Finite Group Databasebeta

← #32977430

Subgroups — #32977430

Order 18688.

1276 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556570C211yesmaximal, characteristic
2C2×#17988325C214yesmaximal, complemented
3#22608154C211yesmaximal, characteristic
4C73×#1779C211yesmaximal, characteristic
5C23×Dic146C411yescharacteristic, complemented
6C2×#14556570—28no—
7C2×#14556570—21no—
8C2×#14556570—21no—
9C2×#14556570C412yescomplemented
10C2×#14556570C2212yes—
11C22×C4⋊Dic73C411yescharacteristic, complemented
12C22×#11924007—21no—
13C22×C22⋊Dic73—21no—
14C22×C22⋊Dic73—21no—
15C2×#14556498—21no—
16C2×#14556498C2212yes—
17#17988325—28no—
18C24×C4×C73C2211yescharacteristic
19C2×C22⋊C8×C73—21no—
20C2×C22⋊C8×C73—21no—
21C2×C22⋊C8×C73C2212yes—
22C22×Dic146—24no—
23C22×Dic146—21no—
24C22×Dic146—42no—
25C22×Dic146—42no—
26C22×Dic146C2×C412yes—
27C23×Dic73—21no—
28C23×Dic73—21no—
29C23×Dic73—22no—
30#14556570—28no—
31#14556570—28no—
32#14556570—24no—
33#14556570—24no—
34#14556570—24no—
35#14556570D418yes—
36C2×C4⋊Dic73—24no—
37C2×C4⋊Dic73—21no—
38C2×C4⋊Dic73C2×C412yes—
39C2×#11924007—28no—
40C2×#11924007—22no—
41C2×#11924007—22no—
42C2×C22⋊Dic73—28no—
43C2×C22⋊Dic73—24no—
44C2×C22⋊Dic73—22no—
45C2×C22⋊Dic73—22no—
46C2×C22⋊Dic73—42no—
47C2×C22⋊Dic73—42no—
48#14556498—24no—
49#14556498—42no—
50C25×C73D411yescharacteristic
51C23×C4×C73—24no—
52C23×C4×C73—42no—
53C23×C4×C73—42no—
54C23×C4×C73C2×C411yescharacteristic
55C23×C4×C73C2×C411yescharacteristic
56C23×C4×C73D411yescharacteristic
57C23×C4×C73D411yescharacteristic
58C23×C4×C73D411yescharacteristic
59C23×C4×C73C2311yescharacteristic
60C22×C8×C73—22no—
61C22⋊C8×C73—24no—
62C22⋊C8×C73—42no—
63C22⋊C8×C73—42no—
64C2×Dic146—24no—
65C2×Dic146—22no—
66C2×Dic146—42no—
67C2×Dic146—416no—
68C2×Dic146—42no—
69C2×Dic146—42no—
70C2×Dic146—42no—
71C2×Dic146C22⋊C414yescomplemented
72C22×Dic73—24no—
73C22×Dic73—24no—
74C22×Dic73—22no—
75C22×Dic73—22no—
76C22×Dic73—24no—
77C22×Dic73—42no—
78C22×Dic73—42no—
79C22×Dic73—42no—
80C22×Dic73—42no—
81C22×Dic73—42no—
82C22×Dic73—42no—
83C22×Dic73—42no—
84C22×Dic73—42no—
85C22×Dic73—42no—
86C22×Dic73—42no—
87C4⋊Dic73—24no—
88C4⋊Dic73—22no—
89C4⋊Dic73C22⋊C414yescomplemented
90#11924007—28no—
91#11924007—28no—
92C22⋊Dic73—28no—
93C22⋊Dic73—28no—
94C22⋊Dic73—48no—
95C24×C73—22no—
96C24×C73—22no—
97C24×C73—22no—
98C24×C73—22no—
99C24×C73—41no—
100C24×C73—41no—
101C24×C73C22⋊C411yescharacteristic
102C24×C73C22⋊C411yescharacteristic
103C24×C73SD1612yes—
104C24×C73Q1612yes—
105C24×C73C2×D411yescharacteristic
106C22×C4×C73—22no—
107C22×C4×C73—22no—
108C22×C4×C73—22no—
109C22×C4×C73—22no—
110C22×C4×C73—22no—
111C22×C4×C73—22no—
112C22×C4×C73—22no—
113C22×C4×C73—22no—
114C22×C4×C73—22no—
115C22×C4×C73—22no—
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—41no—
123C22×C4×C73—416no—
124C22×C4×C73C22⋊C411yescharacteristic
125C22×C4×C73C22⋊C411yescharacteristic
126C22×C4×C73C22×C411yescharacteristic
127C22×C4×C73C2×D414yes—
128C22×C4×C73C2×D411yescharacteristic
129C2×C8×C73—42no—
130C2×C8×C73—42no—
131C2×C8×C73—42no—
132C23×C73—21no—
133C23×C73—21no—
134C23×C73—21no—
135C23×C73—21no—
136C23×C73—21no—
137C23×C73—21no—
138C23×C73—21no—
139C23×C73—21no—
140C23×C73—24no—
141C23×C73—24no—
142C23×C73—21no—
143C23×C73—21no—
144C23×C73—21no—
145C23×C73—21no—
146C23×C73—21no—
147C23×C73—21no—
148C23×C73—24no—
149C23×C73—24no—
150C23×C73—42no—
151C23×C73—42no—
152C23×C73—44no—
153C23×C73—44no—
154C23×C73—44no—
155C23×C73—44no—
156C23×C73#9912yes—
157C23×C73#10312yes—
158C23×C73#10312yes—
159C23×C73#10412yes—
160C23×C73C2×C22⋊C411yescharacteristic
161C23×C73#12012yes—
162C23×C73C2×SD1611yescharacteristic
163C23×C73C2×Q1611yescharacteristic
164C23×C73#13712yes—
165C2×C4×C73—28no—
166C2×C4×C73—21no—
167C2×C4×C73—21no—
168C2×C4×C73—21no—
169C2×C4×C73—21no—
170C2×C4×C73—21no—
171C2×C4×C73—21no—
172C2×C4×C73—21no—
173C2×C4×C73—21no—
174C2×C4×C73—21no—
175C2×C4×C73—44no—
176C2×C4×C73—44no—
177C2×C4×C73—44no—
178C2×C4×C73—44no—
179C2×C4×C73—44no—
180C2×C4×C73#9912yes—
181C2×C4×C73C2×C22⋊C412yes—
182C2×C4×C73#12012yes—
183C2×Dic73—24no—
184C2×Dic73—24no—
185C2×Dic73—48no—
186C2×Dic73—48no—
187C2×Dic73—42no—
188C2×Dic73—42no—
189C2×Dic73—42no—
190C2×Dic73—42no—
191C2×Dic73—44no—
192C2×Dic73—44no—
193C2×Dic73—44no—
194C2×Dic73—82no—
195C2×Dic73—82no—
196C2×Dic73—82no—
197C2×Dic73—82no—
198Dic146—48no—
199Dic146—44no—
200Dic146—44no—
201C8×C73—82no—
202C22×C73—21no—
203C22×C73—21no—
204C22×C73—22no—
205C22×C73—22no—
206C22×C73—22no—
207C22×C73—22no—
208C22×C73—21no—
209C22×C73—22no—
210C22×C73—21no—
211C22×C73—22no—
212C22×C73—22no—
213C22×C73—22no—
214C22×C73—22no—
215C22×C73—22no—
216C22×C73—22no—
217C22×C73—22no—
218C22×C73—22no—
219C22×C73—48no—
220C22×C73—48no—
221C22×C73—41no—
222C22×C73—41no—
223C22×C73—41no—
224C22×C73—41no—
225C22×C73#32814yescomplemented
226C22×C73#37911yescharacteristic
227C22×C73C2×#9911yescharacteristic
228C22×C73C2×#9911yescharacteristic
229C22×C73C2×#10311yescharacteristic
230C22×C73#41911yescharacteristic
231C22×C73C2×#10411yescharacteristic
232C22×C73#42111yescharacteristic
233C22×C73#44812yes—
234C22×C73#45112yes—
235C4×C73—22no—
236C4×C73—22no—
237C4×C73—22no—
238C4×C73—41no—
239Dic73—44no—
240Dic73—44no—
241Dic73—84no—
242#8329—731nomaximal, Sylow
243C2×C73—22no—
244C2×C73—24no—
245C2×C73—22no—
246C2×C73—42no—
247C2×C73C2×#32811yescharacteristic
248C2×C73#150811yescharacteristic
249C2×C73#151111yescharacteristic
250C2×C73#152011yescharacteristic
251C2×C73#178111yescharacteristic
252C2×C73#178711yescharacteristic
253C2×C73#178911yescharacteristic
254C22×C22⋊Q8—731no—
255#1779D7311yescharacteristic
256C2×#328—734no—
257C22⋊#95—731no—
258C73#832911yescharacteristic, complemented, Sylow
259C23×Q8—731no—
260C24×C4C2×D7311yescharacteristic
261C2×C22⋊Q8—732no—
262C2×C22⋊Q8—732no—
263C2×C22⋊Q8—1468no—
264C2×C22⋊Q8—1461no—
265C2×C22⋊Q8—1461no—
266C22×C4⋊C4—731no—
267C22×C4⋊C4—1461no—
268C22×C22⋊C4—1461no—
269C22×C22⋊C4—1461no—
270C2×C22⋊C8—21no—
271C2×C22⋊C8—21no—
272C2×C22⋊C8C2×D7312yes—
273C2×#95—732no—
274C2×#95—1461no—
275#328—1468no—
276C25D29211yescharacteristic
277C22×Q8—2922no—
278C22×Q8—2922no—
279C22×Q8—732no—
280C22×Q8—1464no—
281C22×Q8—1461no—
282C23×C4—24no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—1462no—
286C23×C4—1461no—
287C23×C4—1461no—
288C23×C4C4×D7311yescharacteristic
289C23×C4C4×D7311yescharacteristic
290C23×C4D29211yescharacteristic
291C23×C4C22⋊D7311yescharacteristic
292C23×C4C22⋊D7311yescharacteristic
293C23×C4C22×D7311yescharacteristic
294C22×C8—22no—
295C22⋊Q8—738no—
296C22⋊Q8—1464no—
297C22⋊Q8—1464no—
298C22⋊Q8—1468no—
299C22⋊Q8—1468no—
300C22⋊Q8—1464no—
301C2×C4⋊C4—732no—
302C2×C4⋊C4—1464no—
303C2×C4⋊C4—1468no—
304C2×C4⋊C4—1461no—
305C2×C4⋊C4—1462no—
306C2×C4⋊C4—1462no—
307C2×C22⋊C4—2922no—
308C2×C22⋊C4—2922no—
309C2×C22⋊C4—1464no—
310C2×C22⋊C4—1468no—
311C2×C22⋊C4—1462no—
312C2×C22⋊C4—1462no—
313C22⋊C8—24no—
314C22⋊C8—42no—
315C22⋊C8—42no—
316#95—2922no—
317#95—1464no—
318C24—22no—
319C24—22no—
320C24—22no—
321C24—22no—
322C24—41no—
323C24—41no—
324C24#1192400511yescharacteristic
325C24#1192400511yescharacteristic
326C24#1192401712yes—
327C24Dic29212yes—
328C24C2×D29211yescharacteristic
329C2×Q8—29216no—
330C2×Q8—2922no—
331C2×Q8—2922no—
332C2×Q8—2922no—
333C2×Q8—2922no—
334C2×Q8—734no—
335C2×Q8—1464no—
336C2×Q8—1462no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—416no—
355C22×C4—2922no—
356C22×C4—2922no—
357C22×C4—2922no—
358C22×C4—2922no—
359C22×C4—2922no—
360C22×C4—2922no—
361C22×C4—2922no—
362C22×C4—2922no—
363C22×C4—2922no—
364C22×C4—2922no—
365C22×C4—1464no—
366C22×C4—1464no—
367C22×C4—1464no—
368C22×C4—1462no—
369C22×C4—1462no—
370C22×C4#1192400511yescharacteristic
371C22×C4#1192400511yescharacteristic
372C22×C4C2×C4×D7311yescharacteristic
373C22×C4D4×D7314yes—
374C22×C4C2×C22⋊D7311yescharacteristic
375C2×C8—42no—
376C2×C8—42no—
377C2×C8—42no—
378C4⋊C4—734no—
379C4⋊C4—1468no—
380C4⋊C4—1464no—
381C4⋊C4—1462no—
382C4⋊C4—1468no—
383C22⋊C4—2928no—
384C22⋊C4—1468no—
385C22⋊C4—1468no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—24no—
396C23—24no—
397C23—21no—
398C23—21no—
399C23—24no—
400C23—24no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—42no—
405C23—42no—
406C23—44no—
407C23—44no—
408C23—44no—
409C23—44no—
410C23#1455650512yes—
411C23#1455651612yes—
412C23#1455651612yes—
413C23#1455651712yes—
414C23C2×#1192400511yescharacteristic
415C23#1455656112yes—
416C23C2×#1192401711yescharacteristic
417C23C2×Dic29211yescharacteristic
418C23#1455662412yes—
419Q8—2924no—
420Q8—2928no—
421Q8—2924no—
422C2×C4—28no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4—2928no—
438C2×C4—2928no—
439C2×C4—2922no—
440C2×C4—2922no—
441C2×C4—2922no—
442C2×C4—2922no—
443C2×C4—2924no—
444C2×C4—2924no—
445C2×C4—2924no—
446C2×C4—5842no—
447C2×C4—5842no—
448C2×C4—5842no—
449C2×C4—5842no—
450C2×C4—1464no—
451C2×C4—1464no—
452C2×C4#1455650512yes—
453C2×C4C22⋊C4×D7312yes—
454C2×C4#1455655912yes—
455C8—82no—
456C22—21no—
457C22—21no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—21no—
463C22—22no—
464C22—21no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—22no—
473C22—48no—
474C22—48no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22#1798832514yescomplemented
480C22#1798844211yescharacteristic
481C22C2×#1455650511yescharacteristic
482C22C2×#1455650511yescharacteristic
483C22C2×#1455651611yescharacteristic
484C22#1798859711yescharacteristic
485C22C2×#1455651711yescharacteristic
486C22#1798860311yescharacteristic
487C22#1798872812yes—
488C22#1798874512yes—
489C4—22no—
490C4—22no—
491C4—22no—
492C4—41no—
493C4—2924no—
494C4—2924no—
495C4—5844no—
496C2—22no—
497C2—22no—
498C2—24no—
499C2—42no—
500C2C2×#1798832511yescharacteristic
501C2#2260845211yescharacteristic
502C2#2260846511yescharacteristic
503C2#2260850411yescharacteristic
504C2#2260984511yescharacteristic
505C2#2260986711yescharacteristic
506C2#2260987411yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1779C2
socleC23×C73C2×C22⋊C4
prime radicalC25×C73D4
cosocleC23×C4×C73C23
hypercenter#1779D73
hypocenterC73#8329
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#17988325C2semidirect
5. C23×Dic146C4semidirect
9. C2×#14556570C4semidirect
11. C22×C4⋊Dic73C4semidirect
71. C2×Dic146C22⋊C4semidirect
89. C4⋊Dic73C22⋊C4semidirect
225. C22×C73#328semidirect
258. C73#8329semidirect
479. C22#17988325semidirect

Maximal subgroups

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

subgroupindex
C22×#145565702
C2×#179883252
#226081542
C73×#17792
#832973