Finite Group Databasebeta

← C4×#88676 #13150868

Subgroups — C4×#88676 #13150868

Order 1728.

1585 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
2C2×#88676C211yesmaximal, characteristic
3C2×C4×((C3⋊D3)⋊C3)⋊C2C211yesmaximal, characteristic, complemented
4C4×#6235C211yesmaximal, characteristic, complemented
5C4×#638⋊C3C211yesmaximal, characteristic, complemented
6#11721314C211yesmaximal, characteristic, complemented
7#11721310C211yesmaximal, characteristic, complemented
8#11721293C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721154C211yesmaximal, characteristic, complemented
11C4×#6200C211yesmaximal, characteristic, complemented
12C4×#6198C211yesmaximal, characteristic, complemented
13#11721122C211yesmaximal, characteristic, complemented
14#11721119C211yesmaximal, characteristic, complemented
15C4×((C3⋊D3)⋊C3)⋊C4C211yesmaximal, characteristic, complemented
16C4×#3811—31nomaximal
17C4×D3×#67—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
21C2×#6235C2211yescharacteristic
22C2×C4×#272C2211yescharacteristic, complemented
23C2×#638⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
25C2×C4×(C3⋊D3)⋊C3—24no—
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
29C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
30C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
31#88676C418yesdirect product factor
32C2×#6200C2211yescharacteristic
33C2×#6199C2211yescharacteristic, complemented
34C2×#6198C2211yescharacteristic
35C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
36C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
37C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
38C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
39C4×((C3⋊D3)⋊C3)⋊C2—24no—
40#88552C2211yescharacteristic, complemented
41#88542C2211yescharacteristic, complemented
42#88540C2211yescharacteristic, complemented
43C4×#1084C2211yescharacteristic, complemented
44#3757⋊C3C2211yescharacteristic, complemented
45#3752⋊C3C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
48#88451C2211yescharacteristic, complemented
49#88450C2211yescharacteristic, complemented
50#88450C2211yescharacteristic, complemented
51#88450C2211yescharacteristic, complemented
52#88449C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88447C2211yescharacteristic, complemented
55#88447C2211yescharacteristic, complemented
56C22×C4×C3⋊D3D311yescharacteristic, complemented
57C22×C3×C4×D3—31no—
58C2×#3811—31no—
59C2×D3×#67—31no—
60C2×C4×D32—31no—
61C2×C4×D32—31no—
62C4×#638D311yescharacteristic, complemented
63C3×C4×#67—31no—
64C3×C4×#67—31no—
65C3×C4×#67—31no—
66C3×C4×#67—61no—
67#63974—31no—
68#67⋊Dic3—31no—
69#67⋊Dic3—31no—
70Dic3×#67—31no—
71D3×#217—31no—
72#63952—31no—
73#63921—31no—
74D3×(C2×D3)⋊C4—31no—
75#63904—31no—
76C4×#626—31no—
77C4×#626—31no—
78C4×#626—31no—
79C4×#625—31no—
80#63883—31no—
81C4×#624—31no—
82#63881—31no—
83#63881—31no—
84#63879—31no—
85D3×Dic3⋊C4—31no—
86C4×D3×Dic3—31no—
87C23×H(3,𝔽3)C2311yescharacteristic
88C22×#272C2311yescharacteristic
89C22×(C3⋊D3)⋊C3—22no—
90C22×(C3⋊D3)⋊C3—22no—
91C22×(C3⋊D3)⋊C3C2×C414yescomplemented
92C22×(C3⋊D3)⋊C3C2311yescharacteristic
93C22×(C3⋊D3)⋊C3C2311yescharacteristic
94C22×(C3⋊D3)⋊C3C2311yescharacteristic
95C2×((C3⋊D3)⋊C3)⋊C2—22no—
96C2×((C3⋊D3)⋊C3)⋊C2—22no—
97C2×((C3⋊D3)⋊C3)⋊C2C2×C414yescomplemented
98C2×C4×H(3,𝔽3)—22no—
99C2×C4×H(3,𝔽3)C2311yescharacteristic
100C2×C4×H(3,𝔽3)C2311yescharacteristic
101#6235C2×C414yescomplemented
102C2×#1084C2311yescharacteristic
103C2×#1084C2311yescharacteristic
104C2×#1084C2311yescharacteristic
105C4×#272—22no—
106#638⋊C3C2×C414yescomplemented
107C2×(C3⋊Dic3)⋊C3—22no—
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
113C4×(C3⋊D3)⋊C3—22no—
114C4×(C3⋊D3)⋊C3—22no—
115C4×(C3⋊D3)⋊C3—22no—
116C4×(C3⋊D3)⋊C3—22no—
117C4×(C3⋊D3)⋊C3D414yescomplemented
118#6200C2×C414yescomplemented
119#6199—22no—
120#6198C2×C414yescomplemented
121((C3⋊D3)⋊C3)⋊C4—22no—
122((C3⋊D3)⋊C3)⋊C4—22no—
123((C3⋊D3)⋊C3)⋊C4—22no—
124((C3⋊D3)⋊C3)⋊C4C2×C414yescomplemented
125C2×C4×#67—91no—
126C4×D3×D4—91no—
127C4×D3×D4—91no—
128C23×C3⋊D3C2×D311yescharacteristic
129C23×C3×D3—31no—
130C22×D32—31no—
131C22×D32—31no—
132C22×C32×C4—21no—
133C22×C32×C4C2×D311yescharacteristic, complemented
134C22×C32×C4C2×D311yescharacteristic, complemented
135C2×#638C2×D311yescharacteristic
136C22×C3⋊Dic3C2×D311yescharacteristic, complemented
137C2×C4×C3⋊D3—24no—
138C2×C4×C3⋊D3C2×D311yescharacteristic
139C2×C4×C3⋊D3C2×D311yescharacteristic
140C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
141C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
142C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—61no—
147C22×C3×Dic3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—64no—
156C2×C3×C4×D3—61no—
157#3811—38no—
158D3×#67—38no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#625—31no—
163C2×#624—31no—
164C2×#624—31no—
165C2×#624—31no—
166C2×#624—31no—
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173C4×D32—64no—
174C4×D32—64no—
175#3757C2×D311yescharacteristic, complemented
176#3752C2×D311yescharacteristic, complemented
177#3750C2×D311yescharacteristic, complemented
178C4×C3⋊Dic3C2×D311yescharacteristic, complemented
179C3×#217—31no—
180C3×#217—31no—
181C3×#217—31no—
182C3×#217—61no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—61no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—61no—
191C3×C4×Dic3—31no—
192C3×C4×Dic3—31no—
193C3×C4×Dic3—31no—
194C3×C4×Dic3—61no—
195#3724—31no—
196Dic3⋊Dic3—31no—
197Dic3⋊Dic3—31no—
198Dic3⋊Dic3—31no—
199#3722—31no—
200#3722—31no—
201#3722—31no—
202(C2×D3)⋊Dic3—31no—
203(C2×D3)⋊Dic3—31no—
204(C2×D3)⋊Dic3—31no—
205(C2×D3)⋊Dic3—31no—
206(C2×D3)⋊Dic3—31no—
207Dic32—31no—
208Dic32—31no—
209Dic32—31no—
210Dic32—31no—
211C22×H(3,𝔽3)—21no—
212C22×H(3,𝔽3)—21no—
213C22×H(3,𝔽3)C22×C412yescomplemented
214C22×H(3,𝔽3)C2411yescharacteristic
215C2×#272—21no—
216C2×#272—21no—
217C2×#272C22×C412yescomplemented
218C2×(C3⋊D3)⋊C3—21no—
219C2×(C3⋊D3)⋊C3—21no—
220C2×(C3⋊D3)⋊C3—21no—
221C2×(C3⋊D3)⋊C3—21no—
222C2×(C3⋊D3)⋊C3—28no—
223C2×(C3⋊D3)⋊C3C22×C412yes—
224C2×(C3⋊D3)⋊C3C22×C412yescomplemented
225C2×(C3⋊D3)⋊C3C22×C412yescomplemented
226C2×(C3⋊D3)⋊C3C2×D412yes—
227C2×(C3⋊D3)⋊C3#4112yes—
228((C3⋊D3)⋊C3)⋊C2—28no—
229C4×H(3,𝔽3)—21no—
230C4×H(3,𝔽3)C2×D412yescomplemented
231#1084—21no—
232#1084—21no—
233#1084C22×C412yescomplemented
234(C3⋊Dic3)⋊C3—21no—
235(C3⋊Dic3)⋊C3—21no—
236(C3⋊Dic3)⋊C3—21no—
237(C3⋊Dic3)⋊C3C22×C412yescomplemented
238(C3⋊Dic3)⋊C3C2×D412yescomplemented
239C23×C3×C4—91no—
240C22×#67—91no—
241C2×D3×D4—91no—
242C2×D3×D4—91no—
243C22×C4×D3—31no—
244C22×C4×D3—91no—
245C22×C4×D3—91no—
246C22×C4×D3—91no—
247C22×C4×D3—91no—
248C3×C4×D4—91no—
249C3×C4×D4—91no—
250C2×#217—91no—
251D4×Dic3—91no—
252D4×Dic3—91no—
253C4×#67—31no—
254C4×#67—31no—
255C4×#67—31no—
256C4×#67—61no—
257C4×#67—91no—
258C4×#67—91no—
259C4×#67—91no—
260C4×#67—91no—
261C4×#67—91no—
262C4×#67—91no—
263C4×#67—91no—
264C4×#67—91no—
265C4×#67—91no—
266C2×(C2×D3)⋊C4—91no—
267C2×Dic3⋊C4—91no—
268C2×C4×Dic3—91no—
269#893—91no—
270#893—91no—
271D3×C4⋊C4—91no—
272D3×C4⋊C4—91no—
273#67⋊C4—91no—
274#67⋊C4—91no—
275#67⋊C4—91no—
276#67⋊C4—91no—
277D3×C22⋊C4—91no—
278D3×C22⋊C4—91no—
279D3×C22⋊C4—91no—
280D3×C22⋊C4—91no—
281C4×D12—91no—
282C4×D12—91no—
283C42×D3—91no—
284C42×D3—91no—
285C23×C32—21no—
286C23×C32C22×D311yescharacteristic
287C23×C32C22×D311yescharacteristic
288C22×C3⋊D3—22no—
289C22×C3⋊D3—22no—
290C22×C3⋊D3C4×D314yescomplemented
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3⋊D3C22×D311yescharacteristic
294C22×C3×D3—31no—
295C22×C3×D3—34no—
296C22×C3×D3—31no—
297C22×C3×D3—31no—
298C22×C3×D3—31no—
299C22×C3×D3—31no—
300C22×C3×D3—61no—
301C22×C3×D3—62no—
302C22×C3×D3—62no—
303C2×D32—34no—
304C2×D32—34no—
305C2×D32—62no—
306C2×D32—62no—
307C2×D32—62no—
308C2×D32—62no—
309C2×C32×C4—22no—
310C2×C32×C4—22no—
311C2×C32×C4—21no—
312C2×C32×C4—21no—
313C2×C32×C4—42no—
314C2×C32×C4C22×D311yescharacteristic
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C22×D311yescharacteristic
317C2×C32×C4C22×D311yescharacteristic
318#638C4×D314yescomplemented
319C2×C3⋊Dic3—22no—
320C2×C3⋊Dic3C22×D311yescharacteristic
321C2×C3⋊Dic3C22×D311yescharacteristic
322C2×C3⋊Dic3C22×D311yescharacteristic
323C2×C3⋊Dic3C22×D311yescharacteristic
324C2×C3⋊Dic3C22×D311yescharacteristic
325C4×C3⋊D3—22no—
326C4×C3⋊D3—22no—
327C4×C3⋊D3—22no—
328C4×C3⋊D3—22no—
329C4×C3⋊D3#6714yescomplemented
330C3×#67—34no—
331C3×#67—34no—
332C3×#67—34no—
333C3×#67—64no—
334C2×C3×Dic3—31no—
335C2×C3×Dic3—31no—
336C2×C3×Dic3—31no—
337C2×C3×Dic3—31no—
338C2×C3×Dic3—31no—
339C2×C3×Dic3—31no—
340C2×C3×Dic3—31no—
341C2×C3×Dic3—31no—
342C2×C3×Dic3—31no—
343C2×C3×Dic3—31no—
344C2×C3×Dic3—31no—
345C2×C3×Dic3—61no—
346C2×C3×Dic3—61no—
347C2×C3×Dic3—61no—
348C2×C3×Dic3—62no—
349C3×C4×D3—34no—
350C3×C4×D3—62no—
351C3×C4×D3—62no—
352C3×C4×D3—62no—
353C3×C4×D3—62no—
354C3×C4×D3—62no—
355C3×C4×D3—62no—
356C3×C4×D3—122no—
357#626—34no—
358#626—34no—
359#626—34no—
360#625—34no—
361#624—34no—
362#624—62no—
363#624—62no—
364#624—62no—
365D3×Dic3—34no—
366D3×Dic3—62no—
367D3×Dic3—62no—
368D3×Dic3—62no—
369D3×Dic3—62no—
370D3×Dic3—62no—
371C2×C4×D4—271noSylow
372C2×H(3,𝔽3)—22no—
373C2×H(3,𝔽3)C23×C411yescharacteristic
374C2×H(3,𝔽3)C22×D411yescharacteristic
375C2×H(3,𝔽3)C2×#4111yescharacteristic
376#272—22no—
377(C3⋊D3)⋊C3—22no—
378(C3⋊D3)⋊C3—22no—
379(C3⋊D3)⋊C3C4×D414yescomplemented
380C24×C3—91no—
381C23×D3—31no—
382C23×D3—91no—
383C23×D3—91no—
384C23×D3—91no—
385C23×D3—91no—
386C2×C3×D4—91no—
387C2×C3×D4—91no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—61no—
391C22×C3×C4—91no—
392C22×C3×C4—91no—
393C22×C3×C4—91no—
394C22×C3×C4—91no—
395C22×C3×C4—91no—
396C22×C3×C4—91no—
397C22×C3×C4—91no—
398C22×C3×C4—184no—
399C22×C3×C4D3211yescharacteristic
400C2×#67—31no—
401C2×#67—31no—
402C2×#67—31no—
403C2×#67—61no—
404C2×#67—91no—
405C2×#67—91no—
406C2×#67—91no—
407C2×#67—91no—
408C2×#67—98no—
409C2×#67—91no—
410C22×Dic3—31no—
411C22×Dic3—91no—
412C22×Dic3—91no—
413C22×Dic3—91no—
414C22×Dic3—91no—
415C22×Dic3—91no—
416C22×Dic3—91no—
417D3×D4—98no—
418D3×D4—98no—
419C2×D12—91no—
420C2×D12—91no—
421C2×C4×D3—31no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—61no—
429C2×C4×D3—64no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×C4×D3—91no—
438C2×C4×D3—91no—
439C2×C4×D3—91no—
440C2×C4×D3—91no—
441C2×C4×D3—91no—
442C2×C4×D3—91no—
443C2×C4×D3—91no—
444C2×C4×D3—91no—
445C2×C4×D3—184no—
446C2×C4×D3—184no—
447C2×C4×D3—184no—
448C2×C4×D3—184no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C22⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C42—91no—
456C3×C42—91no—
457#217—31no—
458#217—31no—
459#217—31no—
460#217—61no—
461#217—91no—
462#217—91no—
463#217—91no—
464#217—91no—
465#217—91no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—31no—
469(C2×D3)⋊C4—61no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—91no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479C4⋊Dic3—91no—
480C4⋊Dic3—91no—
481Dic3⋊C4—31no—
482Dic3⋊C4—31no—
483Dic3⋊C4—31no—
484Dic3⋊C4—61no—
485Dic3⋊C4—91no—
486Dic3⋊C4—91no—
487Dic3⋊C4—91no—
488Dic3⋊C4—91no—
489Dic3⋊C4—91no—
490C4×Dic3—31no—
491C4×Dic3—31no—
492C4×Dic3—31no—
493C4×Dic3—61no—
494C4×Dic3—91no—
495C4×Dic3—91no—
496C4×Dic3—91no—
497C4×Dic3—91no—
498C4×Dic3—91no—
499C4×Dic3—91no—
500C4×Dic3—91no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32—21no—
506C22×C32—22no—
507C22×C32—41no—
508C22×C32—41no—
509C22×C32C2×C4×D312yescomplemented
510C22×C32C2×C4×D312yescomplemented
511C22×C32C23×D311yescharacteristic
512C22×C32C23×D311yescharacteristic
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3—28no—
518C2×C3⋊D3C2×C4×D312yes—
519C2×C3⋊D3C2×C4×D312yescomplemented
520C2×C3⋊D3C2×C4×D312yescomplemented
521C2×C3⋊D3#23512yes—
522C2×C3⋊D3C2×#6712yes—
523C2×C3×D3—32no—
524C2×C3×D3—32no—
525C2×C3×D3—32no—
526C2×C3×D3—32no—
527C2×C3×D3—32no—
528C2×C3×D3—32no—
529C2×C3×D3—32no—
530C2×C3×D3—62no—
531C2×C3×D3—68no—
532C2×C3×D3—61no—
533C2×C3×D3—61no—
534C2×C3×D3—61no—
535C2×C3×D3—61no—
536C2×C3×D3—61no—
537C2×C3×D3—61no—
538C2×C3×D3—61no—
539C2×C3×D3—61no—
540C2×C3×D3—121no—
541C2×C3×D3—121no—
542D32—68no—
543D32—68no—
544C32×C4—21no—
545C32×C4—21no—
546C32×C4—22no—
547C32×C4—41no—
548C32×C4D3×D412yescomplemented
549C32×C4C2×#6712yescomplemented
550C3⋊Dic3—21no—
551C3⋊Dic3—21no—
552C3⋊Dic3—21no—
553C3⋊Dic3C2×C4×D312yescomplemented
554C3⋊Dic3C2×#6712yescomplemented
555C3×Dic3—32no—
556C3×Dic3—32no—
557C3×Dic3—32no—
558C3×Dic3—32no—
559C3×Dic3—62no—
560C3×Dic3—61no—
561C3×Dic3—61no—
562C3×Dic3—61no—
563C3×Dic3—61no—
564C3×Dic3—61no—
565C3×Dic3—61no—
566C3×Dic3—61no—
567C3×Dic3—121no—
568C3×Dic3—121no—
569C22×D4—271no—
570C23×C4—91no—
571C23×C4—271no—
572C4×D4—91no—
573C4×D4—91no—
574C4×D4—271no—
575C4×D4—271no—
576C4×D4—271no—
577C4×D4—271no—
578C4×D4—271no—
579C4×D4—271no—
580C2×C4⋊C4—271no—
581C2×C22⋊C4—271no—
582C2×C22⋊C4—271no—
583C2×C42—271no—
584H(3,𝔽3)C2×C4×D411yescharacteristic, complemented, Sylow
585C23×C3—31no—
586C23×C3—31no—
587C23×C3—61no—
588C23×C3—91no—
589C23×C3—91no—
590C23×C3—91no—
591C23×C3—94no—
592C23×C3—91no—
593C23×C3—182no—
594C23×C3—182no—
595C23×C3C2×D3211yescharacteristic
596C22×D3—31no—
597C22×D3—31no—
598C22×D3—31no—
599C22×D3—31no—
600C22×D3—31no—
601C22×D3—34no—
602C22×D3—61no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—91no—
606C22×D3—94no—
607C22×D3—91no—
608C22×D3—91no—
609C22×D3—94no—
610C22×D3—94no—
611C22×D3—94no—
612C22×D3—182no—
613C22×D3—182no—
614C22×D3—182no—
615C22×D3—182no—
616C22×D3—182no—
617C22×D3—182no—
618C22×D3—182no—
619C22×D3—182no—
620C3×D4—94no—
621C3×D4—94no—
622C2×C3×C4—22no—
623C2×C3×C4—31no—
624C2×C3×C4—31no—
625C2×C3×C4—31no—
626C2×C3×C4—31no—
627C2×C3×C4—62no—
628C2×C3×C4—62no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—94no—
632C2×C3×C4—91no—
633C2×C3×C4—91no—
634C2×C3×C4—91no—
635C2×C3×C4—91no—
636C2×C3×C4—91no—
637C2×C3×C4—91no—
638C2×C3×C4—91no—
639C2×C3×C4—91no—
640C2×C3×C4—122no—
641C2×C3×C4—182no—
642C2×C3×C4—182no—
643C2×C3×C4—182no—
644C2×C3×C4—182no—
645C2×C3×C4—182no—
646C2×C3×C4—182no—
647C2×C3×C4C2×D3211yescharacteristic
648C2×C3×C4C2×D3211yescharacteristic
649#67—34no—
650#67—34no—
651#67—34no—
652#67—64no—
653#67—94no—
654#67—94no—
655#67—94no—
656#67—94no—
657#67—94no—
658C2×Dic3—31no—
659C2×Dic3—31no—
660C2×Dic3—31no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—31no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—31no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—62no—
673C2×Dic3—91no—
674C2×Dic3—91no—
675C2×Dic3—91no—
676C2×Dic3—91no—
677C2×Dic3—91no—
678C2×Dic3—94no—
679C2×Dic3—182no—
680C2×Dic3—182no—
681C2×Dic3—182no—
682C2×Dic3—182no—
683C2×Dic3—182no—
684D12—94no—
685D12—94no—
686C4×D3—34no—
687C4×D3—62no—
688C4×D3—62no—
689C4×D3—62no—
690C4×D3—62no—
691C4×D3—62no—
692C4×D3—62no—
693C4×D3—94no—
694C4×D3—94no—
695C4×D3—94no—
696C4×D3—122no—
697C4×D3—182no—
698C4×D3—182no—
699C4×D3—182no—
700C4×D3—182no—
701C4×D3—182no—
702C4×D3—182no—
703C4×D3—182no—
704C4×D3—182no—
705C4×D3—182no—
706C4×D3—182no—
707C4×D3—182no—
708C4×D3—182no—
709C2×C32—22no—
710C2×C32—22no—
711C2×C32—21no—
712C2×C32—21no—
713C2×C32—21no—
714C2×C32—42no—
715C2×C32C22×C4×D311yescharacteristic
716C2×C32C22×C4×D311yescharacteristic
717C2×C32C2×#23511yescharacteristic
718C2×C32C2×D3×D411yescharacteristic
719C2×C32D3×#4111yescharacteristic
720C2×C32C22×#6711yescharacteristic
721C3⋊D3—22no—
722C3⋊D3—22no—
723C3⋊D3C4×#6714yescomplemented
724C3×D3—34no—
725C3×D3—62no—
726C3×D3—62no—
727C3×D3—62no—
728C3×D3—62no—
729C3×D3—122no—
730C24—91no—
731C24—271no—
732C2×D4—91no—
733C2×D4—91no—
734C2×D4—271no—
735C2×D4—271no—
736C2×D4—278no—
737C22×C4—91no—
738C22×C4—91no—
739C22×C4—91no—
740C22×C4—91no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—91no—
744C22×C4—184no—
745C22×C4—271no—
746C22×C4—271no—
747C22×C4—271no—
748C22×C4—271no—
749C22×C4—271no—
750C22×C4—544no—
751C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
752C4⋊C4—91no—
753C4⋊C4—91no—
754C4⋊C4—271no—
755C4⋊C4—271no—
756C22⋊C4—91no—
757C22⋊C4—91no—
758C22⋊C4—91no—
759C22⋊C4—91no—
760C22⋊C4—271no—
761C22⋊C4—271no—
762C22⋊C4—271no—
763C22⋊C4—271no—
764C42—91no—
765C42—91no—
766C42—271no—
767C42—271no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—31no—
771C22×C3—31no—
772C22×C3—32no—
773C22×C3—32no—
774C22×C3—61no—
775C22×C3—61no—
776C22×C3—61no—
777C22×C3—61no—
778C22×C3—61no—
779C22×C3—62no—
780C22×C3—92no—
781C22×C3—92no—
782C22×C3—92no—
783C22×C3—92no—
784C22×C3—92no—
785C22×C3—92no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—181no—
789C22×C3—181no—
790C22×C3—181no—
791C22×C3—181no—
792C22×C3—188no—
793C22×C3—181no—
794C22×C3—181no—
795C22×C3C4×D3212yes—
796C22×C3C22×D3211yescharacteristic
797C2×D3—32no—
798C2×D3—32no—
799C2×D3—32no—
800C2×D3—32no—
801C2×D3—32no—
802C2×D3—32no—
803C2×D3—32no—
804C2×D3—62no—
805C2×D3—68no—
806C2×D3—61no—
807C2×D3—61no—
808C2×D3—61no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—61no—
814C2×D3—92no—
815C2×D3—92no—
816C2×D3—92no—
817C2×D3—92no—
818C2×D3—92no—
819C2×D3—121no—
820C2×D3—121no—
821C2×D3—188no—
822C2×D3—181no—
823C2×D3—181no—
824C2×D3—181no—
825C2×D3—181no—
826C2×D3—188no—
827C2×D3—188no—
828C2×D3—188no—
829C3×C4—21no—
830C3×C4—32no—
831C3×C4—32no—
832C3×C4—61no—
833C3×C4—61no—
834C3×C4—62no—
835C3×C4—92no—
836C3×C4—92no—
837C3×C4—92no—
838C3×C4—121no—
839C3×C4—181no—
840C3×C4—181no—
841C3×C4—181no—
842C3×C4—181no—
843C3×C4—181no—
844C3×C4D3×#6712yes—
845Dic3—32no—
846Dic3—32no—
847Dic3—32no—
848Dic3—32no—
849Dic3—62no—
850Dic3—61no—
851Dic3—61no—
852Dic3—61no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—92no—
858Dic3—92no—
859Dic3—121no—
860Dic3—121no—
861Dic3—181no—
862Dic3—181no—
863Dic3—181no—
864C32—21no—
865C32C4×D3×D411yescharacteristic, complemented
866C32C2×C4×#6711yescharacteristic, complemented
867C23—91no—
868C23—91no—
869C23—91no—
870C23—91no—
871C23—94no—
872C23—182no—
873C23—182no—
874C23—274no—
875C23—542no—
876C23—542no—
877C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
878D4—94no—
879D4—94no—
880D4—274no—
881D4—274no—
882C2×C4—22no—
883C2×C4—91no—
884C2×C4—91no—
885C2×C4—91no—
886C2×C4—94no—
887C2×C4—91no—
888C2×C4—91no—
889C2×C4—91no—
890C2×C4—91no—
891C2×C4—91no—
892C2×C4—182no—
893C2×C4—182no—
894C2×C4—182no—
895C2×C4—182no—
896C2×C4—182no—
897C2×C4—182no—
898C2×C4—274no—
899C2×C4—542no—
900C2×C4—542no—
901C2×C4—542no—
902C2×C4—542no—
903C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
904C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
905C2×C3—22no—
906C2×C3—31no—
907C2×C3—31no—
908C2×C3—31no—
909C2×C3—31no—
910C2×C3—31no—
911C2×C3—31no—
912C2×C3—62no—
913C2×C3—62no—
914C2×C3—61no—
915C2×C3—61no—
916C2×C3—61no—
917C2×C3—94no—
918C2×C3—122no—
919C2×C3—182no—
920C2×C3—182no—
921C2×C3—182no—
922C2×C3C2×C4×D3211yescharacteristic
923C2×C3D3×#23511yescharacteristic
924C2×C3C2×D3×#6711yescharacteristic
925D3—34no—
926D3—62no—
927D3—62no—
928D3—62no—
929D3—62no—
930D3—94no—
931D3—122no—
932D3—182no—
933D3—182no—
934C22—21no—
935C22—21no—
936C22—92no—
937C22—92no—
938C22—92no—
939C22—92no—
940C22—92no—
941C22—92no—
942C22—188no—
943C22—181no—
944C22—181no—
945C22—181no—
946C22—181no—
947C22—181no—
948C22—181no—
949C22—548no—
950C22C4×((C3⋊D3)⋊C3)⋊C212yescomplemented
951C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
952C4—21no—
953C4—92no—
954C4—92no—
955C4—92no—
956C4—181no—
957C4—181no—
958C4—181no—
959C4—181no—
960C4—181no—
961C4#8867612yesdirect product factor
962C3—31no—
963C3—31no—
964C3—61no—
965C3C4×D3×#6711yescharacteristic
966C2—22no—
967C2—94no—
968C2—182no—
969C2—182no—
970C2—182no—
971C2C2×C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
972C2#1172249011yescharacteristic
973C2C2×#8867611yescharacteristic
subgroupG/H
centerC2×C4C2×((C3⋊D3)⋊C3)⋊C2
commutatorC2×H(3,𝔽3)C23×C4
Frattini, socleC22×C3C22×D32
FittingC22×C4×H(3,𝔽3)C22
prime radicalC2×#88676C2
cosocleC22×H(3,𝔽3)C24
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×C4×D4
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×(C3⋊D3)⋊C3C2semidirect
3. C2×C4×((C3⋊D3)⋊C3)⋊C2C2semidirect
4. C4×#6235C2semidirect
5. C4×#638⋊C3C2semidirect
6. #11721314C2semidirect
7. #11721310C2semidirect
8. #11721293C2semidirect
9. #11721160C2semidirect
10. #11721154C2semidirect
11. C4×#6200C2semidirect
12. C4×#6198C2semidirect
13. #11721122C2semidirect
14. #11721119C2semidirect
15. C4×((C3⋊D3)⋊C3)⋊C4C2semidirect
20. C22×C4×H(3,𝔽3)C22semidirect
22. C2×C4×#272C22semidirect
24. C22×(C3⋊Dic3)⋊C3C22semidirect
28. C2×C4×(C3⋊D3)⋊C3C22semidirect
29. C2×C4×(C3⋊D3)⋊C3C22semidirect
30. C2×C4×(C3⋊D3)⋊C3C22semidirect
31. #88676C4direct (N × H)
33. C2×#6199C22semidirect
38. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
40. #88552C22semidirect
41. #88542C22semidirect
42. #88540C22semidirect
43. C4×#1084C22semidirect
44. #3757⋊C3C22semidirect
45. #3752⋊C3C22semidirect
46. #3750⋊C3C22semidirect
47. C4×(C3⋊Dic3)⋊C3C22semidirect
48. #88451C22semidirect
49. #88450C22semidirect
50. #88450C22semidirect
51. #88450C22semidirect
52. #88449C22semidirect
53. #88448C22semidirect
54. #88447C22semidirect
55. #88447C22semidirect
56. C22×C4×C3⋊D3D3semidirect
62. C4×#638D3semidirect
91. C22×(C3⋊D3)⋊C3C2×C4semidirect
97. C2×((C3⋊D3)⋊C3)⋊C2C2×C4semidirect
101. #6235C2×C4semidirect
106. #638⋊C3C2×C4semidirect
117. C4×(C3⋊D3)⋊C3D4semidirect
118. #6200C2×C4semidirect
120. #6198C2×C4semidirect
124. ((C3⋊D3)⋊C3)⋊C4C2×C4semidirect
133. C22×C32×C4C2×D3semidirect
134. C22×C32×C4C2×D3semidirect
136. C22×C3⋊Dic3C2×D3semidirect
140. C2×C4×C3⋊D3C2×D3semidirect
141. C2×C4×C3⋊D3C2×D3semidirect
142. C2×C4×C3⋊D3C2×D3semidirect
175. #3757C2×D3semidirect
176. #3752C2×D3semidirect
177. #3750C2×D3semidirect
178. C4×C3⋊Dic3C2×D3semidirect
213. C22×H(3,𝔽3)C22×C4semidirect
217. C2×#272C22×C4semidirect
224. C2×(C3⋊D3)⋊C3C22×C4semidirect
225. C2×(C3⋊D3)⋊C3C22×C4semidirect
230. C4×H(3,𝔽3)C2×D4semidirect
233. #1084C22×C4semidirect
237. (C3⋊Dic3)⋊C3C22×C4semidirect
238. (C3⋊Dic3)⋊C3C2×D4semidirect
290. C22×C3⋊D3C4×D3semidirect
318. #638C4×D3semidirect
329. C4×C3⋊D3#67semidirect
379. (C3⋊D3)⋊C3C4×D4semidirect
509. C22×C32C2×C4×D3semidirect
510. C22×C32C2×C4×D3semidirect
519. C2×C3⋊D3C2×C4×D3semidirect
520. C2×C3⋊D3C2×C4×D3semidirect
548. C32×C4D3×D4semidirect
549. C32×C4C2×#67semidirect
553. C3⋊Dic3C2×C4×D3semidirect
554. C3⋊Dic3C2×#67semidirect
584. H(3,𝔽3)C2×C4×D4semidirect
723. C3⋊D3C4×#67semidirect
751. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
865. C32C4×D3×D4semidirect
866. C32C2×C4×#67semidirect
950. C22C4×((C3⋊D3)⋊C3)⋊C2semidirect
961. C4#88676direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×(C3⋊D3)⋊C32
C2×#886762
C2×C4×((C3⋊D3)⋊C3)⋊C22
C4×#62352
C4×#638⋊C32
#117213142
#117213102
#117212932
#117211602
#117211542
C4×#62002
C4×#61982
#117211222
#117211192
C4×((C3⋊D3)⋊C3)⋊C42
C4×#38113
C4×D3×#673