C2×C22⋊C4—1462no—
281C2×C22⋊C4—1462no—
282C2×C22⋊C4—1461no—
283C2×C42—1462no—
284C2×C42—1461no—
285C2×C42C22×D7311yescharacteristic
286C4⋊C8—732no—
287C4⋊C8—1461no—
288C4⋊C8—1461no—
289C4⋊C8—1461no—
290#103—1464no—
291C4×C8—21no—
292C4×C8—21no—
293#95—1462no—
294#95—1461no—
295C24—1461no—
296C2×Q8—22no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×D4—732no—
303C2×D4—1461no—
304C2×D4—1461no—
305C2×D4—1461no—
306C2×D4—1461no—
307C2×D4—1461no—
308C22×C4—22no—
309C22×C4—41no—
310C22×C4—2921no—
311C22×C4—2921no—
312C22×C4—2921no—
313C22×C4—2921no—
314C22×C4—1461no—
315C22×C4—1461no—
316C22×C4—1461no—
317C22×C4—1462no—
318C22×C4—1462no—
319C22×C4D4×D7311yescharacteristic
320C22×C4D4×D7311yescharacteristic
321C22×C4C2×C22⋊D7311yescharacteristic
322SD16—2928no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—2921no—
327C2×C8—2921no—
328C2×C8—2921no—
329C2×C8—2921no—
330C2×C8—2921no—
331C2×C8—1462no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—42no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—732no—
342C4⋊C4—732no—
343C4⋊C4—1461no—
344C4⋊C4—1461no—
345C4⋊C4—1461no—
346C4⋊C4—1461no—
347C22⋊C4—2924no—
348C22⋊C4—5842no—
349C22⋊C4—1462no—
350C22⋊C4—1462no—
351C42—2924no—
352C42—2921no—
353C42—2921no—
354C42C2×C4×D7311yescharacteristic
355C42D4×D7311yescharacteristic
356C42#1192402711yescharacteristic
357C42#1192402811yescharacteristic
358C23—2921no—
359C23—2921no—
360C23—2921no—
361C23—2921no—
362C23—2921no—
363C23—2921no—
364C23—1462no—
365C23#1455655911yescharacteristic
366Q8—42no—
367Q8—42no—
368Q8—81no—
369Q8—81no—
370D4—2921no—
371D4—2921no—
372D4—1462no—
373D4—1462no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—2921no—
383C2×C4—2921no—
384C2×C4—2921no—
385C2×C4—2921no—
386C2×C4—2922no—
387C2×C4—2922no—
388C2×C4—2922no—
389C2×C4—2922no—
390C2×C4—2921no—
391C2×C4—2921no—
392C2×C4—2921no—
393C2×C4—1462no—
394C2×C4—1462no—
395C2×C4C22⋊C4×D7311yescharacteristic
396C2×C4#1455655111yescharacteristic
397C2×C4C4×C22⋊D7311yescharacteristic
398C2×C4#1455656211yescharacteristic
399C2×C4#1455656411yescharacteristic
400C2×C4#1455657311yescharacteristic
401C2×C4SD16×D7311yescharacteristic
402C2×C4#1455661011yescharacteristic
403C2×C4#1455661211yescharacteristic
404C2×C4#1455661411yescharacteristic
405C2×C4#1455661511yescharacteristic
406C2×C4#1455661811yescharacteristic
407C2×C4#1455661811yescharacteristic
408C2×C4#1455662311yescharacteristic
409C8—42no—
410C8—2922no—
411C8—5841no—
412C22—2922no—
413C22—2922no—
414C22—2922no—
415C22—5841no—
416C22—5841no—
417C22—5841no—
418C22—5841no—
419C22#1798846311yescharacteristic
420C22#1798872911yescharacteristic
421C22#1798873111yescharacteristic
422C22#1798873611yescharacteristic
423C22#1798874811yescharacteristic
424C22#1798876411yescharacteristic
425C22#1798876911yescharacteristic
426C4—21no—
427C4—21no—
428C4—82no—
429C4—82no—
430C4—2922no—
431C4—2922no—
432C4—5841no—
433C4#1798858011yescharacteristic
434C4#1798859011yescharacteristic
435C4#1798867211yescharacteristic
436C4#1798869011yescharacteristic
437C4#1798879111yescharacteristic
438C4#1798880511yescharacteristic
439C4#1798890911yescharacteristic
440C4#1798891011yescharacteristic
441C2—5842no—
442C2#2260912811yescharacteristic
443C2#2260915611yescharacteristic
444C2#2260918411yescharacteristic
445C2#2260921211yescharacteristic
446C2#2261025011yescharacteristic
447C2#2261026211yescharacteristic
448C2#2261030311yescharacteristic
subgroupG/H
centerC23#14556559
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1990C2
socleC23×C73#120
prime radicalC22×D292D4
cosocleC2×C42×C73C23
hypercenter#1990D73
hypocenterC73#8988
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
3. #22610884C2semidirect
5. #22607814C2semidirect
6. #22607771C2semidirect
7. C73×#1990C2semidirect
12. #17988789C4semidirect
98. C4⋊Dic73SD16semidirect
227. #1990D73semidirect
232. C73#8988semidirect

Maximal subgroups

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

subgroupindex
C2×#179887892
#226128822
#226108842
C2×#179883162
#226078142
#226077712
C73×#19902
#898873