Finite Group Databasebeta

← C2×#22627151 #34034834

Subgroups — C2×#22627151 #34034834

Order 18688.

654 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989709C211yesmaximal, characteristic, complemented
2C2×#17989708C211yesmaximal, characteristic, complemented
3#22627151C218yesmaximal, direct product factor
4C2×#17989692C211yesmaximal, characteristic, complemented
5C2×#17989688C211yesmaximal, characteristic, complemented
6C2×#17989687C211yesmaximal, characteristic, complemented
7C2×#17989682C211yesmaximal, characteristic, complemented
8C2×#17989630C211yesmaximal, characteristic
9#17989709—22no—
10#17989709C2214yescomplemented
11#17989708—22no—
12#17989708C2214yescomplemented
13C2×#14556688—21no—
14C2×#14556688C2211yescharacteristic
15C2×#14556688C2211yescharacteristic
16C2×#14556687—21no—
17C2×#14556686—21no—
18C2×#14556686C2211yescharacteristic
19C2×#14556686C2211yescharacteristic
20C22×#11924040—21no—
21#17989692C2214yescomplemented
22#17989688C2214yescomplemented
23#17989687C2214yescomplemented
24#17989682C2214yescomplemented
25C2×#14556679C2211yescharacteristic
26C2×#14556678C2211yescharacteristic
27#17989630C414yes—
28#17989630C2214yes—
29C2×#14556661C411yescharacteristic
30C2×#14556656C411yescharacteristic
31C2×#14556655C411yescharacteristic
32C2×C8×#64408C2211yescharacteristic
33C2×#14556612C411yescharacteristic
34#14556688—24no—
35#14556688—21no—
36#14556688—21no—
37#14556688C2312yes—
38#14556688C2312yes—
39#14556687—24no—
40#14556686—24no—
41#14556686—21no—
42#14556686D412yes—
43#14556686C2312yes—
44#14556686C2312yes—
45C2×#11924040—24no—
46C2×#11924040—21no—
47C2×#11924040—21no—
48C2×#11924040—21no—
49C2×#11924040D411yescharacteristic
50C2×#11924040D411yescharacteristic
51#14556679—21no—
52#14556679—21no—
53#14556679C2×C412yes—
54#14556679C2312yes—
55#14556678—21no—
56#14556678—21no—
57#14556678C2×C412yes—
58#14556678C2312yes—
59C2×#11924038—21no—
60C2×#11924038C2×C411yescharacteristic
61C2×#11924038C2×C411yescharacteristic
62C2×#11924037—21no—
63C2×#11924036—21no—
64C2×#11924036C2311yescharacteristic
65C22×#10596833—21no—
66C2×C4×#64408C2×C411yescharacteristic
67#14556661C2×C414yes—
68#14556656C2×C414yes—
69#14556655C2×C414yes—
70C8×#64408C2×C412yes—
71C8×#64408C2312yes—
72C2×#11924029C2×C411yescharacteristic
73C2×#11924027C2×C411yescharacteristic
74#14556612C814yes—
75#14556612C2×C414yes—
76C2×#11924018C811yescharacteristic
77C2×#11924017C811yescharacteristic
78C2×#11924013C811yescharacteristic
79C2×C8×D73C2×C411yescharacteristic
80C2×SD16×C73C811yescharacteristic
81#11924040—22no—
82#11924040—22no—
83#11924040—22no—
84#11924040C2×D412yes—
85#11924040C2×D412yes—
86C22×#64408—21no—
87#11924038—21no—
88#11924038—21no—
89#11924038—22no—
90#11924038—22no—
91#11924038C22×C412yes—
92#11924038C22×C412yes—
93#11924037—22no—
94#11924037—22no—
95#11924036—22no—
96#11924036—22no—
97#11924036C22×C411yescharacteristic
98#11924036C2×D411yescharacteristic
99#11924036#4111yescharacteristic
100#11924036C2411yescharacteristic
101C2×#10596833—21no—
102C2×#10596833—21no—
103C2×#10596833—22no—
104C2×#10596833—22no—
105C2×#10596833C2×D411yescharacteristic
106C2×#10596833#4111yescharacteristic
107C4×#64408—21no—
108C4×#64408C22×C412yes—
109#11924029—21no—
110#11924029—21no—
111#11924029C2×C812yes—
112#11924029C22×C412yes—
113#11924027—21no—
114#11924027—21no—
115#11924027C2×C812yes—
116#11924027C22×C412yes—
117C2×Dic146C2×C811yescharacteristic
118C2×D292—21no—
119C2×D292C2×C811yescharacteristic
120C2×C22⋊D73—21no—
121C22×Dic73—21no—
122C2×C4×D73—21no—
123C2×C4×D73C22×C411yescharacteristic
124#11924018C2×C814yes—
125#11924017C2×C814yes—
126#11924013C2×C814yes—
127C2×#10596831C2×C811yescharacteristic
128C8×D73C2×C812yes—
129C8×D73C22×C412yes—
130C2×Q8×C73C2×C811yescharacteristic
131C2×D4×C73C2×C811yescharacteristic
132SD16×C73C2×C814yes—
133C2×C8×C73C2×C811yescharacteristic
134C23×C73—21no—
135C22×D73—21no—
136C22×D73#13111yescharacteristic
137C2×#64408—22no—
138C2×#64408—42no—
139Q8×C73—21no—
140Q8×C73C22×C812yes—
141D4×C73—21no—
142D4×C73C22×C812yes—
143C2×C4×C73—21no—
144C2×C4×C73C22×C811yescharacteristic
145C22⋊D73—22no—
146C22⋊D73—22no—
147C2×Dic73—21no—
148C2×Dic73—22no—
149C2×Dic73—22no—
150C2×Dic73C4×D411yescharacteristic
151D292—22no—
152D292—22no—
153D292—21no—
154D292C22×C812yes—
155C4×D73—22no—
156C4×D73—22no—
157C4×D73C4×D411yescharacteristic
158C4×D73C22×C811yescharacteristic
159C4×D73#13111yescharacteristic
160C4×D73C23×C411yescharacteristic
161Dic146—21no—
162Dic146C22×C812yes—
163#10596833—22no—
164#10596833—22no—
165#10596833C4×D411yescharacteristic
166#10596833C4×D411yescharacteristic
167#10596833C22×D411yescharacteristic
168#10596833C2×#4111yescharacteristic
169C8×C73C22×C812yes—
170#10596831C22×C812yes—
171C22×C73—22no—
172C22×C73—42no—
173C22×C73C8×D411yescharacteristic
174C2×D73—22no—
175C2×D73—22no—
176C2×D73—42no—
177C2×D73C8×D411yescharacteristic
178C2×D73C2×#13111yescharacteristic
179#64408—42no—
180C4×C73—22no—
181C4×C73C8×D411yescharacteristic
182C4×C73C23×C811yescharacteristic
183Dic73—22no—
184Dic73C8×D411yescharacteristic
185Dic73C2×C4×D411yescharacteristic
186C2×#2171—731nomaximal, Sylow
187C2×C73—42no—
188C2×C73#217112yescomplemented
189C2×C73C2×C8×D411yescharacteristic
190D73—21no—
191D73—21no—
192D73—42no—
193C2×#504—731no—
194C2×#504—731no—
195C2×#443—731no—
196#2171—738no—
197C2×#364—731no—
198C2×#350—731no—
199C2×#350—731no—
200C2×#346—731no—
201C73C2×#217111yescharacteristic, complemented, Sylow
202C2×#135—731no—
203C2×#131—731no—
204C2×#131—731no—
205#504—734no—
206#504—734no—
207#504—1462no—
208#504—1462no—
209C2×M32—731no—
210C2×M32—731no—
211C2×M32—1461no—
212C2×M32—1461no—
213C22×C16—731no—
214C22×C16—731no—
215C22×C16—1461no—
216C22×C16—1461no—
217#443—734no—
218#443—734no—
219C2×#108—731no—
220C2×#104—731no—
221C2×#104—731no—
222C2×C4×C8—731no—
223#364—734no—
224#350—734no—
225#350—734no—
226#346—734no—
227C2×#41—731no—
228C2×#41—731no—
229#135—734no—
230#135—734no—
231C2×Q16—731no—
232C2×SD16—731no—
233C2×SD16#1059684211yescharacteristic
234C2×D8—731no—
235#131—732no—
236#131—732no—
237#131—732no—
238#131—732no—
239#131—1461no—
240#131—1461no—
241#131—1461no—
242#131—1461no—
243C2×M16—731no—
244C2×M16—731no—
245C2×M16—1461no—
246C2×M16—1461no—
247C22×C8—731no—
248C22×C8—731no—
249C22×C8—1461no—
250C22×C8—1461no—
251C2×C42—731no—
252M32—732no—
253M32—732no—
254M32—1464no—
255M32—1464no—
256M32—1461no—
257M32—1461no—
258C2×C16—731no—
259C2×C16—731no—
260C2×C16—732no—
261C2×C16—732no—
262C2×C16—732no—
263C2×C16—1464no—
264C2×C16—1464no—
265C2×C16—1461no—
266C2×C16—1461no—
267C2×C16—1461no—
268C2×C16—1461no—
269#108—734no—
270#104—734no—
271#104—734no—
272C4×C8—732no—
273C4×C8—732no—
274#41—732no—
275#41—732no—
276#41—732no—
277#41—732no—
278#41—1461no—
279#41—1461no—
280#41—1461no—
281#41—1461no—
282C2×Q8—731no—
283C2×Q8C2×#1059684211yescharacteristic
284C2×D4—731no—
285C2×D4—1461no—
286C2×D4—1461no—
287C2×D4C2×#1059684211yescharacteristic
288C22×C4—731no—
289C22×C4—1461no—
290C22×C4—1461no—
291C22×C4—1461no—
292Q16—734no—
293SD16—734no—
294SD16C2×#1059684214yes—
295D8—734no—
296M16—732no—
297M16—732no—
298M16—1462no—
299M16—1462no—
300M16—1462no—
301M16—1462no—
302M16—1461no—
303M16—1461no—
304C2×C8—731no—
305C2×C8—731no—
306C2×C8—731no—
307C2×C8—731no—
308C2×C8—731no—
309C2×C8—731no—
310C2×C8—731no—
311C2×C8—732no—
312C2×C8—732no—
313C2×C8—1462no—
314C2×C8—1462no—
315C2×C8—1462no—
316C2×C8—1462no—
317C2×C8—1461no—
318C2×C8—1461no—
319C2×C8C2×#1059684211yescharacteristic
320C42—732no—
321C42—1461no—
322C16—732no—
323C16—732no—
324C16—1462no—
325C16—1462no—
326C16—1462no—
327C23—21no—
328C23—731no—
329C23—1461no—
330Q8—21no—
331Q8—732no—
332Q8—1461no—
333Q8C22×#1059684212yes—
334D4—21no—
335D4—732no—
336D4—1462no—
337D4—1462no—
338D4—1462no—
339D4—1462no—
340D4—1461no—
341D4C22×#1059684212yes—
342C2×C4—21no—
343C2×C4—2922no—
344C2×C4—731no—
345C2×C4—731no—
346C2×C4—731no—
347C2×C4—731no—
348C2×C4—731no—
349C2×C4—1462no—
350C2×C4—1462no—
351C2×C4—1462no—
352C2×C4—1462no—
353C2×C4—1462no—
354C2×C4—1461no—
355C2×C4C22×#1059684211yescharacteristic
356C8—731no—
357C8—731no—
358C8—731no—
359C8—731no—
360C8—732no—
361C8—1462no—
362C8—1462no—
363C8C22×#1059684212yes—
364C22—22no—
365C22—42no—
366C22—2922no—
367C22—731no—
368C22—731no—
369C22—1462no—
370C22—1462no—
371C22D4×#1059684211yescharacteristic
372C4—22no—
373C4—2922no—
374C4—731no—
375C4—731no—
376C4—1462no—
377C4D4×#1059684211yescharacteristic
378C4C23×#1059684211yescharacteristic
379C2—42no—
380C2—2922no—
381C2—1461no—
382C2—1461no—
383C2#2262715112yesdirect product factor
384C2C2×D4×#1059684211yescharacteristic
subgroupG/H
centerC22D4×#10596842
commutatorC4×C73C23×C8
FrattiniC4C23×#10596842
FittingC2×SD16×C73C8
socleC22×C73C8×D4
prime radicalC2×#14556612C4
cosocle#11924036C24
hypercenterC2×SD16#10596842
hypocenterC73C2×#2171
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#17989709C2semidirect
2. C2×#17989708C2semidirect
3. #22627151C2direct (N × H)
4. C2×#17989692C2semidirect
5. C2×#17989688C2semidirect
6. C2×#17989687C2semidirect
7. C2×#17989682C2semidirect
10. #17989709C22semidirect
12. #17989708C22semidirect
21. #17989692C22semidirect
22. #17989688C22semidirect
23. #17989687C22semidirect
24. #17989682C22semidirect
188. C2×C73#2171semidirect
201. C73C2×#2171semidirect
383. C2#22627151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179897092
C2×#179897082
#226271512
C2×#179896922
C2×#179896882
C2×#179896872
C2×#179896822
C2×#179896302
C2×#217173