Finite Group Databasebeta

← #13175953

Subgroups — #13175953

Order 1728.

1800 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723924C211yesmaximal, characteristic, complemented
2C3×#64092C211yesmaximal, characteristic, complemented
3C32×#886C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic
5#11723618C211yesmaximal, characteristic, complemented
6Dic3×#638C211yesmaximal, characteristic, complemented
7#11723600C211yesmaximal, characteristic, complemented
8#11723539C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723502C211yesmaximal, characteristic, complemented
11#11723495C211yesmaximal, characteristic, complemented
12#11723430C211yesmaximal, characteristic, complemented
13#11723427C211yesmaximal, characteristic, complemented
14#11723413C211yesmaximal, characteristic, complemented
15#11723404C211yesmaximal, characteristic, complemented
16#10596130—31nomaximal
17#10594304—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic, complemented
25C2×#6293C2211yescharacteristic, complemented
26C2×#6289C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C33×C22⋊C4C2211yescharacteristic, complemented
29#88864C2211yescharacteristic, complemented
30#88859C2211yescharacteristic
31C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
32#88857C2211yescharacteristic, complemented
33C3×#3757C2211yescharacteristic, complemented
34C3×#3752C2211yescharacteristic
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C3×#3750C2211yescharacteristic, complemented
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×C4⋊Dic3C2211yescharacteristic, complemented
40C32×C4⋊Dic3C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88804C2211yescharacteristic
44#88804C2211yescharacteristic
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50Dic3×C3⋊Dic3C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#123—31no—
54#64146—31no—
55#64145—31no—
56C4×#638—31no—
57C4×#638—31no—
58#64105—31no—
59#64105—31no—
60#64101—31no—
61#64101—31no—
62#64092—31no—
63#64092—34no—
64#64092—64no—
65#64092D311yescharacteristic, complemented
66C22⋊C4×C3⋊D3—31no—
67C22⋊C4×C3⋊D3—31no—
68#64088—31no—
69#64088—31no—
70C3×#886D314yescomplemented
71C3×#883—34no—
72#63983—34no—
73Dic3×#67—34no—
74#63959—34no—
75#63952—34no—
76#63921—34no—
77D3×(C2×D3)⋊C4—34no—
78#63899—34no—
79#63895—34no—
80#63861—34no—
81#63858—34no—
82#63849—34no—
83#63841—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×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93#6312—22no—
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C4×C3⋊(C3⋊D3)—22no—
98C3×#638—22no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C3×C4×C3⋊D3—22no—
103C32×#67—41no—
104C2×C32×Dic3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108#6293—41no—
109#6289—41no—
110Dic3×C3⋊D3—41no—
111#5659—94no—
112#5658—91no—
113C23×C3⋊D3—31no—
114C22×D32—34no—
115C2×C32×D4—31no—
116C22×C32×C4—31no—
117C2×#638—31no—
118C2×#638—34no—
119C2×#638—64no—
120C2×#638C2×D311yescharacteristic
121C2×C4×C3⋊D3—31no—
122C2×C4×C3⋊D3—34no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—64no—
126C2×C4×C3⋊D3C2×D311yescharacteristic
127C2×#634—31no—
128C2×C3×#67—34no—
129C2×C3×#67C2×D314yes—
130C22×C3×Dic3C2×D314yescomplemented
131C2×C3×C4×D3—34no—
132C2×#627—34no—
133C2×#624—34no—
134C2×D3×Dic3—34no—
135C32×C4⋊C4—31no—
136C32×C4⋊C4—31no—
137C32×C22⋊C4—24no—
138C32×C22⋊C4—31no—
139C32×C22⋊C4—31no—
140C32×C22⋊C4C2×D314yescomplemented
141C32×C22⋊C4C2×D311yescharacteristic, complemented
142#3757—31no—
143#3757—34no—
144#3757—31no—
145#3757—31no—
146#3757—31no—
147#3757—64no—
148#3757C2×D311yescharacteristic, complemented
149#3752—31no—
150#3752—31no—
151#3752—31no—
152#3752—34no—
153#3752—31no—
154#3752—31no—
155#3752—64no—
156#3752C2×D311yescharacteristic
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—34no—
159C4⋊(C3⋊Dic3)—64no—
160C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
161#3750—31no—
162#3750—34no—
163#3750—31no—
164#3750—31no—
165#3750—64no—
166#3750C2×D311yescharacteristic, complemented
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3—31no—
170C3×#217—34no—
171C3×(C2×D3)⋊C4—34no—
172C3×(C2×D3)⋊C4C2×D314yes—
173C3×(C2×D3)⋊C4C2×D314yes—
174C3×C4⋊Dic3—34no—
175C3×C4⋊Dic3C2×D314yescomplemented
176C3×C4⋊Dic3C2×D314yescomplemented
177C3×Dic3⋊C4—34no—
178#3724—34no—
179Dic3⋊Dic3—34no—
180#3722—34no—
181#3722—34no—
182(C2×D3)⋊Dic3—34no—
183(C2×D3)⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187Dic32—34no—
188Dic32—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×#123—91no—
217#937—94no—
218#937—91no—
219#936—94no—
220D4×Dic3—91no—
221C4×#67—94no—
222C4×#67—94no—
223C2×(C2×D3)⋊C4—91no—
224#926—91no—
225#898—91no—
226#898—91no—
227#897—91no—
228#896—94no—
229#896—94no—
230#892—94no—
231#892—94no—
232#892—91no—
233#886C3⋊D311yescharacteristic, complemented
234#885—91no—
235#883—34no—
236#883—94no—
237#883—91no—
238#883—184no—
239#67⋊C4—91no—
240D3×C22⋊C4—94no—
241D3×C22⋊C4—94no—
242D3×C22⋊C4—91no—
243#879—94no—
244#879—94no—
245#878—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—121no—
269C2×C32×C4C22×D314yes—
270C2×C32×C4C22×D314yes—
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273#638—22no—
274#638—62no—
275#638—68no—
276#638—128no—
277C2×C3⋊Dic3—31no—
278C2×C3⋊Dic3—31no—
279C2×C3⋊Dic3—31no—
280C2×C3⋊Dic3—34no—
281C2×C3⋊Dic3—34no—
282C2×C3⋊Dic3—34no—
283C2×C3⋊Dic3—64no—
284C2×C3⋊Dic3—64no—
285C2×C3⋊Dic3—64no—
286C2×C3⋊Dic3C22×D311yescharacteristic
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3⋊Dic3C22×D311yescharacteristic
289C4×C3⋊D3—22no—
290C4×C3⋊D3—62no—
291C4×C3⋊D3—68no—
292C4×C3⋊D3—128no—
293C4×C3⋊D3—121no—
294C4×C3⋊D3—121no—
295#634—121no—
296C3×#67—44no—
297C3×#67—68no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—44no—
302C2×C3×Dic3C22×D314yes—
303C2×C3×Dic3C22×D314yes—
304C2×C3×Dic3C22×D314yes—
305C3×C4×D3—68no—
306#627—124no—
307#624—124no—
308D3×Dic3—124no—
309#551—271noSylow
310C2×C33—41no—
311C2×C33C2×#4111yescharacteristic
312C2×C33C2×#4111yescharacteristic
313C2×C33H(5,𝔽2)11yescharacteristic
314C3⋊(C3⋊D3)—22no—
315C3×C3⋊D3—22no—
316C32×D3—41no—
317C23×D3—94no—
318C23×D3—91no—
319C2×C3×D4—34no—
320C2×C3×D4—91no—
321C22×C3×C4—34no—
322C22×C3×C4—91no—
323C2×#67—34no—
324C2×#67—94no—
325C2×#67—91no—
326C2×#67—184no—
327C2×#67C2×C3⋊D311yescharacteristic
328C22×Dic3—91no—
329C22×Dic3C2×C3⋊D311yescharacteristic, complemented
330C2×C4×D3—34no—
331C2×C4×D3—94no—
332C2×C4×D3—91no—
333C2×C4×D3—94no—
334C2×C4×D3—94no—
335C2×C4×D3—91no—
336C2×C4×D3—184no—
337C2×Dic6—94no—
338C2×Dic6—91no—
339C3×C4⋊C4—34no—
340C3×C4⋊C4—34no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C22⋊C4—24no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4D3214yescomplemented
349C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
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(C2×D3)⋊C4—34no—
360(C2×D3)⋊C4—94no—
361(C2×D3)⋊C4—94no—
362(C2×D3)⋊C4—94no—
363(C2×D3)⋊C4—94no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—94no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—184no—
372(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
373(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
374C4⋊Dic3—34no—
375C4⋊Dic3—94no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—184no—
379C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
380C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
381Dic3⋊C4—34no—
382Dic3⋊C4—94no—
383Dic3⋊C4—94no—
384Dic3⋊C4—94no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—184no—
388C4×Dic3—94no—
389C4×Dic3—94no—
390C4×Dic3—94no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—24no—
398C22×C32—24no—
399C22×C32—24no—
400C22×C32—24no—
401C22×C32—44no—
402C22×C32—44no—
403C22×C32—44no—
404C22×C32—61no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32C23×D314yes—
408C22×C32C23×D311yescharacteristic
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—32no—
412C2×C3⋊D3—38no—
413C2×C3⋊D3—68no—
414C2×C3⋊D3—61no—
415C2×C3⋊D3—61no—
416C2×C3⋊D3—64no—
417C2×C3⋊D3—64no—
418C2×C3⋊D3—124no—
419C2×C3⋊D3—124no—
420C2×C3⋊D3—124no—
421C2×C3⋊D3#23712yes—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—24no—
425C2×C3×D3—38no—
426C2×C3×D3—64no—
427C2×C3×D3—64no—
428D32—1216no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4—24no—
432C32×C4—24no—
433C32×C4—44no—
434C32×C4—44no—
435C32×C4—61no—
436C32×C4—61no—
437C32×C4—61no—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—61no—
442C3⋊Dic3—61no—
443C3⋊Dic3—61no—
444C3⋊Dic3—64no—
445C3⋊Dic3—64no—
446C3⋊Dic3—64no—
447C3⋊Dic3—124no—
448C3⋊Dic3—124no—
449C3⋊Dic3—124no—
450C3×Dic3—24no—
451C3×Dic3—24no—
452C3×Dic3—24no—
453C3×Dic3—64no—
454C3×Dic3—64no—
455C3×Dic3—64no—
456#126—271no—
457#126—271no—
458#124—271no—
459#123—31no—
460#123—91no—
461#123—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464#120—271no—
465C4×D4—271no—
466C4×D4—271no—
467#117—271no—
468#117—271no—
469C2×C22⋊C4—271no—
470C2×C22⋊C4—271no—
471C33#55111yescharacteristic, complemented, Sylow
472C23×C3—24no—
473C23×C3—34no—
474C23×C3—91no—
475C23×C3C2×D3214yes—
476C23×C3C22×C3⋊D311yescharacteristic
477C22×D3—34no—
478C22×D3—94no—
479C22×D3—91no—
480C22×D3—184no—
481C22×D3—182no—
482C22×D3—182no—
483C22×D3—188no—
484C22×D3—188no—
485C22×D3—361no—
486C22×D3—364no—
487C22×D3C22×C3⋊D311yescharacteristic
488C3×D4—124no—
489C3×D4—182no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—34no—
493C2×C3×C4—34no—
494C2×C3×C4—34no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—124no—
499C2×C3×C4—182no—
500C2×C3×C4C2×D3214yes—
501C2×C3×C4C2×D3214yes—
502C2×C3×C4C22×C3⋊D311yescharacteristic
503C2×C3×C4C22×C3⋊D311yescharacteristic
504#67—41no—
505#67—68no—
506#67—182no—
507#67—188no—
508#67—368no—
509C2×Dic3—34no—
510C2×Dic3—34no—
511C2×Dic3—34no—
512C2×Dic3—41no—
513C2×Dic3—94no—
514C2×Dic3—94no—
515C2×Dic3—94no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—184no—
520C2×Dic3—184no—
521C2×Dic3—184no—
522C2×Dic3—361no—
523C2×Dic3C22×C3⋊D311yescharacteristic
524C2×Dic3C22×C3⋊D311yescharacteristic
525C2×Dic3C22×C3⋊D311yescharacteristic
526C4×D3—68no—
527C4×D3—182no—
528C4×D3—188no—
529C4×D3—368no—
530C4×D3—361no—
531C4×D3—364no—
532C4×D3—364no—
533Dic6—361no—
534Dic6—364no—
535C2×C32—24no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—41no—
539C2×C32—44no—
540C2×C32—84no—
541C2×C32—121no—
542C2×C32C2×#23711yescharacteristic
543C2×C32#100414yes—
544C2×C32D3×#4114yes—
545C2×C32D3×#4114yes—
546C2×C32D3×#4111yescharacteristic
547C2×C32#100911yescharacteristic
548C3⋊D3—22no—
549C3⋊D3—62no—
550C3⋊D3—68no—
551C3⋊D3—128no—
552C3×D3—44no—
553C3×D3—68no—
554C24—271no—
555C2×Q8—271no—
556C2×D4—31no—
557C2×D4—91no—
558C2×D4—271no—
559C22×C4—31no—
560C22×C4—91no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—91no—
575C22⋊C4—91no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4D3×C3⋊D311yescharacteristic, complemented
586C42—271no—
587C42—271no—
588C42—271no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—24no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—44no—
599C22×C3—64no—
600C22×C3—64no—
601C22×C3—64no—
602C22×C3—92no—
603C22×C3—181no—
604C22×C3—181no—
605C22×C3C22×D3214yes—
606C22×C3C23×C3⋊D311yescharacteristic
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—38no—
611C2×D3—64no—
612C2×D3—64no—
613C2×D3—98no—
614C2×D3—92no—
615C2×D3—188no—
616C2×D3—184no—
617C2×D3—184no—
618C2×D3—181no—
619C2×D3—181no—
620C2×D3—364no—
621C2×D3—364no—
622C2×D3—364no—
623C2×D3—3616no—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—44no—
629C3×C4—44no—
630C3×C4—64no—
631C3×C4—64no—
632C3×C4—64no—
633C3×C4—181no—
634C3×C4—181no—
635C3×C4—181no—
636Dic3—21no—
637Dic3—21no—
638Dic3—21no—
639Dic3—64no—
640Dic3—64no—
641Dic3—64no—
642Dic3—184no—
643Dic3—184no—
644Dic3—184no—
645Dic3—181no—
646Dic3—181no—
647Dic3—181no—
648Dic3—364no—
649Dic3—364no—
650Dic3—364no—
651C32—24no—
652C32#565811yescharacteristic, complemented
653C32#565914yescomplemented
654C23—31no—
655C23—91no—
656C23—271no—
657C23—542no—
658C23—542no—
659C23—1081no—
660C23C2×D3×C3⋊D311yescharacteristic
661Q8—1081no—
662D4—121no—
663D4—182no—
664D4—542no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—91no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—121no—
672C2×C4—182no—
673C2×C4—271no—
674C2×C4—271no—
675C2×C4—271no—
676C2×C4—542no—
677C2×C4—1081no—
678C2×C4—1081no—
679C2×C4C2×D3×C3⋊D311yescharacteristic
680C2×C4C2×D3×C3⋊D311yescharacteristic
681C2×C3—24no—
682C2×C3—24no—
683C2×C3—24no—
684C2×C3—44no—
685C2×C3—41no—
686C2×C3—84no—
687C2×C3—124no—
688C2×C3—182no—
689C2×C3#6430714yes—
690C2×C3D3×#23714yes—
691C2×C3#6431214yes—
692C2×C3#6436111yescharacteristic
693C2×C3#41×C3⋊D311yescharacteristic
694C2×C3#41×C3⋊D311yescharacteristic
695D3—41no—
696D3—68no—
697D3—188no—
698D3—182no—
699D3—368no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—61no—
704C22—61no—
705C22—61no—
706C22—92no—
707C22—181no—
708C22—181no—
709C22—272no—
710C22—541no—
711C22—541no—
712C22—1084no—
713C22C22×D3×C3⋊D311yescharacteristic
714C4—21no—
715C4—21no—
716C4—61no—
717C4—61no—
718C4—61no—
719C4—181no—
720C4—181no—
721C4—181no—
722C4—541no—
723C4—541no—
724C4—541no—
725C3—24no—
726C3#1059430414yescomplemented
727C3#1059613011yescharacteristic, complemented
728C2—41no—
729C2—121no—
730C2—182no—
731C2—542no—
732C2#1172457911yescharacteristic
733C2C3⋊D3×#23711yescharacteristic
734C2#1172458611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊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. #11723924C2semidirect
2. C3×#64092C2semidirect
3. C32×#886C2semidirect
5. #11723618C2semidirect
6. Dic3×#638C2semidirect
7. #11723600C2semidirect
8. #11723539C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723502C2semidirect
11. #11723495C2semidirect
12. #11723430C2semidirect
13. #11723427C2semidirect
14. #11723413C2semidirect
15. #11723404C2semidirect
24. C22×C32×Dic3C22semidirect
25. C2×#6293C22semidirect
28. C33×C22⋊C4C22semidirect
29. #88864C22semidirect
31. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
32. #88857C22semidirect
33. C3×#3757C22semidirect
35. C3×C4⋊(C3⋊Dic3)C22semidirect
36. C3×#3750C22semidirect
39. C32×C4⋊Dic3C22semidirect
40. C32×C4⋊Dic3C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
50. Dic3×C3⋊Dic3C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
65. #64092D3semidirect
70. C3×#886D3semidirect
130. C22×C3×Dic3C2×D3semidirect
140. C32×C22⋊C4C2×D3semidirect
141. C32×C22⋊C4C2×D3semidirect
148. #3757C2×D3semidirect
160. C4⋊(C3⋊Dic3)C2×D3semidirect
166. #3750C2×D3semidirect
175. C3×C4⋊Dic3C2×D3semidirect
176. C3×C4⋊Dic3C2×D3semidirect
233. #886C3⋊D3semidirect
329. C22×Dic3C2×C3⋊D3semidirect
348. C3×C22⋊C4D32semidirect
349. C3×C22⋊C4C2×C3⋊D3semidirect
379. C4⋊Dic3C2×C3⋊D3semidirect
380. C4⋊Dic3C2×C3⋊D3semidirect
471. C33#551semidirect
585. C22⋊C4D3×C3⋊D3semidirect
652. C32#5658semidirect
653. C32#5659semidirect
726. C3#10594304semidirect
727. C3#10596130semidirect

Maximal subgroups

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

subgroupindex
#117239242
C3×#640922
C32×#8862
#117236432
#117236182
Dic3×#6382
#117236002
#117235392
C3⋊D3×(C2×D3)⋊C42
#117235022
#117234952
#117234302
#117234272
#117234132
#117234042
#105961303
#105943043