Finite Group Databasebeta

← #33055330

Subgroups — #33055330

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619061C211yesmaximal, characteristic
2#22619052C211yesmaximal, characteristic
3#22618892C211yesmaximal, characteristic
4#22608720C211yesmaximal, characteristic, complemented
5#22608710C212yesmaximal, complemented
6#22608700C212yesmaximal, complemented
7#22608697C212yesmaximal, complemented
8#22608686C211yesmaximal, characteristic, complemented
9#22608680C212yesmaximal, complemented
10#22608677C211yesmaximal, characteristic, complemented
11C73×#1574C211yesmaximal, characteristic, complemented
12C4×#11924028C2211yescharacteristic
13#17988717—21no—
14#17988714C411yescharacteristic
15#17988714C411yescharacteristic
16#17988711—21no—
17#17988664—21no—
18#17988664C411yescharacteristic
19#17988664C411yescharacteristic
20#17988663—22no—
21#17988661—22no—
22#17988655C412yes—
23#17988655C412yes—
24C8×D292—21no—
25#17988643C2212yes—
26#17988640C2211yescharacteristic
27#17988639C2212yes—
28#17988638C2212yes—
29#17988611C2211yescharacteristic
30#17988609C2212yes—
31C4⋊C8×D73C2212yes—
32C4×#11924011C2212yes—
33C2×C4×#10596831C2211yescharacteristic
34#17988340C2212yes—
35#17988339C2211yescharacteristic
36#17988339C2211yescharacteristic
37#17988338C2212yes—
38#17988337C2211yescharacteristic
39#17988337C2211yescharacteristic
40#17988337C2212yes—
41#17988337C2212yes—
42#431×C73C2211yescharacteristic
43#431×C73C2211yescharacteristic
44#423×C73C2211yescharacteristic
45#335×C73C2212yes—
46#334×C73C2212yes—
47C2×#11924028Q811yescharacteristic
48C2×#11924012—21no—
49C2×#11924011—22no—
50C2×#11924011C2×C412yes—
51C2×#11924011C2×C412yes—
52C22×#10596831C2×C411yescharacteristic
53C22×#10596831C2×C411yescharacteristic
54C2×C8×D73—22no—
55C4×Dic146C2×C411yescharacteristic
56C4×Dic146D411yescharacteristic
57C4×D292C2×C411yescharacteristic
58C4×D292D411yescharacteristic
59C4×C22⋊D73C2×C412yes—
60C4×C22⋊D73D412yes—
61#14556550Q811yescharacteristic
62#14556548Q812yes—
63C42×D73C2312yes—
64C4⋊#10596831—21no—
65C4⋊#10596831C2311yescharacteristic
66C4⋊#10596831C2312yes—
67C4⋊#10596831C2311yescharacteristic
68#14556520—22no—
69#14556520—22no—
70#14556520C2×C412yes—
71#14556520C2×C412yes—
72C22⋊#10596831—21no—
73#14556503—22no—
74#14556503—22no—
75#14556503C2×C412yes—
76#14556503C2×C412yes—
77#14556501—22no—
78#14556501C2×C412yes—
79#14556501C2×C412yes—
80C4×#10596831—21no—
81C4×#10596831C2×C411yescharacteristic
82C4×#10596831C2×C411yescharacteristic
83C4×#10596831C2311yescharacteristic
84C4×#10596831C2311yescharacteristic
85C8×Dic73—22no—
86C2×M16×C73—21no—
87C2×C42×C73C2311yescharacteristic
88C4⋊C8×C73—21no—
89C4⋊C8×C73C2×C411yescharacteristic
90C4⋊C8×C73C2×C411yescharacteristic
91C4⋊C8×C73C2312yes—
92C4⋊C8×C73C2311yescharacteristic
93C4⋊C8×C73C2311yescharacteristic
94C22⋊C8×C73—21no—
95C22⋊C8×C73C2×C412yes—
96C4×C8×C73—21no—
97C4×C8×C73C2312yes—
98#11924028—42no—
99C2×Dic146C4⋊C411yescharacteristic
100C2×D292C4⋊C411yescharacteristic
101C2×C22⋊D73C4⋊C412yes—
102C2×C4×D73C22×C412yes—
103C2×C4×D73C2×D412yes—
104C2×C4×D73C2×Q812yes—
105#11924012—81no—
106#11924011—24no—
107#11924011—42no—
108#11924011—82no—
109C2×#10596831—22no—
110C2×#10596831—21no—
111C2×#10596831—21no—
112C2×#10596831—22no—
113C2×#10596831—41no—
114C2×#10596831C22×C411yescharacteristic
115C2×#10596831C22×C411yescharacteristic
116C2×#10596831C22×C411yescharacteristic
117C2×#10596831C22×C411yescharacteristic
118C8×D73—82no—
119C4⋊Dic73C4⋊C411yescharacteristic
120C4⋊Dic73C4⋊C411yescharacteristic
121#11924007C4⋊C412yes—
122#11924007C4⋊C412yes—
123C22⋊Dic73C4⋊C412yes—
124#11924005C4⋊C412yes—
125#11924005C4⋊C412yes—
126C4×Dic73C22×C412yes—
127C4×Dic73C2×D412yes—
128C4×Dic73C2×Q812yes—
129C22×C4×C73C22×C411yescharacteristic
130C22×C4×C73C2×D411yescharacteristic
131C22×C4×C73C2×Q811yescharacteristic
132M16×C73—81no—
133C2×C8×C73—21no—
134C2×C8×C73—21no—
135C2×C8×C73—22no—
136C2×C8×C73C22×C412yes—
137C2×C8×C73C22×C412yes—
138C42×C73C22×C411yescharacteristic
139C42×C73C2×D411yescharacteristic
140C42×C73C2×Q811yescharacteristic
141C42×C73C2411yescharacteristic
142C23×C73C2×C4⋊C411yescharacteristic
143C22×D73C2×C4⋊C412yes—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—22no—
149C2×C4×C73C2×C4⋊C411yescharacteristic
150C2×C4×C73C2×C4⋊C411yescharacteristic
151C2×C4×C73C2×C4⋊C411yescharacteristic
152C2×C4×C73C23×C411yescharacteristic
153C2×C4×C73C22×D411yescharacteristic
154C2×C4×C73C22×Q811yescharacteristic
155C22⋊D73—42no—
156C2×Dic73C2×C4⋊C412yes—
157C2×Dic73C2×C4⋊C412yes—
158C2×Dic73C2×C4⋊C412yes—
159D292—22no—
160C4×D73—22no—
161C4×D73—22no—
162C4×D73—22no—
163C4×D73—22no—
164C4×D73—42no—
165Dic146—22no—
166C8×C73—22no—
167C8×C73—22no—
168C8×C73—41no—
169C8×C73—42no—
170C8×C73—41no—
171#10596831—21no—
172#10596831—21no—
173#10596831—21no—
174#10596831—42no—
175#10596831—41no—
176#10596831—41no—
177#10596831#13112yes—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73C22×C4⋊C411yescharacteristic
182C2×D73—22no—
183C2×D73—22no—
184C2×D73—22no—
185C4×C73—21no—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73#43012yes—
189C4×C73C2×#13111yescharacteristic
190C4×C73#56811yescharacteristic
191C4×C73#57711yescharacteristic
192C4×C73#57711yescharacteristic
193Dic73—22no—
194Dic73—22no—
195Dic73—22no—
196#17841—731nomaximal, Sylow
197C2×C73—41no—
198C2×C73#290611yescharacteristic
199C2×C73#291211yescharacteristic
200C2×C73C2×#43011yescharacteristic
201D73—42no—
202#2991—731no—
203#2990—731no—
204#2965—731no—
205#1574—731no—
206#1574D7311yescharacteristic, complemented
207#1572—732no—
208#1570—732no—
209#1569—732no—
210#1566—731no—
211#1565—732no—
212#1564—731no—
213C73#1784111yescharacteristic, complemented, Sylow
214C4×#41—731no—
215#446—731no—
216#446—731no—
217#446—1461no—
218C8×Q8—1461no—
219#436—731no—
220#436—731no—
221#436—1461no—
222#436—1462no—
223#435—732no—
224#435—732no—
225#435—1462no—
226C8×D4—1461no—
227#432—732no—
228#431—732no—
229#431—731no—
230#431—732no—
231#431C2×D7311yescharacteristic
232#431C2×D7311yescharacteristic
233#423—731no—
234#423—732no—
235#423C2×D7311yescharacteristic
236C2×C4⋊C8—732no—
237C4×M16—732no—
238C2×C4×C8—731no—
239#335—731no—
240#335—731no—
241#335—732no—
242#335C2×D7312yes—
243#334—731no—
244#334—731no—
245#334—732no—
246#334—732no—
247#334—732no—
248#334C2×D7312yes—
249C2×#41—731no—
250C2×M16—21no—
251C2×M16—732no—
252C2×M16—732no—
253C2×M16—1462no—
254C2×M16—1461no—
255C22×C8—731no—
256C22×C8—731no—
257C22×C8—1462no—
258C4×Q8—731no—
259C4×Q8—731no—
260C4×D4—732no—
261C4×D4—732no—
262C4×D4—731no—
263C4×D4—731no—
264#117—731no—
265#117—732no—
266C2×C42—732no—
267C2×C42C22×D7311yescharacteristic
268C4⋊C8—21no—
269C4⋊C8—732no—
270C4⋊C8—732no—
271C4⋊C8—732no—
272C4⋊C8—731no—
273C4⋊C8—731no—
274C4⋊C8—1462no—
275C4⋊C8—1462no—
276C4⋊C8—1461no—
277C4⋊C8C4×D7311yescharacteristic
278C4⋊C8C4×D7311yescharacteristic
279C4⋊C8C22×D7312yes—
280C4⋊C8C22×D7311yescharacteristic
281C4⋊C8C22×D7311yescharacteristic
282C22⋊C8—21no—
283C22⋊C8—732no—
284C22⋊C8—732no—
285C22⋊C8—1462no—
286C22⋊C8—1462no—
287C22⋊C8—1461no—
288C22⋊C8C4×D7312yes—
289#97—732no—
290#97—732no—
291#97—1462no—
292C4×C8—21no—
293C4×C8—731no—
294C4×C8—731no—
295C4×C8—731no—
296C4×C8—731no—
297C4×C8—1462no—
298C4×C8—1461no—
299C4×C8C22×D7312yes—
300#41—2922no—
301C2×Q8—731no—
302C2×D4—732no—
303C2×D4—731no—
304C22×C4—732no—
305C22×C4—732no—
306C22×C4—732no—
307C22×C4C2×C4×D7311yescharacteristic
308C22×C4D4×D7311yescharacteristic
309C22×C4Q8×D7311yescharacteristic
310M16—81no—
311M16—2922no—
312M16—5842no—
313M16—5841no—
314M16—1464no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—22no—
318C2×C8—2921no—
319C2×C8—5842no—
320C2×C8—731no—
321C2×C8—731no—
322C2×C8—731no—
323C2×C8—731no—
324C2×C8—1461no—
325C2×C8—1461no—
326C2×C8—1462no—
327C2×C8—1462no—
328C2×C8C2×C4×D7312yes—
329C2×C8C2×C4×D7312yes—
330C4⋊C4—732no—
331C4⋊C4—732no—
332C4⋊C4—731no—
333C4⋊C4—731no—
334C22⋊C4—732no—
335C22⋊C4—732no—
336C22⋊C4—732no—
337C42—732no—
338C42—732no—
339C42—732no—
340C42C2×C4×D7311yescharacteristic
341C42D4×D7311yescharacteristic
342C42Q8×D7311yescharacteristic
343C42C23×D7311yescharacteristic
344C23—732no—
345C23C4⋊C4×D7311yescharacteristic
346Q8—1462no—
347D4—2922no—
348D4—1462no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—2922no—
355C2×C4—732no—
356C2×C4—732no—
357C2×C4—732no—
358C2×C4—1462no—
359C2×C4—1462no—
360C2×C4—1462no—
361C2×C4—1462no—
362C2×C4C4⋊C4×D7311yescharacteristic
363C2×C4C4⋊C4×D7311yescharacteristic
364C2×C4C4⋊C4×D7311yescharacteristic
365C2×C4C22×C4×D7311yescharacteristic
366C2×C4C2×D4×D7311yescharacteristic
367C2×C4C2×Q8×D7311yescharacteristic
368C8—22no—
369C8—22no—
370C8—41no—
371C8—42no—
372C8—41no—
373C8—2922no—
374C8—2921no—
375C8—2921no—
376C8—732no—
377C8—1461no—
378C8—1461no—
379C8—1461no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—1462no—
384C22—1462no—
385C22—1462no—
386C22C2×C4⋊C4×D7311yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—1462no—
391C4—1462no—
392C4—1462no—
393C4#1798863412yes—
394C4#131×D7311yescharacteristic
395C4#1798935211yescharacteristic
396C4#1798939611yescharacteristic
397C4#1798939711yescharacteristic
398C2—41no—
399C2—2922no—
400C2#2261849811yescharacteristic
401C2#2261852511yescharacteristic
402C2C2×#1798863411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1574C2
socleC22×C73C22×C4⋊C4
prime radicalC2×#11924028Q8
cosocleC42×C73C24
hypercenter#1574D73
hypocenterC73#17841
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
4. #22608720C2semidirect
5. #22608710C2semidirect
6. #22608700C2semidirect
7. #22608697C2semidirect
8. #22608686C2semidirect
9. #22608680C2semidirect
10. #22608677C2semidirect
11. C73×#1574C2semidirect
206. #1574D73semidirect
213. C73#17841semidirect

Maximal subgroups

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

subgroupindex
#226190612
#226190522
#226188922
#226087202
#226087102
#226087002
#226086972
#226086862
#226086802
#226086772
C73×#15742
#1784173