Finite Group Databasebeta

← #34030249

Subgroups — #34030249

Order 18688.

648 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
1#22626900C211yesmaximal, characteristic, complemented
2#22626898C211yesmaximal, characteristic, complemented
3#22626322C214yesmaximal, complemented
4#22626319C214yesmaximal, complemented
5C2×#17989510C211yesmaximal, characteristic, complemented
6#22626175C211yesmaximal, characteristic, complemented
7#22626173C211yesmaximal, characteristic, complemented
8C4×#14556665C211yesmaximal, characteristic, complemented
9C2×#17988701C211yesmaximal, characteristic
10#17989646—22no—
11#17989646C2214yescomplemented
12#17989645—22no—
13#17989645C2214yescomplemented
14#17989643—22no—
15C2×#14556665—22no—
16C2×#14556665C2211yescharacteristic
17C2×#14556665C2211yescharacteristic
18C2×#14556665C2211yescharacteristic
19C2×#14556665C2211yescharacteristic
20#17989510C2212yescomplemented
21#17989510C2212yescomplemented
22#17989486C2214yescomplemented
23#17989485C2214yescomplemented
24#17989475C2212yescomplemented
25C4×#11924031C2212yescomplemented
26C2×#14556611C411yescharacteristic
27C2×#14556599C2211yescharacteristic
28C2×#14556598C2211yescharacteristic
29#17988701C412yes—
30#17988701C412yes—
31#17988701C2212yes—
32#17988701C2212yes—
33C2×#14556526C411yescharacteristic
34C2×#14556519C411yescharacteristic
35C2×C4×#10596831C2211yescharacteristic
36C2×#104×C73C411yescharacteristic
37#14556666—24no—
38#14556665—24no—
39#14556665—21no—
40#14556665—21no—
41#14556665—21no—
42#14556665—21no—
43#14556665D412yes—
44#14556665D412yes—
45#14556665C2312yes—
46#14556665C2312yes—
47#14556664—24no—
48C2×#11924031—24no—
49C2×#11924031—21no—
50C2×#11924031—21no—
51C2×#11924031C2312yes—
52C2×#11924031C2312yes—
53C2×#11924028C2×C411yescharacteristic
54#14556611C812yes—
55#14556611C812yes—
56#14556611C2×C412yes—
57#14556611C2×C412yes—
58C2×#11924018C811yescharacteristic
59C2×#11924016C811yescharacteristic
60C2×#11924015C811yescharacteristic
61C2×#11924013C811yescharacteristic
62#14556599—21no—
63#14556599—21no—
64#14556599C2×C412yes—
65#14556599C2312yes—
66#14556598—21no—
67#14556598—21no—
68#14556598C2×C412yes—
69#14556598C2312yes—
70C2×#11924012—21no—
71C2×#11924012C2×C411yescharacteristic
72C2×#11924011—21no—
73C22×#10596831—21no—
74C22×#10596831C2×C411yescharacteristic
75C22×#10596831C2311yescharacteristic
76C2×C8×D73—21no—
77#14556526C2×C412yes—
78#14556526C2×C412yes—
79#14556519C2×C412yes—
80#14556519C2×C412yes—
81C4×#10596831C2×C411yescharacteristic
82C4×#10596831C2×C411yescharacteristic
83C4×#10596831C2311yescharacteristic
84C4×#10596831C2311yescharacteristic
85C2×#41×C73C2×C411yescharacteristic
86C2×M16×C73C2×C411yescharacteristic
87C2×C42×C73C2×C411yescharacteristic
88#104×C73C2×C412yes—
89#104×C73C2×C412yes—
90#11924031—22no—
91#11924031—22no—
92#11924031—22no—
93#11924031C2×D414yes—
94#11924028—21no—
95#11924028—21no—
96#11924028C2×C812yes—
97#11924028C22×C412yes—
98C2×Dic146C2×C811yescharacteristic
99C2×D292C2×C811yescharacteristic
100C2×C22⋊D73—21no—
101C2×C4×D73—21no—
102#11924018C2×C812yes—
103#11924018C2×C812yes—
104#11924016C2×C812yes—
105#11924016C2×C812yes—
106#11924015C2×C812yes—
107#11924015C2×C812yes—
108#11924013C2×C812yes—
109#11924013C2×C812yes—
110#11924012—21no—
111#11924012—22no—
112#11924012—22no—
113#11924012C22×C412yes—
114#11924011—22no—
115#11924011—22no—
116C2×#10596831—21no—
117C2×#10596831—22no—
118C2×#10596831—22no—
119C2×#10596831C2×C811yescharacteristic
120C2×#10596831C2×C811yescharacteristic
121C2×#10596831C2×C811yescharacteristic
122C2×#10596831C2×C811yescharacteristic
123C2×#10596831C22×C411yescharacteristic
124C2×#10596831C22×C411yescharacteristic
125C2×#10596831C22×C411yescharacteristic
126C2×#10596831C2×D411yescharacteristic
127C2×#10596831C2×D411yescharacteristic
128C2×#10596831#4111yescharacteristic
129C2×#10596831#4111yescharacteristic
130C2×#10596831C2411yescharacteristic
131C8×D73—22no—
132C8×D73—22no—
133#41×C73—21no—
134#41×C73—21no—
135#41×C73C2×C812yes—
136#41×C73C22×C412yes—
137C2×Q8×C73C2×C811yescharacteristic
138C2×D4×C73—21no—
139C2×D4×C73C2×C811yescharacteristic
140C22×C4×C73—21no—
141C22×C4×C73—21no—
142C22×C4×C73C22×C411yescharacteristic
143M16×C73—21no—
144M16×C73C22×C412yes—
145C2×C8×C73—21no—
146C42×C73—21no—
147C42×C73C22×C411yescharacteristic
148C42×C73C22×C411yescharacteristic
149C23×C73—21no—
150C23×C73#13111yescharacteristic
151C22×D73—21no—
152Q8×C73—21no—
153Q8×C73C22×C812yes—
154D4×C73—22no—
155D4×C73—22no—
156D4×C73—21no—
157D4×C73C22×C812yes—
158C2×C4×C73—21no—
159C2×C4×C73—21no—
160C2×C4×C73—22no—
161C2×C4×C73—22no—
162C2×C4×C73—21no—
163C2×C4×C73—42no—
164C2×C4×C73C4×D411yescharacteristic
165C2×C4×C73C4×D411yescharacteristic
166C2×C4×C73C22×C811yescharacteristic
167C2×C4×C73C22×C811yescharacteristic
168C2×C4×C73#13111yescharacteristic
169C2×C4×C73C23×C411yescharacteristic
170C22⋊D73—22no—
171C22⋊D73—22no—
172C2×Dic73—21no—
173D292—21no—
174D292C22×C812yes—
175C4×D73—22no—
176C4×D73—22no—
177Dic146—21no—
178Dic146C22×C812yes—
179C8×C73—22no—
180#10596831—22no—
181#10596831C4×D411yescharacteristic
182#10596831C4×D411yescharacteristic
183#10596831C22×C811yescharacteristic
184#10596831C22×C811yescharacteristic
185#10596831C22×C811yescharacteristic
186#10596831C22×C811yescharacteristic
187#10596831C22×D411yescharacteristic
188#10596831C2×#4111yescharacteristic
189C22×C73—22no—
190C22×C73—41no—
191C22×C73—81no—
192C22×C73C8×D411yescharacteristic
193C22×C73C8×D411yescharacteristic
194C22×C73C2×#13111yescharacteristic
195C2×D73—22no—
196C2×D73—81no—
197C4×C73—22no—
198C4×C73—22no—
199C4×C73—41no—
200C4×C73C8×D411yescharacteristic
201C4×C73C8×D411yescharacteristic
202C4×C73C2×C4×D411yescharacteristic
203C4×C73C23×C811yescharacteristic
204Dic73—22no—
205#33443—731nomaximal, Sylow
206C2×C73—21no—
207C2×C73—21no—
208C2×C73—21no—
209C2×C73—42no—
210C2×C73C2×C8×D411yescharacteristic
211D73—42no—
212#3407—731no—
213#3407—731no—
214C2×#443—731no—
215#2171—734no—
216#2170—734no—
217C2×#364—731no—
218#2117—731no—
219#2117—731no—
220C4×M32—731no—
221C73#3344311yescharacteristic, complemented, Sylow
222C2×#135—731no—
223C2×#131—731no—
224C2×#131—731no—
225#504—734no—
226#504—734no—
227#504—1462no—
228#504—1462no—
229C2×M32—731no—
230C2×M32—731no—
231C2×M32—731no—
232C2×M32—731no—
233C2×M32—1462no—
234C2×M32—1462no—
235#443—732no—
236#443—732no—
237#443—732no—
238#443—732no—
239C2×#108—731no—
240C2×#104—731no—
241C2×#104#6440811yescharacteristic
242C2×C4×C8—731no—
243#364—732no—
244#364—732no—
245#350—734no—
246#350—734no—
247#346—732no—
248C4×C16—732no—
249C2×#41—731no—
250C2×#41C2×#6440811yescharacteristic
251#135—732no—
252#135—732no—
253#135—732no—
254#135—732no—
255C2×Q16—731no—
256C2×SD16—731no—
257C2×SD16—731no—
258C2×D8—731no—
259#131—732no—
260#131—732no—
261#131—732no—
262#131—732no—
263#131—1461no—
264#131—1461no—
265#131—1461no—
266#131—1461no—
267C2×M16—731no—
268C2×M16—1461no—
269C2×M16—1461no—
270C2×M16C2×#6440811yescharacteristic
271C22×C8—731no—
272C22×C8—731no—
273C22×C8—1461no—
274C22×C8—1461no—
275C2×C42C2×#6440811yescharacteristic
276M32—732no—
277M32—732no—
278M32—732no—
279M32—732no—
280M32—1464no—
281M32—1464no—
282M32—1461no—
283M32—1461no—
284M32—1461no—
285M32—1461no—
286C2×C16—732no—
287C2×C16—732no—
288C2×C16—1464no—
289C2×C16—1464no—
290C2×C16—1461no—
291C2×C16—1461no—
292#108—732no—
293#108—732no—
294#104—732no—
295#104—732no—
296#104C2×#6440812yes—
297#104C2×#6440812yes—
298C4×C8—731no—
299C4×C8—731no—
300C4×C8—731no—
301C4×C8—731no—
302#41—21no—
303#41—21no—
304#41—732no—
305#41—732no—
306#41—1461no—
307#41—1461no—
308#41#1192403612yes—
309#41C22×#6440812yes—
310C2×Q8—731no—
311C2×Q8#1192403611yescharacteristic
312C2×D4—21no—
313C2×D4—731no—
314C2×D4—1461no—
315C2×D4#1192403611yescharacteristic
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—1461no—
319C22×C4C22×#6440811yescharacteristic
320Q16—732no—
321Q16—732no—
322SD16—732no—
323SD16—732no—
324SD16—732no—
325SD16—732no—
326D8—732no—
327D8—732no—
328M16—21no—
329M16—732no—
330M16—1462no—
331M16—1462no—
332M16—1462no—
333M16—1462no—
334M16—1461no—
335M16C22×#6440812yes—
336C2×C8—21no—
337C2×C8—731no—
338C2×C8—731no—
339C2×C8—731no—
340C2×C8—731no—
341C2×C8—731no—
342C2×C8—731no—
343C2×C8—731no—
344C2×C8—731no—
345C2×C8—731no—
346C2×C8—731no—
347C2×C8—731no—
348C2×C8—731no—
349C2×C8—1462no—
350C2×C8—1462no—
351C2×C8—1462no—
352C2×C8—1462no—
353C2×C8—1461no—
354C42—21no—
355C42C22×#6440811yescharacteristic
356C42C22×#6440811yescharacteristic
357C16—734no—
358C16—1462no—
359C16—1462no—
360C16—1462no—
361C23—21no—
362C23—1461no—
363C23#1455667811yescharacteristic
364Q8—21no—
365Q8—732no—
366Q8—1461no—
367Q8C2×#1192403612yes—
368D4—22no—
369D4—22no—
370D4—21no—
371D4—732no—
372D4—1462no—
373D4—1462no—
374D4—1461no—
375D4C2×#1192403612yes—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—1461no—
383C2×C4—1462no—
384C2×C4—1462no—
385C2×C4D4×#6440811yescharacteristic
386C2×C4D4×#6440811yescharacteristic
387C2×C4C2×#1192403611yescharacteristic
388C2×C4C2×#1192403611yescharacteristic
389C2×C4#1455667811yescharacteristic
390C2×C4C23×#6440811yescharacteristic
391C8—22no—
392C8—731no—
393C8—731no—
394C8—731no—
395C8—731no—
396C8—731no—
397C8—731no—
398C8—731no—
399C8—731no—
400C8—1462no—
401C22—22no—
402C22—41no—
403C22—81no—
404C22—5841no—
405C22—1462no—
406C22#1798961411yescharacteristic
407C22#1798961411yescharacteristic
408C22C2×#1455667811yescharacteristic
409C4—22no—
410C4—22no—
411C4—41no—
412C4—1462no—
413C4#1798961411yescharacteristic
414C4#1798961411yescharacteristic
415C4C2×D4×#6440811yescharacteristic
416C4C22×#1192403611yescharacteristic
417C2—21no—
418C2—21no—
419C2—21no—
420C2—42no—
421C2—2922no—
422C2C2×#1798961411yescharacteristic
subgroupG/H
centerC4C2×D4×#64408
commutatorC4×C73C23×C8
FrattiniC2×C4C23×#64408
FittingC2×#104×C73C4
socleC2×C73C2×C8×D4
prime radicalC2×#14556611C4
cosocleC2×#10596831C24
hypercenterC2×#104#64408
hypocenterC73#33443
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. #22626900C2semidirect
2. #22626898C2semidirect
3. #22626322C2semidirect
4. #22626319C2semidirect
5. C2×#17989510C2semidirect
6. #22626175C2semidirect
7. #22626173C2semidirect
8. C4×#14556665C2semidirect
11. #17989646C22semidirect
13. #17989645C22semidirect
20. #17989510C22semidirect
21. #17989510C22semidirect
22. #17989486C22semidirect
23. #17989485C22semidirect
24. #17989475C22semidirect
25. C4×#11924031C22semidirect
221. C73#33443semidirect

Maximal subgroups

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

subgroupindex
#226269002
#226268982
#226263222
#226263192
C2×#179895102
#226261752
#226261732
C4×#145566652
C2×#179887012
#3344373