Finite Group Databasebeta

← #34016004

Subgroups — #34016004

Order 18688.

1098 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626830C212yesmaximal, complemented
2#22625194C212yesmaximal, complemented
3#22625193C212yesmaximal, complemented
4#22625185C212yesmaximal
5#22625184C212yesmaximal
6#22625173C212yesmaximal, complemented
7#22625165C212yesmaximal
8C2×#17989063C211yesmaximal, characteristic
9#17989639—28no—
10#17989608C2214yes—
11#17989607C2214yes—
12#17989604C2214yes—
13#17989433C2214yes—
14#17989432C2214yes—
15#17989432C2214yes—
16#17989431C2214yes—
17C22×Q8×D73C411yescharacteristic
18#17989063—28no—
19C2×Q8×Dic73C2211yescharacteristic
20C2×C4×Dic146C411yescharacteristic
21C2×C4×Dic146C2211yescharacteristic
22C2×C4×Dic146C2211yescharacteristic
23C2×#14556556C411yescharacteristic
24C2×#14556556C411yescharacteristic
25C2×#14556556C2211yescharacteristic
26C2×#14556549C411yescharacteristic
27C2×#14556549C2211yescharacteristic
28C2×#14556549C2211yescharacteristic
29C2×#14556548C411yescharacteristic
30C2×#14556548C411yescharacteristic
31C2×#14556548C2211yescharacteristic
32C2×C4×Q8×C73C411yescharacteristic
33#14556658—24no—
34#14556658—24no—
35C4⋊#10596833—24no—
36C22⋊#10596833C2318yes—
37#14556646—24no—
38#14556646—24no—
39C4×#10596833—24no—
40C22×Dic146C2×C411yescharacteristic
41C22×Dic146C2×C411yescharacteristic
42C22×Dic146C2×C411yescharacteristic
43C2×Q8×D73—24no—
44C2×Q8×D73—24no—
45C2×Q8×D73—24no—
46C22×C4×D73C2×C411yescharacteristic
47C22×C4×D73C2×C411yescharacteristic
48C22×C4×D73C2×C411yescharacteristic
49Q8×Dic73—24no—
50C4×Dic146—24no—
51C4×Dic146—24no—
52C4×Dic146—24no—
53#14556556—24no—
54#14556556—24no—
55#14556556D418yes—
56#14556549—24no—
57#14556549—24no—
58#14556549—24no—
59#14556548—24no—
60#14556548—24no—
61#14556548—24no—
62C2×C4⋊Dic73C2×C411yescharacteristic
63C2×C4⋊Dic73C2311yescharacteristic
64C2×C4⋊Dic73C2311yescharacteristic
65C2×#11924007C2×C411yescharacteristic
66C2×#11924007C2×C411yescharacteristic
67C2×#11924007C2×C411yescharacteristic
68C2×#11924007C2×C411yescharacteristic
69C2×#11924007C2×C411yescharacteristic
70C2×#11924007C2311yescharacteristic
71C2×#11924005C2×C411yescharacteristic
72C2×#11924005C2×C411yescharacteristic
73C2×#11924005C2×C411yescharacteristic
74C2×#11924005C2311yescharacteristic
75C2×C4×Dic73C2×C411yescharacteristic
76C2×C4×Dic73C2×C411yescharacteristic
77C2×C4×Dic73C2×C411yescharacteristic
78C2×C4×Dic73C2×C411yescharacteristic
79C2×C4×Dic73C2×C411yescharacteristic
80C2×C4×Dic73C2×C411yescharacteristic
81C2×C4×Dic73C2311yescharacteristic
82C2×C4×Dic73C2311yescharacteristic
83C2×C4×Dic73C2311yescharacteristic
84C22×Q8×C73C2×C411yescharacteristic
85C4×Q8×C73—24no—
86C2×C4⋊C4×C73C2×C411yescharacteristic
87C2×C4⋊C4×C73C2×C411yescharacteristic
88C2×C4⋊C4×C73C2×C411yescharacteristic
89C2×C42×C73C2×C411yescharacteristic
90C2×C42×C73C2×C411yescharacteristic
91C2×C42×C73C2×C411yescharacteristic
92C2×#10596833—28no—
93C23×D73C22×C411yescharacteristic
94C2×Dic146—22no—
95C2×Dic146—22no—
96C2×Dic146—22no—
97C2×Dic146—22no—
98C2×Dic146—22no—
99C2×Dic146—22no—
100C2×Dic146—22no—
101C2×Dic146C22⋊C414yes—
102C2×Dic146M1614yes—
103Q8×D73—232no—
104C22×Dic73C22×C411yescharacteristic
105C22×Dic73C22×C411yescharacteristic
106C22×Dic73C22×C411yescharacteristic
107C22×Dic73C22×C411yescharacteristic
108C22×Dic73C22×C411yescharacteristic
109C22×Dic73C22×C411yescharacteristic
110C22×Dic73C2411yescharacteristic
111C2×C4×D73—22no—
112C2×C4×D73—22no—
113C2×C4×D73—22no—
114C2×C4×D73—22no—
115C2×C4×D73—22no—
116C2×C4×D73—22no—
117C2×C4×D73—22no—
118C2×C4×D73—22no—
119C2×C4×D73M1614yes—
120C4⋊Dic73—22no—
121C4⋊Dic73—22no—
122C4⋊Dic73—22no—
123#11924007—22no—
124#11924007—22no—
125#11924007—22no—
126#11924007—22no—
127#11924007C22⋊C414yes—
128#11924007C22⋊C414yes—
129#11924005—22no—
130#11924005—22no—
131#11924005—22no—
132#11924005—22no—
133C4×Dic73—22no—
134C4×Dic73—22no—
135C4×Dic73—22no—
136C4×Dic73—22no—
137C4×Dic73—22no—
138C4×Dic73—22no—
139C4×Dic73C2×D414yes—
140C4×Dic73C2×D414yes—
141C4×Dic73C2×D414yes—
142C2×Q8×C73—22no—
143C2×Q8×C73—22no—
144C2×Q8×C73—22no—
145C22×C4×C73C22×C411yescharacteristic
146C22×C4×C73C22×C411yescharacteristic
147C22×C4×C73C22×C411yescharacteristic
148C22×C4×C73C22×C411yescharacteristic
149C22×C4×C73C22×C411yescharacteristic
150C22×C4×C73C22×C411yescharacteristic
151C22×C4×C73C22×C411yescharacteristic
152C4⋊C4×C73—22no—
153C4⋊C4×C73—22no—
154C4⋊C4×C73C22⋊C414yes—
155C42×C73—22no—
156C42×C73—22no—
157C42×C73—22no—
158C23×C73C23×C411yescharacteristic
159C22×D73—21no—
160C22×D73—21no—
161C22×D73—41no—
162C22×D73—41no—
163C22×D73C2×M1612yes—
164Q8×C73—28no—
165C2×C4×C73—21no—
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—41no—
174C2×C4×C73—41no—
175C2×C4×C73—41no—
176C2×C4×C73—41no—
177C2×C4×C73C2×C22⋊C412yes—
178C2×C4×C73C2×C22⋊C412yes—
179C2×C4×C73C2×C22⋊C412yes—
180C2×C4×C73C2×M1612yes—
181C2×C4×C73C2×M1612yes—
182C2×Dic73—21no—
183C2×Dic73—21no—
184C2×Dic73—21no—
185C2×Dic73—21no—
186C2×Dic73—21no—
187C2×Dic73—21no—
188C2×Dic73—41no—
189C2×Dic73—41no—
190C2×Dic73—41no—
191C2×Dic73—41no—
192C2×Dic73C2×C22⋊C412yes—
193C2×Dic73C2×C22⋊C412yes—
194C2×Dic73C2×C22⋊C412yes—
195C2×Dic73C2×M1612yes—
196C2×Dic73C2×M1612yes—
197C2×Dic73C2×M1612yes—
198C2×Dic73C22×D412yes—
199C4×D73—28no—
200C4×D73—28no—
201C4×D73—28no—
202Dic146—28no—
203Dic146—28no—
204Dic146—28no—
205#10596833—48no—
206C22×C73—21no—
207C22×C73—21no—
208C22×C73C22×C22⋊C411yescharacteristic
209C22×C73C22×M1611yescharacteristic
210C22×C73C22×M1611yescharacteristic
211C2×D73—22no—
212C2×D73—42no—
213C2×D73—41no—
214C2×D73—41no—
215C2×D73—42no—
216C4×C73—22no—
217C4×C73—22no—
218C4×C73—22no—
219C4×C73—22no—
220C4×C73—22no—
221C4×C73—41no—
222C4×C73—41no—
223Dic73—22no—
224Dic73—22no—
225Dic73—22no—
226Dic73—22no—
227Dic73—41no—
228Dic73—41no—
229Dic73#40714yes—
230#17371—731nomaximal, Sylow
231C2×C73—21no—
232C2×C73—21no—
233C2×C73C2×#40711yescharacteristic
234C2×C73#288411yescharacteristic
235C2×C73#288911yescharacteristic
236D73—42no—
237C2×#519—731no—
238#2983—732no—
239#1467—732no—
240#1467—732no—
241#1464—732no—
242#1464—732no—
243#1461—732no—
244#1458—732no—
245C73#1737111yescharacteristic, complemented, Sylow
246C23×Q8—731no—
247#519—1468no—
248C2×C4×Q8—731no—
249C2×C4×Q8—731no—
250C2×C4×Q8—731no—
251C2×C4×Q8—731no—
252C2×C4×Q8—731no—
253C2×C4×Q8—731no—
254C2×C4×Q8—731no—
255C2×C4×Q8#6440811yescharacteristic
256C2×#117—731no—
257C2×#117—731no—
258C2×#117—731no—
259C2×#117—731no—
260C2×#117—731no—
261C2×#117—731no—
262#446—1468no—
263#432—734no—
264#432—734no—
265#431—734no—
266#324—734no—
267#324—734no—
268#324—734no—
269#323—734no—
270C22×Q8—731no—
271C22×Q8—731no—
272C22×Q8—731no—
273C22×Q8—1464no—
274C22×Q8—1464no—
275C22×Q8—1464no—
276C22×Q8C2×#6440811yescharacteristic
277C23×C4—731no—
278C23×C4—731no—
279C23×C4—731no—
280C4×Q8—24no—
281C4×Q8—738no—
282C4×Q8—1464no—
283C4×Q8—1464no—
284C4×Q8—1464no—
285C4×Q8—1464no—
286C4×Q8—1464no—
287C4×Q8—1464no—
288#117—1464no—
289#117—1464no—
290#117—1464no—
291#117—1464no—
292#117—1464no—
293#117—1464no—
294C2×C4⋊C4—731no—
295C2×C4⋊C4—731no—
296C2×C4⋊C4—731no—
297C2×C4⋊C4—731no—
298C2×C4⋊C4—731no—
299C2×C4⋊C4—731no—
300C2×C4⋊C4—731no—
301C2×C4⋊C4—731no—
302C2×C4⋊C4—731no—
303C2×C4⋊C4C2×#6440811yescharacteristic
304C2×C4⋊C4C2×#6440811yescharacteristic
305C2×C4⋊C4C2×#6440811yescharacteristic
306C2×C22⋊C4—731no—
307C2×C22⋊C4—731no—
308C2×C22⋊C4—731no—
309C2×C22⋊C4—731no—
310C2×C42—731no—
311C2×C42—731no—
312C2×C42—731no—
313C2×C42—731no—
314C2×C42—731no—
315C2×C42—731no—
316C2×C42—731no—
317C2×C42—731no—
318C2×C42—731no—
319C2×C42C2×#6440811yescharacteristic
320C2×C42C2×#6440811yescharacteristic
321C2×C42C2×#6440811yescharacteristic
322C4⋊C8—1464no—
323C4⋊C8—1464no—
324C4⋊C8—1464no—
325C22⋊C8—738no—
326#97—1464no—
327#97—1464no—
328C4×C8—1464no—
329C24—731no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—734no—
334C2×Q8—734no—
335C2×Q8—1462no—
336C2×Q8—1462no—
337C2×Q8—1462no—
338C2×Q8—1462no—
339C2×Q8—1462no—
340C2×Q8—1462no—
341C2×Q8—14632no—
342C2×Q8—1462no—
343C22×C4—731no—
344C22×C4—731no—
345C22×C4—731no—
346C22×C4—731no—
347C22×C4—731no—
348C22×C4—731no—
349C22×C4—731no—
350C22×C4—734no—
351C22×C4—1462no—
352C22×C4—1462no—
353C22×C4—1462no—
354C22×C4—1462no—
355C22×C4—1462no—
356C22×C4—1462no—
357C22×C4—1462no—
358C22×C4—1462no—
359C22×C4C22×#6440811yescharacteristic
360C22×C4C22×#6440811yescharacteristic
361C22×C4C22×#6440811yescharacteristic
362C22×C4C22×#6440811yescharacteristic
363C22×C4C22×#6440811yescharacteristic
364C22×C4C22×#6440811yescharacteristic
365C22×C4C22×#6440811yescharacteristic
366C2×C8—1468no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—734no—
370C4⋊C4—734no—
371C4⋊C4—1462no—
372C4⋊C4—1462no—
373C4⋊C4—1462no—
374C4⋊C4—1462no—
375C4⋊C4—1462no—
376C4⋊C4—1462no—
377C4⋊C4—1462no—
378C4⋊C4C22⋊#6440814yes—
379C22⋊C4—1462no—
380C22⋊C4—1462no—
381C22⋊C4—1462no—
382C22⋊C4—1462no—
383C42—22no—
384C42—22no—
385C42—22no—
386C42—734no—
387C42—734no—
388C42—734no—
389C42—1462no—
390C42—1462no—
391C42—1462no—
392C42—1462no—
393C42—1462no—
394C42—1462no—
395C23—2921no—
396C23—2921no—
397C23—732no—
398C23—1461no—
399C23—1461no—
400C23C23×#6440811yescharacteristic
401Q8—28no—
402Q8—1468no—
403Q8—1468no—
404Q8—1468no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—2921no—
418C2×C4—2921no—
419C2×C4—2921no—
420C2×C4—2921no—
421C2×C4—732no—
422C2×C4—732no—
423C2×C4—732no—
424C2×C4—732no—
425C2×C4—732no—
426C2×C4—732no—
427C2×C4—732no—
428C2×C4—1468no—
429C2×C4—1468no—
430C2×C4—1468no—
431C2×C4—1461no—
432C2×C4—1461no—
433C2×C4—1461no—
434C2×C4—1461no—
435C2×C4—1461no—
436C2×C4—1461no—
437C2×C4C2×C22⋊#6440812yes—
438C2×C4C2×C22⋊#6440812yes—
439C2×C4C2×C22⋊#6440812yes—
440C2×C4D73⋊M1612yes—
441C2×C4D73⋊M1612yes—
442C8—2928no—
443C22—21no—
444C22—21no—
445C22—2922no—
446C22—2922no—
447C22—2921no—
448C22—2921no—
449C22—1462no—
450C22C22×C22⋊#6440811yescharacteristic
451C22C2×D73⋊M1611yescharacteristic
452C22C2×D73⋊M1611yescharacteristic
453C4—22no—
454C4—22no—
455C4—22no—
456C4—22no—
457C4—22no—
458C4—41no—
459C4—41no—
460C4—2921no—
461C4—2921no—
462C4—734no—
463C4—1462no—
464C4—1462no—
465C4—1462no—
466C4—1462no—
467C2—21no—
468C2—21no—
469C2—2922no—
470C2D73⋊#40711yescharacteristic
471C2#2262653211yescharacteristic
472C2#2262654311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#64408
commutatorC23×C73C23×C4
FrattiniC23C23×#64408
FittingC2×C4×Q8×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC23×D73C22×C4
cosocleC22×Dic73C24
hypercenterC2×C4×Q8#64408
hypocenterC73#17371
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #22626830C2semidirect
2. #22625194C2semidirect
3. #22625193C2semidirect
6. #22625173C2semidirect
245. C73#17371semidirect

Maximal subgroups

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

subgroupindex
#226268302
#226251942
#226251932
#226251852
#226251842
#226251732
#226251652
C2×#179890632
#1737173