Finite Group Databasebeta

← #32975076

Subgroups — #32975076

Order 18688.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22611459C211yesmaximal, characteristic, complemented
2#22611339C211yesmaximal, characteristic, complemented
3#22611334C211yesmaximal, characteristic, complemented
4#22607757C211yesmaximal, characteristic, complemented
5#22607752C211yesmaximal, characteristic, complemented
6#22607752C211yesmaximal, characteristic, complemented
7C73×#2733C211yesmaximal, characteristic
8C2×#14556524—21no—
9C2×#14556515—21no—
10C2×#14556512—21no—
11C2×#14556512—21no—
12#17988457C2211yescharacteristic
13#17988349—21no—
14#17988349—21no—
15#17988342C2211yescharacteristic
16#17988342C2211yescharacteristic
17#17988342C2211yescharacteristic
18C2×#124×C73—21no—
19#394×C73—21no—
20#392×C73—21no—
21#392×C73—21no—
22#391×C73C2211yescharacteristic
23#390×C73C2211yescharacteristic
24#390×C73C2211yescharacteristic
25#388×C73—21no—
26#388×C73—21no—
27C22×#10596831—21no—
28C22×#10596831—21no—
29C22×#10596831—21no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33#14556524—42no—
34#14556515—42no—
35#14556512—42no—
36#14556512—42no—
37C22×Q8×C73D411yescharacteristic
38C22×D4×C73—21no—
39C22×D4×C73—21no—
40C22×D4×C73D411yescharacteristic
41C22×D4×C73D411yescharacteristic
42#124×C73—42no—
43#124×C73—42no—
44C2×C4⋊C4×C73D411yescharacteristic
45C2×C4⋊C4×C73D411yescharacteristic
46C2×C4⋊C4×C73D411yescharacteristic
47C2×C22⋊C4×C73—21no—
48C2×C22⋊C4×C73—21no—
49C2×C22⋊C4×C73—21no—
50C2×C22⋊C4×C73—21no—
51C2×C22⋊C4×C73—21no—
52C2×C22⋊C4×C73—21no—
53C2×C22⋊C4×C73—21no—
54C2×C22⋊C4×C73—21no—
55C2×C42×C73—21no—
56C2×C42×C73C2311yescharacteristic
57#95×C73—21no—
58#95×C73—21no—
59#95×C73—21no—
60C22×Dic73—41no—
61C2×#10596831—22no—
62C2×#10596831—41no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C2×#10596831—41no—
67C2×#10596831—41no—
68C2×#10596831—41no—
69C2×#10596831—41no—
70C4⋊Dic73—41no—
71C4⋊Dic73—41no—
72C4⋊Dic73—41no—
73C4⋊Dic73—41no—
74C4⋊Dic73—41no—
75C4⋊Dic73—41no—
76C24×C73—21no—
77C24×C73—21no—
78C2×Q8×C73—21no—
79C2×Q8×C73—41no—
80C2×Q8×C73—41no—
81C2×Q8×C73D812yes—
82C2×D4×C73—21no—
83C2×D4×C73—21no—
84C2×D4×C73—21no—
85C2×D4×C73—21no—
86C2×D4×C73—41no—
87C2×D4×C73—41no—
88C2×D4×C73—41no—
89C2×D4×C73—41no—
90C2×D4×C73—42no—
91C2×D4×C73—81no—
92C2×D4×C73—81no—
93C2×D4×C73—81no—
94C2×D4×C73—81no—
95C2×D4×C73—81no—
96C22×C4×C73—21no—
97C22×C4×C73—21no—
98C22×C4×C73—21no—
99C22×C4×C73—21no—
100C22×C4×C73C2×D411yescharacteristic
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73C2×D411yescharacteristic
103C4⋊C4×C73—41no—
104C4⋊C4×C73—41no—
105C4⋊C4×C73—41no—
106C22⋊C4×C73—42no—
107C22⋊C4×C73—42no—
108C22⋊C4×C73—41no—
109C22⋊C4×C73—41no—
110C22⋊C4×C73—41no—
111C22⋊C4×C73—41no—
112C22⋊C4×C73—41no—
113C22⋊C4×C73—41no—
114C22⋊C4×C73—41no—
115C22⋊C4×C73—41no—
116C22⋊C4×C73—81no—
117C22⋊C4×C73—81no—
118C42×C73—41no—
119C42×C73—42no—
120C23×C73—41no—
121C23×C73—41no—
122C23×C73—41no—
123C23×C73—41no—
124C23×C73—41no—
125C23×C73—41no—
126C23×C73—41no—
127C23×C73—41no—
128C23×C73—41no—
129C23×C73—41no—
130C23×C73—41no—
131C23×C73—41no—
132C23×C73—41no—
133C23×C73—41no—
134C23×C73#12011yescharacteristic
135Q8×C73—42no—
136Q8×C73—81no—
137D4×C73—42no—
138D4×C73—42no—
139D4×C73—81no—
140D4×C73—81no—
141D4×C73—84no—
142D4×C73—84no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—22no—
150C2×C4×C73—41no—
151C2×C4×C73—41no—
152C2×C4×C73—41no—
153C2×C4×C73—41no—
154C2×C4×C73—41no—
155C2×C4×C73—41no—
156C2×C4×C73—41no—
157C2×C4×C73—41no—
158C2×C4×C73—41no—
159C2×C4×C73—41no—
160C2×C4×C73—41no—
161C2×C4×C73C2×D811yescharacteristic
162C2×C4×C73#13511yescharacteristic
163C2×C4×C73#13511yescharacteristic
164C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C73#13711yescharacteristic
167C2×Dic73—81no—
168C2×Dic73—81no—
169C2×Dic73—81no—
170#10596831—42no—
171#10596831—81no—
172#10596831—81no—
173C22×C73—81no—
174C22×C73—81no—
175C22×C73—81no—
176C22×C73—81no—
177C22×C73—81no—
178C22×C73—81no—
179C22×C73—81no—
180C22×C73—81no—
181C22×C73—81no—
182C22×C73—81no—
183C22×C73—81no—
184C22×C73—81no—
185C22×C73—81no—
186C22×C73—81no—
187C22×C73#44711yescharacteristic
188C22×C73#44911yescharacteristic
189C22×C73#45211yescharacteristic
190C22×C73#45311yescharacteristic
191C22×C73#45511yescharacteristic
192C22×C73#45511yescharacteristic
193C22×C73#45811yescharacteristic
194C4×C73—21no—
195C4×C73—21no—
196C4×C73—21no—
197C4×C73—21no—
198C4×C73—21no—
199C4×C73—21no—
200C4×C73—42no—
201C4×C73—81no—
202C4×C73—81no—
203C4×C73—81no—
204Dic73—161no—
205#7796—731nomaximal, Sylow
206C2×C73—161no—
207C2×C73—161no—
208C2×C73#160711yescharacteristic
209C2×C73#161211yescharacteristic
210C2×C73#161811yescharacteristic
211C2×C73#162111yescharacteristic
212C2×C73#164111yescharacteristic
213C2×C73#164611yescharacteristic
214C2×C73#165911yescharacteristic
215#2733D7311yescharacteristic
216#2093—731no—
217#2072—731no—
218#2071—731no—
219#1272—731no—
220#1270—731no—
221#1270—731no—
222C73#779611yescharacteristic, complemented, Sylow
223C2×#124—21no—
224C2×#107—1461no—
225C2×#103—1461no—
226C2×#102—1461no—
227C2×#102—1461no—
228#394—21no—
229#392—21no—
230#392—21no—
231#391C2×D7311yescharacteristic
232#390C2×D7311yescharacteristic
233#390C2×D7311yescharacteristic
234#388—21no—
235#388—21no—
236#384—731no—
237#340—1461no—
238#340—1461no—
239#336—731no—
240#336—731no—
241#336—731no—
242C22×Q8C22⋊D7311yescharacteristic
243C22×D4—21no—
244C22×D4—21no—
245C22×D4C22⋊D7311yescharacteristic
246C22×D4C22⋊D7311yescharacteristic
247C22×C8—1461no—
248C22×C8—1461no—
249C22×C8—1461no—
250#124—42no—
251#124—42no—
252C2×C4⋊C4—1461no—
253C2×C4⋊C4—1461no—
254C2×C4⋊C4—1461no—
255C2×C4⋊C4C22⋊D7311yescharacteristic
256C2×C4⋊C4C22⋊D7311yescharacteristic
257C2×C4⋊C4C22⋊D7311yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C42—21no—
267C2×C42C22×D7311yescharacteristic
268#107—2922no—
269#103—2922no—
270#102—2922no—
271#102—2922no—
272#95—21no—
273#95—21no—
274#95—21no—
275C24—21no—
276C24—21no—
277C2×Q8—21no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8#1192401312yes—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—42no—
290C2×D4—81no—
291C2×D4—81no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4—81no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—2921no—
300C22×C4C2×C22⋊D7311yescharacteristic
301C22×C4C2×C22⋊D7311yescharacteristic
302C22×C4C2×C22⋊D7311yescharacteristic
303C2×C8—2921no—
304C2×C8—2921no—
305C2×C8—2921no—
306C2×C8—2921no—
307C2×C8—2921no—
308C2×C8—2921no—
309C2×C8—2921no—
310C2×C8—2921no—
311C2×C8—1462no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—2921no—
316C4⋊C4—2921no—
317C4⋊C4—2921no—
318C4⋊C4—2921no—
319C4⋊C4—2921no—
320C4⋊C4—2921no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C42—41no—
334C42—42no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23#1455656011yescharacteristic
350Q8—42no—
351Q8—81no—
352D4—42no—
353D4—42no—
354D4—81no—
355D4—81no—
356D4—84no—
357D4—84no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—5841no—
377C2×C4—5841no—
378C2×C4—5841no—
379C2×C4C2×#1192401311yescharacteristic
380C2×C4#1455661111yescharacteristic
381C2×C4#1455661111yescharacteristic
382C2×C4#1455661611yescharacteristic
383C2×C4#1455661711yescharacteristic
384C2×C4#1455662111yescharacteristic
385C8—2922no—
386C8—5841no—
387C8—5841no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22#1798872111yescharacteristic
403C22#1798873211yescharacteristic
404C22#1798874911yescharacteristic
405C22#1798875511yescharacteristic
406C22#1798876511yescharacteristic
407C22#1798876511yescharacteristic
408C22#1798877711yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—81no—
417C4—81no—
418C4—81no—
419C4—11681no—
420C2—161no—
421C2—161no—
422C2#2260891711yescharacteristic
423C2#2260894511yescharacteristic
424C2#2260897911yescharacteristic
425C2#2260899611yescharacteristic
426C2#2260912411yescharacteristic
427C2#2260915911yescharacteristic
428C2#2260923711yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
Fitting, prime radicalC73×#2733C2
socleC23×C73#120
hypercenter#2733D73
hypocenterC73#7796
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #22611459C2semidirect
2. #22611339C2semidirect
3. #22611334C2semidirect
4. #22607757C2semidirect
5. #22607752C2semidirect
6. #22607752C2semidirect
222. C73#7796semidirect

Maximal subgroups

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

subgroupindex
#226114592
#226113392
#226113342
#226077572
#226077522
C73×#27332
#779673