Finite Group Databasebeta

← #33002284

Subgroups — #33002284

Order 18688.

404 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#427×D73C211yesmaximal, characteristic
2C2×#17988366C211yesmaximal, characteristic
3#22609966C211yesmaximal, characteristic
4#22608028C211yesmaximal, characteristic, complemented
5#22608027C211yesmaximal, characteristic, complemented
6#22608026C211yesmaximal, characteristic, complemented
7C73×#1382C211yesmaximal, characteristic, complemented
8C22×C8×D73C2211yescharacteristic
9#117×D73—21no—
10C22×#11924003C2211yescharacteristic
11C2×#14556527C2211yescharacteristic
12#17988625C2211yescharacteristic
13#17988624C411yescharacteristic
14#17988624C411yescharacteristic
15#17988623—21no—
16#17988622—21no—
17#107×D73C411yescharacteristic
18#107×D73C411yescharacteristic
19#106×D73—21no—
20#17988550—21no—
21#17988366—21no—
22#17988366—21no—
23#17988351—21no—
24C22×C16×C73C2211yescharacteristic
25C2×#108×C73C2211yescharacteristic
26#427×C73C2211yescharacteristic
27C22×C4×D73D411yescharacteristic
28C2×#11924012—21no—
29C22×#10596831D411yescharacteristic
30C2×C8×D73—21no—
31C2×C8×D73—21no—
32C2×C8×D73—21no—
33C2×C8×D73—21no—
34C2×C8×D73C2×C411yescharacteristic
35C2×C8×D73C2×C411yescharacteristic
36C2×C8×D73D411yescharacteristic
37C2×C8×D73D411yescharacteristic
38#14556550—21no—
39#14556549—21no—
40#14556549—21no—
41#14556548—41no—
42#14556547—41no—
43C4⋊C4×D73—21no—
44C4⋊C4×D73—21no—
45C22⋊C4×D73—41no—
46C42×D73—41no—
47C2×#11924003—21no—
48C2×#11924003—21no—
49C2×#11924003—21no—
50#14556527—21no—
51#14556527—21no—
52#14556525C2×C411yescharacteristic
53#14556525C2×C411yescharacteristic
54#14556524—21no—
55#14556524—21no—
56#14556523—21no—
57#14556522—21no—
58#14556522—21no—
59#14556503—41no—
60#14556503—41no—
61C2×M16×C73—21no—
62C22×C8×C73C2311yescharacteristic
63#117×C73—21no—
64C2×C16×C73—21no—
65C2×C16×C73—21no—
66C2×C16×C73—21no—
67#108×C73—21no—
68#108×C73—21no—
69#107×C73C2×C411yescharacteristic
70#107×C73C2×C411yescharacteristic
71#106×C73—21no—
72C23×D73SD1611yescharacteristic
73C22×Dic73SD1611yescharacteristic
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77C2×C4×D73—21no—
78C2×C4×D73—41no—
79C2×C4×D73—41no—
80C2×C4×D73C22⋊C411yescharacteristic
81C2×C4×D73C22⋊C411yescharacteristic
82C2×C4×D73D811yescharacteristic
83C2×C4×D73D811yescharacteristic
84#11924012—41no—
85#11924012—41no—
86C2×#10596831—21no—
87C2×#10596831—21no—
88C2×#10596831—41no—
89C2×#10596831C22⋊C411yescharacteristic
90C2×#10596831C22⋊C411yescharacteristic
91C8×D73—21no—
92C8×D73—21no—
93C8×D73—21no—
94C8×D73—21no—
95C8×D73—21no—
96C8×D73—21no—
97C8×D73—21no—
98C8×D73—21no—
99C4⋊Dic73—21no—
100C4⋊Dic73—21no—
101#11924007—41no—
102#11924007—41no—
103C22⋊Dic73—41no—
104#11924005—41no—
105#11924005—41no—
106C4×Dic73—41no—
107C4×Dic73—41no—
108C4×Dic73—41no—
109#11924003—41no—
110C22×C4×C73C2×D411yescharacteristic
111M16×C73—41no—
112M16×C73—41no—
113C2×C8×C73—41no—
114C2×C8×C73C22×C411yescharacteristic
115C2×C8×C73C2×D411yescharacteristic
116C2×C8×C73#4111yescharacteristic
117C2×C8×C73#4111yescharacteristic
118C2×C8×C73#4111yescharacteristic
119C2×C8×C73#4111yescharacteristic
120C4⋊C4×C73—21no—
121C4⋊C4×C73—21no—
122C22⋊C4×C73—41no—
123C42×C73—41no—
124C16×C73—41no—
125C23×C73C2×SD1611yescharacteristic
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—22no—
129C22×D73—41no—
130C22×D73#10211yescharacteristic
131C22×D73#10211yescharacteristic
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73C2×C22⋊C411yescharacteristic
135C2×C4×C73#12311yescharacteristic
136C2×C4×C73#12311yescharacteristic
137C2×C4×C73C2×D811yescharacteristic
138C2×C4×C73#13711yescharacteristic
139C2×C4×C73#13711yescharacteristic
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73#10211yescharacteristic
145C2×Dic73#10211yescharacteristic
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—21no—
149C4×D73—21no—
150C4×D73—21no—
151C4×D73—21no—
152C4×D73—21no—
153C4×D73—21no—
154C4×D73—82no—
155C4×D73—82no—
156C8×C73—81no—
157C8×C73#11711yescharacteristic
158C8×C73#11711yescharacteristic
159C8×C73#12311yescharacteristic
160C8×C73#12311yescharacteristic
161#10596831—21no—
162#10596831—21no—
163#10596831—81no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73C2×#10211yescharacteristic
167C22×C73#48311yescharacteristic
168C22×C73#48311yescharacteristic
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—21no—
172C2×D73—21no—
173C2×D73—21no—
174C2×D73—42no—
175C2×D73—42no—
176C2×D73#35912yes—
177C4×C73—81no—
178C4×C73—81no—
179C4×C73#38111yescharacteristic
180C4×C73#41911yescharacteristic
181C4×C73#48011yescharacteristic
182C4×C73#48011yescharacteristic
183Dic73—21no—
184Dic73—21no—
185Dic73—81no—
186Dic73—81no—
187#12869—731nomaximal, Sylow
188C2×C73—21no—
189C2×C73—21no—
190C2×C73#182311yescharacteristic
191C2×C73C2×#35911yescharacteristic
192C2×C73#214311yescharacteristic
193D73—22no—
194D73—41no—
195C2×#427—731no—
196C2×C22⋊C16—731no—
197#1810—731no—
198#1382—731no—
199#1382—731no—
200#1382—731no—
201#1382D7311yescharacteristic, complemented
202C73#1286911yescharacteristic, complemented, Sylow
203C23×C8—731no—
204C2×#117—1461no—
205C22×C16—731no—
206C22×C16C2×D7311yescharacteristic
207C2×#108—731no—
208C2×#108C2×D7311yescharacteristic
209#427—731no—
210#427—731no—
211#427—731no—
212#427—1461no—
213#427—1461no—
214#427C2×D7311yescharacteristic
215C2×#107—731no—
216C2×#107—731no—
217C2×#106—1461no—
218#407—1461no—
219C22⋊C16—1461no—
220C22⋊C16—1461no—
221#341—1461no—
222C23×C4—731no—
223C2×M16—21no—
224C2×M16—1461no—
225C22×C8—731no—
226C22×C8—731no—
227C22×C8—731no—
228C22×C8—731no—
229C22×C8—731no—
230C22×C8—1461no—
231C22×C8—1461no—
232C22×C8—1461no—
233C22×C8—1461no—
234C22×C8C22×D7311yescharacteristic
235#117—21no—
236#117—2921no—
237#117—2921no—
238#117—1461no—
239#117—1461no—
240#117—1461no—
241C2×C4⋊C4—1461no—
242C2×C4⋊C4—1461no—
243C2×C22⋊C4—2921no—
244C2×C42—2921no—
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—1461no—
249C2×C16—1461no—
250C2×C16—1461no—
251#108—21no—
252#108—21no—
253#108—1461no—
254#108—1461no—
255#107—731no—
256#107—731no—
257#107—1461no—
258#107—1461no—
259#107C4×D7311yescharacteristic
260#107C4×D7311yescharacteristic
261#106—21no—
262#106—1461no—
263#106—1461no—
264#106—1461no—
265C22⋊C8—2921no—
266C22⋊C8—2921no—
267C24—731no—
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—731no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4—1461no—
278C22×C4—1461no—
279C22×C4D4×D7311yescharacteristic
280M16—41no—
281M16—41no—
282M16—2921no—
283M16—2921no—
284C2×C8—41no—
285C2×C8—2921no—
286C2×C8—731no—
287C2×C8—731no—
288C2×C8—1461no—
289C2×C8—1461no—
290C2×C8—1461no—
291C2×C8—1461no—
292C2×C8—1461no—
293C2×C8—1461no—
294C2×C8—1461no—
295C2×C8—1461no—
296C2×C8—1461no—
297C2×C8—1461no—
298C2×C8C2×C4×D7311yescharacteristic
299C2×C8D4×D7311yescharacteristic
300C2×C8#1192402711yescharacteristic
301C2×C8#1192402811yescharacteristic
302C2×C8#1192402811yescharacteristic
303C2×C8#1192402911yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—2921no—
307C4⋊C4—2921no—
308C4⋊C4—1461no—
309C4⋊C4—1461no—
310C22⋊C4—41no—
311C22⋊C4—2921no—
312C22⋊C4—2921no—
313C22⋊C4—2921no—
314C42—41no—
315C42—2921no—
316C42—2921no—
317C42—2921no—
318C16—41no—
319C16—2921no—
320C23—2921no—
321C23—731no—
322C23—731no—
323C23—1462no—
324C23—1461no—
325C23—1461no—
326C23SD16×D7311yescharacteristic
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—5842no—
332C2×C4—5842no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4C22⋊C4×D7311yescharacteristic
346C2×C4#1455657311yescharacteristic
347C2×C4#1455657611yescharacteristic
348C2×C4D8×D7311yescharacteristic
349C2×C4#1455662011yescharacteristic
350C2×C4#1455662311yescharacteristic
351C8—81no—
352C8—5841no—
353C8—1461no—
354C8—1461no—
355C8#1455654811yescharacteristic
356C8#1455654911yescharacteristic
357C8#1455657311yescharacteristic
358C8#1455657611yescharacteristic
359C22—21no—
360C22—21no—
361C22—2922no—
362C22—2922no—
363C22—732no—
364C22—1461no—
365C22—1461no—
366C22—1461no—
367C22—1461no—
368C22—1461no—
369C22#102×D7311yescharacteristic
370C22#1798891611yescharacteristic
371C22#1798891911yescharacteristic
372C4—81no—
373C4—81no—
374C4—5841no—
375C4—5841no—
376C4—1461no—
377C4—1461no—
378C4#1798844911yescharacteristic
379C4#1798859411yescharacteristic
380C4#1798889911yescharacteristic
381C4#1798890211yescharacteristic
382C2—21no—
383C2—21no—
384C2—2921no—
385C2—1462no—
386C2#2261001611yescharacteristic
387C2#359×D7311yescharacteristic
388C2#2261165711yescharacteristic
subgroupG/H
centerC2×C4D8×D73
commutatorC2×C8×C73C22×C4
FrattiniC22×C8C22×D73
FittingC73×#1382C2
socleC22×C73C2×#102
prime radicalC23×D73SD16
cosocleC22×C8×C73C23
hypercenter#1382D73
hypocenterC73#12869
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
4. #22608028C2semidirect
5. #22608027C2semidirect
6. #22608026C2semidirect
7. C73×#1382C2semidirect
201. #1382D73semidirect
202. C73#12869semidirect

Maximal subgroups

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

subgroupindex
#427×D732
C2×#179883662
#226099662
#226080282
#226080272
#226080262
C73×#13822
#1286973