Finite Group Databasebeta

← #2232×D73 #33240738

Subgroups — #2232×D73 #33240738

Order 18688.

682 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
1#466×D73C211yesmaximal, characteristic
2C2×#107×D73C211yesmaximal, characteristic, complemented
3#22612113C212yesmaximal, complemented
4#22612112C211yesmaximal, characteristic, complemented
5#22612111C211yesmaximal, characteristic, complemented
6#22612110C212yesmaximal, complemented
7#22612109C211yesmaximal, characteristic, complemented
8#366×D73C212yesmaximal, complemented
9#357×D73C212yesmaximal, complemented
10C22⋊C16×D73C211yesmaximal, characteristic, complemented
11C73×#2232C211yesmaximal, characteristic, complemented
12C2×D8×D73C2211yescharacteristic
13C22×C8×D73C2211yescharacteristic
14#121×D73—21no—
15C2×C4⋊C4×D73—21no—
16C2×C16×D73C2212yes—
17#17988824C2211yescharacteristic
18#17988823C2211yescharacteristic
19#17988822—21no—
20#17988821—21no—
21#17988820C2211yescharacteristic
22C2×#14556525C2211yescharacteristic, complemented
23C2×#14556524—21no—
24#107×D73—21no—
25#107×D73—21no—
26#107×D73C2211yescharacteristic
27#107×D73C2212yes—
28#107×D73C2212yescomplemented
29#102×D73—21no—
30#17988413C2212yescomplemented
31#17988412C2212yescomplemented
32#17988412C2212yescomplemented
33#17988389C2212yescomplemented
34#17988388C2212yescomplemented
35#17988387C2212yescomplemented
36C22⋊#11924003C2211yescharacteristic, complemented
37#17988366C2212yescomplemented
38#466×C73C2211yescharacteristic
39C2×#107×C73C2211yescharacteristic, complemented
40#366×C73C2212yescomplemented
41#357×C73C2212yescomplemented
42C22⋊C16×C73C2211yescharacteristic, complemented
43C2×D4×D73—21no—
44C2×D4×D73—41no—
45C22×C4×D73—41no—
46C22×C4×D73D411yescharacteristic
47C2×D584C2311yescharacteristic
48C2×#11924013—21no—
49D8×D73—24no—
50C22×#10596831D411yescharacteristic
51C2×C8×D73—24no—
52C2×C8×D73D411yescharacteristic
53C2×C8×D73D411yescharacteristic
54C2×C8×D73C2311yescharacteristic
55C2×C8×D73C2311yescharacteristic
56#14556566—21no—
57#14556565—21no—
58#14556564—41no—
59#14556563—41no—
60#14556562—21no—
61C2×C4⋊Dic73—21no—
62C2×#11924007—41no—
63C4⋊C4×D73—22no—
64C4⋊C4×D73—22no—
65C4⋊C4×D73—21no—
66C4⋊C4×D73—41no—
67C4⋊C4×D73—41no—
68C22⋊C4×D73—41no—
69C2×#11924003C2312yes—
70C16×D73—24no—
71#14556525—21no—
72#14556525C2312yes—
73#14556525C2311yescharacteristic
74#14556524—22no—
75#14556524—22no—
76#14556524—21no—
77#14556513—21no—
78#14556512—21no—
79#14556511—21no—
80C2×D8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82#121×C73—21no—
83C2×C4⋊C4×C73—21no—
84C2×C16×C73C2312yes—
85#107×C73—21no—
86#107×C73C2312yes—
87#107×C73C2311yescharacteristic
88#102×C73—21no—
89C23×D73—41no—
90C23×D73D811yescharacteristic
91C2×D292—21no—
92C2×D292—41no—
93C2×C22⋊D73—41no—
94C2×C22⋊D73—41no—
95C2×C22⋊D73—41no—
96D4×D73—42no—
97D4×D73—42no—
98D4×D73—84no—
99C22×Dic73—41no—
100C22×Dic73D811yescharacteristic
101C2×C4×D73—22no—
102C2×C4×D73—22no—
103C2×C4×D73—41no—
104C2×C4×D73—42no—
105C2×C4×D73—42no—
106C2×C4×D73—84no—
107C2×C4×D73D811yescharacteristic
108C2×C4×D73D811yescharacteristic
109C2×C4×D73C2×D411yescharacteristic
110C2×C4×D73C2×D411yescharacteristic
111D584—22no—
112#11924013—42no—
113C2×#10596831—22no—
114C2×#10596831C2×D411yescharacteristic
115C2×#10596831C2×D411yescharacteristic
116C8×D73—22no—
117C8×D73—22no—
118C8×D73—22no—
119C8×D73#4114yes—
120C4⋊Dic73—21no—
121C4⋊Dic73—22no—
122C4⋊Dic73—41no—
123#11924007—42no—
124#11924007—42no—
125#11924007—41no—
126C22⋊Dic73—41no—
127#11924005—41no—
128#11924005—41no—
129#11924003—22no—
130C2×D4×C73—21no—
131C2×D4×C73—41no—
132C22×C4×C73—41no—
133C22×C4×C73C2×D411yescharacteristic
134D8×C73—22no—
135C2×C8×C73—22no—
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73C2411yescharacteristic
138C4⋊C4×C73—21no—
139C4⋊C4×C73—22no—
140C4⋊C4×C73—41no—
141C22⋊C4×C73—41no—
142C16×C73—22no—
143C23×C73—41no—
144C23×C73C2×D811yescharacteristic
145C22×D73—22no—
146C22×D73—22no—
147C22×D73—41no—
148C22×D73—82no—
149C22×D73—82no—
150C22×D73—82no—
151C22×D73D1614yes—
152C22×D73C2×D811yescharacteristic
153C22×D73C2×D811yescharacteristic
154D4×C73—41no—
155D4×C73—41no—
156D4×C73—82no—
157C2×C4×C73—21no—
158C2×C4×C73—21no—
159C2×C4×C73—41no—
160C2×C4×C73—42no—
161C2×C4×C73—82no—
162C2×C4×C73C2×D811yescharacteristic
163C2×C4×C73C22×D411yescharacteristic
164C22⋊D73—82no—
165C22⋊D73—82no—
166C22⋊D73—82no—
167C2×Dic73—22no—
168C2×Dic73—41no—
169C2×Dic73—42no—
170C2×Dic73—82no—
171C2×Dic73C2×D811yescharacteristic
172C2×Dic73C2×D811yescharacteristic
173D292—41no—
174D292—41no—
175D292—82no—
176C4×D73—22no—
177C4×D73—21no—
178C4×D73—21no—
179C4×D73—22no—
180C4×D73—84no—
181C4×D73—84no—
182C4×D73—82no—
183C4×D73#12312yes—
184C4×D73#13712yes—
185C8×C73—21no—
186C8×C73C2×#4112yes—
187#10596831—21no—
188#10596831#12312yes—
189C22×C73—21no—
190C22×C73—21no—
191C22×C73—81no—
192C22×C73—81no—
193C22×C73—81no—
194C22×C73C2×D1612yes—
195C22×C73C22×D811yescharacteristic
196C2×D73—21no—
197C2×D73—21no—
198C2×D73—28no—
199C2×D73—81no—
200C2×D73—81no—
201C2×D73—81no—
202C2×D73—164no—
203C2×D73#48012yes—
204C2×D73C2×D1612yes—
205C2×D73C2×D1612yes—
206C2×D73#51012yes—
207C4×C73—21no—
208C4×C73—82no—
209C4×C73—81no—
210C4×C73C2×#12311yescharacteristic
211C4×C73C2×#13711yescharacteristic
212Dic73—21no—
213Dic73—82no—
214Dic73—81no—
215Dic73#48012yes—
216C2×#2232—731nomaximal, Sylow
217C2×C73—22no—
218C2×C73—161no—
219C2×C73C2×#48011yescharacteristic
220C2×C73C22×D1611yescharacteristic
221C2×C73C2×#51011yescharacteristic
222D73—22no—
223D73—161no—
224D73#223214yesdirect product factor
225C2×#466—731no—
226C22×#107—731no—
227#2232—731no—
228#2232—731no—
229#2232—732no—
230#2232—732no—
231#2232—731no—
232#2232D7311yescharacteristic, direct product factor
233C2×#366—732no—
234C2×#357—732no—
235C2×C22⋊C16—731no—
236C73C2×#223211yescharacteristic, complemented, Sylow
237C22×D8—731no—
238C23×C8—731no—
239C2×#121—1461no—
240C22×C4⋊C4—1461no—
241C22×C16—732no—
242#466—731no—
243#466—731no—
244#466—731no—
245#466—1461no—
246#466—1461no—
247#466C2×D7311yescharacteristic
248C2×#107—731no—
249C2×#107—732no—
250C2×#107—731no—
251C2×#107—732no—
252C2×#107—1461no—
253C2×#107—1461no—
254C2×#107—1461no—
255C2×#107C2×D7311yescharacteristic, complemented
256C2×#102—1461no—
257#366—732no—
258#366—732no—
259#366—732no—
260#366C2×D7312yescomplemented
261#357—732no—
262#357—732no—
263#357—732no—
264#357C2×D7312yescomplemented
265C22⋊C16—731no—
266C22⋊C16—732no—
267C22⋊C16C2×D7311yescharacteristic, complemented
268C22×D4—2921no—
269C22×D4—1461no—
270C23×C4—2921no—
271C23×C4—731no—
272C2×D8—731no—
273C2×D8—1464no—
274C2×D8—1461no—
275C2×D8C22×D7311yescharacteristic
276C22×C8—731no—
277C22×C8—731no—
278C22×C8—731no—
279C22×C8—731no—
280C22×C8—731no—
281C22×C8—1464no—
282C22×C8C22×D7311yescharacteristic
283#121—21no—
284#121—2921no—
285#121—2921no—
286#121—1461no—
287#121—1461no—
288#121—1461no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—2921no—
291C2×C4⋊C4—2921no—
292C2×C4⋊C4—2921no—
293C2×C4⋊C4—1462no—
294C2×C4⋊C4—1462no—
295C2×C4⋊C4—1461no—
296C2×C4⋊C4—1461no—
297C2×C22⋊C4—2921no—
298C2×C16—732no—
299C2×C16—1464no—
300C2×C16C22×D7312yes—
301#107—21no—
302#107—732no—
303#107—731no—
304#107—1462no—
305#107—1462no—
306#107—1461no—
307#107—1461no—
308#107C22×D7312yes—
309#107C22×D7311yescharacteristic
310#102—21no—
311#102—1461no—
312#102—1461no—
313#102—1461no—
314C24—2921no—
315C24—731no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—2921no—
319C2×D4—2921no—
320C2×D4—2921no—
321C2×D4—2922no—
322C2×D4—2922no—
323C2×D4—2921no—
324C2×D4—5844no—
325C2×D4—1461no—
326C22×C4—41no—
327C22×C4—2921no—
328C22×C4—2922no—
329C22×C4—2922no—
330C22×C4—2921no—
331C22×C4—5844no—
332C22×C4—731no—
333C22×C4—731no—
334C22×C4—731no—
335C22×C4—731no—
336C22×C4—731no—
337C22×C4—1462no—
338C22×C4—1462no—
339C22×C4D4×D7311yescharacteristic
340D8—22no—
341D8—2922no—
342D8—1462no—
343C2×C8—22no—
344C2×C8—731no—
345C2×C8—734no—
346C2×C8—731no—
347C2×C8—1462no—
348C2×C8—1462no—
349C2×C8—1462no—
350C2×C8—1462no—
351C2×C8D4×D7311yescharacteristic
352C2×C8C23×D7311yescharacteristic
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4—41no—
356C4⋊C4—2922no—
357C4⋊C4—2922no—
358C4⋊C4—2921no—
359C4⋊C4—2921no—
360C4⋊C4—1461no—
361C4⋊C4—1462no—
362C22⋊C4—41no—
363C22⋊C4—2921no—
364C22⋊C4—2921no—
365C22⋊C4—2921no—
366C16—22no—
367C16—1462no—
368C23—41no—
369C23—2921no—
370C23—5842no—
371C23—5842no—
372C23—5842no—
373C23—731no—
374C23—734no—
375C23—731no—
376C23—1462no—
377C23—1462no—
378C23D8×D7311yescharacteristic
379D4—41no—
380D4—41no—
381D4—82no—
382D4—2921no—
383D4—2921no—
384D4—5842no—
385D4—5842no—
386D4—5842no—
387D4—5842no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—82no—
393C2×C4—2921no—
394C2×C4—2922no—
395C2×C4—5844no—
396C2×C4—5844no—
397C2×C4—5842no—
398C2×C4—5842no—
399C2×C4—731no—
400C2×C4—732no—
401C2×C4—732no—
402C2×C4—731no—
403C2×C4—1462no—
404C2×C4—1462no—
405C2×C4—1462no—
406C2×C4—1461no—
407C2×C4—1461no—
408C2×C4D8×D7311yescharacteristic
409C2×C4C2×D4×D7311yescharacteristic
410C8—21no—
411C8—732no—
412C8—1461no—
413C8#41×D7312yes—
414C22—21no—
415C22—21no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—5841no—
420C22—5841no—
421C22—5841no—
422C22—732no—
423C22—732no—
424C22—732no—
425C22—732no—
426C22—11684no—
427C22—1468no—
428C22—1461no—
429C22—1461no—
430C22D16×D7312yes—
431C22C2×D8×D7311yescharacteristic
432C4—21no—
433C4—82no—
434C4—81no—
435C4—5842no—
436C4—5841no—
437C4—732no—
438C4—1461no—
439C4#123×D7311yescharacteristic
440C4#137×D7311yescharacteristic
441C2—22no—
442C2—161no—
443C2—734no—
444C2—11681no—
445C2—1462no—
446C2#480×D7311yescharacteristic
447C2C2×D16×D7311yescharacteristic
448C2#510×D7311yescharacteristic
subgroupG/H
centerC22C2×D8×D73
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#2232C2
socleC22×C73C22×D8
prime radical#466×D73C2
hypercenter#2232D73
hypocenterC73C2×#2232
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
2. C2×#107×D73C2semidirect
3. #22612113C2semidirect
4. #22612112C2semidirect
5. #22612111C2semidirect
6. #22612110C2semidirect
7. #22612109C2semidirect
8. #366×D73C2semidirect
9. #357×D73C2semidirect
10. C22⋊C16×D73C2semidirect
11. C73×#2232C2semidirect
22. C2×#14556525C22semidirect
28. #107×D73C22semidirect
30. #17988413C22semidirect
31. #17988412C22semidirect
32. #17988412C22semidirect
33. #17988389C22semidirect
34. #17988388C22semidirect
35. #17988387C22semidirect
36. C22⋊#11924003C22semidirect
37. #17988366C22semidirect
39. C2×#107×C73C22semidirect
40. #366×C73C22semidirect
41. #357×C73C22semidirect
42. C22⋊C16×C73C22semidirect
224. D73#2232direct (N × H)
232. #2232D73direct (N × H)
236. C73C2×#2232semidirect
255. C2×#107C2×D73semidirect
260. #366C2×D73semidirect
264. #357C2×D73semidirect
267. C22⋊C16C2×D73semidirect

Maximal subgroups

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

subgroupindex
#466×D732
C2×#107×D732
#226121132
#226121122
#226121112
#226121102
#226121092
#366×D732
#357×D732
C22⋊C16×D732
C73×#22322
C2×#223273