Finite Group Databasebeta

← #13177345

Subgroups — #13177345

Order 1728.

1864 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6312C211yesmaximal, characteristic, complemented
2C3×C4×#638C211yesmaximal, characteristic, complemented
3C32×#929C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic
5#11723628C211yesmaximal, characteristic, complemented
6#11723621C211yesmaximal, characteristic, complemented
7#11723600C211yesmaximal, characteristic, complemented
8#11723539C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723469C211yesmaximal, characteristic, complemented
11#11723466C211yesmaximal, characteristic, complemented
12#11723442C211yesmaximal, characteristic, complemented
13#11723432C211yesmaximal, characteristic, complemented
14#11723428C211yesmaximal, characteristic, complemented
15#11723418C211yesmaximal, characteristic, complemented
16#10596130—31nomaximal
17#10595088—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic, complemented
20C2×#6312C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×#6293C2211yescharacteristic, complemented
26C2×#6289C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28#88864C2211yescharacteristic, complemented
29#88859C2211yescharacteristic
30#88857C2211yescharacteristic, complemented
31C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
32C3×#3757C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3750C2211yescharacteristic, complemented
35C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C32×#217C2211yescharacteristic, complemented
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#123—31no—
54#64146—31no—
55#64145—31no—
56C4×#638—31no—
57C4×#638—34no—
58C4×#638—64no—
59C4×#638D311yescharacteristic, complemented
60#64105—31no—
61#64105—31no—
62#64101—31no—
63#64101—31no—
64#64092—31no—
65#64092—31no—
66C22⋊C4×C3⋊D3—31no—
67C22⋊C4×C3⋊D3—31no—
68#64088—31no—
69#64088—31no—
70C3×#929D314yescomplemented
71C3×C4×#67—34no—
72#63983—34no—
73#63975—34no—
74#63969—34no—
75#63959—34no—
76#63921—34no—
77D3×(C2×D3)⋊C4—34no—
78#63878—34no—
79#63865—34no—
80#63862—34no—
81#63859—34no—
82#63851—34no—
83#63836—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C2×D3×C3⋊D3—22no—
89C2×D3×C3⋊D3—22no—
90C2×D3×C3⋊D3—41no—
91C2×C33×C4—41no—
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94#6312—22no—
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C4×C3⋊(C3⋊D3)—41no—
99C3×#638—22no—
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C3×C4×C3⋊D3—41no—
104C32×#67—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108#6293—41no—
109#6289—22no—
110Dic3×C3⋊D3—22no—
111#5659—94no—
112#5556—91no—
113C23×C3⋊D3—31no—
114C22×D32—34no—
115C2×C32×D4—31no—
116C22×C32×C4—24no—
117C22×C32×C4C2×D314yescomplemented
118C22×C32×C4C2×D311yescharacteristic, complemented
119C2×#638—31no—
120C2×#638—34no—
121C2×#638—64no—
122C2×#638C2×D311yescharacteristic
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—34no—
127C2×C4×C3⋊D3—64no—
128C2×C4×C3⋊D3C2×D311yescharacteristic
129C2×#634—31no—
130C2×C3×#67—34no—
131C2×C3×#67C2×D314yes—
132C2×C3×C4×D3—34no—
133C2×#627—34no—
134C2×#624—34no—
135C2×D3×Dic3—34no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4—31no—
138C32×C22⋊C4—31no—
139C32×C22⋊C4—31no—
140C32×C22⋊C4—31no—
141#3757—31no—
142#3757—34no—
143#3757—31no—
144#3757—31no—
145#3757—31no—
146#3757—64no—
147#3757C2×D311yescharacteristic, complemented
148#3752—31no—
149#3752—31no—
150#3752—31no—
151#3752—34no—
152#3752—31no—
153#3752—31no—
154#3752—64no—
155#3752C2×D311yescharacteristic
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—31no—
158#3750—31no—
159#3750—34no—
160#3750—31no—
161#3750—31no—
162#3750—64no—
163#3750C2×D311yescharacteristic, complemented
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3—34no—
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—64no—
168C4×C3⋊Dic3C2×D311yescharacteristic, complemented
169C3×#217—34no—
170C3×#217C2×D314yescomplemented
171C3×(C2×D3)⋊C4—34no—
172C3×(C2×D3)⋊C4C2×D314yes—
173C3×(C2×D3)⋊C4C2×D314yes—
174C3×Dic3⋊C4—34no—
175C3×Dic3⋊C4C2×D314yescomplemented
176C3×Dic3⋊C4C2×D314yescomplemented
177C3×C4×Dic3—34no—
178#3724—34no—
179Dic3⋊Dic3—34no—
180Dic3⋊Dic3—34no—
181Dic3⋊Dic3—34no—
182#3722—34no—
183#3722—34no—
184(C2×D3)⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189Dic32—34no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33C2411yescharacteristic
194C2×C3⋊(C3⋊D3)—21no—
195C2×C3⋊(C3⋊D3)—21no—
196C2×C3⋊(C3⋊D3)#4112yes—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3#4112yes—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203D3×C3⋊D3—44no—
204C33×C4—21no—
205C33×C4—21no—
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3⋊(C3⋊Dic3)—21no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C3×#123—34no—
216C3×C4×D4—91no—
217#937—94no—
218#937—91no—
219#936—94no—
220#935—91no—
221#929C3⋊D311yescharacteristic, complemented
222C4×#67—34no—
223C4×#67—94no—
224C4×#67—91no—
225C4×#67—184no—
226C2×(C2×D3)⋊C4—91no—
227#924—91no—
228#898—91no—
229#896—94no—
230#896—94no—
231#896—91no—
232#892—94no—
233#892—94no—
234#885—91no—
235#883—94no—
236#883—94no—
237#883—91no—
238D3×C22⋊C4—94no—
239D3×C22⋊C4—94no—
240D3×C22⋊C4—91no—
241#879—94no—
242#879—94no—
243#877—91no—
244#876—91no—
245#872—91no—
246C23×C32—24no—
247C23×C32—31no—
248C23×C32C22×D314yes—
249C23×C32C22×D311yescharacteristic
250C22×C3⋊D3—31no—
251C22×C3⋊D3—34no—
252C22×C3⋊D3—64no—
253C22×C3⋊D3—62no—
254C22×C3⋊D3—62no—
255C22×C3⋊D3—121no—
256C22×C3⋊D3C22×D311yescharacteristic
257C22×C3×D3—34no—
258C22×C3×D3C22×D314yes—
259C2×D32—68no—
260C2×D32—68no—
261C2×D32—124no—
262C32×D4—121no—
263C2×C32×C4—24no—
264C2×C32×C4—24no—
265C2×C32×C4—31no—
266C2×C32×C4—31no—
267C2×C32×C4—31no—
268C2×C32×C4—41no—
269C2×C32×C4—44no—
270C2×C32×C4—48no—
271C2×C32×C4C22×D314yes—
272C2×C32×C4C22×D314yes—
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275#638—22no—
276#638—62no—
277#638—68no—
278#638—616no—
279C2×C3⋊Dic3—31no—
280C2×C3⋊Dic3—31no—
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—34no—
283C2×C3⋊Dic3—34no—
284C2×C3⋊Dic3—34no—
285C2×C3⋊Dic3—64no—
286C2×C3⋊Dic3—64no—
287C2×C3⋊Dic3—64no—
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C2×C3⋊Dic3C22×D311yescharacteristic
291C4×C3⋊D3—41no—
292C4×C3⋊D3—62no—
293C4×C3⋊D3—62no—
294C4×C3⋊D3—121no—
295C4×C3⋊D3—124no—
296C4×C3⋊D3—128no—
297#634—121no—
298C3×#67—44no—
299C3×#67—68no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3—34no—
303C2×C3×Dic3C22×D314yes—
304C2×C3×Dic3C22×D314yes—
305C2×C3×Dic3C22×D314yes—
306C3×C4×D3—124no—
307#627—124no—
308#624—68no—
309D3×Dic3—68no—
310#551—271noSylow
311C2×C33—41no—
312C2×C33C2×#4111yescharacteristic
313C2×C33C2×#4111yescharacteristic
314C2×C33H(5,𝔽2)11yescharacteristic
315C3⋊(C3⋊D3)—22no—
316C3×C3⋊D3—22no—
317C32×D3—41no—
318C23×D3—94no—
319C23×D3—91no—
320C2×C3×D4—34no—
321C2×C3×D4—91no—
322C22×C3×C4—24no—
323C22×C3×C4—91no—
324C22×C3×C4D3214yescomplemented
325C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
326C2×#67—34no—
327C2×#67—94no—
328C2×#67—91no—
329C2×#67—184no—
330C2×#67C2×C3⋊D311yescharacteristic
331C22×Dic3—91no—
332C2×C4×D3—34no—
333C2×C4×D3—94no—
334C2×C4×D3—94no—
335C2×C4×D3—91no—
336C2×C4×D3—94no—
337C2×C4×D3—91no—
338C2×C4×D3—184no—
339C2×Dic6—94no—
340C2×Dic6—91no—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4—91no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349C3×C42—91no—
350#217—34no—
351#217—94no—
352#217—94no—
353#217—94no—
354#217—94no—
355#217—91no—
356#217—91no—
357#217—91no—
358#217—184no—
359#217C2×C3⋊D311yescharacteristic, complemented
360(C2×D3)⋊C4—34no—
361(C2×D3)⋊C4—94no—
362(C2×D3)⋊C4—94no—
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—94no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—94no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—184no—
373(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
374(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
375C4⋊Dic3—94no—
376C4⋊Dic3—94no—
377C4⋊Dic3—91no—
378Dic3⋊C4—34no—
379Dic3⋊C4—94no—
380Dic3⋊C4—94no—
381Dic3⋊C4—94no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—184no—
387Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
388Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
389C4×Dic3—34no—
390C4×Dic3—94no—
391C4×Dic3—94no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—184no—
395C22×C32—28no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—24no—
399C22×C32—21no—
400C22×C32—24no—
401C22×C32—24no—
402C22×C32—24no—
403C22×C32—44no—
404C22×C32—44no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32—61no—
408C22×C32C23×D314yes—
409C22×C32C23×D311yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—32no—
413C2×C3⋊D3—38no—
414C2×C3⋊D3—68no—
415C2×C3⋊D3—61no—
416C2×C3⋊D3—61no—
417C2×C3⋊D3—64no—
418C2×C3⋊D3—64no—
419C2×C3⋊D3—124no—
420C2×C3⋊D3—124no—
421C2×C3⋊D3—124no—
422C2×C3⋊D3#23512yes—
423C2×C3×D3—24no—
424C2×C3×D3—24no—
425C2×C3×D3—24no—
426C2×C3×D3—38no—
427C2×C3×D3—64no—
428C2×C3×D3—64no—
429D32—1216no—
430C32×C4—28no—
431C32×C4—21no—
432C32×C4—24no—
433C32×C4—21no—
434C32×C4—24no—
435C32×C4—44no—
436C32×C4—61no—
437C32×C4—61no—
438C32×C4—61no—
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—68no—
443C3⋊Dic3—61no—
444C3⋊Dic3—61no—
445C3⋊Dic3—64no—
446C3⋊Dic3—61no—
447C3⋊Dic3—64no—
448C3⋊Dic3—64no—
449C3⋊Dic3—124no—
450C3⋊Dic3—124no—
451C3×Dic3—24no—
452C3×Dic3—24no—
453C3×Dic3—24no—
454C3×Dic3—64no—
455C3×Dic3—64no—
456C3×Dic3—64no—
457#126—271no—
458#126—271no—
459#124—271no—
460#123—31no—
461#123—271no—
462#123—271no—
463C22⋊Q8—271no—
464C22⋊Q8—271no—
465#120—271no—
466C4×D4—91no—
467C4×D4—271no—
468#117—271no—
469#117—271no—
470C2×C22⋊C4—271no—
471C2×C22⋊C4—271no—
472C33#55111yescharacteristic, complemented, Sylow
473C23×C3—24no—
474C23×C3—34no—
475C23×C3—91no—
476C23×C3C2×D3214yes—
477C23×C3C22×C3⋊D311yescharacteristic
478C22×D3—34no—
479C22×D3—94no—
480C22×D3—91no—
481C22×D3—184no—
482C22×D3—182no—
483C22×D3—182no—
484C22×D3—188no—
485C22×D3—188no—
486C22×D3—361no—
487C22×D3—364no—
488C22×D3C22×C3⋊D311yescharacteristic
489C3×D4—124no—
490C3×D4—182no—
491C2×C3×C4—24no—
492C2×C3×C4—24no—
493C2×C3×C4—34no—
494C2×C3×C4—34no—
495C2×C3×C4—34no—
496C2×C3×C4—44no—
497C2×C3×C4—41no—
498C2×C3×C4—48no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—361no—
503C2×C3×C4C2×D3214yes—
504C2×C3×C4C2×D3214yes—
505C2×C3×C4C22×C3⋊D311yescharacteristic
506C2×C3×C4C22×C3⋊D311yescharacteristic
507#67—41no—
508#67—68no—
509#67—188no—
510#67—182no—
511#67—1816no—
512C2×Dic3—34no—
513C2×Dic3—34no—
514C2×Dic3—34no—
515C2×Dic3—94no—
516C2×Dic3—94no—
517C2×Dic3—94no—
518C2×Dic3—91no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—184no—
522C2×Dic3—184no—
523C2×Dic3—184no—
524C2×Dic3—182no—
525C2×Dic3C22×C3⋊D311yescharacteristic
526C2×Dic3C22×C3⋊D311yescharacteristic
527C2×Dic3C22×C3⋊D311yescharacteristic
528C4×D3—124no—
529C4×D3—182no—
530C4×D3—188no—
531C4×D3—188no—
532C4×D3—364no—
533C4×D3—361no—
534C4×D3—368no—
535Dic6—361no—
536Dic6—364no—
537C2×C32—24no—
538C2×C32—24no—
539C2×C32—24no—
540C2×C32—48no—
541C2×C32—44no—
542C2×C32—41no—
543C2×C32—121no—
544C2×C32C2×#23511yescharacteristic
545C2×C32#100414yes—
546C2×C32#100411yescharacteristic
547C2×C32D3×#4114yes—
548C2×C32D3×#4114yes—
549C2×C32D3×#4111yescharacteristic
550C3⋊D3—22no—
551C3⋊D3—62no—
552C3⋊D3—68no—
553C3⋊D3—128no—
554C3×D3—44no—
555C3×D3—68no—
556C24—271no—
557C2×Q8—271no—
558C2×D4—31no—
559C2×D4—91no—
560C2×D4—271no—
561C22×C4—91no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4D3×C3⋊D311yescharacteristic, complemented
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—91no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C42—91no—
589C42—271no—
590C42—271no—
591C22×C3—28no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—24no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—24no—
599C22×C3—44no—
600C22×C3—44no—
601C22×C3—64no—
602C22×C3—64no—
603C22×C3—64no—
604C22×C3—92no—
605C22×C3—181no—
606C22×C3—181no—
607C22×C3C22×D3214yes—
608C22×C3C23×C3⋊D311yescharacteristic
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—21no—
612C2×D3—38no—
613C2×D3—64no—
614C2×D3—64no—
615C2×D3—98no—
616C2×D3—92no—
617C2×D3—188no—
618C2×D3—184no—
619C2×D3—184no—
620C2×D3—181no—
621C2×D3—181no—
622C2×D3—364no—
623C2×D3—364no—
624C2×D3—364no—
625C2×D3—3616no—
626C3×C4—28no—
627C3×C4—24no—
628C3×C4—24no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—44no—
632C3×C4—64no—
633C3×C4—64no—
634C3×C4—64no—
635C3×C4—181no—
636C3×C4—181no—
637C3×C4—181no—
638Dic3—21no—
639Dic3—21no—
640Dic3—21no—
641Dic3—64no—
642Dic3—64no—
643Dic3—64no—
644Dic3—188no—
645Dic3—184no—
646Dic3—184no—
647Dic3—184no—
648Dic3—181no—
649Dic3—181no—
650Dic3—181no—
651Dic3—364no—
652Dic3—364no—
653C32—24no—
654C32#555611yescharacteristic, complemented
655C32#565914yescomplemented
656C23—31no—
657C23—91no—
658C23—271no—
659C23—542no—
660C23—542no—
661C23—1081no—
662C23C2×D3×C3⋊D311yescharacteristic
663Q8—1081no—
664D4—121no—
665D4—182no—
666D4—542no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—41no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—91no—
674C2×C4—271no—
675C2×C4—271no—
676C2×C4—271no—
677C2×C4—361no—
678C2×C4—542no—
679C2×C4—542no—
680C2×C4—1081no—
681C2×C4C2×D3×C3⋊D311yescharacteristic
682C2×C4C2×D3×C3⋊D311yescharacteristic
683C2×C3—24no—
684C2×C3—24no—
685C2×C3—24no—
686C2×C3—48no—
687C2×C3—44no—
688C2×C3—41no—
689C2×C3—124no—
690C2×C3—182no—
691C2×C3D3×#23514yes—
692C2×C3#6430614yes—
693C2×C3#6433014yes—
694C2×C3#6436111yescharacteristic
695C2×C3#41×C3⋊D311yescharacteristic
696C2×C3#41×C3⋊D311yescharacteristic
697D3—41no—
698D3—68no—
699D3—188no—
700D3—182no—
701D3—368no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—61no—
706C22—61no—
707C22—61no—
708C22—92no—
709C22—181no—
710C22—181no—
711C22—272no—
712C22—541no—
713C22—541no—
714C22—1084no—
715C22C22×D3×C3⋊D311yescharacteristic
716C4—21no—
717C4—21no—
718C4—61no—
719C4—61no—
720C4—61no—
721C4—181no—
722C4—181no—
723C4—181no—
724C4—541no—
725C4—541no—
726C4—541no—
727C3—24no—
728C3#1059508814yescomplemented
729C3#1059613011yescharacteristic, complemented
730C2—41no—
731C2—121no—
732C2—182no—
733C2—542no—
734C2C3⋊D3×#23511yescharacteristic
735C2#1172457811yescharacteristic
736C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
prime radical#11723643C2
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C4×#6312C2semidirect
2. C3×C4×#638C2semidirect
3. C32×#929C2semidirect
5. #11723628C2semidirect
6. #11723621C2semidirect
7. #11723600C2semidirect
8. #11723539C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723469C2semidirect
11. #11723466C2semidirect
12. #11723442C2semidirect
13. #11723432C2semidirect
14. #11723428C2semidirect
15. #11723418C2semidirect
19. C22×C33×C4C22semidirect
25. C2×#6293C22semidirect
28. #88864C22semidirect
30. #88857C22semidirect
31. C4×C3⋊(C3⋊Dic3)C22semidirect
32. C3×#3757C22semidirect
34. C3×#3750C22semidirect
35. C3×C4×C3⋊Dic3C22semidirect
36. C32×#217C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
59. C4×#638D3semidirect
70. C3×#929D3semidirect
117. C22×C32×C4C2×D3semidirect
118. C22×C32×C4C2×D3semidirect
147. #3757C2×D3semidirect
163. #3750C2×D3semidirect
168. C4×C3⋊Dic3C2×D3semidirect
170. C3×#217C2×D3semidirect
175. C3×Dic3⋊C4C2×D3semidirect
176. C3×Dic3⋊C4C2×D3semidirect
221. #929C3⋊D3semidirect
324. C22×C3×C4D32semidirect
325. C22×C3×C4C2×C3⋊D3semidirect
359. #217C2×C3⋊D3semidirect
387. Dic3⋊C4C2×C3⋊D3semidirect
388. Dic3⋊C4C2×C3⋊D3semidirect
472. C33#551semidirect
565. C22×C4D3×C3⋊D3semidirect
654. C32#5556semidirect
655. C32#5659semidirect
728. C3#10595088semidirect
729. C3#10596130semidirect

Maximal subgroups

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

subgroupindex
C4×#63122
C3×C4×#6382
C32×#9292
#117236432
#117236282
#117236212
#117236002
#117235392
C3⋊D3×(C2×D3)⋊C42
#117234692
#117234662
#117234422
#117234322
#117234282
#117234182
#105961303
#105950883