Finite Group Databasebeta

← #13177464

Subgroups — #13177464

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#11723976C211yesmaximal, characteristic, complemented
2C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C32×#937C211yesmaximal, characteristic
4#11723641C211yesmaximal, characteristic, complemented
5#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#11723614C211yesmaximal, characteristic, complemented
7D3×#3757C211yesmaximal, characteristic, complemented
8#11723602C211yesmaximal, characteristic, complemented
9C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
10#11723600C211yesmaximal, characteristic, complemented
11#11723598C211yesmaximal, characteristic, complemented
12#11723500C211yesmaximal, characteristic, complemented
13#11723459C211yesmaximal, characteristic, complemented
14#11723428C211yesmaximal, characteristic, complemented
15#11723427C211yesmaximal, characteristic, complemented
16#10596058—31nomaximal
17#10595175—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×#6293C2211yescharacteristic, complemented
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28#88864C2211yescharacteristic
29#88864C2211yescharacteristic, complemented
30#88864C2211yescharacteristic, complemented
31#88857C2211yescharacteristic, complemented
32#88857C2211yescharacteristic, complemented
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic, complemented
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
37C32×#217C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#120—31no—
54C2×#3757—31no—
55C2×#3757—31no—
56#64145—31no—
57#64144—31no—
58#64144—31no—
59#64144—31no—
60#64144—34no—
61#64144—64no—
62D4×C3⋊Dic3—31no—
63D4×C3⋊Dic3D311yescharacteristic, complemented
64#64088—31no—
65#64088—31no—
66#64087—31no—
67#64087—31no—
68#64086—31no—
69#64086—31no—
70C3×#937D314yes—
71C3×D4×Dic3—34no—
72Dic3×#67—34no—
73#63969—34no—
74D3×#217—34no—
75#63964—34no—
76#63961—34no—
77C2×(C2×D3)⋊Dic3—34no—
78#63959—34no—
79#63957—34no—
80#63899—34no—
81#63877—34no—
82#63859—34no—
83#63858—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C32×D3—22no—
87C22×C32×D3—22no—
88C22×C32×D3—41no—
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C33×D4—22no—
92C2×C33×C4C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)—22no—
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3×C3⋊Dic3—41no—
99C2×C3×C3⋊Dic3—41no—
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C32×#67—22no—
105C32×#67—41no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108#6293—41no—
109D3×C3⋊Dic3—22no—
110D3×C3⋊Dic3—41no—
111#5587—94no—
112#5556—91no—
113C24×C32—31no—
114C23×C3×D3C2×D314yes—
115C2×C32×D4—24no—
116C2×C32×D4—31no—
117C2×C32×D4—31no—
118C2×C32×D4C2×D314yes—
119C2×C32×D4C2×D311yescharacteristic
120C22×C3⋊Dic3—31no—
121C22×C3⋊Dic3—34no—
122C22×C3⋊Dic3—31no—
123C22×C3⋊Dic3—31no—
124C22×C3⋊Dic3—64no—
125C22×C3⋊Dic3C2×D311yescharacteristic
126C22×C3⋊Dic3C2×D311yescharacteristic, complemented
127C2×#634—31no—
128C2×C3×#67C2×D314yes—
129C2×C3×#67C2×D314yes—
130C22×C3×Dic3—34no—
131C22×C3×Dic3—34no—
132C2×#627—34no—
133C2×D3×Dic3—34no—
134C2×D3×Dic3—34no—
135C32×C22⋊C4—31no—
136C32×C22⋊C4—31no—
137C32×C22⋊C4—31no—
138#3757—31no—
139#3757—31no—
140#3757—31no—
141#3757—34no—
142#3757—34no—
143#3757—34no—
144#3757—31no—
145#3757—31no—
146#3757—31no—
147#3757—31no—
148#3757—31no—
149#3757—31no—
150#3757—64no—
151#3757—64no—
152#3757—64no—
153#3757C2×D311yescharacteristic
154#3757C2×D311yescharacteristic, complemented
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
157#3750—31no—
158#3750—31no—
159#3750—34no—
160#3750—34no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750—64no—
166#3750—64no—
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3C2×D311yescharacteristic, complemented
170C3×#217—34no—
171C3×#217—34no—
172C3×#217C2×D314yes—
173C3×(C2×D3)⋊C4C2×D314yes—
174C3×(C2×D3)⋊C4C2×D314yes—
175C3×C4⋊Dic3—34no—
176C3×C4×Dic3—34no—
177#3724—34no—
178#3724—34no—
179#3724—34no—
180Dic3⋊Dic3—34no—
181Dic3⋊Dic3—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—
187(C2×D3)⋊Dic3—34no—
188Dic32—34no—
189Dic32—34no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33#4112yes—
196C22×C33C2411yescharacteristic
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—44no—
203C2×C32×D3#4112yes—
204C33×C4—21no—
205C3⋊(C3⋊Dic3)—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—
212C3×C3⋊Dic3—21no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C3×#120—34no—
216C3×C4×D4—91no—
217C2×#217—94no—
218C2×#217—94no—
219#937C3⋊D311yescharacteristic
220#936—94no—
221#935—94no—
222#935—94no—
223#935—94no—
224#935—91no—
225#935—184no—
226D4×Dic3—34no—
227D4×Dic3—94no—
228#929—91no—
229C4×#67—91no—
230C2×(C2×D3)⋊C4—91no—
231#924—91no—
232#898—91no—
233#896—91no—
234#885—91no—
235#883—91no—
236D3×C22⋊C4—91no—
237#879—94no—
238#879—94no—
239#878—94no—
240#878—94no—
241#877—94no—
242#877—94no—
243#877—91no—
244#876—91no—
245#872—91no—
246C23×C32—24no—
247C23×C32—24no—
248C23×C32—31no—
249C23×C32—31no—
250C23×C32—62no—
251C23×C32—62no—
252C23×C32—121no—
253C23×C32C22×D314yes—
254C23×C32C22×D314yes—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C22×C3×D3—28no—
258C22×C3×D3—28no—
259C22×C3×D3—44no—
260C22×C3×D3C22×D314yes—
261C22×C3×D3C22×D314yes—
262C32×D4—22no—
263C32×D4—28no—
264C32×D4—48no—
265C32×D4—62no—
266C32×D4—121no—
267C2×C32×C4—24no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4C22×D314yes—
271C2×C32×C4C22×D311yescharacteristic
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—34no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—41no—
281C2×C3⋊Dic3—41no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3—64no—
284C2×C3⋊Dic3—64no—
285C2×C3⋊Dic3—64no—
286C2×C3⋊Dic3—62no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—68no—
289C2×C3⋊Dic3—128no—
290C2×C3⋊Dic3—121no—
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295#634—121no—
296C3×#67—28no—
297C3×#67—44no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3—124no—
303C2×C3×Dic3—124no—
304C2×C3×Dic3C22×D314yes—
305C2×C3×Dic3C22×D314yes—
306#627—124no—
307D3×Dic3—68no—
308D3×Dic3—124no—
309#551—271noSylow
310C2×C33—22no—
311C2×C33—41no—
312C2×C33C2×#4111yescharacteristic
313C2×C33C2×#4111yescharacteristic
314C2×C33H(5,𝔽2)11yescharacteristic
315C32×D3—22no—
316C32×D3—41no—
317C24×C3—34no—
318C23×D3C2×C3⋊D311yescharacteristic
319C2×C3×D4—24no—
320C2×C3×D4—34no—
321C2×C3×D4—34no—
322C2×C3×D4D3214yes—
323C2×C3×D4C2×C3⋊D311yescharacteristic
324C22×C3×C4—91no—
325C22×C3×C4—91no—
326C2×#67C2×C3⋊D311yescharacteristic
327C2×#67C2×C3⋊D311yescharacteristic
328C22×Dic3—34no—
329C22×Dic3—34no—
330C22×Dic3—94no—
331C22×Dic3—94no—
332C22×Dic3—94no—
333C22×Dic3—91no—
334C22×Dic3—184no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×Dic6—94no—
338C2×Dic6—91no—
339C3×C4⋊C4—91no—
340C3×C22⋊C4—34no—
341C3×C22⋊C4—34no—
342C3×C22⋊C4—34no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C42—91no—
346#217—34no—
347#217—34no—
348#217—94no—
349#217—94no—
350#217—94no—
351#217—94no—
352#217—94no—
353#217—94no—
354#217—94no—
355#217—94no—
356#217—94no—
357#217—91no—
358#217—91no—
359#217—91no—
360#217—184no—
361#217—184no—
362#217—184no—
363#217C2×C3⋊D311yescharacteristic
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
371(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
372C4⋊Dic3—34no—
373C4⋊Dic3—94no—
374C4⋊Dic3—91no—
375Dic3⋊C4—94no—
376Dic3⋊C4—94no—
377Dic3⋊C4—94no—
378Dic3⋊C4—94no—
379Dic3⋊C4—94no—
380Dic3⋊C4—94no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—184no—
388Dic3⋊C4—184no—
389C4×Dic3—34no—
390C4×Dic3—94no—
391C4×Dic3—94no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—24no—
400C22×C32—28no—
401C22×C32—24no—
402C22×C32—24no—
403C22×C32—24no—
404C22×C32—24no—
405C22×C32—24no—
406C22×C32—32no—
407C22×C32—44no—
408C22×C32—44no—
409C22×C32—44no—
410C22×C32—44no—
411C22×C32—44no—
412C22×C32—61no—
413C22×C32—61no—
414C22×C32—61no—
415C22×C32—61no—
416C22×C32—61no—
417C22×C32—124no—
418C22×C32#23512yes—
419C22×C32#23718yes—
420C22×C32C23×D314yes—
421C22×C32C23×D311yescharacteristic
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—24no—
425C2×C3×D3—24no—
426C2×C3×D3—24no—
427C2×C3×D3—416no—
428C2×C3×D3#23718yes—
429C32×C4—21no—
430C32×C4—24no—
431C32×C4—44no—
432C32×C4—61no—
433C32×C4—61no—
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—61no—
439C3⋊Dic3—61no—
440C3⋊Dic3—61no—
441C3⋊Dic3—61no—
442C3⋊Dic3—64no—
443C3⋊Dic3—64no—
444C3⋊Dic3—64no—
445C3⋊Dic3—64no—
446C3⋊Dic3—124no—
447C3⋊Dic3—124no—
448C3⋊Dic3—124no—
449C3⋊Dic3—124no—
450C3×Dic3—24no—
451C3×Dic3—24no—
452C3×Dic3—64no—
453C3×Dic3—64no—
454C3×Dic3—64no—
455C3×Dic3—64no—
456#126—271no—
457#126—271no—
458#124—271no—
459#123—271no—
460#123—271no—
461#123—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464#120—31no—
465C4×D4—91no—
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—24no—
474C23×C3—34no—
475C23×C3—34no—
476C23×C3—68no—
477C23×C3—68no—
478C23×C3—124no—
479C23×C3C2×D3214yes—
480C23×C3C2×D3214yes—
481C23×C3C22×C3⋊D311yescharacteristic
482C23×C3C22×C3⋊D311yescharacteristic
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—41no—
486C22×D3C22×C3⋊D311yescharacteristic
487C22×D3C22×C3⋊D311yescharacteristic
488C3×D4—28no—
489C3×D4—22no—
490C3×D4—48no—
491C3×D4—68no—
492C3×D4—124no—
493C2×C3×C4—24no—
494C2×C3×C4—34no—
495C2×C3×C4—34no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—91no—
499C2×C3×C4—91no—
500C2×C3×C4—361no—
501C2×C3×C4—361no—
502C2×C3×C4C2×D3214yes—
503C2×C3×C4C22×C3⋊D311yescharacteristic
504#67—22no—
505#67—41no—
506C2×Dic3—34no—
507C2×Dic3—34no—
508C2×Dic3—34no—
509C2×Dic3—34no—
510C2×Dic3—94no—
511C2×Dic3—94no—
512C2×Dic3—94no—
513C2×Dic3—94no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—124no—
519C2×Dic3—124no—
520C2×Dic3—184no—
521C2×Dic3—184no—
522C2×Dic3—184no—
523C2×Dic3—184no—
524C2×Dic3—188no—
525C2×Dic3—188no—
526C2×Dic3—182no—
527C2×Dic3—368no—
528C2×Dic3—364no—
529C2×Dic3C22×C3⋊D311yescharacteristic
530C2×Dic3C22×C3⋊D311yescharacteristic
531C4×D3—182no—
532C4×D3—361no—
533Dic6—361no—
534Dic6—364no—
535C2×C32—22no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—24no—
539C2×C32—28no—
540C2×C32—48no—
541C2×C32—41no—
542C2×C32—44no—
543C2×C32—62no—
544C2×C32—84no—
545C2×C32—121no—
546C2×C32C2×#23511yescharacteristic
547C2×C32C2×#23714yes—
548C2×C32C2×#23714yes—
549C2×C32#100414yes—
550C2×C32#100411yescharacteristic
551C2×C32D3×#4111yescharacteristic
552C3×D3—28no—
553C3×D3—44no—
554C24—31no—
555C2×Q8—271no—
556C2×D4—31no—
557C2×D4—31no—
558C2×D4D3×C3⋊D311yescharacteristic
559C22×C4—91no—
560C22×C4—91no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C4⋊C4—91no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—91no—
576C22⋊C4—91no—
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⋊C4—271no—
586C42—91no—
587C42—271no—
588C42—271no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—24no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—24no—
600C22×C3—28no—
601C22×C3—38no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—44no—
606C22×C3—44no—
607C22×C3—64no—
608C22×C3—64no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3—64no—
612C22×C3—1216no—
613C22×C3#380418yes—
614C22×C3#383012yes—
615C22×C3C22×D3214yes—
616C22×C3C23×C3⋊D311yescharacteristic
617C2×D3—21no—
618C2×D3—21no—
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—44no—
623C2×D3#383012yes—
624C3×C4—24no—
625C3×C4—21no—
626C3×C4—44no—
627C3×C4—64no—
628C3×C4—64no—
629C3×C4—181no—
630C3×C4—181no—
631C3×C4—181no—
632C3×C4—181no—
633Dic3—21no—
634Dic3—21no—
635Dic3—64no—
636Dic3—64no—
637Dic3—64no—
638Dic3—64no—
639Dic3—184no—
640Dic3—184no—
641Dic3—184no—
642Dic3—184no—
643Dic3—181no—
644Dic3—181no—
645Dic3—181no—
646Dic3—181no—
647Dic3—364no—
648Dic3—364no—
649Dic3—364no—
650Dic3—364no—
651C32—24no—
652C32#555611yescharacteristic, complemented
653C32#558714yescomplemented
654C23—31no—
655C23—31no—
656C23—62no—
657C23—62no—
658C23—121no—
659C23C2×D3×C3⋊D311yescharacteristic
660C23C2×D3×C3⋊D311yescharacteristic
661Q8—1081no—
662D4—22no—
663D4—62no—
664D4—121no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—271no—
672C2×C4—271no—
673C2×C4—271no—
674C2×C4—271no—
675C2×C4—361no—
676C2×C4—361no—
677C2×C4—542no—
678C2×C4—542no—
679C2×C4—1081no—
680C2×C4C2×D3×C3⋊D311yescharacteristic
681C2×C3—28no—
682C2×C3—22no—
683C2×C3—24no—
684C2×C3—24no—
685C2×C3—24no—
686C2×C3—48no—
687C2×C3—44no—
688C2×C3—41no—
689C2×C3—68no—
690C2×C3—84no—
691C2×C3—124no—
692C2×C3D3×#23714yes—
693C2×C3#6431314yes—
694C2×C3C2×#380414yes—
695C2×C3C2×#383011yescharacteristic
696C2×C3C2×#383011yescharacteristic
697C2×C3#6436111yescharacteristic
698D3—22no—
699D3—41no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—32no—
706C22—61no—
707C22—61no—
708C22—61no—
709C22—61no—
710C22—61no—
711C22—124no—
712C22#8902812yes—
713C22C22×D3×C3⋊D311yescharacteristic
714C4—21no—
715C4—61no—
716C4—61no—
717C4—181no—
718C4—181no—
719C4—181no—
720C4—181no—
721C4—541no—
722C4—541no—
723C4—541no—
724C4—541no—
725C3—24no—
726C3#1059517514yescomplemented
727C3#1059605811yescharacteristic, complemented
728C2—22no—
729C2—41no—
730C2—62no—
731C2—121no—
732C2D3×#383011yescharacteristic
733C2#1172458711yescharacteristic
734C2C2×#8902811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
prime radicalC32×#937C2
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11723976C2semidirect
2. C3×D4×C3⋊Dic3C2semidirect
4. #11723641C2semidirect
5. #67×C3⋊Dic3C2semidirect
6. #11723614C2semidirect
7. D3×#3757C2semidirect
8. #11723602C2semidirect
9. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
10. #11723600C2semidirect
11. #11723598C2semidirect
12. #11723500C2semidirect
13. #11723459C2semidirect
14. #11723428C2semidirect
15. #11723427C2semidirect
22. C22×C3×C3⋊Dic3C22semidirect
25. C2×#6293C22semidirect
29. #88864C22semidirect
30. #88864C22semidirect
31. #88857C22semidirect
32. #88857C22semidirect
34. C3×#3757C22semidirect
35. C3×C4⋊(C3⋊Dic3)C22semidirect
36. C3×C4×C3⋊Dic3C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
42. #88806C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
63. D4×C3⋊Dic3D3semidirect
126. C22×C3⋊Dic3C2×D3semidirect
154. #3757C2×D3semidirect
156. C4⋊(C3⋊Dic3)C2×D3semidirect
169. C4×C3⋊Dic3C2×D3semidirect
471. C33#551semidirect
652. C32#5556semidirect
653. C32#5587semidirect
726. C3#10595175semidirect
727. C3#10596058semidirect

Maximal subgroups

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

subgroupindex
#117239762
C3×D4×C3⋊Dic32
C32×#9372
#117236412
#67×C3⋊Dic32
#117236142
D3×#37572
#117236022
C2×(C2×D3)⋊(C3⋊Dic3)2
#117236002
#117235982
#117235002
#117234592
#117234282
#117234272
#105960583
#105951753