Finite Group Databasebeta

← #33052059

Subgroups — #33052059

Order 18688.

970 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556581C211yesmaximal, characteristic
2#22618560C212yesmaximal
3#22608285C218yesmaximal, complemented
4#22608261C211yesmaximal, characteristic
5#22608260C212yesmaximal
6C73×#1463C211yesmaximal, characteristic
7C2×#14556581—22no—
8C2×#14556581—22no—
9C2×#14556581—22no—
10C2×#14556581—22no—
11C2×#14556581C414yes—
12C2×#14556581C2214yes—
13C22×C4⋊Dic73C411yescharacteristic
14C22×#11924007C411yescharacteristic
15C22×#11924007C411yescharacteristic
16C22×#11924007C411yescharacteristic
17C22×#11924007C2211yescharacteristic
18C22×C4×Dic73C2211yescharacteristic
19#17988641—22no—
20#17988641C2214yes—
21#17988637—22no—
22#17988637C2214yes—
23#17988610—22no—
24#17988551C2212yes—
25M16×Dic73—22no—
26#17988313C2214yes—
27#17988312C2218yes—
28C22×C4⋊C4×C73C2211yescharacteristic
29#407×C73C2212yes—
30#324×C73C2214yes—
31C23×Dic73C2×C411yescharacteristic
32C23×Dic73C2×C411yescharacteristic
33C23×Dic73C2×C411yescharacteristic
34C23×Dic73C2×C411yescharacteristic
35C2×#11924012—22no—
36#14556581—24no—
37#14556581—24no—
38#14556581—24no—
39#14556581—24no—
40#14556581—24no—
41#14556581—24no—
42#14556581—24no—
43#14556581—24no—
44C2×C4⋊Dic73—22no—
45C2×C4⋊Dic73—21no—
46C2×C4⋊Dic73—21no—
47C2×C4⋊Dic73C2×C414yes—
48C2×#11924007—21no—
49C2×#11924007—21no—
50C2×#11924007—22no—
51C2×#11924007—22no—
52C2×#11924007—21no—
53C2×#11924007—21no—
54C2×#11924007—21no—
55C2×#11924007—22no—
56C2×#11924007—21no—
57C2×#11924007—22no—
58C2×#11924007—22no—
59C2×#11924007C2×C414yes—
60C2×#11924007C2×C414yes—
61C2×#11924007C2×C414yes—
62C2×#11924007C2×C412yes—
63C2×#11924007C2312yes—
64C2×C4×Dic73C2×C412yes—
65C2×C4×Dic73D412yes—
66C2×C4×Dic73D412yes—
67C2×C4×Dic73D412yes—
68C2×C4×Dic73D412yes—
69C2×C4×Dic73C2312yes—
70#14556520—24no—
71#14556520—24no—
72C22⋊#10596831—22no—
73C22⋊#10596831C2314yes—
74#14556501—24no—
75C8×Dic73—24no—
76C23×C4×C73C2×C411yescharacteristic
77C23×C4×C73C2×C411yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C2×M16×C73—22no—
80C2×C4⋊C4×C73—22no—
81C2×C4⋊C4×C73—22no—
82C2×C4⋊C4×C73C2×C412yes—
83C2×C4⋊C4×C73C2312yes—
84C22⋊C8×C73—22no—
85C22⋊C8×C73C2314yes—
86C22×Dic73—24no—
87C22×Dic73—21no—
88C22×Dic73—21no—
89C22×Dic73—21no—
90C22×Dic73—21no—
91C22×Dic73—42no—
92C22×Dic73—42no—
93C22×Dic73—42no—
94C22×Dic73C22⋊C411yescharacteristic
95C22×Dic73C22⋊C412yes—
96C22×Dic73C22⋊C411yescharacteristic
97C22×Dic73C22⋊C411yescharacteristic
98C22×Dic73C22⋊C412yes—
99C22×Dic73C22⋊C411yescharacteristic
100C22×Dic73C22×C412yes—
101C22×Dic73C22×C412yes—
102C22×Dic73C22×C412yes—
103C22×Dic73C22×C412yes—
104#11924012—44no—
105C2×#10596831—24no—
106C4⋊Dic73—24no—
107C4⋊Dic73—24no—
108#11924007—24no—
109#11924007—24no—
110#11924007—24no—
111#11924007—24no—
112#11924007—24no—
113#11924007—24no—
114#11924007—24no—
115#11924007—24no—
116C4×Dic73C22⋊C412yes—
117C4×Dic73C22⋊C412yes—
118C4×Dic73C22⋊C412yes—
119C4×Dic73C22⋊C412yes—
120C4×Dic73C2×D412yes—
121C4×Dic73C2×D412yes—
122C4×Dic73C2×D412yes—
123C4×Dic73C2×D412yes—
124C24×C73C22×C411yescharacteristic
125C22×C4×C73—21no—
126C22×C4×C73—21no—
127C22×C4×C73—21no—
128C22×C4×C73—21no—
129C22×C4×C73—42no—
130C22×C4×C73—42no—
131C22×C4×C73—42no—
132C22×C4×C73C22×C412yes—
133C22×C4×C73C22×C412yes—
134C22×C4×C73C22×C411yescharacteristic
135C22×C4×C73C2×D412yes—
136C22×C4×C73C2×D412yes—
137C22×C4×C73C2411yescharacteristic
138M16×C73—44no—
139C2×C8×C73—24no—
140C4⋊C4×C73—24no—
141C4⋊C4×C73—24no—
142C23×C73—22no—
143C23×C73—22no—
144C23×C73—22no—
145C23×C73C2×C22⋊C411yescharacteristic
146C23×C73C2×C22⋊C411yescharacteristic
147C23×C73C23×C411yescharacteristic
148C2×C4×C73—24no—
149C2×C4×C73—22no—
150C2×C4×C73—22no—
151C2×C4×C73—24no—
152C2×C4×C73—41no—
153C2×C4×C73—42no—
154C2×C4×C73—41no—
155C2×C4×C73—42no—
156C2×C4×C73—42no—
157C2×C4×C73—42no—
158C2×C4×C73—42no—
159C2×C4×C73—42no—
160C2×C4×C73C2×C22⋊C412yes—
161C2×C4×C73C22×D412yes—
162C2×Dic73—24no—
163C2×Dic73—22no—
164C2×Dic73—24no—
165C2×Dic73—24no—
166C2×Dic73—22no—
167C2×Dic73—22no—
168C2×Dic73—24no—
169C2×Dic73—41no—
170C2×Dic73—41no—
171C2×Dic73—42no—
172C2×Dic73—42no—
173C2×Dic73—42no—
174C2×Dic73—42no—
175C2×Dic73—42no—
176C2×Dic73—42no—
177C2×Dic73#10114yes—
178C2×Dic73C2×C22⋊C412yes—
179C2×Dic73C2×C22⋊C412yes—
180C2×Dic73C2×C22⋊C412yes—
181C2×Dic73C2×C22⋊C412yes—
182C8×C73—44no—
183#10596831—44no—
184C22×C73—28no—
185C22×C73—21no—
186C22×C73—21no—
187C22×C73—21no—
188C22×C73—21no—
189C22×C73—21no—
190C22×C73—21no—
191C22×C73#41012yes—
192C22×C73C2×#10112yes—
193C22×C73C22×C22⋊C411yescharacteristic
194C22×C73#56812yes—
195C4×C73—22no—
196C4×C73—22no—
197C4×C73—42no—
198C4×C73—42no—
199Dic73—22no—
200Dic73—22no—
201Dic73—22no—
202Dic73—42no—
203Dic73—42no—
204Dic73C2×#10114yes—
205#17394—731nomaximal, Sylow
206C2×C73—22no—
207C2×C73—22no—
208C2×C73—22no—
209C2×C73#287911yescharacteristic
210C2×C73C2×#41011yescharacteristic
211C2×C73C22×#10111yescharacteristic
212C22×#125—731no—
213#2920—732no—
214#1470—738no—
215#1463—732no—
216#1463—731no—
217#1463D7311yescharacteristic
218C73#1739411yescharacteristic, complemented, Sylow
219C2×#125—734no—
220C2×#125—734no—
221C2×#125—1462no—
222C2×#125—1462no—
223C2×#125—1462no—
224C2×#125—1462no—
225C22×C4⋊C4—731no—
226C22×C4⋊C4—731no—
227C22×C4⋊C4—731no—
228C22×C4⋊C4—731no—
229C22×C4⋊C4—731no—
230C22×C4⋊C4C2×D7311yescharacteristic
231C22×C42—731no—
232#432—734no—
233#432—1462no—
234#431—734no—
235#431—1462no—
236#423—1462no—
237#407—732no—
238#407C2×D7312yes—
239C4×M16—1462no—
240#324—734no—
241#324—738no—
242#324C2×D7314yes—
243C23×C4—731no—
244C23×C4—731no—
245C23×C4—731no—
246C23×C4—731no—
247C23×C4C4×D7311yescharacteristic
248C23×C4C4×D7311yescharacteristic
249C23×C4C22×D7311yescharacteristic
250C2×M16—22no—
251C2×M16—1462no—
252#125—1464no—
253#125—1464no—
254#125—1464no—
255#125—1464no—
256#125—1464no—
257#125—1464no—
258#125—1464no—
259#125—1464no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—734no—
263C2×C4⋊C4—734no—
264C2×C4⋊C4—734no—
265C2×C4⋊C4—732no—
266C2×C4⋊C4—734no—
267C2×C4⋊C4—732no—
268C2×C4⋊C4—1461no—
269C2×C4⋊C4—1461no—
270C2×C4⋊C4—1462no—
271C2×C4⋊C4—1461no—
272C2×C4⋊C4—1461no—
273C2×C4⋊C4—1462no—
274C2×C4⋊C4—1462no—
275C2×C4⋊C4—1461no—
276C2×C4⋊C4—1461no—
277C2×C4⋊C4—1462no—
278C2×C4⋊C4—1461no—
279C2×C4⋊C4—1461no—
280C2×C4⋊C4—1462no—
281C2×C4⋊C4—1462no—
282C2×C4⋊C4C4×D7312yes—
283C2×C4⋊C4C22×D7312yes—
284C2×C42—732no—
285C2×C42—732no—
286C2×C42—732no—
287C2×C42—732no—
288C2×C42—732no—
289C2×C42—732no—
290C4⋊C8—1464no—
291C4⋊C8—1464no—
292C22⋊C8—22no—
293C22⋊C8—734no—
294C22⋊C8—1462no—
295C22⋊C8C22×D7314yes—
296#97—1464no—
297C4×C8—1464no—
298C24C2×C4×D7311yescharacteristic
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—2922no—
307C22×C4—2922no—
308C22×C4—2922no—
309C22×C4—731no—
310C22×C4—731no—
311C22×C4—732no—
312C22×C4—732no—
313C22×C4—731no—
314C22×C4—732no—
315C22×C4—731no—
316C22×C4—732no—
317C22×C4—732no—
318C22×C4—732no—
319C22×C4—1461no—
320C22×C4—1461no—
321C22×C4—1461no—
322C22×C4—1461no—
323C22×C4—1464no—
324C22×C4C2×C4×D7312yes—
325C22×C4C2×C4×D7312yes—
326C22×C4C2×C4×D7311yescharacteristic
327C22×C4D4×D7312yes—
328C22×C4D4×D7312yes—
329C22×C4C23×D7311yescharacteristic
330M16—44no—
331M16—2924no—
332C2×C8—24no—
333C2×C8—1464no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—1464no—
337C4⋊C4—1464no—
338C4⋊C4—1464no—
339C4⋊C4—1464no—
340C4⋊C4—1464no—
341C4⋊C4—1464no—
342C4⋊C4—1464no—
343C4⋊C4—1464no—
344C4⋊C4—1464no—
345C4⋊C4—1464no—
346C42—732no—
347C42—732no—
348C42—732no—
349C42—732no—
350C42—732no—
351C42—732no—
352C42—732no—
353C42—732no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23C22⋊C4×D7311yescharacteristic
358C23C22⋊C4×D7311yescharacteristic
359C23C22×C4×D7311yescharacteristic
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—2922no—
373C2×C4—2922no—
374C2×C4—2922no—
375C2×C4—2922no—
376C2×C4—2922no—
377C2×C4—2921no—
378C2×C4—2921no—
379C2×C4—2922no—
380C2×C4—732no—
381C2×C4—734no—
382C2×C4—732no—
383C2×C4—732no—
384C2×C4—732no—
385C2×C4—1462no—
386C2×C4—1462no—
387C2×C4—1464no—
388C2×C4—1464no—
389C2×C4—1464no—
390C2×C4—1462no—
391C2×C4—1464no—
392C2×C4C22⋊C4×D7312yes—
393C2×C4C2×D4×D7312yes—
394C8—44no—
395C8—2924no—
396C22—28no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22#1798855912yes—
404C22#101×D7312yes—
405C22C2×C22⋊C4×D7311yescharacteristic
406C22#1798935312yes—
407C4—22no—
408C4—22no—
409C4—42no—
410C4—42no—
411C4—2922no—
412C4—2922no—
413C4—734no—
414C4—1462no—
415C4—1462no—
416C4—1462no—
417C2—22no—
418C2—22no—
419C2—22no—
420C2#2261837411yescharacteristic
421C2C2×#1798855911yescharacteristic
422C2C2×#101×D7311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1463C2
socleC22×C73C22×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenter#1463D73
hypocenterC73#17394
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #22608285C2semidirect
218. C73#17394semidirect

Maximal subgroups

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

subgroupindex
C22×#145565812
#226185602
#226082852
#226082612
#226082602
C73×#14632
#1739473