Finite Group Databasebeta

← C4×#89031 #13176904

Subgroups — C4×#89031 #13176904

Order 1728.

2236 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89031C211yesmaximal, characteristic
2C4×#6312C211yesmaximal, characteristic, complemented
3C3×C4×#638C211yesmaximal, characteristic, complemented
4C2×C32×C4×Dic3C211yesmaximal, characteristic, complemented
5#11723618C211yesmaximal, characteristic, complemented
6Dic3×#638C211yesmaximal, characteristic, complemented
7#11723594C211yesmaximal, characteristic, complemented
8C4×#6293C211yesmaximal, characteristic, complemented
9C4×#6292C211yesmaximal, characteristic, complemented
10#11723471C211yesmaximal, characteristic, complemented
11#11723468C211yesmaximal, characteristic, complemented
12C4×#6289C211yesmaximal, characteristic, complemented
13#11723464C211yesmaximal, characteristic, complemented
14C4×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
15#11723389C211yesmaximal, characteristic, complemented
16C4×#3828—31nomaximal
17C4×#3804—34nomaximal
18C22×C33×C4C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29#89031C418yesdirect product factor
30C2×Dic3×C3⋊D3C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic
32#88864C2211yescharacteristic
33#88859C2211yescharacteristic
34#88857C2211yescharacteristic
35C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
36C3×#3757C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×C4×C3⋊Dic3C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41C32×C4×Dic3C2211yescharacteristic
42C32×C4×Dic3C2211yescharacteristic
43C32×C4×Dic3C2211yescharacteristic
44#88807C2211yescharacteristic
45#88806C2211yescharacteristic
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic
48#88804C2211yescharacteristic
49#88803C2211yescharacteristic
50Dic3×C3⋊Dic3C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53Dic3×C3⋊Dic3C2211yescharacteristic
54C2×#3828—31no—
55C2×#3804—34no—
56C2×C32×C42—31no—
57C4×#638—31no—
58C4×#638—31no—
59C4×#638—31no—
60C4×#638—34no—
61C4×#638—64no—
62C4×#638D311yescharacteristic, complemented
63#64135—31no—
64C4×C4⋊(C3⋊D3)—31no—
65C4×C4⋊(C3⋊D3)—31no—
66#64081—31no—
67#64081—31no—
68C42×C3⋊D3—31no—
69C42×C3⋊D3—31no—
70C4×#634—31no—
71C4×#634—31no—
72C3×C4×#67—34no—
73C2×C3×C4×Dic3D314yescomplemented
74Dic3×#67—34no—
75#63955—34no—
76#63952—34no—
77C4×#627—34no—
78C4×#626—34no—
79C4×#624—34no—
80#63880—34no—
81#63877—34no—
82C4×D3×Dic3—34no—
83#63837—34no—
84#63836—34no—
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C2×C33×C4—22no—
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91#6312C2×C414yescomplemented
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C4×C3⋊(C3⋊D3)—22no—
96C3×#638C2×C414yescomplemented
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C3×C4×C3⋊D3—22no—
101C2×C32×Dic3—22no—
102C2×C32×Dic3C2×C414yescomplemented
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107#6293C2×C414yescomplemented
108#6292C2×C414yescomplemented
109#6289—22no—
110#6289C2×C414yescomplemented
111Dic3×C3⋊D3—22no—
112Dic3×C3⋊D3C2×C414yescomplemented
113C4×#237—91no—
114C4×#235—94no—
115C22×C32×C4—24no—
116C22×C32×C4—31no—
117C22×C32×C4—31no—
118C22×C32×C4C2×D314yes—
119C22×C32×C4C2×D311yescharacteristic
120C2×#638—31no—
121C2×#638—34no—
122C2×#638—64no—
123C2×#638C2×D311yescharacteristic
124#3828—38no—
125C2×C4⋊(C3⋊D3)—31no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3—31no—
130C2×C4×C3⋊D3—34no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—64no—
133C2×C4×C3⋊D3C2×D311yescharacteristic
134C2×#634—31no—
135C2×C3×#67—34no—
136C22×C3×Dic3C2×D314yes—
137C22×C3×Dic3C2×D314yes—
138C2×C3×C4×D3—34no—
139C2×#627—34no—
140C2×#626—34no—
141C2×#624—34no—
142C2×#624—34no—
143#3804—332no—
144C2×D3×Dic3—34no—
145C2×D3×Dic3—34no—
146C32×C42—31no—
147C32×C42—31no—
148C32×C42—31no—
149C32×C42—31no—
150#3757—31no—
151#3757—34no—
152#3757—64no—
153#3757C2×D311yescharacteristic
154#3752—31no—
155#3752—31no—
156#3752—34no—
157#3752—31no—
158#3752—64no—
159#3752C2×D311yescharacteristic
160C4⋊(C3⋊Dic3)—31no—
161C4⋊(C3⋊Dic3)—31no—
162#3750—31no—
163#3750—34no—
164#3750—31no—
165#3750—31no—
166#3750—64no—
167#3750C2×D311yescharacteristic
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3—34no—
170C4×C3⋊Dic3—31no—
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3—31no—
173C4×C3⋊Dic3—31no—
174C4×C3⋊Dic3—64no—
175C4×C3⋊Dic3C2×D311yescharacteristic
176C3×#217—34no—
177C3×(C2×D3)⋊C4—34no—
178C3×Dic3⋊C4—34no—
179C3×C4×Dic3—34no—
180C3×C4×Dic3C2×D314yes—
181C3×C4×Dic3C2×D314yes—
182C3×C4×Dic3C2×D314yes—
183C3×C4×Dic3C2×D314yes—
184#3724—34no—
185Dic3⋊Dic3—34no—
186Dic3⋊Dic3—34no—
187Dic3⋊Dic3—34no—
188#3722—34no—
189(C2×D3)⋊Dic3—34no—
190Dic32—34no—
191Dic32—34no—
192Dic32—34no—
193Dic32—34no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33C22×C412yes—
197C22×C33C2411yescharacteristic
198C2×C3⋊(C3⋊D3)—21no—
199C2×C3⋊(C3⋊D3)—21no—
200C2×C3⋊(C3⋊D3)C22×C412yes—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3C22×C412yes—
204C33×C4—21no—
205C33×C4#4112yescomplemented
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3⋊(C3⋊Dic3)C22×C412yes—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3C22×C412yes—
212C32×Dic3—21no—
213C32×Dic3C22×C412yes—
214C32×Dic3C22×C412yes—
215C32×Dic3#4112yescomplemented
216C2×#237—91no—
217C2×#235—94no—
218C3×C4×D4—91no—
219C2×C3×C42—34no—
220D4×Dic3—91no—
221C4×#67—34no—
222C4×#67—94no—
223C4×#67—94no—
224C4×#67—94no—
225C4×#67—91no—
226C4×#67—91no—
227C4×#67—184no—
228#926—94no—
229C2×C4×Dic3—91no—
230C2×C4×Dic3C3⋊D311yescharacteristic, complemented
231#892—91no—
232#887—91no—
233#67⋊C4—91no—
234#67⋊C4—91no—
235#877—91no—
236#877—91no—
237C4×D12—94no—
238C4×D12—94no—
239#872—94no—
240#872—94no—
241C42×D3—94no—
242C42×D3—94no—
243C42×D3—91no—
244C4×Dic6—94no—
245C4×Dic6—94no—
246C4×Dic6—91no—
247C23×C32—24no—
248C23×C32C22×D314yes—
249C23×C32C22×D311yescharacteristic
250C22×C3⋊D3—31no—
251C22×C3⋊D3—34no—
252C22×C3⋊D3—64no—
253C22×C3⋊D3C22×D311yescharacteristic
254C22×C3×D3—34no—
255C2×C32×C4—22no—
256C2×C32×C4—24no—
257C2×C32×C4—24no—
258C2×C32×C4—28no—
259C2×C32×C4—34no—
260C2×C32×C4—31no—
261C2×C32×C4—31no—
262C2×C32×C4—31no—
263C2×C32×C4—31no—
264C2×C32×C4—48no—
265C2×C32×C4—62no—
266C2×C32×C4C22×D314yes—
267C2×C32×C4C22×D314yes—
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270#638—34no—
271#638—316no—
272#638—616no—
273#638C4×D314yescomplemented
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C4⋊(C3⋊D3)—34no—
287C4×C3⋊D3—22no—
288C4×C3⋊D3—34no—
289C4×C3⋊D3—34no—
290C4×C3⋊D3—62no—
291C4×C3⋊D3—62no—
292C4×C3⋊D3—62no—
293C4×C3⋊D3—68no—
294C4×C3⋊D3—128no—
295#634—34no—
296C3×#67—316no—
297C2×C3×Dic3—28no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3C4×D3116yescomplemented
302C2×C3×Dic3C22×D314yes—
303C2×C3×Dic3C22×D314yes—
304C2×C3×Dic3C22×D314yes—
305C2×C3×Dic3C22×D314yes—
306C3×C4×D3—68no—
307#627—316no—
308#626—316no—
309#624—316no—
310#624—68no—
311D3×Dic3—316no—
312D3×Dic3—68no—
313C4×#41—271noSylow
314C2×C33—22no—
315C2×C33C23×C411yescharacteristic
316C2×C33C2×#4111yescharacteristic
317C2×C33C2×#4111yescharacteristic
318C3⋊(C3⋊D3)—22no—
319C3×C3⋊D3—22no—
320C2×C3×D4—91no—
321C22×C3×C4—24no—
322C22×C3×C4—34no—
323C22×C3×C4—34no—
324C22×C3×C4—91no—
325C22×C3×C4D3214yes—
326C22×C3×C4C2×C3⋊D311yescharacteristic
327C2×#67—34no—
328C2×#67—94no—
329C2×#67—91no—
330C2×#67—91no—
331C2×#67—184no—
332C22×Dic3—91no—
333C22×Dic3—91no—
334C22×Dic3C2×C3⋊D311yescharacteristic
335C22×Dic3C2×C3⋊D311yescharacteristic
336#237—98no—
337#235—932no—
338C2×D12—94no—
339C2×C4×D3—34no—
340C2×C4×D3—94no—
341C2×C4×D3—94no—
342C2×C4×D3—91no—
343C2×C4×D3—94no—
344C2×C4×D3—94no—
345C2×C4×D3—94no—
346C2×C4×D3—91no—
347C2×C4×D3—91no—
348C2×C4×D3—184no—
349C2×Dic6—94no—
350C2×Dic6—91no—
351C3×C4⋊C4—91no—
352C3×C22⋊C4—91no—
353C3×C22⋊C4—91no—
354C3×C42—34no—
355C3×C42—34no—
356C3×C42—34no—
357C3×C42—34no—
358C3×C42—91no—
359#217—34no—
360#217—94no—
361#217—91no—
362#217—91no—
363#217—184no—
364(C2×D3)⋊C4—34no—
365(C2×D3)⋊C4—94no—
366(C2×D3)⋊C4—94no—
367(C2×D3)⋊C4—94no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—184no—
371C4⋊Dic3—94no—
372C4⋊Dic3—94no—
373C4⋊Dic3—91no—
374Dic3⋊C4—34no—
375Dic3⋊C4—94no—
376Dic3⋊C4—94no—
377Dic3⋊C4—94no—
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—184no—
383C4×Dic3—34no—
384C4×Dic3—94no—
385C4×Dic3—94no—
386C4×Dic3—94no—
387C4×Dic3—94no—
388C4×Dic3—94no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—184no—
395C4×Dic3C2×C3⋊D311yescharacteristic
396C4×Dic3C2×C3⋊D311yescharacteristic
397C4×Dic3C2×C3⋊D311yescharacteristic
398C4×Dic3C2×C3⋊D311yescharacteristic
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—24no—
402C22×C32—28no—
403C22×C32—24no—
404C22×C32—24no—
405C22×C32—44no—
406C22×C32—44no—
407C22×C32C2×C4×D318yes—
408C22×C32C2×C4×D312yes—
409C22×C32C23×D314yes—
410C22×C32C23×D311yescharacteristic
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3—32no—
414C2×C3⋊D3—38no—
415C2×C3⋊D3—68no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—64no—
419C2×C3⋊D3—64no—
420C2×C3⋊D3—124no—
421C2×C3⋊D3—124no—
422C2×C3⋊D3C2×C4×D312yes—
423C2×C3×D3—38no—
424C2×C3×D3—64no—
425C2×C3×D3—64no—
426C32×C4—21no—
427C32×C4—28no—
428C32×C4—24no—
429C32×C4—32no—
430C32×C4—32no—
431C32×C4—32no—
432C32×C4—44no—
433C32×C4—61no—
434C32×C4#23518yescomplemented
435C32×C4#23712yescomplemented
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—32no—
439C3⋊Dic3—38no—
440C3⋊Dic3—68no—
441C3⋊Dic3—61no—
442C3⋊Dic3—61no—
443C3⋊Dic3—64no—
444C3⋊Dic3—64no—
445C3⋊Dic3—124no—
446C3⋊Dic3—124no—
447C3⋊Dic3C2×C4×D312yes—
448C3×Dic3—24no—
449C3×Dic3—38no—
450C3×Dic3—64no—
451C3×Dic3—64no—
452C3×Dic3C2×C4×D318yes—
453C3×Dic3C2×C4×D318yes—
454C3×Dic3#23518yescomplemented
455C2×#41—271no—
456C4×Q8—271no—
457C4×Q8—271no—
458C4×D4—91no—
459C4×D4—271no—
460C4×D4—271no—
461C4×D4—271no—
462C4×D4—271no—
463C4×D4—271no—
464#117—271no—
465#117—271no—
466#117—271no—
467C2×C42—31no—
468C2×C42—271no—
469C2×C42—271no—
470C33C4×#4111yescharacteristic, complemented, Sylow
471C23×C3—24no—
472C23×C3—91no—
473C23×C3C2×D3214yes—
474C23×C3C22×C3⋊D311yescharacteristic
475C22×D3—34no—
476C22×D3—94no—
477C22×D3—91no—
478C22×D3—184no—
479C3×D4—94no—
480C2×C3×C4—28no—
481C2×C3×C4—22no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—34no—
485C2×C3×C4—34no—
486C2×C3×C4—34no—
487C2×C3×C4—316no—
488C2×C3×C4—34no—
489C2×C3×C4—48no—
490C2×C3×C4—68no—
491C2×C3×C4—91no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—182no—
495C2×C3×C4C2×D3214yes—
496C2×C3×C4C2×D3214yes—
497C2×C3×C4C22×C3⋊D311yescharacteristic
498C2×C3×C4C22×C3⋊D311yescharacteristic
499#67—316no—
500#67—916no—
501#67—94no—
502#67—94no—
503#67—1816no—
504C2×Dic3—22no—
505C2×Dic3—34no—
506C2×Dic3—34no—
507C2×Dic3—34no—
508C2×Dic3—94no—
509C2×Dic3—91no—
510C2×Dic3—94no—
511C2×Dic3—94no—
512C2×Dic3—94no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—184no—
516C2×Dic3—184no—
517C2×Dic3—184no—
518C2×Dic3—182no—
519C2×Dic3C4×C3⋊D314yescomplemented
520C2×Dic3C22×C3⋊D311yescharacteristic
521C2×Dic3C22×C3⋊D311yescharacteristic
522C2×Dic3C22×C3⋊D311yescharacteristic
523C2×Dic3C22×C3⋊D311yescharacteristic
524D12—916no—
525C4×D3—68no—
526C4×D3—916no—
527C4×D3—916no—
528C4×D3—94no—
529C4×D3—188no—
530C4×D3—188no—
531C4×D3—188no—
532C4×D3—182no—
533C4×D3—182no—
534C4×D3—368no—
535Dic6—916no—
536Dic6—94no—
537C2×C32—22no—
538C2×C32—24no—
539C2×C32—24no—
540C2×C32—24no—
541C2×C32—28no—
542C2×C32—48no—
543C2×C32C22×C4×D314yes—
544C2×C32C22×C4×D311yescharacteristic
545C2×C32C2×#23514yes—
546C2×C32C2×#23514yes—
547C2×C32C2×#23711yescharacteristic
548C2×C32D3×#4111yescharacteristic
549C3⋊D3—22no—
550C3⋊D3—62no—
551C3⋊D3—68no—
552C3⋊D3—128no—
553C3×D3—68no—
554#41—278no—
555C2×Q8—271no—
556C2×D4—91no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—91no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C22×C4—271no—
567C22×C4D3×C3⋊D311yescharacteristic
568C4⋊C4—91no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C22⋊C4—91no—
575C22⋊C4—91no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C42—31no—
581C42—31no—
582C42—31no—
583C42—31no—
584C42—91no—
585C42—271no—
586C42—271no—
587C42—271no—
588C42—271no—
589C42—271no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—24no—
595C22×C3—28no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—92no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3C4×D3218yes—
602C22×C3C2×C4×C3⋊D312yes—
603C22×C3C22×D3214yes—
604C22×C3C23×C3⋊D311yescharacteristic
605C2×D3—38no—
606C2×D3—64no—
607C2×D3—64no—
608C2×D3—98no—
609C2×D3—92no—
610C2×D3—188no—
611C2×D3—184no—
612C2×D3—184no—
613C2×D3—181no—
614C2×D3—181no—
615C2×D3—364no—
616C2×D3—364no—
617C3×C4—24no—
618C3×C4—21no—
619C3×C4—28no—
620C3×C4—38no—
621C3×C4—38no—
622C3×C4—38no—
623C3×C4—44no—
624C3×C4—64no—
625C3×C4—92no—
626C3×C4—181no—
627C3×C4—181no—
628C3×C4#380418yescomplemented
629C3×C4#382812yescomplemented
630Dic3—21no—
631Dic3—38no—
632Dic3—64no—
633Dic3—64no—
634Dic3—98no—
635Dic3—92no—
636Dic3—188no—
637Dic3—184no—
638Dic3—184no—
639Dic3—181no—
640Dic3—181no—
641Dic3—364no—
642Dic3—364no—
643Dic3C2×C4×C3⋊D312yes—
644Dic3C2×C4×C3⋊D312yes—
645Dic3#382812yescomplemented
646C32—24no—
647C32C4×#23514yescomplemented
648C32C4×#23711yescharacteristic, complemented
649C23—91no—
650C23—271no—
651C23C2×D3×C3⋊D311yescharacteristic
652Q8—274no—
653D4—94no—
654D4—274no—
655D4—274no—
656C2×C4—22no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—34no—
661C2×C4—31no—
662C2×C4—62no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—182no—
667C2×C4—274no—
668C2×C4—274no—
669C2×C4—271no—
670C2×C4—271no—
671C2×C4—271no—
672C2×C4—542no—
673C2×C4—542no—
674C2×C4—542no—
675C2×C4C2×D3×C3⋊D311yescharacteristic
676C2×C4C2×D3×C3⋊D311yescharacteristic
677C2×C3—28no—
678C2×C3—22no—
679C2×C3—24no—
680C2×C3—24no—
681C2×C3—24no—
682C2×C3—48no—
683C2×C3—182no—
684C2×C3C2×C4×D3214yes—
685C2×C3D3×#23514yes—
686C2×C3C2×#380414yes—
687C2×C3C22×C4×C3⋊D311yescharacteristic
688C2×C3C2×#382811yescharacteristic
689C2×C3C2×#382811yescharacteristic
690D3—68no—
691D3—188no—
692D3—182no—
693D3—368no—
694C22—21no—
695C22—21no—
696C22—92no—
697C22—181no—
698C22—181no—
699C22—272no—
700C22—541no—
701C22—541no—
702C22C4×D3×C3⋊D312yes—
703C22C22×D3×C3⋊D311yescharacteristic
704C4—21no—
705C4—32no—
706C4—32no—
707C4—32no—
708C4—61no—
709C4—92no—
710C4—181no—
711C4—181no—
712C4—272no—
713C4—541no—
714C4—541no—
715C4#8903112yesdirect product factor
716C3—24no—
717C3C4×#380414yescomplemented
718C3C4×#382811yescharacteristic, complemented
719C2—22no—
720C2—182no—
721C2—542no—
722C2C2×C4×D3×C3⋊D311yescharacteristic
723C2D3×#382811yescharacteristic
724C2C2×#8903111yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutatorC2×C33C23×C4
FrattiniC22C22×D3×C3⋊D3
FittingC22×C33×C4C22
socle, cosocleC22×C33C24
prime radicalC2×#89031C2
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C4×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6312C2semidirect
3. C3×C4×#638C2semidirect
4. C2×C32×C4×Dic3C2semidirect
5. #11723618C2semidirect
6. Dic3×#638C2semidirect
7. #11723594C2semidirect
8. C4×#6293C2semidirect
9. C4×#6292C2semidirect
10. #11723471C2semidirect
11. #11723468C2semidirect
12. C4×#6289C2semidirect
13. #11723464C2semidirect
14. C4×Dic3×C3⋊D3C2semidirect
15. #11723389C2semidirect
29. #89031C4direct (N × H)
62. C4×#638D3semidirect
73. C2×C3×C4×Dic3D3semidirect
91. #6312C2×C4semidirect
96. C3×#638C2×C4semidirect
102. C2×C32×Dic3C2×C4semidirect
107. #6293C2×C4semidirect
108. #6292C2×C4semidirect
110. #6289C2×C4semidirect
112. Dic3×C3⋊D3C2×C4semidirect
205. C33×C4#41semidirect
215. C32×Dic3#41semidirect
230. C2×C4×Dic3C3⋊D3semidirect
273. #638C4×D3semidirect
301. C2×C3×Dic3C4×D3semidirect
434. C32×C4#235semidirect
435. C32×C4#237semidirect
454. C3×Dic3#235semidirect
470. C33C4×#41semidirect
519. C2×Dic3C4×C3⋊D3semidirect
628. C3×C4#3804semidirect
629. C3×C4#3828semidirect
645. Dic3#3828semidirect
647. C32C4×#235semidirect
648. C32C4×#237semidirect
715. C4#89031direct (N × H)
717. C3C4×#3804semidirect
718. C3C4×#3828semidirect

Maximal subgroups

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

subgroupindex
C2×#890312
C4×#63122
C3×C4×#6382
C2×C32×C4×Dic32
#117236182
Dic3×#6382
#117235942
C4×#62932
C4×#62922
#117234712
#117234682
C4×#62892
#117234642
C4×Dic3×C3⋊D32
#117233892
C4×#38283
C4×#38043