Finite Group Databasebeta

← #32975102

Subgroups — #32975102

Order 18688.

516 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 91 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#22611407C211yesmaximal, characteristic, complemented
3#22611334C211yesmaximal, characteristic, complemented
4#22607754C211yesmaximal, characteristic, complemented
5#22607752C211yesmaximal, characteristic, complemented
6#22607752C211yesmaximal, characteristic, complemented
7C73×#2682C211yesmaximal, characteristic
8C2×#14556524—21no—
9C2×#14556522—21no—
10C2×#14556512—21no—
11C2×#14556512—21no—
12#17988457C2211yescharacteristic
13#17988349—21no—
14#17988349—21no—
15#17988342C2211yescharacteristic
16#17988342C2211yescharacteristic
17#17988342C2211yescharacteristic
18C2×#123×C73—21no—
19C2×#121×C73—21no—
20#396×C73—21no—
21#394×C73—21no—
22#392×C73—21no—
23#390×C73C2211yescharacteristic
24#390×C73C2211yescharacteristic
25#389×C73C2211yescharacteristic
26#385×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#14556522—42no—
35#14556512—42no—
36#14556512—42no—
37C22×D4×C73—21no—
38C22×D4×C73—21no—
39C22×D4×C73D411yescharacteristic
40C22×D4×C73D411yescharacteristic
41C23×C4×C73—21no—
42#123×C73—42no—
43#123×C73—42no—
44#121×C73—42no—
45#121×C73—42no—
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73—21no—
48C2×C4⋊C4×C73D411yescharacteristic
49C2×C4⋊C4×C73D411yescharacteristic
50C2×C4⋊C4×C73D411yescharacteristic
51C2×C4⋊C4×C73D411yescharacteristic
52C2×C22⋊C4×C73—21no—
53C2×C22⋊C4×C73—21no—
54C2×C22⋊C4×C73—21no—
55C2×C22⋊C4×C73—21no—
56C2×C22⋊C4×C73—21no—
57C2×C22⋊C4×C73—21no—
58C2×C22⋊C4×C73—21no—
59C2×C42×C73C2311yescharacteristic
60#95×C73—21no—
61#95×C73—21no—
62C22×Dic73—41no—
63C2×#10596831—22no—
64C2×#10596831—22no—
65C2×#10596831—41no—
66C2×#10596831—41no—
67C2×#10596831—41no—
68C2×#10596831—41no—
69C2×#10596831—41no—
70C2×#10596831—41no—
71C2×#10596831—41no—
72C4⋊Dic73—41no—
73C4⋊Dic73—41no—
74C4⋊Dic73—41no—
75C4⋊Dic73—41no—
76C4⋊Dic73—41no—
77C4⋊Dic73—41no—
78C24×C73—21no—
79C24×C73—21no—
80C2×D4×C73—21no—
81C2×D4×C73—21no—
82C2×D4×C73—21no—
83C2×D4×C73—41no—
84C2×D4×C73—41no—
85C2×D4×C73—41no—
86C2×D4×C73—41no—
87C2×D4×C73—42no—
88C2×D4×C73—42no—
89C2×D4×C73—42no—
90C2×D4×C73—81no—
91C2×D4×C73—81no—
92C2×D4×C73—81no—
93C2×D4×C73SD1612yes—
94C22×C4×C73—21no—
95C22×C4×C73—21no—
96C22×C4×C73—21no—
97C22×C4×C73—21no—
98C22×C4×C73—42no—
99C22×C4×C73—42no—
100C22×C4×C73—81no—
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73C2×D411yescharacteristic
104C4⋊C4×C73—21no—
105C4⋊C4×C73—41no—
106C4⋊C4×C73—41no—
107C4⋊C4×C73—41no—
108C4⋊C4×C73—42no—
109C4⋊C4×C73—41no—
110C4⋊C4×C73—41no—
111C4⋊C4×C73D812yes—
112C22⋊C4×C73—42no—
113C22⋊C4×C73—42no—
114C22⋊C4×C73—41no—
115C22⋊C4×C73—41no—
116C22⋊C4×C73—41no—
117C22⋊C4×C73—41no—
118C22⋊C4×C73—41no—
119C22⋊C4×C73—41no—
120C22⋊C4×C73—41no—
121C22⋊C4×C73—41no—
122C22⋊C4×C73—81no—
123C42×C73—41no—
124C23×C73—22no—
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—41no—
135C23×C73—41no—
136C23×C73—41no—
137C23×C73—41no—
138C23×C73#12011yescharacteristic
139D4×C73—42no—
140D4×C73—42no—
141D4×C73—81no—
142D4×C73—81no—
143D4×C73—84no—
144D4×C73—84no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—22no—
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×C73—41no—
162C2×C4×C73—41no—
163C2×C4×C73—84no—
164C2×C4×C73C2×D811yescharacteristic
165C2×C4×C73C2×SD1611yescharacteristic
166C2×C4×C73#13511yescharacteristic
167C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
170C2×Dic73—81no—
171C2×Dic73—81no—
172C2×Dic73—81no—
173#10596831—42no—
174#10596831—42no—
175#10596831—81no—
176C22×C73—42no—
177C22×C73—42no—
178C22×C73—42no—
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—81no—
188C22×C73—81no—
189C22×C73—81no—
190C22×C73#44711yescharacteristic
191C22×C73#44911yescharacteristic
192C22×C73#45011yescharacteristic
193C22×C73#45311yescharacteristic
194C22×C73#45511yescharacteristic
195C22×C73#45611yescharacteristic
196C22×C73#45811yescharacteristic
197C4×C73—21no—
198C4×C73—21no—
199C4×C73—21no—
200C4×C73—21no—
201C4×C73—21no—
202C4×C73—21no—
203C4×C73—42no—
204C4×C73—81no—
205C4×C73—81no—
206C4×C73—81no—
207Dic73—161no—
208#7800—731nomaximal, Sylow
209C2×C73—82no—
210C2×C73—161no—
211C2×C73#161011yescharacteristic
212C2×C73#161211yescharacteristic
213C2×C73#161311yescharacteristic
214C2×C73#162111yescharacteristic
215C2×C73#163911yescharacteristic
216C2×C73#165411yescharacteristic
217C2×C73#166111yescharacteristic
218#2682D7311yescharacteristic
219#2093—731no—
220#2084—731no—
221#2071—731no—
222#1271—731no—
223#1270—731no—
224#1270—731no—
225C73#780011yescharacteristic, complemented, Sylow
226C2×#123—21no—
227C2×#121—21no—
228C2×#107—1461no—
229C2×#106—1461no—
230C2×#102—1461no—
231C2×#102—1461no—
232#396—21no—
233#394—21no—
234#392—21no—
235#390C2×D7311yescharacteristic
236#390C2×D7311yescharacteristic
237#389C2×D7311yescharacteristic
238#385—21no—
239#384—731no—
240#340—1461no—
241#340—1461no—
242#336—731no—
243#336—731no—
244#336—731no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4C22⋊D7311yescharacteristic
248C22×D4C22⋊D7311yescharacteristic
249C23×C4—21no—
250C22×C8—1461no—
251C22×C8—1461no—
252C22×C8—1461no—
253#123—42no—
254#123—42no—
255#121—42no—
256#121—42no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—1461no—
260C2×C4⋊C4—1461no—
261C2×C4⋊C4—1461no—
262C2×C4⋊C4C22⋊D7311yescharacteristic
263C2×C4⋊C4C22⋊D7311yescharacteristic
264C2×C4⋊C4C22⋊D7311yescharacteristic
265C2×C4⋊C4C22⋊D7311yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C42C22×D7311yescharacteristic
274#107—2922no—
275#106—2922no—
276#102—2922no—
277#102—2922no—
278#95—21no—
279#95—21no—
280C24—21no—
281C24—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—42no—
291C2×D4—42no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4—81no—
295C2×D4#1192401612yes—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—81no—
303C22×C4—2921no—
304C22×C4C2×C22⋊D7311yescharacteristic
305C22×C4C2×C22⋊D7311yescharacteristic
306C22×C4C2×C22⋊D7311yescharacteristic
307C2×C8—2921no—
308C2×C8—2921no—
309C2×C8—2921no—
310C2×C8—2921no—
311C2×C8—2921no—
312C2×C8—2921no—
313C2×C8—2921no—
314C2×C8—1462no—
315C2×C8—1462no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—2921no—
324C4⋊C4—2921no—
325C4⋊C4—2921no—
326C4⋊C4—2921no—
327C4⋊C4—2921no—
328C4⋊C4—2921no—
329C4⋊C4#1192401312yes—
330C22⋊C4—42no—
331C22⋊C4—42no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—81no—
341C42—41no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23#1455656011yescharacteristic
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—84no—
362D4—84no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—84no—
382C2×C4—5841no—
383C2×C4—5841no—
384C2×C4—5841no—
385C2×C4C2×#1192401311yescharacteristic
386C2×C4C2×#1192401611yescharacteristic
387C2×C4#1455661111yescharacteristic
388C2×C4#1455661611yescharacteristic
389C2×C4#1455661711yescharacteristic
390C2×C4#1455661711yescharacteristic
391C8—2922no—
392C8—2922no—
393C8—5841no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22#1798872111yescharacteristic
409C22#1798873211yescharacteristic
410C22#1798873811yescharacteristic
411C22#1798875511yescharacteristic
412C22#1798876511yescharacteristic
413C22#1798877011yescharacteristic
414C22#1798877711yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—11681no—
426C2—82no—
427C2—161no—
428C2#2260893411yescharacteristic
429C2#2260894511yescharacteristic
430C2#2260895111yescharacteristic
431C2#2260899611yescharacteristic
432C2#2260911011yescharacteristic
433C2#2260921511yescharacteristic
434C2#2260924811yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
Fitting, prime radicalC73×#2682C2
socleC23×C73#120
hypercenter#2682D73
hypocenterC73#7800
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2682

Complements

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

NH ≅ G/Ntype
1. #22611459C2semidirect
2. #22611407C2semidirect
3. #22611334C2semidirect
4. #22607754C2semidirect
5. #22607752C2semidirect
6. #22607752C2semidirect
225. C73#7800semidirect

Maximal subgroups

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

subgroupindex
#226114592
#226114072
#226113342
#226077542
#226077522
C73×#26822
#780073