Finite Group Databasebeta

← #33095484

Subgroups — #33095484

Order 18688.

1042 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D73C211yesmaximal, characteristic
2C2×#17988639C211yesmaximal, characteristic
3#22612327C211yesmaximal, characteristic
4#22610894C212yesmaximal, complemented
5#22610894C212yesmaximal, complemented
6#22610889C211yesmaximal, characteristic, complemented
7#22610888C211yesmaximal, characteristic, complemented
8#22610886C211yesmaximal, characteristic, complemented
9#22610020C212yesmaximal
10#22610016C212yesmaximal
11C73×#1989C211yesmaximal, characteristic, complemented
12C2×#14556583C2211yescharacteristic
13C2×#14556582C2211yescharacteristic
14C2×#14556582C2211yescharacteristic
15C2×#14556581—21no—
16C2×#14556581—21no—
17#125×D73—24no—
18#125×D73C418yescomplemented
19C2×C4⋊C4×D73—21no—
20C2×C4⋊C4×D73—21no—
21C2×C4⋊C4×D73C2211yescharacteristic
22C2×C4⋊C4×D73C2211yescharacteristic
23C2×C42×D73C2211yescharacteristic
24#17988639—24no—
25C2×C4⋊#10596831C2211yescharacteristic
26C2×#14556503C2212yes—
27C2×C8×Dic73C2212yes—
28#17988454—21no—
29#17988452C2212yes—
30#17988449—21no—
31#17988444C2212yes—
32C4×C4⋊Dic73C2211yescharacteristic
33C4×#11924005—21no—
34#17988433—21no—
35#17988350C2212yes—
36#17988350C2212yes—
37#17988349C2212yes—
38#17988349C2212yes—
39#17988349C2212yes—
40#17988349C2212yes—
41C2×#125×C73C2211yescharacteristic
42C2×C4⋊C8×C73C2211yescharacteristic
43C4×C4⋊C4×C73C2211yescharacteristic
44#340×C73C2212yes—
45#340×C73C2212yes—
46C22×C4×D73—21no—
47C22×C4×D73—21no—
48C22×C4×D73D411yescharacteristic
49C22×C4×D73D411yescharacteristic
50C22×C4×D73C2311yescharacteristic
51C22×#10596831C2312yes—
52#14556583—22no—
53#14556583C2×C414yes—
54#14556582—22no—
55#14556582—22no—
56#14556582C2×C414yes—
57#14556582C2×C414yes—
58#14556581—28no—
59#14556581—28no—
60C2×C4⋊Dic73—21no—
61C2×C4⋊Dic73—21no—
62C2×C4⋊Dic73C2312yes—
63C2×C4⋊Dic73C2311yescharacteristic
64C2×C4⋊Dic73C2311yescharacteristic
65C2×#11924007—21no—
66C2×#11924007—21no—
67C2×#11924007—21no—
68C2×#11924007—21no—
69C2×#11924007—21no—
70C2×#11924007—21no—
71C4⋊C4×D73—28no—
72C4⋊C4×D73—28no—
73C4⋊C4×D73—22no—
74C4⋊C4×D73—22no—
75C4⋊C4×D73C2×C414yes—
76C4⋊C4×D73C2×C414yes—
77C2×#11924005—22no—
78C2×C4×Dic73—21no—
79C2×C4×Dic73D411yescharacteristic
80C2×C4×Dic73D411yescharacteristic
81C2×C4×Dic73C2311yescharacteristic
82C42×D73C2×C414yes—
83C42×D73D414yes—
84C4⋊#10596831—22no—
85#14556503—24no—
86C8×Dic73—24no—
87#14556498—22no—
88#14556498—22no—
89#14556498—22no—
90#14556498—21no—
91C22×C8×C73C2312yes—
92#125×C73—22no—
93#125×C73C2×C414yes—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73C2312yes—
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C42×C73—21no—
100C2×C42×C73C2311yescharacteristic
101C4⋊C8×C73—22no—
102#95×C73—21no—
103C23×D73C2×D411yescharacteristic
104C22×Dic73—21no—
105C22×Dic73—21no—
106C22×Dic73—22no—
107C22×Dic73C2×D411yescharacteristic
108C22×Dic73C2×D411yescharacteristic
109C22×Dic73C2×D411yescharacteristic
110C2×C4×D73—24no—
111C2×C4×D73—22no—
112C2×C4×D73—22no—
113C2×C4×D73—24no—
114C2×C4×D73—24no—
115C2×C4×D73—41no—
116C2×C4×D73—41no—
117C2×C4×D73—42no—
118C2×C4×D73—42no—
119C2×C4×D73—44no—
120C2×C4×D73C22⋊C414yes—
121C2×C4×D73C22⋊C414yes—
122C2×C4×D73C22×C412yes—
123C2×C4×D73C2×D412yes—
124C2×#10596831—22no—
125C2×#10596831—24no—
126C4⋊Dic73—21no—
127C4⋊Dic73—21no—
128C4⋊Dic73—24no—
129C4⋊Dic73—24no—
130C4⋊Dic73—22no—
131C4⋊Dic73—22no—
132C4⋊Dic73C22×C412yes—
133C4⋊Dic73C22×C412yes—
134#11924007—24no—
135#11924007—24no—
136#11924007—24no—
137#11924007—24no—
138#11924007—24no—
139#11924007—24no—
140#11924005—44no—
141C4×Dic73—42no—
142C4×Dic73C22⋊C414yes—
143C4×Dic73C22⋊C414yes—
144C4×Dic73C22×C412yes—
145C4×Dic73C2×D412yes—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—22no—
149C22×C4×C73C2×D411yescharacteristic
150C22×C4×C73C2×D411yescharacteristic
151C22×C4×C73C2411yescharacteristic
152C2×C8×C73—22no—
153C2×C8×C73—24no—
154C4⋊C4×C73—24no—
155C4⋊C4×C73—24no—
156C4⋊C4×C73—21no—
157C4⋊C4×C73—21no—
158C4⋊C4×C73—22no—
159C4⋊C4×C73—22no—
160C4⋊C4×C73C22×C412yes—
161C4⋊C4×C73C22×C412yes—
162C42×C73—42no—
163C42×C73C22×C412yes—
164C42×C73C2×D412yes—
165C23×C73C22×D411yescharacteristic
166C22×D73—22no—
167C22×D73—21no—
168C22×D73—21no—
169C22×D73C2×C22⋊C412yes—
170C22×D73#13514yes—
171C2×C4×C73—22no—
172C2×C4×C73—21no—
173C2×C4×C73—21no—
174C2×C4×C73—22no—
175C2×C4×C73—22no—
176C2×C4×C73—42no—
177C2×C4×C73—41no—
178C2×C4×C73—41no—
179C2×C4×C73—42no—
180C2×C4×C73—42no—
181C2×C4×C73—42no—
182C2×C4×C73C2×C22⋊C412yes—
183C2×C4×C73C2×C22⋊C412yes—
184C2×C4×C73C23×C411yescharacteristic
185C2×C4×C73C22×D411yescharacteristic
186C2×C4×C732−1+412yes—
187C2×C4×C732−1+412yes—
188C2×Dic73—22no—
189C2×Dic73—22no—
190C2×Dic73—21no—
191C2×Dic73—21no—
192C2×Dic73—22no—
193C2×Dic73—22no—
194C2×Dic73—42no—
195C2×Dic73—41no—
196C2×Dic73—41no—
197C2×Dic73—42no—
198C2×Dic73—42no—
199C2×Dic73—42no—
200C2×Dic73C2×C22⋊C412yes—
201C2×Dic73C2×C22⋊C412yes—
202C2×Dic73C2×C22⋊C412yes—
203C4×D73—28no—
204C4×D73—24no—
205C4×D73—22no—
206C4×D73—22no—
207C4×D73—44no—
208C4×D73—48no—
209C4×D73—48no—
210C8×C73—42no—
211#10596831—42no—
212C22×C73C22×C22⋊C411yescharacteristic
213C22×C73#53612yes—
214C22×C73C2×#13512yes—
215C22×C73#57511yescharacteristic
216C22×C73#57511yescharacteristic
217C2×D73—22no—
218C2×D73—22no—
219C2×D73—24no—
220C2×D73—24no—
221C2×D73#41614yes—
222C4×C73—22no—
223C4×C73—22no—
224C4×C73—42no—
225C4×C73—42no—
226C4×C73—82no—
227C4×C73#51912yes—
228C4×C73#53611yescharacteristic
229C4×C73#53611yescharacteristic
230Dic73—22no—
231Dic73—22no—
232Dic73—22no—
233Dic73—42no—
234Dic73—42no—
235Dic73—82no—
236#21836—731nomaximal, Sylow
237C2×C73#231011yescharacteristic
238C2×C73C2×#41611yescharacteristic
239C2×C73#289611yescharacteristic
240C2×C73#323212yes—
241C2×C73#323212yes—
242D73—24no—
243C22×#125—731no—
244C2×#431—731no—
245#2283—731no—
246#1991—732no—
247#1991—732no—
248#1989—731no—
249#1989—731no—
250#1989—731no—
251#1989D7311yescharacteristic, complemented
252#1824—732no—
253#1823—732no—
254C73#2183611yescharacteristic, complemented, Sylow
255C2×#125—738no—
256C2×#125—731no—
257C2×#125—731no—
258C2×#125—731no—
259C2×#125—1461no—
260C2×#125—1461no—
261C2×#125—1464no—
262C2×#125C2×D7311yescharacteristic
263C22×C4⋊C4—731no—
264C22×C4⋊C4—731no—
265C22×C4⋊C4—1461no—
266C22×C4⋊C4—1461no—
267C22×C42—731no—
268#431—1464no—
269C2×C4⋊C8—731no—
270C2×C4⋊C8C2×D7311yescharacteristic
271C2×C22⋊C8—732no—
272C2×C4×C8—732no—
273#383—1461no—
274#382—732no—
275#381—1461no—
276#380—732no—
277C4×C4⋊C4—731no—
278C4×C4⋊C4C2×D7311yescharacteristic
279C4×C22⋊C4—1461no—
280#376—1461no—
281#340—732no—
282#340—732no—
283#340—732no—
284#340—732no—
285#340—732no—
286#340—732no—
287#340C2×D7312yes—
288#340C2×D7312yes—
289C23×C4—731no—
290C23×C4—731no—
291C23×C4—731no—
292C23×C4—1461no—
293C23×C4—1461no—
294C22×C8—732no—
295C22×C8C22×D7312yes—
296#125—22no—
297#125—734no—
298#125—734no—
299#125—734no—
300#125—1468no—
301#125—1468no—
302#125—1462no—
303#125—1462no—
304#125—1462no—
305#125C4×D7314yes—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—731no—
309C2×C4⋊C4—731no—
310C2×C4⋊C4—734no—
311C2×C4⋊C4—734no—
312C2×C4⋊C4—732no—
313C2×C4⋊C4—1462no—
314C2×C4⋊C4—1462no—
315C2×C4⋊C4—1468no—
316C2×C4⋊C4—1468no—
317C2×C4⋊C4—1461no—
318C2×C4⋊C4—1461no—
319C2×C4⋊C4—1461no—
320C2×C4⋊C4—1461no—
321C2×C4⋊C4—1461no—
322C2×C4⋊C4—1461no—
323C2×C4⋊C4—1461no—
324C2×C4⋊C4—1461no—
325C2×C4⋊C4C22×D7312yes—
326C2×C4⋊C4C22×D7311yescharacteristic
327C2×C4⋊C4C22×D7311yescharacteristic
328C2×C22⋊C4—1462no—
329C2×C42—21no—
330C2×C42—731no—
331C2×C42—731no—
332C2×C42—731no—
333C2×C42—734no—
334C2×C42—734no—
335C2×C42—1461no—
336C2×C42C22×D7311yescharacteristic
337C4⋊C8—22no—
338C4⋊C8—1462no—
339C22⋊C8—1464no—
340C4×C8—1464no—
341#95—21no—
342#95—1462no—
343#95—1462no—
344#95—1462no—
345#95—1461no—
346C24—731no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—2921no—
351C22×C4—2921no—
352C22×C4—2924no—
353C22×C4—2922no—
354C22×C4—2922no—
355C22×C4—734no—
356C22×C4—731no—
357C22×C4—731no—
358C22×C4—731no—
359C22×C4—734no—
360C22×C4—732no—
361C22×C4—732no—
362C22×C4—1464no—
363C22×C4—1464no—
364C22×C4—1464no—
365C22×C4—1462no—
366C22×C4—1461no—
367C22×C4—1461no—
368C22×C4—1462no—
369C22×C4—1462no—
370C22×C4D4×D7311yescharacteristic
371C22×C4D4×D7311yescharacteristic
372C22×C4C23×D7311yescharacteristic
373C2×C8—22no—
374C2×C8—24no—
375C2×C8—1462no—
376C2×C8—1464no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—732no—
384C4⋊C4—732no—
385C4⋊C4—1464no—
386C4⋊C4—1464no—
387C4⋊C4—1464no—
388C4⋊C4—1464no—
389C4⋊C4—1464no—
390C4⋊C4—1464no—
391C4⋊C4—1462no—
392C4⋊C4—1462no—
393C4⋊C4—1464no—
394C4⋊C4—1464no—
395C4⋊C4—1461no—
396C4⋊C4—1461no—
397C4⋊C4C2×C4×D7312yes—
398C4⋊C4C2×C4×D7312yes—
399C22⋊C4—2924no—
400C42—42no—
401C42—2922no—
402C42—734no—
403C42—734no—
404C42—732no—
405C42—732no—
406C42C2×C4×D7312yes—
407C42D4×D7312yes—
408C23—732no—
409C23—734no—
410C23—1461no—
411C23—1461no—
412C23—1462no—
413C23C2×D4×D7311yescharacteristic
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—2924no—
426C2×C4—2928no—
427C2×C4—2928no—
428C2×C4—2921no—
429C2×C4—2921no—
430C2×C4—2922no—
431C2×C4—2922no—
432C2×C4—2922no—
433C2×C4—2922no—
434C2×C4—732no—
435C2×C4—732no—
436C2×C4—732no—
437C2×C4—1468no—
438C2×C4—1462no—
439C2×C4—1462no—
440C2×C4—1461no—
441C2×C4—1461no—
442C2×C4—1462no—
443C2×C4—1462no—
444C2×C4—1462no—
445C2×C4—1462no—
446C2×C4—1464no—
447C2×C4C22⋊C4×D7312yes—
448C2×C4C22⋊C4×D7312yes—
449C2×C4C22×C4×D7311yescharacteristic
450C2×C4C2×D4×D7311yescharacteristic
451C2×C4#1455663812yes—
452C2×C4#1455663912yes—
453C8—42no—
454C8—2922no—
455C22—734no—
456C22—1462no—
457C22—1462no—
458C22—1464no—
459C22—1464no—
460C22C2×C22⋊C4×D7311yescharacteristic
461C22#1798916012yes—
462C22#135×D7312yes—
463C22#1798938311yescharacteristic
464C22#1798938611yescharacteristic
465C4—22no—
466C4—22no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4—2922no—
471C4—2922no—
472C4—5842no—
473C4—1462no—
474C4—1462no—
475C4—1462no—
476C4#1798906312yes—
477C4#1798915711yescharacteristic
478C4#1798916211yescharacteristic
479C2—1464no—
480C2#2261251411yescharacteristic
481C2#416×D7311yescharacteristic
482C2#2261844711yescharacteristic
483C2#2262109712yes—
484C2#2262110312yes—
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1989C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1989D73
hypocenterC73#21836
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
4. #22610894C2semidirect
5. #22610894C2semidirect
6. #22610889C2semidirect
7. #22610888C2semidirect
8. #22610886C2semidirect
11. C73×#1989C2semidirect
18. #125×D73C4semidirect
251. #1989D73semidirect
254. C73#21836semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D732
C2×#179886392
#226123272
#226108942
#226108892
#226108882
#226108862
#226100202
#226100162
C73×#19892
#2183673