Finite Group Databasebeta

← #32979358

Subgroups — #32979358

Order 18688.

940 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988447C211yesmaximal, characteristic
2#22608154C211yesmaximal, characteristic
3#22607811C214yesmaximal, complemented
4C73×#1779C211yesmaximal, characteristic
5C22×C4⋊Dic73C411yescharacteristic, complemented
6C22×C4⋊Dic73C411yescharacteristic, complemented
7C22×C22⋊Dic73—21no—
8C22×C22⋊Dic73—21no—
9#17988447—21no—
10#17988447—21no—
11#17988447C412yescomplemented
12#17988447C2212yes—
13C2×#14556498—21no—
14C2×#14556498—21no—
15C2×#14556498C2212yes—
16C24×C4×C73C2211yescharacteristic
17C2×C22⋊C8×C73—21no—
18C2×C22⋊C8×C73—21no—
19C2×C22⋊C8×C73C2212yes—
20C23×Dic73—21no—
21C23×Dic73—21no—
22C23×Dic73—22no—
23C2×C4⋊Dic73—21no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73—42no—
26C2×C4⋊Dic73—42no—
27C2×C4⋊Dic73C2×C412yes—
28C2×C4⋊Dic73C2×C412yes—
29C2×C22⋊Dic73—24no—
30C2×C22⋊Dic73—22no—
31C2×C22⋊Dic73—22no—
32C2×C22⋊Dic73—42no—
33C2×C22⋊Dic73—42no—
34C2×C22⋊Dic73—42no—
35C2×C22⋊Dic73—42no—
36#14556498—22no—
37#14556498—22no—
38#14556498—24no—
39#14556498—42no—
40C25×C73D411yescharacteristic
41C23×C4×C73—24no—
42C23×C4×C73—42no—
43C23×C4×C73—42no—
44C23×C4×C73C2×C411yescharacteristic
45C23×C4×C73C2×C411yescharacteristic
46C23×C4×C73D411yescharacteristic
47C23×C4×C73D411yescharacteristic
48C23×C4×C73D411yescharacteristic
49C23×C4×C73C2311yescharacteristic
50C22×C8×C73—22no—
51C22⋊C8×C73—24no—
52C22⋊C8×C73—42no—
53C22⋊C8×C73—42no—
54C22×Dic73—24no—
55C22×Dic73—22no—
56C22×Dic73—22no—
57C22×Dic73—42no—
58C22×Dic73—42no—
59C22×Dic73—42no—
60C22×Dic73—42no—
61C22×Dic73—42no—
62C22×Dic73—42no—
63C22×Dic73—42no—
64C22×Dic73—42no—
65C22×Dic73—42no—
66C22×Dic73—42no—
67C22×Dic73—42no—
68C22×Dic73—42no—
69C4⋊Dic73—42no—
70C4⋊Dic73—42no—
71C4⋊Dic73—42no—
72C4⋊Dic73—42no—
73C22⋊Dic73—48no—
74C22⋊Dic73—44no—
75C22⋊Dic73—42no—
76C22⋊Dic73—42no—
77C24×C73—22no—
78C24×C73—22no—
79C24×C73—22no—
80C24×C73—22no—
81C24×C73—41no—
82C24×C73—41no—
83C24×C73C22⋊C411yescharacteristic
84C24×C73C22⋊C411yescharacteristic
85C24×C73D812yes—
86C24×C73SD1612yes—
87C24×C73C2×D411yescharacteristic
88C22×C4×C73—22no—
89C22×C4×C73—22no—
90C22×C4×C73—22no—
91C22×C4×C73—22no—
92C22×C4×C73—22no—
93C22×C4×C73—22no—
94C22×C4×C73—22no—
95C22×C4×C73—22no—
96C22×C4×C73—22no—
97C22×C4×C73—22no—
98C22×C4×C73—41no—
99C22×C4×C73—41no—
100C22×C4×C73—41no—
101C22×C4×C73—41no—
102C22×C4×C73—41no—
103C22×C4×C73—41no—
104C22×C4×C73—41no—
105C22×C4×C73—416no—
106C22×C4×C73C22⋊C411yescharacteristic
107C22×C4×C73C22⋊C411yescharacteristic
108C22×C4×C73C22×C411yescharacteristic
109C22×C4×C73C2×D411yescharacteristic
110C22×C4×C73#4114yes—
111C2×C8×C73—42no—
112C2×C8×C73—42no—
113C2×C8×C73—42no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—24no—
123C23×C73—24no—
124C23×C73—21no—
125C23×C73—21no—
126C23×C73—21no—
127C23×C73—21no—
128C23×C73—21no—
129C23×C73—21no—
130C23×C73—24no—
131C23×C73—24no—
132C23×C73—42no—
133C23×C73—42no—
134C23×C73—44no—
135C23×C73—44no—
136C23×C73—44no—
137C23×C73—44no—
138C23×C73#9912yes—
139C23×C73#10212yes—
140C23×C73#10212yes—
141C23×C73#10412yes—
142C23×C73C2×C22⋊C411yescharacteristic
143C23×C73#12312yes—
144C23×C73C2×D811yescharacteristic
145C23×C73C2×SD1611yescharacteristic
146C23×C73#13712yes—
147C2×C4×C73—28no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—21no—
155C2×C4×C73—21no—
156C2×C4×C73—21no—
157C2×C4×C73—44no—
158C2×C4×C73—44no—
159C2×C4×C73—44no—
160C2×C4×C73—44no—
161C2×C4×C73—44no—
162C2×C4×C73#9912yes—
163C2×C4×C73#11712yes—
164C2×C4×C73#12312yes—
165C2×Dic73—44no—
166C2×Dic73—44no—
167C2×Dic73—44no—
168C2×Dic73—42no—
169C2×Dic73—42no—
170C2×Dic73—42no—
171C2×Dic73—42no—
172C2×Dic73—42no—
173C2×Dic73—42no—
174C2×Dic73—82no—
175C2×Dic73—82no—
176C2×Dic73—82no—
177C2×Dic73—84no—
178C2×Dic73—84no—
179C2×Dic73—82no—
180C8×C73—82no—
181C22×C73—22no—
182C22×C73—22no—
183C22×C73—22no—
184C22×C73—22no—
185C22×C73—22no—
186C22×C73—21no—
187C22×C73—21no—
188C22×C73—22no—
189C22×C73—22no—
190C22×C73—22no—
191C22×C73—22no—
192C22×C73—22no—
193C22×C73—21no—
194C22×C73—21no—
195C22×C73—22no—
196C22×C73—22no—
197C22×C73—22no—
198C22×C73—48no—
199C22×C73—48no—
200C22×C73—41no—
201C22×C73—41no—
202C22×C73—41no—
203C22×C73—41no—
204C22×C73#32714yes—
205C22×C73#38111yescharacteristic
206C22×C73C2×#9911yescharacteristic
207C22×C73C2×#9911yescharacteristic
208C22×C73C2×#10211yescharacteristic
209C22×C73#41911yescharacteristic
210C22×C73C2×#10411yescharacteristic
211C22×C73#42111yescharacteristic
212C22×C73#48012yes—
213C22×C73#48312yes—
214C4×C73—22no—
215C4×C73—22no—
216C4×C73—22no—
217C4×C73—41no—
218Dic73—84no—
219Dic73—82no—
220Dic73—82no—
221#8712—731nomaximal, Sylow
222C2×C73—22no—
223C2×C73—24no—
224C2×C73—22no—
225C2×C73—42no—
226C2×C73C2×#32711yescharacteristic
227C2×C73#150811yescharacteristic
228C2×C73#151111yescharacteristic
229C2×C73#151911yescharacteristic
230C2×C73#181911yescharacteristic
231C2×C73#182311yescharacteristic
232C2×C73#182611yescharacteristic
233C2×#380—731no—
234#1779D7311yescharacteristic
235C22⋊#95—731no—
236#1294—734no—
237C73#871211yescharacteristic, complemented, Sylow
238C24×C4C2×D7311yescharacteristic
239C22×C4⋊C4—731no—
240C22×C4⋊C4—731no—
241C22×C22⋊C4—1461no—
242C22×C22⋊C4—1461no—
243C2×C22⋊C8—21no—
244C2×C22⋊C8—21no—
245C2×C22⋊C8C2×D7312yes—
246#380—732no—
247#380—732no—
248#380—1461no—
249#380—1461no—
250C2×#95—732no—
251C2×#95—1461no—
252C2×#95—1461no—
253C25D29211yescharacteristic
254C23×C4—24no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—1461no—
258C23×C4—1461no—
259C23×C4—1462no—
260C23×C4C4×D7311yescharacteristic
261C23×C4C4×D7311yescharacteristic
262C23×C4D29211yescharacteristic
263C23×C4C22⋊D7311yescharacteristic
264C23×C4C22⋊D7311yescharacteristic
265C23×C4C22×D7311yescharacteristic
266C22×C8—22no—
267C2×C4⋊C4—2922no—
268C2×C4⋊C4—2922no—
269C2×C4⋊C4—732no—
270C2×C4⋊C4—732no—
271C2×C4⋊C4—1461no—
272C2×C4⋊C4—1461no—
273C2×C22⋊C4—2922no—
274C2×C22⋊C4—2922no—
275C2×C22⋊C4—2922no—
276C2×C22⋊C4—2922no—
277C2×C22⋊C4—1464no—
278C2×C22⋊C4—1462no—
279C2×C22⋊C4—1462no—
280C22⋊C8—24no—
281C22⋊C8—42no—
282C22⋊C8—42no—
283#95—2922no—
284#95—1464no—
285#95—1462no—
286#95—1462no—
287C24—22no—
288C24—22no—
289C24—22no—
290C24—22no—
291C24—41no—
292C24—41no—
293C24#1192400511yescharacteristic
294C24#1192400511yescharacteristic
295C24D58412yes—
296C24#1192401712yes—
297C24C2×D29211yescharacteristic
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—416no—
316C22×C4—2922no—
317C22×C4—2922no—
318C22×C4—2922no—
319C22×C4—2922no—
320C22×C4—2922no—
321C22×C4—2922no—
322C22×C4—2922no—
323C22×C4—2922no—
324C22×C4—2922no—
325C22×C4—2922no—
326C22×C4—2922no—
327C22×C4—2922no—
328C22×C4—1464no—
329C22×C4—1462no—
330C22×C4—1462no—
331C22×C4#1192400511yescharacteristic
332C22×C4#1192400511yescharacteristic
333C22×C4C2×C4×D7311yescharacteristic
334C22×C4C2×C22⋊D7311yescharacteristic
335C22×C4#1192402714yes—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—42no—
339C4⋊C4—2922no—
340C4⋊C4—2922no—
341C4⋊C4—2922no—
342C4⋊C4—2922no—
343C22⋊C4—2928no—
344C22⋊C4—2924no—
345C22⋊C4—2922no—
346C22⋊C4—2922no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—24no—
356C23—24no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—24no—
361C23—24no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—42no—
366C23—42no—
367C23—44no—
368C23—44no—
369C23—44no—
370C23—44no—
371C23#1455650512yes—
372C23#1455651312yes—
373C23#1455651312yes—
374C23#1455651712yes—
375C23C2×#1192400511yescharacteristic
376C23#1455657512yes—
377C23C2×D58411yescharacteristic
378C23C2×#1192401711yescharacteristic
379C23#1455662412yes—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—2924no—
396C2×C4—2924no—
397C2×C4—2924no—
398C2×C4—2922no—
399C2×C4—2922no—
400C2×C4—2922no—
401C2×C4—2922no—
402C2×C4—2922no—
403C2×C4—2922no—
404C2×C4—5842no—
405C2×C4—5842no—
406C2×C4—5842no—
407C2×C4—5844no—
408C2×C4—5842no—
409C2×C4—5844no—
410C2×C4#1455650512yes—
411C2×C4#1455654712yes—
412C2×C4#1455657212yes—
413C8—82no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—21no—
427C22—21no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—48no—
432C22—48no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22#1798832214yes—
438C22#1798844811yescharacteristic
439C22C2×#1455650511yescharacteristic
440C22C2×#1455650511yescharacteristic
441C22C2×#1455651311yescharacteristic
442C22#1798859711yescharacteristic
443C22C2×#1455651711yescharacteristic
444C22#1798860311yescharacteristic
445C22#1798890112yes—
446C22#1798891812yes—
447C4—22no—
448C4—22no—
449C4—22no—
450C4—41no—
451C4—5844no—
452C4—5842no—
453C4—5842no—
454C2—22no—
455C2—22no—
456C2—24no—
457C2—42no—
458C2C2×#1798832211yescharacteristic
459C2#2260845211yescharacteristic
460C2#2260846511yescharacteristic
461C2#2260850011yescharacteristic
462C2#2261000311yescharacteristic
463C2#2261001811yescharacteristic
464C2#2261002811yescharacteristic
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#8712
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
3. #22607811C2semidirect
5. C22×C4⋊Dic73C4semidirect
6. C22×C4⋊Dic73C4semidirect
11. #17988447C4semidirect
237. C73#8712semidirect

Maximal subgroups

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

subgroupindex
C2×#179884472
#226081542
#226078112
C73×#17792
#871273