Finite Group Databasebeta

← C2×#10590729 #11859289

Subgroups — C2×#10590729 #11859289

Order 1152.

1253 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3743C211yesmaximal, characteristic, complemented
2C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3C2×C4×#626C211yesmaximal, characteristic
4C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63557C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590729C218yesmaximal, direct product factor
9C2×#5128—31nomaximal
10C2×#4688—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×#626C411yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×#3743—24no—
17C2×#3743C2214yescomplemented
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)—24no—
22C2×C3×ΓL(1,𝔽25)C2214yescomplemented
23C2×Dic3⋊Dic3C411yescharacteristic
24C2×#3722C411yescharacteristic
25C2×(C2×D3)⋊Dic3C411yescharacteristic
26C4×#626C414yes—
27C4×#626C2214yes—
28C3×C8×Dic3C2214yescomplemented
29Dic3⋊(C3⋊C8)C2214yescomplemented
30#63557C2214yescomplemented
31(C2×D3)⋊(C3⋊C8)C2214yescomplemented
32C22×C3×M16—31no—
33C2×C4×#67—31no—
34C22×ΓL(1,𝔽25)—31no—
35C22×ΓL(1,𝔽25)—31no—
36C22×ΓL(1,𝔽25)—61no—
37C22×ΓL(1,𝔽25)D311yescharacteristic, complemented
38C2×C4×D12—31no—
39C2×C3×C4×C8—31no—
40C2×#830—31no—
41#5128—38no—
42C2×(C2×D3)⋊C8—31no—
43C2×(C2×D3)⋊C8—31no—
44C2×(C2×D3)⋊C8—31no—
45C2×Dic3⋊C8—31no—
46C2×C8×Dic3D311yescharacteristic, complemented
47C2×C4⋊(C3⋊C8)—31no—
48#4688—38no—
49C23×C3⋊D3C2×C411yescharacteristic
50C23×C3×D3C2×C411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2×C411yescharacteristic
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3C2×C412yes—
56C2×C4×C3⋊D3C2312yes—
57C22×C3×Dic3C2×C411yescharacteristic
58C22×C3×Dic3C2×C411yescharacteristic
59C22×C3×Dic3C2×C411yescharacteristic
60C2×C3×C4×D3—22no—
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3C2×C412yes—
63C2×C3×C4×D3C2312yes—
64C2×#626—24no—
65C2×#626C2×C414yes—
66C2×C32×C8D414yescomplemented
67C2×C32×C8C2312yes—
68C2×C3⋊(C3⋊C8)—22no—
69C2×C3⋊(C3⋊C8)C2312yes—
70#3743—28no—
71C3×C4×Dic3C2×C412yes—
72C3×C4×Dic3C2312yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2312yes—
76C2×C3×C3⋊C8C2312yes—
77C3×ΓL(1,𝔽25)—28no—
78Dic3⋊Dic3C2×C414yes—
79#3722C2×C414yes—
80(C2×D3)⋊Dic3C2×C414yes—
81C2×#436—91noSylow
82C23×C3×C4—31no—
83C22×#67—31no—
84C22×D12—31no—
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C22×C4×D3C2×D311yescharacteristic
89C2×C3×M16—34no—
90C2×C3×M16—64no—
91C22×C3×C8—21no—
92C22×C3×C8—31no—
93C22×C3×C8—31no—
94C22×C3×C8C2×D311yescharacteristic
95C22×C3×C8C2×D311yescharacteristic
96C2×C3×C42—31no—
97C2×#217—31no—
98C4×#67—34no—
99C4×#67—34no—
100C2×(C2×D3)⋊C4—31no—
101C2×(C2×D3)⋊C4—31no—
102C2×(C2×D3)⋊C4—31no—
103C2×C4⋊Dic3—31no—
104C2×Dic3⋊C4—31no—
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C22×C3⋊C8C2×D311yescharacteristic
111C2×ΓL(1,𝔽25)—24no—
112C2×ΓL(1,𝔽25)—34no—
113C2×ΓL(1,𝔽25)—34no—
114C2×ΓL(1,𝔽25)—64no—
115C2×ΓL(1,𝔽25)—68no—
116C2×ΓL(1,𝔽25)—64no—
117C2×ΓL(1,𝔽25)—64no—
118C2×ΓL(1,𝔽25)C2×D314yescomplemented
119C4×D12—34no—
120C4×D12—34no—
121C3×C4×C8—34no—
122#830—34no—
123(C2×D3)⋊C8—34no—
124(C2×D3)⋊C8—34no—
125(C2×D3)⋊C8—34no—
126Dic3⋊C8—34no—
127C8×Dic3C2×D314yescomplemented
128C4⋊(C3⋊C8)—34no—
129C23×C32C22×C411yescharacteristic
130C22×C3⋊D3—22no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3C22×C412yes—
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3C22×C412yes—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D412yes—
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3C22×C412yes—
144C4×C3⋊D3—24no—
145C4×C3⋊D3—22no—
146C4×C3⋊D3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3M1614yescomplemented
150C2×C3×Dic3C22×C412yes—
151C2×C3×Dic3C22×C412yes—
152C2×C3×Dic3C22×C412yes—
153C3×C4×D3—24no—
154C3×C4×D3—22no—
155C3×C4×D3—22no—
156#626—28no—
157C32×C8C2×D414yescomplemented
158C3⋊(C3⋊C8)—22no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—22no—
161C22×M16—31no—
162C22×M16—91no—
163C2×C4×D4—91no—
164#436—98no—
165C2×C4⋊C8—91no—
166C2×C22⋊C8—91no—
167C2×C22⋊C8—91no—
168C2×C4×C8—31no—
169C24×C3—31no—
170C23×D3—31no—
171C23×D3—31no—
172C23×D3—61no—
173C23×D3C4×D311yescharacteristic
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4—62no—
181C22×C3×C4—62no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—34no—
185C2×#67—64no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—61no—
189C22×Dic3C4×D311yescharacteristic
190C22×Dic3C4×D311yescharacteristic
191C22×Dic3C4×D311yescharacteristic
192C2×D12—34no—
193C2×D12—64no—
194C2×C4×D3—22no—
195C2×C4×D3—22no—
196C2×C4×D3—32no—
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—64no—
203C2×C4×D3—64no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3C4×D312yes—
209C2×C4×D3C22×D312yes—
210C3×M16—68no—
211C2×C3×C8—24no—
212C2×C3×C8—22no—
213C2×C3×C8—32no—
214C2×C3×C8—32no—
215C2×C3×C8—62no—
216C2×C3×C8—62no—
217C2×C3×C8D1214yescomplemented
218C2×C3×C8#6714yescomplemented
219C2×C3×C8C22×D312yes—
220C2×C3×C8C22×D312yes—
221C3×C42—32no—
222C3×C42—32no—
223#217—34no—
224(C2×D3)⋊C4—34no—
225(C2×D3)⋊C4—34no—
226(C2×D3)⋊C4—34no—
227C4⋊Dic3—34no—
228Dic3⋊C4—34no—
229C4×Dic3C4×D312yes—
230C4×Dic3C22×D312yes—
231C2×C3⋊C8—22no—
232C2×C3⋊C8—22no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—64no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8C22×D312yes—
240C2×C3⋊C8C22×D312yes—
241ΓL(1,𝔽25)—28no—
242ΓL(1,𝔽25)—616no—
243ΓL(1,𝔽25)—68no—
244ΓL(1,𝔽25)—68no—
245C22×C32C4×D412yes—
246C22×C32C2×M1612yes—
247C22×C32#13112yes—
248C22×C32C23×C411yescharacteristic
249C2×C3⋊D3—22no—
250C2×C3⋊D3—22no—
251C2×C3⋊D3—22no—
252C2×C3⋊D3—44no—
253C2×C3×D3—22no—
254C2×C3×D3—22no—
255C2×C3×D3—22no—
256C2×C3×D3—44no—
257C32×C4C4×D412yes—
258C32×C4C22×D411yescharacteristic
259C32×C4C2×#4111yescharacteristic
260C3⋊Dic3—22no—
261C3×Dic3—22no—
262C3×Dic3—22no—
263C3×Dic3C2×M1614yescomplemented
264C22×D4—91no—
265C23×C4—31no—
266C23×C4—91no—
267C2×M16—34no—
268C2×M16—64no—
269C2×M16—94no—
270C2×M16—184no—
271C22×C8—31no—
272C22×C8—31no—
273C22×C8—91no—
274C22×C8D3211yescharacteristic
275C4×D4—94no—
276C4×D4—94no—
277C2×C4⋊C4—91no—
278C2×C22⋊C4—91no—
279C2×C22⋊C4—91no—
280C2×C42—31no—
281C4⋊C8—94no—
282C22⋊C8—94no—
283C22⋊C8—94no—
284C4×C8—34no—
285C23×C3—21no—
286C23×C3—32no—
287C23×C3—62no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3C2×C4×D311yescharacteristic
291C23×C3C2×C4×D311yescharacteristic
292C22×D3—22no—
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—32no—
296C22×D3—32no—
297C22×D3—62no—
298C22×D3—64no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3C2×C4×D312yes—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—34no—
313C2×C3×C4—32no—
314C2×C3×C4—32no—
315C2×C3×C4—32no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—64no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4C2×C4×D311yescharacteristic
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4C2×D1212yes—
324C2×C3×C4#23512yes—
325C2×C3×C4#23512yes—
326C2×C3×C4C2×#6712yes—
327C2×C3×C4C23×D311yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329#67—68no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—62no—
335C2×Dic3—64no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3ΓL(1,𝔽25)14yescomplemented
339C2×Dic3C2×C4×D312yes—
340C2×Dic3C2×C4×D312yes—
341C2×Dic3C2×C4×D312yes—
342D12—68no—
343C4×D3—24no—
344C4×D3—22no—
345C4×D3—22no—
346C4×D3—64no—
347C4×D3—64no—
348C4×D3—68no—
349C4×D3—64no—
350C4×D3—64no—
351C4×D3—62no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—62no—
355C3×C8—24no—
356C3×C8—62no—
357C3×C8—62no—
358C3×C8C2×D1214yescomplemented
359C3×C8C2×#6714yescomplemented
360C3⋊C8—22no—
361C3⋊C8—22no—
362C3⋊C8—64no—
363C3⋊C8—62no—
364C3⋊C8—62no—
365C2×C32#43614yescomplemented
366C2×C32C2×C4×D411yescharacteristic
367C2×C32C22×M1611yescharacteristic
368C2×C32C2×#13111yescharacteristic
369C3⋊D3—42no—
370C3×D3—42no—
371C24—31no—
372C24—91no—
373C2×D4—94no—
374C2×D4—184no—
375C22×C4—31no—
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—32no—
379C22×C4—32no—
380C22×C4—62no—
381C22×C4—62no—
382C22×C4—91no—
383C22×C4—92no—
384C22×C4—92no—
385C22×C4—182no—
386C22×C4—182no—
387C22×C4C2×D3211yescharacteristic
388M16—68no—
389M16—188no—
390C2×C8—32no—
391C2×C8—32no—
392C2×C8—62no—
393C2×C8—62no—
394C2×C8—92no—
395C2×C8—182no—
396C2×C8#62614yescomplemented
397C2×C8C2×D3212yes—
398C4⋊C4—94no—
399C22⋊C4—94no—
400C22⋊C4—94no—
401C42—32no—
402C42—32no—
403C22×C3—22no—
404C22×C3—21no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—62no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3—124no—
411C22×C3C4×D1212yes—
412C22×C3C2×ΓL(1,𝔽25)12yes—
413C22×C3#90112yes—
414C22×C3D3×M1612yes—
415C22×C3#90712yes—
416C22×C3C4×#6712yes—
417C22×C3C22×C4×D311yescharacteristic
418C22×C3C22×C4×D311yescharacteristic
419C2×D3—22no—
420C2×D3—22no—
421C2×D3—22no—
422C2×D3—44no—
423C2×D3—64no—
424C2×D3—62no—
425C2×D3—62no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—128no—
433C2×D3—124no—
434C2×D3—124no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—34no—
439C3×C4—62no—
440C3×C4—62no—
441C3×C4C4×D1212yes—
442C3×C4C4×#6712yes—
443C3×C4C22×D1211yescharacteristic
444C3×C4C2×#23511yescharacteristic
445C3×C4C2×#23511yescharacteristic
446C3×C4C22×#6711yescharacteristic
447Dic3—22no—
448Dic3—22no—
449Dic3—64no—
450Dic3—62no—
451Dic3—62no—
452Dic3C2×ΓL(1,𝔽25)14yescomplemented
453C32C2×#43611yescharacteristic, complemented, Sylow
454C23—32no—
455C23—62no—
456C23—62no—
457C23—62no—
458C23—92no—
459C23—182no—
460C23—182no—
461C23—182no—
462C23C4×D3211yescharacteristic
463D4—188no—
464C2×C4—34no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—64no—
473C2×C4—92no—
474C2×C4—182no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—184no—
478C2×C4#379812yes—
479C2×C4C4×D3211yescharacteristic
480C2×C4C2×#62612yes—
481C2×C4C22×D3211yescharacteristic
482C8—62no—
483C8—62no—
484C8—182no—
485C8C2×#62614yescomplemented
486C2×C3—24no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—122no—
491C2×C3#468814yescomplemented
492C2×C3#512814yescomplemented
493C2×C3C2×C4×D1211yescharacteristic
494C2×C3C22×ΓL(1,𝔽25)11yescharacteristic
495C2×C3C2×#90111yescharacteristic
496C2×C3C2×D3×M1611yescharacteristic
497C2×C3C2×#90711yescharacteristic
498C2×C3C2×C4×#6711yescharacteristic
499D3—42no—
500D3—124no—
501D3—122no—
502D3—122no—
503C22—62no—
504C22—62no—
505C22—62no—
506C22—124no—
507C22—182no—
508C22—182no—
509C22—182no—
510C22—364no—
511C22D3×ΓL(1,𝔽25)12yes—
512C22#6380412yes—
513C22C4×#62612yes—
514C22C2×C4×D3211yescharacteristic
515C4—34no—
516C4—62no—
517C4—62no—
518C4—182no—
519C4C4×#62612yes—
520C4C2×#379811yescharacteristic
521C4C22×#62611yescharacteristic
522C3—21no—
523C3C2×#468811yescharacteristic, complemented
524C3C2×#512811yescharacteristic, complemented
525C2—122no—
526C2—362no—
527C2#1059072914yesdirect product factor
528C2C2×D3×ΓL(1,𝔽25)11yescharacteristic
529C2C2×#6380411yescharacteristic
530C2C2×C4×#62611yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC22×#626C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#436
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3743C2semidirect
2. C22×C3×ΓL(1,𝔽25)C2semidirect
4. C2×C3×C8×Dic3C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C2×#63557C2semidirect
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. #10590729C2direct (N × H)
17. C2×#3743C22semidirect
22. C2×C3×ΓL(1,𝔽25)C22semidirect
28. C3×C8×Dic3C22semidirect
29. Dic3⋊(C3⋊C8)C22semidirect
30. #63557C22semidirect
31. (C2×D3)⋊(C3⋊C8)C22semidirect
37. C22×ΓL(1,𝔽25)D3semidirect
46. C2×C8×Dic3D3semidirect
66. C2×C32×C8D4semidirect
118. C2×ΓL(1,𝔽25)C2×D3semidirect
127. C8×Dic3C2×D3semidirect
149. C2×C3×Dic3M16semidirect
157. C32×C8C2×D4semidirect
217. C2×C3×C8D12semidirect
218. C2×C3×C8#67semidirect
263. C3×Dic3C2×M16semidirect
338. C2×Dic3ΓL(1,𝔽25)semidirect
358. C3×C8C2×D12semidirect
359. C3×C8C2×#67semidirect
365. C2×C32#436semidirect
396. C2×C8#626semidirect
452. Dic3C2×ΓL(1,𝔽25)semidirect
453. C32C2×#436semidirect
485. C8C2×#626semidirect
491. C2×C3#4688semidirect
492. C2×C3#5128semidirect
523. C3C2×#4688semidirect
524. C3C2×#5128semidirect
527. C2#10590729direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37432
C22×C3×ΓL(1,𝔽25)2
C2×C4×#6262
C2×C3×C8×Dic32
C2×Dic3⋊(C3⋊C8)2
C2×#635572
C2×(C2×D3)⋊(C3⋊C8)2
#105907292
C2×#51283
C2×#46883