Finite Group Databasebeta

← C4×#88654 #13147895

Subgroups — C4×#88654 #13147895

Order 1728.

1585 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88654C211yesmaximal, characteristic
2C2×C4×((C3⋊D3)⋊C3)⋊C2C212yesmaximal, complemented
3C4×C4⋊#272C211yesmaximal, characteristic, complemented
4C4×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
5C42×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
6#11721160C212yesmaximal, complemented
7C4×#6200C212yesmaximal, complemented
8#11721149C211yesmaximal, characteristic, complemented
9#11721132C211yesmaximal, characteristic, complemented
10#11721129C211yesmaximal, characteristic, complemented
11#11721123C212yesmaximal, complemented
12C4×#3802—31nomaximal
13C4×D3×D12—31nomaximal
14C22×((C3⋊D3)⋊C3)⋊C2C2212yes—
15C2×C4⋊#272C2211yescharacteristic
16C2×C4×#272C2212yescomplemented
17C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
18C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
19C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
20C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2212yescomplemented
22C2×#6200C2212yes—
23C2×#6199C2212yescomplemented
24C2×((C3⋊D3)⋊C3)⋊C4C2212yes—
25C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
26#88654C418yesdirect product factor
27C4×((C3⋊D3)⋊C3)⋊C2—28no—
28C42×H(3,𝔽3)C2211yescharacteristic, complemented
29#88542C2212yescomplemented
30C4⋊#1084C2211yescharacteristic, complemented
31#3752⋊C3C2212yescomplemented
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
33C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
34C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
35C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
36#88451C2212yescomplemented
37#88450C2212yescomplemented
38#88448C2212yescomplemented
39C2×#3802—31no—
40C2×D3×D12—31no—
41C2×C4×D32—32no—
42C2×C4×D32—32no—
43C4×C4⋊(C3⋊D3)D311yescharacteristic, complemented
44C42×C3⋊D3D311yescharacteristic, complemented
45C3×C4×D12—31no—
46C3×C4×D12—31no—
47C3×C4×D12—31no—
48C3×C4×D12—61no—
49C3×C42×D3—31no—
50#63921—32no—
51D3×(C2×D3)⋊C4—32no—
52C4×#626—32no—
53#63902—32no—
54C4×#625—32no—
55#63900—31no—
56#63898—31no—
57#63898—31no—
58#63894—31no—
59Dic3×D12—31no—
60D3×C4⋊Dic3—31no—
61#63880—32no—
62C22×#272C2312yes—
63C22×(C3⋊D3)⋊C3C2312yes—
64C22×(C3⋊D3)⋊C3C2311yescharacteristic
65C2×((C3⋊D3)⋊C3)⋊C2—24no—
66C2×((C3⋊D3)⋊C3)⋊C2—24no—
67C2×((C3⋊D3)⋊C3)⋊C2C2×C418yescomplemented
68C2×C4×H(3,𝔽3)C2311yescharacteristic
69C2×C4×H(3,𝔽3)C2311yescharacteristic
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71C2×#1084C2312yes—
72C4⋊#272C2×C414yescomplemented
73C4×#272—24no—
74C2×(C3⋊Dic3)⋊C3C2312yes—
75C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
76C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
77C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
78C4⋊((C3⋊D3)⋊C3)C2×C414yescomplemented
79C4×(C3⋊D3)⋊C3—22no—
80C4×(C3⋊D3)⋊C3—24no—
81C4×(C3⋊D3)⋊C3C2×C414yescomplemented
82C4×(C3⋊D3)⋊C3D414yescomplemented
83#6200C2×C418yescomplemented
84#6199—24no—
85((C3⋊D3)⋊C3)⋊C4—24no—
86((C3⋊D3)⋊C3)⋊C4—24no—
87C4×D3×D4—91no—
88C4×D3×D4—91no—
89C2×C4×D12—91no—
90C22×D32—32no—
91C22×D32—32no—
92C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
93C2×C4×C3⋊D3C2×D311yescharacteristic
94C2×C4×C3⋊D3C2×D311yescharacteristic
95C2×C4×C3⋊D3C2×D311yescharacteristic
96C2×C4×C3⋊D3C2×D312yescomplemented
97C2×C3×D12—31no—
98C2×C3×D12—31no—
99C2×C3×D12—31no—
100C2×C3×D12—61no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3—32no—
104C2×C3×C4×D3—32no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—62no—
108C2×#626—32no—
109C2×#625—32no—
110C2×#624—32no—
111C2×#624—32no—
112C2×D3×Dic3—32no—
113C2×D3×Dic3—32no—
114C2×D3×Dic3—32no—
115C2×D3×Dic3—32no—
116#3802—38no—
117D3×D12—38no—
118C4×D32—68no—
119C4×D32—68no—
120C32×C42—21no—
121C32×C42C2×D311yescharacteristic, complemented
122C32×C42C2×D311yescharacteristic, complemented
123#3752C2×D312yescomplemented
124C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
125C4×C3⋊Dic3C2×D311yescharacteristic, complemented
126C4×C3⋊Dic3C2×D311yescharacteristic, complemented
127C4×C3⋊Dic3C2×D311yescharacteristic, complemented
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—32no—
131C3×(C2×D3)⋊C4—62no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—31no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—61no—
136C3×C4×Dic3—31no—
137C3×C4×Dic3—31no—
138C3×C4×Dic3—31no—
139#3724—32no—
140Dic3⋊Dic3—32no—
141#3722—32no—
142(C2×D3)⋊Dic3—32no—
143(C2×D3)⋊Dic3—32no—
144(C2×D3)⋊Dic3—32no—
145C22×H(3,𝔽3)C2411yescharacteristic
146C2×#272—22no—
147C2×#272—22no—
148C2×#272C22×C414yescomplemented
149C2×(C3⋊D3)⋊C3—22no—
150C2×(C3⋊D3)⋊C3—22no—
151C2×(C3⋊D3)⋊C3C22×C412yes—
152C2×(C3⋊D3)⋊C3C22×C414yescomplemented
153C2×(C3⋊D3)⋊C3C2×D412yes—
154C2×(C3⋊D3)⋊C3#4112yes—
155((C3⋊D3)⋊C3)⋊C2—216no—
156C4×H(3,𝔽3)—21no—
157C4×H(3,𝔽3)C22×C412yescomplemented
158C4×H(3,𝔽3)C2×D412yescomplemented
159#1084—22no—
160(C3⋊Dic3)⋊C3—22no—
161(C3⋊Dic3)⋊C3—21no—
162(C3⋊Dic3)⋊C3C22×C412yescomplemented
163(C3⋊Dic3)⋊C3C2×D412yescomplemented
164C2×D3×D4—91no—
165C2×D3×D4—91no—
166C22×D12—91no—
167C22×C4×D3—92no—
168C22×C4×D3—92no—
169C22×C4×D3—92no—
170C3×C4×D4—91no—
171C3×C4×D4—91no—
172C2×C3×C42—91no—
173D4×Dic3—91no—
174D4×Dic3—91no—
175C4×#67—92no—
176C4×#67—92no—
177C2×(C2×D3)⋊C4—92no—
178C2×C4⋊Dic3—91no—
179#893—91no—
180#893—91no—
181D3×C4⋊C4—91no—
182D3×C4⋊C4—91no—
183#67⋊C4—92no—
184#67⋊C4—92no—
185D3×C22⋊C4—92no—
186D3×C22⋊C4—92no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—61no—
191C4×D12—91no—
192C4×D12—91no—
193C4×D12—92no—
194C4×D12—92no—
195C4×D12—91no—
196C42×D3—31no—
197C42×D3—91no—
198C22×C3⋊D3C22×D312yes—
199C22×C3⋊D3C22×D311yescharacteristic
200C22×C3×D3—31no—
201C22×C3×D3—32no—
202C22×C3×D3—32no—
203C22×C3×D3—32no—
204C22×C3×D3—62no—
205C2×D32—38no—
206C2×D32—38no—
207C2×D32—64no—
208C2×D32—64no—
209C2×D32—64no—
210C2×D32—64no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4C22×D311yescharacteristic
215C2×C32×C4C22×D311yescharacteristic
216C2×C32×C4C22×D311yescharacteristic
217C2×C32×C4C22×D311yescharacteristic
218C2×C32×C4C22×D311yescharacteristic
219C2×C32×C4C22×D311yescharacteristic
220C2×C3⋊Dic3C22×D311yescharacteristic
221C2×C3⋊Dic3C22×D312yes—
222C2×C3⋊Dic3C22×D311yescharacteristic
223C2×C3⋊Dic3C22×D311yescharacteristic
224C4⋊(C3⋊D3)C4×D314yescomplemented
225C4×C3⋊D3—22no—
226C4×C3⋊D3—24no—
227C4×C3⋊D3C4×D314yescomplemented
228C4×C3⋊D3D1214yescomplemented
229C2×C3×Dic3—31no—
230C2×C3×Dic3—31no—
231C2×C3×Dic3—31no—
232C2×C3×Dic3—32no—
233C2×C3×Dic3—32no—
234C2×C3×Dic3—32no—
235C2×C3×Dic3—62no—
236C3×D12—34no—
237C3×D12—34no—
238C3×D12—34no—
239C3×D12—64no—
240C3×C4×D3—34no—
241C3×C4×D3—34no—
242C3×C4×D3—62no—
243C3×C4×D3—64no—
244C3×C4×D3—64no—
245C3×C4×D3—64no—
246C3×C4×D3—124no—
247#626—38no—
248#625—38no—
249#624—64no—
250#624—64no—
251D3×Dic3—64no—
252D3×Dic3—64no—
253D3×Dic3—64no—
254D3×Dic3—64no—
255C2×C4×D4—271noSylow
256C2×H(3,𝔽3)C23×C411yescharacteristic
257C2×H(3,𝔽3)C22×D411yescharacteristic
258C2×H(3,𝔽3)C2×#4111yescharacteristic
259#272—24no—
260(C3⋊D3)⋊C3—24no—
261(C3⋊D3)⋊C3C4×D414yescomplemented
262C23×D3—92no—
263C23×D3—92no—
264C23×D3—92no—
265C2×C3×D4—91no—
266C2×C3×D4—91no—
267C22×C3×C4—91no—
268C22×C3×C4—91no—
269C22×C3×C4—91no—
270C22×C3×C4—92no—
271C22×C3×C4—92no—
272C2×#67—92no—
273C2×#67—92no—
274C22×Dic3—92no—
275C22×Dic3—92no—
276C22×Dic3—92no—
277D3×D4—98no—
278D3×D4—98no—
279C2×D12—31no—
280C2×D12—31no—
281C2×D12—31no—
282C2×D12—61no—
283C2×D12—91no—
284C2×D12—98no—
285C2×D12—92no—
286C2×C4×D3—31no—
287C2×C4×D3—31no—
288C2×C4×D3—32no—
289C2×C4×D3—32no—
290C2×C4×D3—31no—
291C2×C4×D3—32no—
292C2×C4×D3—62no—
293C2×C4×D3—91no—
294C2×C4×D3—91no—
295C2×C4×D3—91no—
296C2×C4×D3—92no—
297C2×C4×D3—92no—
298C2×C4×D3—92no—
299C2×C4×D3—92no—
300C2×C4×D3—92no—
301C2×C4×D3—92no—
302C2×C4×D3—92no—
303C2×C4×D3—188no—
304C2×C4×D3—188no—
305C2×C4×D3—188no—
306C3×C4⋊C4—91no—
307C3×C4⋊C4—91no—
308C3×C22⋊C4—92no—
309C3×C22⋊C4—92no—
310C3×C42—31no—
311C3×C42—31no—
312C3×C42—61no—
313C3×C42—91no—
314C3×C42—91no—
315C3×C42—91no—
316C3×C42D3211yescharacteristic
317#217—92no—
318#217—92no—
319(C2×D3)⋊C4—32no—
320(C2×D3)⋊C4—32no—
321(C2×D3)⋊C4—32no—
322(C2×D3)⋊C4—62no—
323(C2×D3)⋊C4—92no—
324(C2×D3)⋊C4—92no—
325(C2×D3)⋊C4—92no—
326(C2×D3)⋊C4—92no—
327(C2×D3)⋊C4—92no—
328C4⋊Dic3—31no—
329C4⋊Dic3—31no—
330C4⋊Dic3—31no—
331C4⋊Dic3—61no—
332C4⋊Dic3—91no—
333C4⋊Dic3—92no—
334Dic3⋊C4—92no—
335Dic3⋊C4—92no—
336C4×Dic3—31no—
337C4×Dic3—31no—
338C4×Dic3—31no—
339C4×Dic3—91no—
340C4×Dic3—91no—
341C4×Dic3—91no—
342C22×C32—21no—
343C22×C32C23×D311yescharacteristic
344C22×C32C23×D311yescharacteristic
345C2×C3⋊D3—22no—
346C2×C3⋊D3—22no—
347C2×C3⋊D3C2×C4×D312yes—
348C2×C3⋊D3C2×C4×D314yescomplemented
349C2×C3⋊D3C2×D1212yes—
350C2×C3⋊D3#23512yes—
351C2×C3×D3—32no—
352C2×C3×D3—32no—
353C2×C3×D3—32no—
354C2×C3×D3—34no—
355C2×C3×D3—34no—
356C2×C3×D3—34no—
357C2×C3×D3—64no—
358C2×C3×D3—62no—
359C2×C3×D3—62no—
360C2×C3×D3—62no—
361C2×C3×D3—62no—
362C2×C3×D3—62no—
363C2×C3×D3—62no—
364C2×C3×D3—122no—
365C2×C3×D3—122no—
366D32—616no—
367D32—616no—
368C32×C4—21no—
369C32×C4—21no—
370C32×C4—22no—
371C32×C4—22no—
372C32×C4—41no—
373C32×C4C2×C4×D312yescomplemented
374C32×C4C2×C4×D312yescomplemented
375C32×C4C2×D1212yescomplemented
376C32×C4D3×D412yescomplemented
377C3⋊Dic3—21no—
378C3⋊Dic3—22no—
379C3⋊Dic3C2×C4×D312yescomplemented
380C3⋊Dic3C2×D1212yescomplemented
381C3×Dic3—32no—
382C3×Dic3—32no—
383C3×Dic3—62no—
384C3×Dic3—62no—
385C3×Dic3—62no—
386C3×Dic3—61no—
387C3×Dic3—122no—
388C22×D4—271no—
389C23×C4—272no—
390C4×D4—91no—
391C4×D4—91no—
392C4×D4—272no—
393C4×D4—271no—
394C4×D4—271no—
395C4×D4—272no—
396C2×C4⋊C4—271no—
397C2×C22⋊C4—272no—
398C2×C42—91no—
399H(3,𝔽3)C2×C4×D411yescharacteristic, complemented, Sylow
400C23×C3—91no—
401C23×C3—92no—
402C23×C3—92no—
403C22×D3—31no—
404C22×D3—32no—
405C22×D3—32no—
406C22×D3—32no—
407C22×D3—62no—
408C22×D3—91no—
409C22×D3—92no—
410C22×D3—98no—
411C22×D3—98no—
412C22×D3—98no—
413C22×D3—184no—
414C22×D3—184no—
415C22×D3—184no—
416C22×D3—184no—
417C22×D3—184no—
418C22×D3—184no—
419C3×D4—94no—
420C3×D4—94no—
421C2×C3×C4—31no—
422C2×C3×C4—31no—
423C2×C3×C4—31no—
424C2×C3×C4—31no—
425C2×C3×C4—31no—
426C2×C3×C4—31no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—94no—
431C2×C3×C4—94no—
432C2×C3×C4—91no—
433C2×C3×C4—91no—
434C2×C3×C4—92no—
435C2×C3×C4—91no—
436C2×C3×C4—92no—
437C2×C3×C4—184no—
438C2×C3×C4—182no—
439C2×C3×C4—184no—
440C2×C3×C4C2×D3211yescharacteristic
441C2×C3×C4C2×D3211yescharacteristic
442C2×C3×C4C2×D3211yescharacteristic
443#67—98no—
444#67—98no—
445C2×Dic3—31no—
446C2×Dic3—31no—
447C2×Dic3—32no—
448C2×Dic3—32no—
449C2×Dic3—31no—
450C2×Dic3—32no—
451C2×Dic3—62no—
452C2×Dic3—91no—
453C2×Dic3—91no—
454C2×Dic3—91no—
455C2×Dic3—92no—
456C2×Dic3—184no—
457C2×Dic3—184no—
458C2×Dic3—184no—
459D12—34no—
460D12—34no—
461D12—34no—
462D12—64no—
463D12—94no—
464D12—98no—
465C4×D3—34no—
466C4×D3—34no—
467C4×D3—62no—
468C4×D3—64no—
469C4×D3—64no—
470C4×D3—64no—
471C4×D3—94no—
472C4×D3—94no—
473C4×D3—124no—
474C4×D3—184no—
475C4×D3—182no—
476C4×D3—184no—
477C4×D3—184no—
478C4×D3—184no—
479C4×D3—184no—
480C4×D3—184no—
481C4×D3—184no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32C22×C4×D311yescharacteristic
486C2×C32C22×C4×D311yescharacteristic
487C2×C32C22×D1211yescharacteristic
488C2×C32C2×#23511yescharacteristic
489C2×C32C2×D3×D411yescharacteristic
490C2×C32D3×#4111yescharacteristic
491C3⋊D3—24no—
492C3⋊D3C4×D1214yescomplemented
493C3×D3—34no—
494C3×D3—64no—
495C3×D3—64no—
496C3×D3—64no—
497C3×D3—124no—
498C24—272no—
499C2×D4—91no—
500C2×D4—91no—
501C2×D4—278no—
502C2×D4—272no—
503C22×C4—91no—
504C22×C4—91no—
505C22×C4—91no—
506C22×C4—92no—
507C22×C4—92no—
508C22×C4—272no—
509C22×C4—272no—
510C22×C4—272no—
511C22×C4—548no—
512C4⋊C4—91no—
513C4⋊C4—91no—
514C4⋊C4—272no—
515C22⋊C4—92no—
516C22⋊C4—92no—
517C22⋊C4—272no—
518C22⋊C4—272no—
519C42—91no—
520C42—91no—
521C42—91no—
522C42((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
523C22×C3—31no—
524C22×C3—31no—
525C22×C3—61no—
526C22×C3—92no—
527C22×C3—92no—
528C22×C3—92no—
529C22×C3—94no—
530C22×C3—94no—
531C22×C3—182no—
532C22×C3—182no—
533C22×C3—182no—
534C22×C3—182no—
535C22×C3C22×D3211yescharacteristic
536C2×D3—32no—
537C2×D3—32no—
538C2×D3—32no—
539C2×D3—34no—
540C2×D3—34no—
541C2×D3—34no—
542C2×D3—64no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—62no—
546C2×D3—62no—
547C2×D3—62no—
548C2×D3—62no—
549C2×D3—92no—
550C2×D3—92no—
551C2×D3—92no—
552C2×D3—94no—
553C2×D3—122no—
554C2×D3—122no—
555C2×D3—182no—
556C2×D3—182no—
557C2×D3—1816no—
558C2×D3—1816no—
559C2×D3—1816no—
560C3×C4—21no—
561C3×C4—32no—
562C3×C4—32no—
563C3×C4—32no—
564C3×C4—32no—
565C3×C4—61no—
566C3×C4—61no—
567C3×C4—62no—
568C3×C4—62no—
569C3×C4—92no—
570C3×C4—92no—
571C3×C4—121no—
572C3×C4—182no—
573C3×C4—181no—
574C3×C4—182no—
575C3×C4C4×D3212yes—
576C3×C4D3×D1212yes—
577Dic3—32no—
578Dic3—32no—
579Dic3—62no—
580Dic3—62no—
581Dic3—62no—
582Dic3—61no—
583Dic3—92no—
584Dic3—92no—
585Dic3—122no—
586Dic3—182no—
587Dic3—181no—
588C32—21no—
589C32C2×C4×D1211yescharacteristic, complemented
590C32C4×D3×D411yescharacteristic, complemented
591C23—91no—
592C23—92no—
593C23—92no—
594C23—278no—
595C23—544no—
596C23—544no—
597D4—94no—
598D4—94no—
599D4—278no—
600C2×C4—91no—
601C2×C4—91no—
602C2×C4—94no—
603C2×C4—94no—
604C2×C4—91no—
605C2×C4—92no—
606C2×C4—92no—
607C2×C4—182no—
608C2×C4—184no—
609C2×C4—184no—
610C2×C4—544no—
611C2×C4—544no—
612C2×C4—544no—
613C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
614C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
615C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
616C2×C3—31no—
617C2×C3—31no—
618C2×C3—31no—
619C2×C3—31no—
620C2×C3—31no—
621C2×C3—31no—
622C2×C3—61no—
623C2×C3—61no—
624C2×C3—61no—
625C2×C3—94no—
626C2×C3—184no—
627C2×C3—184no—
628C2×C3C2×C4×D3211yescharacteristic
629C2×C3C2×D3×D1211yescharacteristic
630C2×C3D3×#23511yescharacteristic
631D3—34no—
632D3—64no—
633D3—64no—
634D3—64no—
635D3—94no—
636D3—124no—
637D3—184no—
638C22—92no—
639C22—92no—
640C22—92no—
641C22—94no—
642C22—94no—
643C22—182no—
644C22—182no—
645C22—182no—
646C22—182no—
647C22—5416no—
648C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
649C4—21no—
650C4—92no—
651C4—92no—
652C4—182no—
653C4—182no—
654C4—181no—
655C4C4×((C3⋊D3)⋊C3)⋊C212yescomplemented
656C4#8865412yesdirect product factor
657C3—31no—
658C3—31no—
659C3—61no—
660C3C4×D3×D1211yescharacteristic
661C2—94no—
662C2—184no—
663C2—184no—
664C2C2×C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
665C2C2×#8865411yescharacteristic
666C2#1172249011yescharacteristic
subgroupG/H
centerC2×C4C2×((C3⋊D3)⋊C3)⋊C2
commutatorC2×H(3,𝔽3)C23×C4
Frattini, socleC22×C3C22×D32
FittingC42×H(3,𝔽3)C22
prime radicalC2×#88654C2
cosocleC22×H(3,𝔽3)C24
hypercenterC42((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×C4×D4
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×((C3⋊D3)⋊C3)⋊C2C2semidirect
3. C4×C4⋊#272C2semidirect
4. C4×C4⋊((C3⋊D3)⋊C3)C2semidirect
5. C42×(C3⋊D3)⋊C3C2semidirect
6. #11721160C2semidirect
7. C4×#6200C2semidirect
8. #11721149C2semidirect
9. #11721132C2semidirect
10. #11721129C2semidirect
11. #11721123C2semidirect
16. C2×C4×#272C22semidirect
21. C2×C4×(C3⋊D3)⋊C3C22semidirect
23. C2×#6199C22semidirect
25. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
26. #88654C4direct (N × H)
28. C42×H(3,𝔽3)C22semidirect
29. #88542C22semidirect
30. C4⋊#1084C22semidirect
31. #3752⋊C3C22semidirect
32. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
33. C4×(C3⋊Dic3)⋊C3C22semidirect
34. C4×(C3⋊Dic3)⋊C3C22semidirect
35. C4×(C3⋊Dic3)⋊C3C22semidirect
36. #88451C22semidirect
37. #88450C22semidirect
38. #88448C22semidirect
43. C4×C4⋊(C3⋊D3)D3semidirect
44. C42×C3⋊D3D3semidirect
67. C2×((C3⋊D3)⋊C3)⋊C2C2×C4semidirect
72. C4⋊#272C2×C4semidirect
78. C4⋊((C3⋊D3)⋊C3)C2×C4semidirect
81. C4×(C3⋊D3)⋊C3C2×C4semidirect
82. C4×(C3⋊D3)⋊C3D4semidirect
83. #6200C2×C4semidirect
96. C2×C4×C3⋊D3C2×D3semidirect
121. C32×C42C2×D3semidirect
122. C32×C42C2×D3semidirect
123. #3752C2×D3semidirect
124. C4⋊(C3⋊Dic3)C2×D3semidirect
125. C4×C3⋊Dic3C2×D3semidirect
126. C4×C3⋊Dic3C2×D3semidirect
127. C4×C3⋊Dic3C2×D3semidirect
148. C2×#272C22×C4semidirect
152. C2×(C3⋊D3)⋊C3C22×C4semidirect
157. C4×H(3,𝔽3)C22×C4semidirect
158. C4×H(3,𝔽3)C2×D4semidirect
162. (C3⋊Dic3)⋊C3C22×C4semidirect
163. (C3⋊Dic3)⋊C3C2×D4semidirect
224. C4⋊(C3⋊D3)C4×D3semidirect
227. C4×C3⋊D3C4×D3semidirect
228. C4×C3⋊D3D12semidirect
261. (C3⋊D3)⋊C3C4×D4semidirect
348. C2×C3⋊D3C2×C4×D3semidirect
373. C32×C4C2×C4×D3semidirect
374. C32×C4C2×C4×D3semidirect
375. C32×C4C2×D12semidirect
376. C32×C4D3×D4semidirect
379. C3⋊Dic3C2×C4×D3semidirect
380. C3⋊Dic3C2×D12semidirect
399. H(3,𝔽3)C2×C4×D4semidirect
492. C3⋊D3C4×D12semidirect
522. C42((C3⋊D3)⋊C3)⋊C2semidirect
589. C32C2×C4×D12semidirect
590. C32C4×D3×D4semidirect
655. C4C4×((C3⋊D3)⋊C3)⋊C2semidirect
656. C4#88654direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#886542
C2×C4×((C3⋊D3)⋊C3)⋊C22
C4×C4⋊#2722
C4×C4⋊((C3⋊D3)⋊C3)2
C42×(C3⋊D3)⋊C32
#117211602
C4×#62002
#117211492
#117211322
#117211292
#117211232
C4×#38023
C4×D3×D123