Finite Group Databasebeta

← #33002893

Subgroups — #33002893

Order 18688.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988707C211yesmaximal, characteristic
2#22611559C211yesmaximal, characteristic, complemented
3#22611558C211yesmaximal, characteristic, complemented
4#22611551C211yesmaximal, characteristic, complemented
5#22608014C211yesmaximal, characteristic, complemented
6#22608010C211yesmaximal, characteristic, complemented
7C73×#3407C211yesmaximal, characteristic, complemented
8C2×#14556611C411yescharacteristic
9C2×#14556597C2211yescharacteristic
10C2×#14556531C2211yescharacteristic
11C2×#14556531C2211yescharacteristic
12#17988707—22no—
13#17988707—22no—
14C2×#14556526C411yescharacteristic
15C2×#14556518C411yescharacteristic
16C2×#14556517C411yescharacteristic
17C2×#14556501C2211yescharacteristic
18#17988371—22no—
19#17988370—22no—
20#17988368—22no—
21C2×#131×C73C2211yescharacteristic
22#504×C73—22no—
23#504×C73—22no—
24C2×M32×C73—22no—
25C2×M32×C73C2211yescharacteristic
26C2×M32×C73C2211yescharacteristic
27C2×#11924028C2×C411yescharacteristic
28#14556611—22no—
29#14556611—22no—
30C2×#11924018C811yescharacteristic
31C2×#11924016C811yescharacteristic
32C2×#11924015C811yescharacteristic
33C2×#11924013C811yescharacteristic
34#14556597—21no—
35#14556597—21no—
36#14556597—21no—
37#14556597—21no—
38C2×#11924012C2×C411yescharacteristic
39C2×#11924011—21no—
40C22×#10596831C2×C411yescharacteristic
41C2×C8×D73—21no—
42C2×C4×Dic73C2×C411yescharacteristic
43#14556531—21no—
44#14556531—21no—
45#14556531—21no—
46#14556531—21no—
47C2×#11924003—21no—
48C2×#11924003—21no—
49#14556526—22no—
50#14556518—22no—
51#14556517—22no—
52#14556501—21no—
53#14556501—21no—
54C2×#41×C73C2×C411yescharacteristic
55#131×C73—21no—
56#131×C73—21no—
57#131×C73D412yes—
58#131×C73D412yes—
59C2×M16×C73—21no—
60C2×M16×C73C2×C411yescharacteristic
61C22×C8×C73—21no—
62C22×C8×C73C2311yescharacteristic
63M32×C73—24no—
64M32×C73—21no—
65M32×C73—21no—
66M32×C73—21no—
67M32×C73D412yes—
68C2×C16×C73—24no—
69C2×C16×C73—21no—
70C2×C16×C73D412yes—
71#11924028—21no—
72#11924028—21no—
73#11924028—21no—
74#11924028—21no—
75C2×Dic146C2×C811yescharacteristic
76C2×D292C2×C811yescharacteristic
77C2×C22⋊D73—21no—
78C22×Dic73—21no—
79C2×C4×D73—21no—
80#11924018—22no—
81#11924016—22no—
82#11924015—22no—
83#11924013—22no—
84#11924012—21no—
85#11924012—21no—
86#11924011—41no—
87#11924011—41no—
88C2×#10596831—21no—
89C2×#10596831—21no—
90C2×#10596831—21no—
91C2×#10596831C2×C811yescharacteristic
92C2×#10596831C2×C811yescharacteristic
93C8×D73—41no—
94C8×D73—41no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97#11924003—41no—
98#11924003—41no—
99#41×C73—21no—
100#41×C73—21no—
101#41×C73C22⋊C412yes—
102#41×C73M1612yes—
103C2×Q8×C73C2×C811yescharacteristic
104C2×D4×C73—21no—
105C2×D4×C73C2×C811yescharacteristic
106C22×C4×C73—21no—
107C22×C4×C73C22×C411yescharacteristic
108M16×C73—21no—
109M16×C73—22no—
110M16×C73—22no—
111M16×C73C22⋊C412yes—
112C2×C8×C73—21no—
113C2×C8×C73—22no—
114C2×C8×C73—22no—
115C2×C8×C73C2×D411yescharacteristic
116C2×C8×C73C2×D411yescharacteristic
117C2×C8×C73C2×D411yescharacteristic
118C2×C8×C73C2×D411yescharacteristic
119C2×C8×C73#4111yescharacteristic
120C2×C8×C73#4111yescharacteristic
121C16×C73—22no—
122C16×C73—22no—
123C23×C73—21no—
124C23×C73#13111yescharacteristic
125C22×D73—21no—
126Q8×C73—21no—
127Q8×C73C22⋊C812yes—
128D4×C73—22no—
129D4×C73—22no—
130D4×C73—21no—
131D4×C73C22⋊C812yes—
132C2×C4×C73—21no—
133C2×C4×C73—22no—
134C2×C4×C73—22no—
135C2×C4×C73C2×C22⋊C411yescharacteristic
136C2×C4×C73C4×D411yescharacteristic
137C2×C4×C73C4×D411yescharacteristic
138C2×C4×C73C22×C811yescharacteristic
139C2×C4×C73C2×M1611yescharacteristic
140C2×C4×C73#13111yescharacteristic
141C22⋊D73—41no—
142C22⋊D73—41no—
143C2×Dic73—21no—
144C2×Dic73—41no—
145C2×Dic73—81no—
146D292—21no—
147D292—21no—
148C4×D73—41no—
149C4×D73—41no—
150Dic146—21no—
151Dic146—21no—
152C8×C73—22no—
153C8×C73#12011yescharacteristic
154C8×C73#12111yescharacteristic
155C8×C73#12111yescharacteristic
156C8×C73#12311yescharacteristic
157#10596831—21no—
158#10596831—21no—
159#10596831—41no—
160C22×C73—22no—
161C22×C73—41no—
162C22×C73—81no—
163C22×C73#40811yescharacteristic
164C22×C73C8×D411yescharacteristic
165C22×C73#43511yescharacteristic
166C2×D73—41no—
167C2×D73—81no—
168C4×C73—22no—
169C4×C73#38611yescharacteristic
170C4×C73C2×C22⋊C811yescharacteristic
171C4×C73C8×D411yescharacteristic
172C4×C73#43511yescharacteristic
173Dic73—41no—
174Dic73—81no—
175#12986—731nomaximal, Sylow
176C2×C73—21no—
177C2×C73—21no—
178C2×C73—21no—
179C2×C73—42no—
180C2×C73#186911yescharacteristic
181D73—81no—
182#3407D7311yescharacteristic, complemented
183C2×#444—731no—
184#2117—731no—
185#2117—731no—
186#2115—731no—
187#1377—731no—
188#1375—731no—
189C73#1298611yescharacteristic, complemented, Sylow
190C2×#135—731no—
191C2×#131—731no—
192C2×#131C2×D7311yescharacteristic
193#504—22no—
194#504—22no—
195C2×M32—22no—
196C2×M32—731no—
197C2×M32—731no—
198C2×M32C2×D7311yescharacteristic
199C2×M32C2×D7311yescharacteristic
200#444—1462no—
201#444—1462no—
202C2×#108—731no—
203C2×#104—731no—
204C2×#104—731no—
205C2×#97—731no—
206#350—1462no—
207#350—1462no—
208#349—1462no—
209C2×#41—731no—
210C2×#41C4×D7311yescharacteristic
211#135—1462no—
212#135—1462no—
213C2×Q16—731no—
214C2×SD16—731no—
215C2×SD16—731no—
216C2×D8—731no—
217#131—21no—
218#131—21no—
219#131—1461no—
220#131—1461no—
221#131—1461no—
222#131—1461no—
223#131D29212yes—
224#131C22⋊D7312yes—
225C2×M16—21no—
226C2×M16—731no—
227C2×M16—1461no—
228C2×M16C4×D7311yescharacteristic
229C22×C8—21no—
230C22×C8—731no—
231C22×C8—1461no—
232C22×C8C22×D7311yescharacteristic
233C2×C42—731no—
234M32—24no—
235M32—21no—
236M32—21no—
237M32—21no—
238M32—1461no—
239M32—1461no—
240M32—1461no—
241M32—1461no—
242M32C22⋊D7312yes—
243C2×C16—24no—
244C2×C16—21no—
245C2×C16—1461no—
246C2×C16—1461no—
247C2×C16C22⋊D7312yes—
248#108—1462no—
249#104—1462no—
250#104—1462no—
251#97—1461no—
252#97—1461no—
253#41—21no—
254#41—21no—
255#41—1461no—
256#41—1461no—
257#41—1461no—
258#41—1461no—
259#41#1192400512yes—
260#41#1192401112yes—
261C2×Q8—731no—
262C2×Q8C8×D7311yescharacteristic
263C2×D4—21no—
264C2×D4—731no—
265C2×D4—1461no—
266C2×D4C8×D7311yescharacteristic
267C22×C4—21no—
268C22×C4—1461no—
269C22×C4—1461no—
270C22×C4C2×C4×D7311yescharacteristic
271Q16—1462no—
272SD16—1462no—
273SD16—1462no—
274D8—1462no—
275M16—21no—
276M16—22no—
277M16—22no—
278M16—2921no—
279M16—2921no—
280M16—1461no—
281M16—1461no—
282M16#1192400512yes—
283C2×C8—21no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—2921no—
287C2×C8—2921no—
288C2×C8—731no—
289C2×C8—731no—
290C2×C8—1461no—
291C2×C8—1461no—
292C2×C8—1461no—
293C2×C8C2×C22⋊D7311yescharacteristic
294C2×C8C2×C22⋊D7311yescharacteristic
295C2×C8C2×C22⋊D7311yescharacteristic
296C2×C8C2×D29211yescharacteristic
297C2×C8#1192402811yescharacteristic
298C2×C8#1192402811yescharacteristic
299C42—1461no—
300C42—1461no—
301C16—22no—
302C16—22no—
303C16—2921no—
304C16—2921no—
305C23—21no—
306C23—1461no—
307C23#1455659711yescharacteristic
308Q8—21no—
309Q8—1461no—
310Q8—1461no—
311Q8#1455650312yes—
312D4—22no—
313D4—22no—
314D4—21no—
315D4—2921no—
316D4—2921no—
317D4—1461no—
318D4—1461no—
319D4#1455650312yes—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—2921no—
324C2×C4—2921no—
325C2×C4—2921no—
326C2×C4—5841no—
327C2×C4—1461no—
328C2×C4C2×#1192400511yescharacteristic
329C2×C4C4×C22⋊D7311yescharacteristic
330C2×C4C4×C22⋊D7311yescharacteristic
331C2×C4C2×C8×D7311yescharacteristic
332C2×C4C2×#1192401111yescharacteristic
333C2×C4#1455659711yescharacteristic
334C8—22no—
335C8—2921no—
336C8—1461no—
337C8—1461no—
338C8#1455656011yescharacteristic
339C8#1455656511yescharacteristic
340C8#1455656511yescharacteristic
341C8#1455657411yescharacteristic
342C22—22no—
343C22—41no—
344C22—81no—
345C22—2921no—
346C22—5841no—
347C22#1798855311yescharacteristic
348C22C8×C22⋊D7311yescharacteristic
349C22#1798865811yescharacteristic
350C4—22no—
351C4—2921no—
352C4—5841no—
353C4#1798846611yescharacteristic
354C4C2×#1455650311yescharacteristic
355C4C8×C22⋊D7311yescharacteristic
356C4#1798865811yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—5841no—
362C2#2261022311yescharacteristic
subgroupG/H
centerC4#17988466
commutatorC2×C4×C73C22×C8
FrattiniC22×C8C22×D73
FittingC73×#3407C2
socleC2×C73#1869
prime radicalC2×#14556611C4
cosocleC22×C8×C73C23
hypercenter#3407D73
hypocenterC73#12986
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C8 ◁ #3407

Complements

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

NH ≅ G/Ntype
2. #22611559C2semidirect
3. #22611558C2semidirect
4. #22611551C2semidirect
5. #22608014C2semidirect
6. #22608010C2semidirect
7. C73×#3407C2semidirect
182. #3407D73semidirect
189. C73#12986semidirect

Maximal subgroups

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

subgroupindex
C2×#179887072
#226115592
#226115582
#226115512
#226080142
#226080102
C73×#34072
#1298673