Finite Group Databasebeta

← C2×#22625203 #34016021

Subgroups — C2×#22625203 #34016021

Order 18688.

1002 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989607C211yesmaximal, characteristic
2C2×#17989603C211yesmaximal, characteristic
3#22625203C218yesmaximal, direct product factor
4C2×#17989433C212yesmaximal
5C2×#17989432C212yesmaximal
6C22×#14556581C211yesmaximal, characteristic
7#17989607—22no—
8#17989607C2214yes—
9#17989603—22no—
10#17989603C2214yes—
11C2×#14556658—21no—
12C2×C4⋊#10596833—21no—
13C2×C22⋊#10596833C2212yes—
14C2×C22⋊#10596833C2212yes—
15C2×#14556646—21no—
16C2×C4×#10596833—21no—
17#17989433C2218yes—
18#17989432C2218yes—
19C2×#14556581—21no—
20C2×#14556581—21no—
21C2×#14556581—21no—
22C2×#14556581—21no—
23C2×#14556581—22no—
24C2×#14556581—22no—
25C2×#14556581C414yes—
26C2×#14556581C2214yes—
27C22×C4⋊Dic73C2211yescharacteristic
28C22×#11924007C411yescharacteristic
29C22×#11924007C411yescharacteristic
30C22×#11924007C411yescharacteristic
31C22×#11924007C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33C22×C4⋊C4×C73C411yescharacteristic
34C22×#10596833—22no—
35C22×#10596833—22no—
36#14556658—24no—
37C4⋊#10596833—24no—
38C22⋊#10596833—22no—
39C22⋊#10596833—22no—
40C22⋊#10596833C2314yes—
41C22⋊#10596833C2314yes—
42#14556646—24no—
43C4×#10596833—24no—
44C23×Dic73C2×C411yescharacteristic
45C23×Dic73C2×C411yescharacteristic
46C23×Dic73C2×C411yescharacteristic
47C23×Dic73C2311yescharacteristic
48#14556581—24no—
49#14556581—24no—
50#14556581—24no—
51#14556581—24no—
52#14556581—24no—
53#14556581—24no—
54#14556581—24no—
55#14556581—24no—
56C2×C4⋊Dic73—21no—
57C2×C4⋊Dic73—21no—
58C2×C4⋊Dic73—21no—
59C2×C4⋊Dic73—21no—
60C2×C4⋊Dic73C2×C412yes—
61C2×C4⋊Dic73C2312yes—
62C2×#11924007—22no—
63C2×#11924007—21no—
64C2×#11924007—21no—
65C2×#11924007—22no—
66C2×#11924007—21no—
67C2×#11924007—21no—
68C2×#11924007—21no—
69C2×#11924007—21no—
70C2×#11924007—21no—
71C2×#11924007—21no—
72C2×#11924007—22no—
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×#11924007C2×C414yes—
76C2×#11924007C2×C414yes—
77C2×#11924007C2×C414yes—
78C2×#11924007C2×C412yes—
79C2×#11924007C2312yes—
80C2×C4×Dic73C2×C412yes—
81C2×C4×Dic73D411yescharacteristic
82C2×C4×Dic73D411yescharacteristic
83C2×C4×Dic73D411yescharacteristic
84C2×C4×Dic73D411yescharacteristic
85C2×C4×Dic73D412yes—
86C2×C4×Dic73D412yes—
87C2×C4×Dic73C2312yes—
88C23×C4×C73C2×C411yescharacteristic
89C23×C4×C73C2×C411yescharacteristic
90C23×C4×C73C2×C411yescharacteristic
91C2×C4⋊C4×C73—22no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73C2×C414yes—
95C2×#10596833—24no—
96C2×#10596833—24no—
97C2×#10596833—44no—
98C2×#10596833—44no—
99C22×Dic73—24no—
100C22×Dic73—21no—
101C22×Dic73—21no—
102C22×Dic73—21no—
103C22×Dic73—21no—
104C22×Dic73—24no—
105C22×Dic73—42no—
106C22×Dic73—42no—
107C22×Dic73C22⋊C412yes—
108C22×Dic73C22⋊C411yescharacteristic
109C22×Dic73C22⋊C411yescharacteristic
110C22×Dic73C22×C412yes—
111C22×Dic73C22×C412yes—
112C22×Dic73C22×C412yes—
113C22×Dic73C22×C411yescharacteristic
114C22×Dic73C2×D411yescharacteristic
115C22×Dic73C2×D411yescharacteristic
116C22×Dic73C2×D411yescharacteristic
117C22×Dic73C2×D411yescharacteristic
118C22×Dic73C2411yescharacteristic
119C4⋊Dic73—22no—
120C4⋊Dic73—22no—
121C4⋊Dic73—22no—
122C4⋊Dic73—22no—
123#11924007—24no—
124#11924007—24no—
125#11924007—22no—
126#11924007—22no—
127#11924007—24no—
128#11924007—24no—
129#11924007—24no—
130#11924007—24no—
131#11924007—22no—
132#11924007—22no—
133C4×Dic73C22⋊C412yes—
134C4×Dic73C22⋊C412yes—
135C4×Dic73C22⋊C412yes—
136C4×Dic73C22⋊C412yes—
137C4×Dic73C2×D412yes—
138C4×Dic73C2×D412yes—
139C4×Dic73C2×D412yes—
140C4×Dic73C2×D412yes—
141C24×C73C22×C411yescharacteristic
142C22×C4×C73—24no—
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—24no—
148C22×C4×C73—42no—
149C22×C4×C73C22⋊C412yes—
150C22×C4×C73C22⋊C411yescharacteristic
151C22×C4×C73C22⋊C411yescharacteristic
152C22×C4×C73C22×C412yes—
153C22×C4×C73C22×C412yes—
154C22×C4×C73C22×C412yes—
155C4⋊C4×C73—24no—
156C4⋊C4×C73—24no—
157C23×C73—22no—
158C23×C73—22no—
159C23×C73C2×C22⋊C411yescharacteristic
160C23×C73C2×C22⋊C411yescharacteristic
161C23×C73#13114yes—
162C23×C73C23×C411yescharacteristic
163C2×C4×C73—24no—
164C2×C4×C73—24no—
165C2×C4×C73—22no—
166C2×C4×C73—22no—
167C2×C4×C73—22no—
168C2×C4×C73—22no—
169C2×C4×C73—24no—
170C2×C4×C73—42no—
171C2×C4×C73—42no—
172C2×C4×C73—42no—
173C2×C4×C73—42no—
174C2×C4×C73—42no—
175C2×C4×C73C2×C22⋊C412yes—
176C2×C4×C73C2×C22⋊C412yes—
177C2×Dic73—22no—
178C2×Dic73—22no—
179C2×Dic73—22no—
180C2×Dic73—24no—
181C2×Dic73—24no—
182C2×Dic73—22no—
183C2×Dic73—22no—
184C2×Dic73—24no—
185C2×Dic73—41no—
186C2×Dic73—41no—
187C2×Dic73—41no—
188C2×Dic73—41no—
189C2×Dic73—42no—
190C2×Dic73—42no—
191C2×Dic73—42no—
192C2×Dic73—42no—
193C2×Dic73—42no—
194C2×Dic73#10114yes—
195C2×Dic73C2×C22⋊C411yescharacteristic
196C2×Dic73C2×C22⋊C411yescharacteristic
197C2×Dic73C2×C22⋊C412yes—
198C2×Dic73C2×C22⋊C412yes—
199C2×Dic73C22×D411yescharacteristic
200C2×Dic73C22×D411yescharacteristic
201#10596833—44no—
202#10596833—44no—
203C22×C73—21no—
204C22×C73—21no—
205C22×C73—21no—
206C22×C73—21no—
207C22×C73—28no—
208C22×C73#40812yes—
209C22×C73#40812yes—
210C22×C73#41012yes—
211C22×C73C2×#10112yes—
212C22×C73C22×C22⋊C411yescharacteristic
213C22×C73C2×#13112yes—
214C4×C73—22no—
215C4×C73—22no—
216C4×C73—42no—
217C4×C73—42no—
218Dic73—21no—
219Dic73—21no—
220Dic73—21no—
221Dic73—21no—
222Dic73—22no—
223Dic73—42no—
224Dic73—42no—
225Dic73C2×#10114yes—
226C2×#1470—731nomaximal, Sylow
227C2×C73—22no—
228C2×C73—22no—
229C2×C73#147014yescomplemented
230C2×C73C2×#40811yescharacteristic
231C2×C73C2×#41011yescharacteristic
232C2×C73C22×#10111yescharacteristic
233C22×#125—731no—
234C2×#432—731no—
235C2×#431—731no—
236#1470—738no—
237C2×#324—732no—
238C2×#324—732no—
239C73C2×#147011yescharacteristic, complemented, Sylow
240C2×#125—734no—
241C2×#125—734no—
242C2×#125—1461no—
243C2×#125—1461no—
244C2×#125—1461no—
245C2×#125—1461no—
246C2×#125—1462no—
247C2×#125—1462no—
248C22×C4⋊C4—731no—
249C22×C4⋊C4—731no—
250C22×C4⋊C4—731no—
251C22×C4⋊C4—731no—
252C22×C4⋊C4—731no—
253C22×C4⋊C4#6440811yescharacteristic
254C22×C42—731no—
255#432—734no—
256#432—1462no—
257#431—734no—
258#431—1462no—
259C2×C4⋊C8—1461no—
260C2×C4⋊C8—1461no—
261C2×C22⋊C8—732no—
262C2×C22⋊C8—732no—
263C2×#97—1461no—
264C2×C4×C8—1461no—
265#324—738no—
266#324—738no—
267C23×C4—731no—
268C23×C4—731no—
269C23×C4—731no—
270C23×C4—731no—
271C23×C4C2×#6440811yescharacteristic
272C23×C4C2×#6440811yescharacteristic
273C23×C4C2×#6440811yescharacteristic
274C22×C8—1462no—
275C22×C8—1462no—
276#125—1464no—
277#125—1464no—
278#125—1464no—
279#125—1464no—
280#125—1464no—
281#125—1464no—
282#125—1464no—
283#125—1464no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—732no—
288C2×C4⋊C4—732no—
289C2×C4⋊C4—732no—
290C2×C4⋊C4—734no—
291C2×C4⋊C4—734no—
292C2×C4⋊C4—734no—
293C2×C4⋊C4—732no—
294C2×C4⋊C4—1461no—
295C2×C4⋊C4—1461no—
296C2×C4⋊C4—1462no—
297C2×C4⋊C4—1462no—
298C2×C4⋊C4—1461no—
299C2×C4⋊C4—1461no—
300C2×C4⋊C4—1461no—
301C2×C4⋊C4—1461no—
302C2×C4⋊C4—1461no—
303C2×C4⋊C4—1461no—
304C2×C4⋊C4—1461no—
305C2×C4⋊C4—1461no—
306C2×C4⋊C4—1461no—
307C2×C4⋊C4—1461no—
308C2×C4⋊C4—1462no—
309C2×C4⋊C4—1461no—
310C2×C4⋊C4—1461no—
311C2×C4⋊C4C2×#6440814yes—
312C2×C42—731no—
313C2×C42—731no—
314C2×C42—731no—
315C2×C42—731no—
316C2×C42—732no—
317C2×C42—732no—
318C2×C42—732no—
319C2×C42—732no—
320C4⋊C8—1464no—
321C4⋊C8—1464no—
322C22⋊C8—734no—
323C22⋊C8—734no—
324C22⋊C8—1462no—
325C22⋊C8—1462no—
326#97—1464no—
327C4×C8—1464no—
328C24C22×#6440811yescharacteristic
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—42no—
336C22×C4—2922no—
337C22×C4—2922no—
338C22×C4—731no—
339C22×C4—731no—
340C22×C4—731no—
341C22×C4—731no—
342C22×C4—732no—
343C22×C4—731no—
344C22×C4—732no—
345C22×C4—732no—
346C22×C4—731no—
347C22×C4—731no—
348C22×C4—731no—
349C22×C4—732no—
350C22×C4—1464no—
351C22×C4—1461no—
352C22×C4—1461no—
353C22×C4—1461no—
354C22×C4—1461no—
355C22×C4—1464no—
356C22×C4C22⋊#6440812yes—
357C22×C4C22⋊#6440811yescharacteristic
358C22×C4C22⋊#6440811yescharacteristic
359C22×C4C22×#6440812yes—
360C22×C4C22×#6440812yes—
361C22×C4C22×#6440812yes—
362C2×C8—2924no—
363C2×C8—2924no—
364C2×C8—1464no—
365C2×C8—1464no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—1464no—
369C4⋊C4—1464no—
370C4⋊C4—1462no—
371C4⋊C4—1462no—
372C4⋊C4—1464no—
373C4⋊C4—1462no—
374C4⋊C4—1462no—
375C4⋊C4—1464no—
376C4⋊C4—1462no—
377C4⋊C4—1462no—
378C4⋊C4—1462no—
379C4⋊C4—1462no—
380C4⋊C4—1464no—
381C4⋊C4—1464no—
382C42—732no—
383C42—732no—
384C42—732no—
385C42—732no—
386C42—732no—
387C42—732no—
388C42—732no—
389C42—732no—
390C23—22no—
391C23—22no—
392C23C2×C22⋊#6440811yescharacteristic
393C23C2×C22⋊#6440811yescharacteristic
394C23#1455667814yes—
395C23C23×#6440811yescharacteristic
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—2922no—
409C2×C4—2922no—
410C2×C4—2922no—
411C2×C4—2922no—
412C2×C4—2922no—
413C2×C4—2921no—
414C2×C4—2921no—
415C2×C4—2921no—
416C2×C4—2921no—
417C2×C4—732no—
418C2×C4—734no—
419C2×C4—731no—
420C2×C4—731no—
421C2×C4—731no—
422C2×C4—731no—
423C2×C4—732no—
424C2×C4—1462no—
425C2×C4—1462no—
426C2×C4—1464no—
427C2×C4—1464no—
428C2×C4—1464no—
429C2×C4—1462no—
430C2×C4—1462no—
431C2×C4—1462no—
432C2×C4C2×C22⋊#6440812yes—
433C2×C4C2×C22⋊#6440812yes—
434C8—2924no—
435C8—2924no—
436C22—28no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22#1798956012yes—
442C22#1798956012yes—
443C22#1798956612yes—
444C22D73⋊#10112yes—
445C22C22×C22⋊#6440811yescharacteristic
446C22C2×#1455667812yes—
447C4—22no—
448C4—22no—
449C4—42no—
450C4—42no—
451C4—2922no—
452C4—2922no—
453C4—734no—
454C4—1461no—
455C4—1461no—
456C4—1461no—
457C4—1461no—
458C4—1462no—
459C2—22no—
460C2—22no—
461C2#2262520314yesdirect product factor
462C2C2×#1798956011yescharacteristic
463C2C2×#1798956611yescharacteristic
464C2C2×D73⋊#10111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC23×C73C23×C4
FrattiniC23C23×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC22×Dic73C24
hypercenterC22×C4⋊C4#64408
hypocenterC73C2×#1470
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22625203C2direct (N × H)
229. C2×C73#1470semidirect
239. C73C2×#1470semidirect
461. C2#22625203direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896072
C2×#179896032
#226252032
C2×#179894332
C2×#179894322
C22×#145565812
C2×#147073