Finite Group Databasebeta

← D73⋊#2916 #34031224

Subgroups — D73⋊#2916 #34031224

Order 18688.

2586 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D73⋊#568C212yesmaximal
2#22626593C218yesmaximal, complemented
3#22626592C218yesmaximal, complemented
4D73⋊#430C216yesmaximal, complemented
5C2×D73⋊#108C216yesmaximal, complemented
6C2×#131×D73C211yesmaximal, characteristic
7#17989667—22no—
8#17989666C22116yes—
9#17989665—26no—
10D73⋊#131—28no—
11C2×D73⋊M16C22112yes—
12#17989602C22148yescomplemented
13C2×#14556662C22112yescomplemented
14D73⋊#108C2214yes—
15D73⋊#108C22112yes—
16D73⋊#108C22112yescomplemented
17D73⋊#108C22112yescomplemented
18C2×#14556661C22112yescomplemented
19C2×#41×D73C2211yescharacteristic
20C2×#14556599C413yes—
21C2×#14556598C411yescharacteristic
22C2×#14556597C413yes—
23#131×D73C414yes—
24#131×D73C414yes—
25#131×D73C2214yes—
26#131×D73C2214yes—
27C2×M16×D73C2213yes—
28C22×C8×D73C2213yes—
29C2×#131×C73C411yescharacteristic
30#14556679—216no—
31#14556678—248no—
32C2×#11924038C23124yes—
33D73⋊M16—212no—
34D73⋊M16—212no—
35D73⋊M16C2318yes—
36D73⋊M16C23124yes—
37C2×#11924037—212no—
38C2×#11924036—212no—
39#14556662C2318yes—
40#14556662C23124yes—
41#14556661C2318yes—
42#14556661C23124yes—
43C2×#11924029D411yescharacteristic
44C2×#11924028C2×C413yes—
45C2×#11924027D413yes—
46#41×D73C2×C414yes—
47#41×D73D414yes—
48#41×D73Q814yes—
49#41×D73C2314yes—
50C2×Q8×D73Q811yescharacteristic
51C2×D4×D73Q813yes—
52C22×C4×D73C2313yes—
53#14556599C2×C4112yes—
54#14556599C2×C4112yes—
55#14556598C2×C414yes—
56#14556598C2×C414yes—
57#14556597C2×C4112yes—
58#14556597C2×C4112yes—
59C2×#11924012C2×C413yes—
60C2×#11924011C2×C416yes—
61M16×D73C2×C4112yes—
62M16×D73C23112yes—
63C22×#10596831C2×C413yes—
64C2×C8×D73C2×C416yes—
65C2×C8×D73C2×C416yes—
66C2×C8×D73C2×C413yes—
67C2×C8×D73C2×C413yes—
68C2×C8×D73C2311yescharacteristic
69C2×C8×D73C2316yes—
70C2×C8×D73C2313yes—
71C2×C8×D73C2316yes—
72C2×#41×C73C2×C411yescharacteristic
73#131×C73C2×C414yes—
74#131×C73C2×C414yes—
75C2×M16×C73C2×C413yes—
76C22×C8×C73C2×C413yes—
77#11924038—224no—
78#11924038C24116yes—
79#11924037—28no—
80#11924037—224no—
81#11924036—28no—
82#11924036—224no—
83C2×#10596833—224no—
84C23×D73C2×Q813yes—
85#11924029C4⋊C414yes—
86#11924029C2×D414yes—
87#11924028C4⋊C4112yes—
88#11924028C22×C4112yes—
89#11924027C4⋊C4112yes—
90#11924027C2×D4112yes—
91C2×Dic146C4⋊C413yes—
92Q8×D73C4⋊C414yes—
93Q8×D73C2×Q814yes—
94C2×D292C4⋊C413yes—
95C2×C22⋊D73C4⋊C416yes—
96D4×D73C4⋊C4112yes—
97D4×D73C2×Q8112yes—
98C22×Dic73C2×D413yes—
99C2×C4×D73C22×C416yes—
100C2×C4×D73C22×C413yes—
101C2×C4×D73C2×D416yes—
102C2×C4×D73C2×D413yes—
103C2×C4×D73C2×Q813yes—
104C2×C4×D73C2×Q816yes—
105C2×C4×D73C2411yescharacteristic
106C2×C4×D73C2416yes—
107#11924012C22×C4112yes—
108#11924011C22×C4124yes—
109C2×#10596831C22×C411yescharacteristic
110C2×#10596831C22×C413yes—
111C2×#10596831C22×C416yes—
112C2×#10596831C22×C416yes—
113C8×D73C22×C411yescharacteristic
114C8×D73C22×C411yescharacteristic
115C8×D73C22×C416yes—
116C8×D73C22×C416yes—
117C8×D73C22×C416yes—
118C8×D73C22×C416yes—
119C8×D73C22×C416yes—
120C8×D73C2411yescharacteristic
121C8×D73C2411yescharacteristic
122C8×D73C2416yes—
123#41×C73C4⋊C414yes—
124#41×C73C22×C414yes—
125C2×Q8×C73C4⋊C411yescharacteristic
126C2×D4×C73C4⋊C413yes—
127C22×C4×C73C22×C413yes—
128M16×C73C22×C4112yes—
129C2×C8×C73C22×C411yescharacteristic
130C2×C8×C73C22×C413yes—
131C2×C8×C73C22×C416yes—
132C2×C8×C73C22×C416yes—
133C23×C73C2×C4⋊C413yes—
134C22×D73—46no—
135C22×D73C2×C4⋊C416yes—
136C22×D73C2×C4⋊C413yes—
137C22×D73C22×Q811yescharacteristic
138C22×D73C22×Q816yes—
139Q8×C73C2×C4⋊C414yes—
140D4×C73C2×C4⋊C4112yes—
141C2×C4×C73C2×C4⋊C413yes—
142C2×C4×C73C2×C4⋊C416yes—
143C2×C4×C73C23×C411yescharacteristic
144C2×C4×C73C23×C416yes—
145C22⋊D73C2×C4⋊C4124yes—
146C2×Dic73C2×C4⋊C413yes—
147C2×Dic73C2×C4⋊C416yes—
148C2×Dic73C22×D411yescharacteristic
149C2×Dic73C22×D416yes—
150D292C2×C4⋊C4112yes—
151C4×D73C2×C4⋊C416yes—
152C4×D73C2×C4⋊C416yes—
153C4×D73C2×C4⋊C416yes—
154C4×D73C23×C411yescharacteristic
155C4×D73C23×C416yes—
156C4×D73C22×D411yescharacteristic
157C4×D73C22×D416yes—
158C4×D73C22×Q811yescharacteristic
159C4×D73C22×Q816yes—
160C4×D73C2511yescharacteristic
161Dic146C2×C4⋊C4112yes—
162#10596833—216no—
163C8×C73C23×C411yescharacteristic
164C8×C73C23×C411yescharacteristic
165C8×C73C23×C416yes—
166#10596831C23×C411yescharacteristic
167#10596831C23×C411yescharacteristic
168#10596831C23×C416yes—
169C22×C73—43no—
170C22×C73C22×C4⋊C411yescharacteristic
171C22×C73C22×C4⋊C416yes—
172C2×D73—22no—
173C2×D73—212no—
174C2×D73—43no—
175C2×D73—46no—
176C2×D73C22×C4⋊C416yes—
177C2×D73C22×C4⋊C411yescharacteristic
178C2×D73C23×Q811yescharacteristic
179C4×C73C22×C4⋊C416yes—
180C4×C73C22×C4⋊C411yescharacteristic
181C4×C73C24×C411yescharacteristic
182Dic73C22×C4⋊C416yes—
183Dic73C22×C4⋊C411yescharacteristic
184Dic73C23×D411yescharacteristic
185C2×#2916—731nomaximal, Sylow
186C2×C73—21no—
187C2×C73—26no—
188C2×C73C23×C4⋊C411yescharacteristic
189D73—21no—
190D73—26no—
191D73#291612yescomplemented
192C2×#568—732no—
193C22×#131—731no—
194#2916—738no—
195#2916—738no—
196C2×#430—736no—
197C22×#108—736no—
198C73C2×#291611yescharacteristic, complemented, Sylow
199C22×#41—731no—
200#568—7316no—
201#568—1466no—
202#568—1462no—
203C2×#131—731no—
204C2×#131—734no—
205C2×#131—734no—
206C2×#131—734no—
207C2×#131—734no—
208C2×#131—733no—
209C2×#131—733no—
210C2×#131—1468no—
211C2×#131#6440811yescharacteristic
212C22×M16—733no—
213C22×M16—7312no—
214C23×C8—733no—
215#430—7348no—
216C2×#108—734no—
217C2×#108—7312no—
218C2×#108—7312no—
219C2×#108—7312no—
220C2×#108—7312no—
221C2×#108—7312no—
222C2×#41—734no—
223C2×#41—734no—
224C2×#41—734no—
225C2×#41—734no—
226C2×#41—731no—
227C2×#41—733no—
228C2×#41—733no—
229C2×#41C2×#6440811yescharacteristic
230C22×Q8—731no—
231C22×D4—733no—
232C23×C4—733no—
233#131—734no—
234#131—734no—
235#131—7312no—
236#131—7312no—
237#131—7312no—
238#131—7312no—
239#131—14648no—
240#131—14616no—
241#131C2×#6440814yes—
242#131C2×#6440814yes—
243C2×M16—733no—
244C2×M16—7312no—
245C2×M16—7312no—
246C2×M16—736no—
247C2×M16—738no—
248C2×M16—7324no—
249C2×M16—7324no—
250C2×M16—14612no—
251C2×M16—14612no—
252C2×M16—14612no—
253C2×M16C2×#6440813yes—
254C22×C8—733no—
255C22×C8—731no—
256C22×C8—733no—
257C22×C8—736no—
258C22×C8—736no—
259C22×C8—733no—
260C22×C8—733no—
261C22×C8—736no—
262C22×C8—736no—
263C22×C8—14612no—
264C22×C8C2×#6440813yes—
265#108—738no—
266#108—738no—
267#108—7324no—
268#108—7324no—
269C24—733no—
270#41—734no—
271#41—734no—
272#41—7312no—
273#41—7312no—
274#41—7312no—
275#41—7312no—
276#41C4⋊#6440814yes—
277#41C22×#6440814yes—
278C2×Q8—734no—
279C2×Q8—734no—
280C2×Q8—733no—
281C2×Q8C4⋊#6440811yescharacteristic
282C2×D4—736no—
283C2×D4—7312no—
284C2×D4—7312no—
285C2×D4—733no—
286C2×D4C4⋊#6440813yes—
287C22×C4—733no—
288C22×C4—733no—
289C22×C4—736no—
290C22×C4—731no—
291C22×C4—736no—
292C22×C4—736no—
293C22×C4—733no—
294C22×C4—733no—
295C22×C4—736no—
296C22×C4C22×#6440813yes—
297M16—7312no—
298M16—7324no—
299M16—7316no—
300M16—1468no—
301M16—14624no—
302M16—14624no—
303M16C22×#64408112yes—
304C2×C8—731no—
305C2×C8—733no—
306C2×C8—736no—
307C2×C8—736no—
308C2×C8—731no—
309C2×C8—731no—
310C2×C8—736no—
311C2×C8—736no—
312C2×C8—736no—
313C2×C8—736no—
314C2×C8—736no—
315C2×C8—731no—
316C2×C8—731no—
317C2×C8—736no—
318C2×C8—14624no—
319C2×C8—1468no—
320C2×C8—14624no—
321C2×C8C22×#6440811yescharacteristic
322C2×C8C22×#6440813yes—
323C2×C8C22×#6440816yes—
324C2×C8C22×#6440816yes—
325C23—2926no—
326C23—733no—
327C23—736no—
328C23—731no—
329C23—736no—
330C23C2×C4⋊#6440813yes—
331Q8—7312no—
332Q8C2×C4⋊#6440814yes—
333D4—7324no—
334D4—7312no—
335D4C2×C4⋊#64408112yes—
336C2×C4—736no—
337C2×C4—731no—
338C2×C4—733no—
339C2×C4—736no—
340C2×C4—736no—
341C2×C4—736no—
342C2×C4—736no—
343C2×C4—736no—
344C2×C4—731no—
345C2×C4—731no—
346C2×C4—736no—
347C2×C4—731no—
348C2×C4—731no—
349C2×C4—736no—
350C2×C4C2×C4⋊#6440813yes—
351C2×C4C2×C4⋊#6440816yes—
352C2×C4C23×#6440816yes—
353C2×C4C23×#6440811yescharacteristic
354C8—731no—
355C8—731no—
356C8—736no—
357C8—14616no—
358C8C23×#6440811yescharacteristic
359C8C23×#6440811yescharacteristic
360C8C23×#6440816yes—
361C22—43no—
362C22—2923no—
363C22—2926no—
364C22—731no—
365C22—731no—
366C22—736no—
367C22—1462no—
368C22—14612no—
369C22C22×C4⋊#6440811yescharacteristic
370C22C22×C4⋊#6440816yes—
371C4—731no—
372C4—731no—
373C4—736no—
374C4C22×C4⋊#6440816yes—
375C4C22×C4⋊#6440811yescharacteristic
376C4C24×#6440811yescharacteristic
377C2—21no—
378C2—26no—
379C2—732no—
380C2—1461no—
381C2—1466no—
382C2C23×C4⋊#6440811yescharacteristic
subgroupG/H
centerC4C22×C4⋊#64408
commutatorC4×C73C24×C4
FrattiniC4C24×#64408
FittingC2×#131×C73C4
socleC2×C73C23×C4⋊C4
prime radicalC2×#41×D73C22
cosocleC4×D73C25
hypercenterC2×#131#64408
hypocenterC73C2×#2916
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. #22626593C2semidirect
3. #22626592C2semidirect
4. D73⋊#430C2semidirect
5. C2×D73⋊#108C2semidirect
12. #17989602C22semidirect
13. C2×#14556662C22semidirect
16. D73⋊#108C22semidirect
17. D73⋊#108C22semidirect
18. C2×#14556661C22semidirect
191. D73#2916semidirect
198. C73C2×#2916semidirect

Maximal subgroups

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

subgroupindex
D73⋊#5682
#226265932
#226265922
D73⋊#4302
C2×D73⋊#1082
C2×#131×D732
C2×#291673