Finite Group Databasebeta

← C2×#22626322 #34030236

Subgroups — C2×#22626322 #34030236

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×#17989646C211yesmaximal, characteristic, complemented
2C2×#17989645C211yesmaximal, characteristic, complemented
3#22626322C218yesmaximal, direct product factor
4C2×#17989510C211yesmaximal, characteristic, complemented
5C2×#17989486C211yesmaximal, characteristic, complemented
6C2×#17989485C211yesmaximal, characteristic, complemented
7C2×#17989475C211yesmaximal, characteristic, complemented
8C2×#17988701C211yesmaximal, characteristic
9#17989646—22no—
10#17989646C2214yescomplemented
11#17989645—22no—
12#17989645C2214yescomplemented
13C2×#14556666—21no—
14C2×#14556665—21no—
15C2×#14556665C2211yescharacteristic
16C2×#14556665C2211yescharacteristic
17C2×#14556664—21no—
18C22×#11924031—21no—
19C22×#11924031C2211yescharacteristic
20C22×#11924031C2211yescharacteristic
21#17989510C2214yescomplemented
22#17989486C2214yescomplemented
23#17989485C2214yescomplemented
24#17989475C2214yescomplemented
25C2×#14556611C411yescharacteristic
26C2×#14556599C2211yescharacteristic
27C2×#14556598C2211yescharacteristic
28#17988701C414yes—
29#17988701C2214yes—
30C2×#14556526C411yescharacteristic
31C2×#14556519C411yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33C2×#104×C73C411yescharacteristic
34#14556666—24no—
35#14556665—24no—
36#14556665—21no—
37#14556665—21no—
38#14556665C2312yes—
39#14556665C2312yes—
40#14556664—24no—
41C2×#11924031—24no—
42C2×#11924031—21no—
43C2×#11924031—21no—
44C2×#11924031—21no—
45C2×#11924031—21no—
46C2×#11924031D411yescharacteristic
47C2×#11924031D411yescharacteristic
48C2×#11924031D412yes—
49C2×#11924031C2312yes—
50C2×#11924031C2312yes—
51C2×#11924028C2×C411yescharacteristic
52#14556611C814yes—
53#14556611C2×C414yes—
54C2×#11924018C811yescharacteristic
55C2×#11924016C811yescharacteristic
56C2×#11924015C811yescharacteristic
57C2×#11924013C811yescharacteristic
58#14556599—21no—
59#14556599—21no—
60#14556599C2×C412yes—
61#14556599C2312yes—
62#14556598—21no—
63#14556598—21no—
64#14556598C2×C412yes—
65#14556598C2312yes—
66C2×#11924012—21no—
67C2×#11924012C2×C411yescharacteristic
68C2×#11924011—21no—
69C22×#10596831—21no—
70C22×#10596831C2×C411yescharacteristic
71C22×#10596831C2311yescharacteristic
72C2×C8×D73—21no—
73#14556526C2×C414yes—
74#14556519C2×C414yes—
75C4×#10596831C2×C412yes—
76C4×#10596831C2312yes—
77C2×#41×C73C2×C411yescharacteristic
78C2×M16×C73C2×C411yescharacteristic
79C2×C42×C73C2×C411yescharacteristic
80#104×C73C2×C414yes—
81#11924031—22no—
82#11924031—22no—
83#11924031—22no—
84#11924031C2×D412yes—
85#11924031C2×D412yes—
86#11924028—21no—
87#11924028—21no—
88#11924028C2×C812yes—
89#11924028C22×C412yes—
90C2×Dic146C2×C811yescharacteristic
91C2×D292C2×C811yescharacteristic
92C2×C22⋊D73—21no—
93C2×C4×D73—21no—
94#11924018C2×C814yes—
95#11924016C2×C814yes—
96#11924015C2×C814yes—
97#11924013C2×C814yes—
98#11924012—21no—
99#11924012—22no—
100#11924012—22no—
101#11924012C22×C412yes—
102#11924011—22no—
103#11924011—22no—
104C2×#10596831—21no—
105C2×#10596831—22no—
106C2×#10596831—22no—
107C2×#10596831C2×C811yescharacteristic
108C2×#10596831C2×C811yescharacteristic
109C2×#10596831C2×C812yes—
110C2×#10596831C22×C411yescharacteristic
111C2×#10596831C22×C412yes—
112C2×#10596831C2×D411yescharacteristic
113C2×#10596831C2×D411yescharacteristic
114C2×#10596831#4111yescharacteristic
115C2×#10596831#4111yescharacteristic
116C2×#10596831C2411yescharacteristic
117C8×D73—22no—
118C8×D73—22no—
119#41×C73—21no—
120#41×C73—21no—
121#41×C73C2×C812yes—
122#41×C73C22×C412yes—
123C2×Q8×C73C2×C811yescharacteristic
124C2×D4×C73—21no—
125C2×D4×C73C2×C811yescharacteristic
126C22×C4×C73—21no—
127C22×C4×C73—21no—
128C22×C4×C73C22×C411yescharacteristic
129M16×C73—21no—
130M16×C73C22×C412yes—
131C2×C8×C73—21no—
132C42×C73—21no—
133C42×C73C22×C412yes—
134C23×C73—21no—
135C23×C73#13111yescharacteristic
136C22×D73—21no—
137Q8×C73—21no—
138Q8×C73C22×C812yes—
139D4×C73—22no—
140D4×C73—22no—
141D4×C73—21no—
142D4×C73C22×C812yes—
143C2×C4×C73—21no—
144C2×C4×C73—22no—
145C2×C4×C73—22no—
146C2×C4×C73—22no—
147C2×C4×C73—42no—
148C2×C4×C73C4×D411yescharacteristic
149C2×C4×C73C4×D411yescharacteristic
150C2×C4×C73C22×C811yescharacteristic
151C2×C4×C73C22×C811yescharacteristic
152C2×C4×C73#13111yescharacteristic
153C2×C4×C73C23×C411yescharacteristic
154C22⋊D73—22no—
155C22⋊D73—22no—
156C2×Dic73—21no—
157D292—21no—
158D292C22×C812yes—
159C4×D73—22no—
160C4×D73—22no—
161Dic146—21no—
162Dic146C22×C812yes—
163C8×C73—22no—
164#10596831—22no—
165#10596831C4×D411yescharacteristic
166#10596831C4×D411yescharacteristic
167#10596831C22×C812yes—
168#10596831C22×C812yes—
169#10596831C22×D411yescharacteristic
170#10596831C2×#4111yescharacteristic
171C22×C73—22no—
172C22×C73—22no—
173C22×C73—42no—
174C22×C73C8×D411yescharacteristic
175C22×C73C8×D411yescharacteristic
176C22×C73C2×#13111yescharacteristic
177C2×D73—22no—
178C2×D73—42no—
179C4×C73—22no—
180C4×C73—42no—
181C4×C73C8×D411yescharacteristic
182C4×C73C8×D411yescharacteristic
183C4×C73C2×C4×D411yescharacteristic
184C4×C73C23×C811yescharacteristic
185Dic73—22no—
186C2×#2171—731nomaximal, Sylow
187C2×C73—21no—
188C2×C73—21no—
189C2×C73—42no—
190C2×C73#217112yescomplemented
191C2×C73C2×C8×D411yescharacteristic
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#6440811yescharacteristic
222C2×C4×C8—731no—
223#364—734no—
224#350—734no—
225#350—734no—
226#346—734no—
227C2×#41—731no—
228C2×#41C2×#6440811yescharacteristic
229#135—734no—
230#135—734no—
231C2×Q16—731no—
232C2×SD16—731no—
233C2×SD16—731no—
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—1461no—
245C2×M16—1461no—
246C2×M16C2×#6440811yescharacteristic
247C22×C8—731no—
248C22×C8—731no—
249C22×C8—1461no—
250C22×C8—1461no—
251C2×C42C2×#6440811yescharacteristic
252M32—732no—
253M32—732no—
254M32—1464no—
255M32—1464no—
256M32—1461no—
257M32—1461no—
258C2×C16—732no—
259C2×C16—731no—
260C2×C16—731no—
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#104C2×#6440814yes—
272C4×C8—732no—
273C4×C8—732no—
274#41—21no—
275#41—21no—
276#41—732no—
277#41—732no—
278#41—1461no—
279#41—1461no—
280#41#1192403612yes—
281#41C22×#6440812yes—
282C2×Q8—731no—
283C2×Q8#1192403611yescharacteristic
284C2×D4—21no—
285C2×D4—731no—
286C2×D4—1461no—
287C2×D4#1192403611yescharacteristic
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—1461no—
291C22×C4C22×#6440811yescharacteristic
292Q16—734no—
293SD16—734no—
294SD16—734no—
295D8—734no—
296M16—21no—
297M16—732no—
298M16—1462no—
299M16—1462no—
300M16—1462no—
301M16—1462no—
302M16—1461no—
303M16C22×#6440812yes—
304C2×C8—21no—
305C2×C8—731no—
306C2×C8—731no—
307C2×C8—732no—
308C2×C8—732no—
309C2×C8—731no—
310C2×C8—731no—
311C2×C8—731no—
312C2×C8—731no—
313C2×C8—731no—
314C2×C8—731no—
315C2×C8—1462no—
316C2×C8—1462no—
317C2×C8—1462no—
318C2×C8—1462no—
319C2×C8—1461no—
320C42—21no—
321C42C22×#6440812yes—
322C16—732no—
323C16—732no—
324C16—1462no—
325C16—1462no—
326C16—1462no—
327C23—21no—
328C23—1461no—
329C23#1455667811yescharacteristic
330Q8—21no—
331Q8—732no—
332Q8—1461no—
333Q8C2×#1192403612yes—
334D4—22no—
335D4—22no—
336D4—21no—
337D4—732no—
338D4—1462no—
339D4—1462no—
340D4—1461no—
341D4C2×#1192403612yes—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—42no—
347C2×C4—1461no—
348C2×C4—1462no—
349C2×C4—1462no—
350C2×C4D4×#6440811yescharacteristic
351C2×C4D4×#6440811yescharacteristic
352C2×C4C2×#1192403611yescharacteristic
353C2×C4C2×#1192403611yescharacteristic
354C2×C4#1455667811yescharacteristic
355C2×C4C23×#6440811yescharacteristic
356C8—22no—
357C8—731no—
358C8—731no—
359C8—731no—
360C8—731no—
361C8—732no—
362C8—732no—
363C8—1462no—
364C22—22no—
365C22—22no—
366C22—42no—
367C22—2922no—
368C22—1462no—
369C22#1798961411yescharacteristic
370C22#1798961411yescharacteristic
371C22C2×#1455667811yescharacteristic
372C4—22no—
373C4—42no—
374C4—1462no—
375C4#1798961411yescharacteristic
376C4#1798961411yescharacteristic
377C4C2×D4×#6440811yescharacteristic
378C4C22×#1192403611yescharacteristic
379C2—21no—
380C2—21no—
381C2—42no—
382C2—2922no—
383C2#2262632212yesdirect product factor
384C2C2×#1798961411yescharacteristic
subgroupG/H
centerC2×C4D4×#64408
commutatorC4×C73C23×C8
FrattiniC2×C4C23×#64408
FittingC2×#104×C73C4
socleC22×C73C8×D4
prime radicalC2×#14556611C4
cosocleC2×#10596831C24
hypercenterC2×#104#64408
hypocenterC73C2×#2171
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#17989646C2semidirect
2. C2×#17989645C2semidirect
3. #22626322C2direct (N × H)
4. C2×#17989510C2semidirect
5. C2×#17989486C2semidirect
6. C2×#17989485C2semidirect
7. C2×#17989475C2semidirect
10. #17989646C22semidirect
12. #17989645C22semidirect
21. #17989510C22semidirect
22. #17989486C22semidirect
23. #17989485C22semidirect
24. #17989475C22semidirect
190. C2×C73#2171semidirect
201. C73C2×#2171semidirect
383. C2#22626322direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896462
C2×#179896452
#226263222
C2×#179895102
C2×#179894862
C2×#179894852
C2×#179894752
C2×#179887012
C2×#217173