Finite Group Databasebeta

← #13177529

Subgroups — #13177529

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723979C211yesmaximal, characteristic, complemented
4C3×#64148C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723628C211yesmaximal, characteristic, complemented
8#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
9#11723615C211yesmaximal, characteristic, complemented
10D3×#3757C211yesmaximal, characteristic, complemented
11#11723591C211yesmaximal, characteristic, complemented
12#11723539C211yesmaximal, characteristic, complemented
13#11723491C211yesmaximal, characteristic, complemented
14#11723480C211yesmaximal, characteristic, complemented
15#11723462C211yesmaximal, characteristic, complemented
16#10596062—31nomaximal
17#10595294—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic, complemented
26C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
27C2×C32×#67C2211yescharacteristic
28C2×C32×#67C2211yescharacteristic, complemented
29D3×#638—24no—
30C2×#6293C2211yescharacteristic, complemented
31C2×#6291C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×#6289C2211yescharacteristic, complemented
34#89028—24no—
35C2×D3×C3⋊Dic3C2211yescharacteristic
36C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#88864C2211yescharacteristic, complemented
39#88864C2211yescharacteristic, complemented
40C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×#3830—31no—
57C2×D3×#67—34no—
58C2×#3804—34no—
59C32×#120—31no—
60C2×#3757—31no—
61#64148—31no—
62#64148D311yescharacteristic, complemented
63#64147—31no—
64#64147—34no—
65#64147—64no—
66#64146—31no—
67D4×C3⋊Dic3—31no—
68#64095—31no—
69#64094—31no—
70#64092—31no—
71#64090—31no—
72C22⋊C4×C3⋊D3—31no—
73#64087—31no—
74C3×#939—34no—
75C3×#937D314yescomplemented
76#63983—34no—
77#63975—34no—
78Dic3×#67—34no—
79#63970—34no—
80D3×#217—34no—
81#63959—34no—
82#63921—34no—
83#63893—34no—
84#63891—34no—
85#63881—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3—41no—
93C22×C32×D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C33×D4—41no—
99C2×C33×C4C2311yescharacteristic
100#6312—22no—
101#6312—22no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C4×C3⋊(C3⋊D3)—41no—
106C3×#638—22no—
107C3×#638—41no—
108C2×C3×C3⋊Dic3—22no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C32×#67—22no—
113C32×#67—22no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116#6293—22no—
117#6291D414yescomplemented
118#6290—22no—
119#6289—22no—
120D3×C3⋊Dic3—22no—
121D3×C3⋊Dic3—22no—
122D3×C3⋊Dic3—41no—
123#5612—91no—
124#5591—94no—
125C24×C32—31no—
126C23×C3⋊D3—31no—
127C23×C3×D3C2×D314yes—
128C22×D32—34no—
129C2×C32×D4—24no—
130C2×C32×D4—31no—
131C2×C32×D4—31no—
132C2×C32×D4C2×D314yescomplemented
133C2×C32×D4C2×D311yescharacteristic, complemented
134C2×#638—31no—
135C2×#638—31no—
136C2×#638—34no—
137C2×#638—34no—
138C2×#638—31no—
139C2×#638—31no—
140C2×#638—64no—
141C2×#638—64no—
142C2×#638—64no—
143C2×#638C2×D311yescharacteristic
144C2×#638C2×D311yescharacteristic, complemented
145C22×C3⋊Dic3—31no—
146C22×C3⋊Dic3—31no—
147C22×C3⋊Dic3—31no—
148C22×C3⋊Dic3C2×D311yescharacteristic, complemented
149#3830—64no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—34no—
153C2×C4×C3⋊D3—64no—
154C2×#634—31no—
155C2×C3×#67—34no—
156C2×C3×#67—34no—
157C2×C3×#67C2×D314yes—
158C2×C3×#67C2×D314yescomplemented
159C22×C3×Dic3—34no—
160D3×#67—616no—
161C2×#627—34no—
162C2×#626—34no—
163C2×#625—34no—
164C2×#624—34no—
165#3804—616no—
166C2×D3×Dic3—34no—
167C2×D3×Dic3—34no—
168C2×D3×Dic3—34no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4—31no—
172#3757—31no—
173#3757—31no—
174#3757—34no—
175#3757—34no—
176#3757—31no—
177#3757—31no—
178#3757—64no—
179#3757—64no—
180#3757C2×D311yescharacteristic, complemented
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752C2×D311yescharacteristic, complemented
185C4⋊(C3⋊Dic3)—31no—
186C4⋊(C3⋊Dic3)—34no—
187C4⋊(C3⋊Dic3)—31no—
188C4⋊(C3⋊Dic3)—64no—
189#3750—31no—
190#3750C2×D311yescharacteristic, complemented
191C4×C3⋊Dic3—31no—
192C3×#217—34no—
193C3×#217C2×D314yescomplemented
194C3×(C2×D3)⋊C4—34no—
195C3×(C2×D3)⋊C4C2×D314yes—
196C3×(C2×D3)⋊C4C2×D314yescomplemented
197C3×Dic3⋊C4—34no—
198Dic3⋊Dic3—34no—
199Dic3⋊Dic3—34no—
200#3722—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205Dic32—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C2411yescharacteristic
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)C2×D412yes—
216C2×C3×C3⋊D3—21no—
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C32×D3—21no—
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—44no—
224C2×C32×D3C2×D412yes—
225C2×C32×D3#4112yescomplemented
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C3⋊(C3⋊Dic3)—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3C2×D412yes—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C22×#67—94no—
237C2×#237—94no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#121—91no—
241C3×#120—34no—
242C2×#217—94no—
243#939—34no—
244#939—94no—
245#938—94no—
246#938—91no—
247#938—91no—
248#938—184no—
249#937—94no—
250#937—91no—
251#937C3⋊D311yescharacteristic, complemented
252#936—91no—
253D4×Dic3—94no—
254C4×#67—91no—
255#897—91no—
256#893—91no—
257#886—94no—
258#885—94no—
259#883—94no—
260#883—91no—
261#883—91no—
262#67⋊C4—94no—
263D3×C22⋊C4—94no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266#878—94no—
267C23×C32—24no—
268C23×C32—24no—
269C23×C32—31no—
270C23×C32—31no—
271C23×C32—62no—
272C23×C32—62no—
273C23×C32—121no—
274C23×C32C22×D314yes—
275C23×C32C22×D314yes—
276C23×C32C22×D311yescharacteristic
277C23×C32C22×D311yescharacteristic
278C22×C3⋊D3—31no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—64no—
281C22×C3⋊D3—62no—
282C22×C3⋊D3—62no—
283C22×C3⋊D3—121no—
284C22×C3⋊D3C22×D311yescharacteristic
285C22×C3×D3—28no—
286C22×C3×D3—28no—
287C22×C3×D3—34no—
288C22×C3×D3—44no—
289C22×C3×D3C22×D314yes—
290C22×C3×D3C22×D314yes—
291C2×D32—68no—
292C2×D32—68no—
293C2×D32—124no—
294C32×D4—41no—
295C32×D4—44no—
296C32×D4—48no—
297C32×D4—62no—
298C32×D4—62no—
299C2×C32×C4—24no—
300C2×C32×C4—31no—
301C2×C32×C4—31no—
302C2×C32×C4C22×D314yes—
303C2×C32×C4C22×D311yescharacteristic
304#638—22no—
305#638—34no—
306#638—41no—
307#638—62no—
308#638—62no—
309#638—62no—
310#638—68no—
311#638—68no—
312#638—128no—
313#638—128no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—31no—
316C2×C3⋊Dic3—31no—
317C2×C3⋊Dic3—31no—
318C2×C3⋊Dic3—34no—
319C2×C3⋊Dic3—34no—
320C2×C3⋊Dic3—34no—
321C2×C3⋊Dic3—64no—
322C2×C3⋊Dic3—64no—
323C2×C3⋊Dic3—64no—
324C2×C3⋊Dic3—62no—
325C2×C3⋊Dic3—62no—
326C2×C3⋊Dic3—121no—
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C4×C3⋊D3—62no—
331C4×C3⋊D3—121no—
332C4×C3⋊D3—124no—
333C4×C3⋊D3—128no—
334#634—62no—
335C3×#67—28no—
336C3×#67—28no—
337C3×#67—68no—
338C3×#67—124no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3—34no—
341C2×C3×Dic3—34no—
342C2×C3×Dic3—68no—
343C2×C3×Dic3C22×D314yes—
344C2×C3×Dic3C22×D314yes—
345#627—68no—
346#626—316no—
347#625—68no—
348#624—68no—
349D3×Dic3—68no—
350D3×Dic3—68no—
351D3×Dic3—124no—
352#546—271noSylow
353C2×C33—41no—
354C2×C33—41no—
355C2×C33C22×D411yescharacteristic
356C2×C33C2×#4111yescharacteristic
357C2×C33H(5,𝔽2)11yescharacteristic
358C3⋊(C3⋊D3)—22no—
359C3×C3⋊D3—41no—
360C32×D3—22no—
361C32×D3—22no—
362C24×C3—34no—
363C23×D3—94no—
364C23×D3—91no—
365C23×D3C2×C3⋊D311yescharacteristic
366C2×C3×D4—24no—
367C2×C3×D4—34no—
368C2×C3×D4—34no—
369C2×C3×D4—91no—
370C2×C3×D4—91no—
371C2×C3×D4D3214yescomplemented
372C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
373C22×C3×C4—91no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—94no—
377C2×#67—94no—
378C2×#67—94no—
379C2×#67—94no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—184no—
384C2×#67—184no—
385C2×#67—1816no—
386C2×#67C2×C3⋊D311yescharacteristic
387C2×#67C2×C3⋊D311yescharacteristic, complemented
388C22×Dic3—34no—
389C22×Dic3—94no—
390C22×Dic3—94no—
391C22×Dic3—94no—
392#237—1816no—
393D3×D4—184no—
394#235—184no—
395C2×D12—91no—
396C2×C4×D3—94no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—94no—
402C2×C4×D3—91no—
403C2×C4×D3—184no—
404C2×Dic6—94no—
405C2×Dic6—91no—
406C3×C4⋊C4—91no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4—91no—
412#217—34no—
413#217—94no—
414#217—94no—
415#217—94no—
416#217—94no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—91no—
421#217—184no—
422#217—184no—
423#217C2×C3⋊D311yescharacteristic, complemented
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—94no—
426(C2×D3)⋊C4—94no—
427(C2×D3)⋊C4—94no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
432(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
433C4⋊Dic3—94no—
434C4⋊Dic3—94no—
435C4⋊Dic3—91no—
436C4⋊Dic3—91no—
437C4⋊Dic3—184no—
438Dic3⋊C4—34no—
439Dic3⋊C4—94no—
440Dic3⋊C4—91no—
441C4×Dic3—94no—
442C4×Dic3—91no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—24no—
450C22×C32—24no—
451C22×C32—24no—
452C22×C32—24no—
453C22×C32—24no—
454C22×C32—24no—
455C22×C32—24no—
456C22×C32—32no—
457C22×C32—32no—
458C22×C32—44no—
459C22×C32—44no—
460C22×C32—44no—
461C22×C32—44no—
462C22×C32—44no—
463C22×C32—44no—
464C22×C32—61no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32—61no—
468C22×C32—124no—
469C22×C32C23×D314yes—
470C22×C32C23×D311yescharacteristic
471C2×C3⋊D3—21no—
472C2×C3⋊D3—21no—
473C2×C3⋊D3—21no—
474C2×C3⋊D3—32no—
475C2×C3⋊D3—38no—
476C2×C3⋊D3—68no—
477C2×C3⋊D3—61no—
478C2×C3⋊D3—61no—
479C2×C3⋊D3—64no—
480C2×C3⋊D3—64no—
481C2×C3⋊D3—124no—
482C2×C3⋊D3—124no—
483C2×C3⋊D3—124no—
484C2×C3×D3—24no—
485C2×C3×D3—24no—
486C2×C3×D3—24no—
487C2×C3×D3—24no—
488C2×C3×D3—416no—
489C2×C3×D3—64no—
490C2×C3×D3—64no—
491C2×C3×D3—64no—
492C2×C3×D3D3×D418yes—
493C2×C3×D3#23718yescomplemented
494D32—1216no—
495C32×C4—28no—
496C32×C4—24no—
497C32×C4—21no—
498C32×C4—61no—
499C32×C4—61no—
500C3⋊Dic3—21no—
501C3⋊Dic3—21no—
502C3⋊Dic3—61no—
503C3⋊Dic3—61no—
504C3⋊Dic3—61no—
505C3⋊Dic3—64no—
506C3⋊Dic3—64no—
507C3⋊Dic3—64no—
508C3⋊Dic3—124no—
509C3⋊Dic3—124no—
510C3⋊Dic3—124no—
511C3⋊Dic3D3×D412yes—
512C3×Dic3—24no—
513C3×Dic3—24no—
514C3×Dic3—38no—
515C3×Dic3—64no—
516C3×Dic3—64no—
517C2×#41—271no—
518C22×D4—271no—
519#124—271no—
520#123—271no—
521#123—271no—
522C22⋊Q8—271no—
523#121—91no—
524#121—271no—
525#121—271no—
526#120—31no—
527#120—271no—
528C4×D4—271no—
529C4×D4—271no—
530C2×C22⋊C4—271no—
531C2×C22⋊C4—271no—
532C33#54611yescharacteristic, complemented, Sylow
533C23×C3—24no—
534C23×C3—24no—
535C23×C3—34no—
536C23×C3—34no—
537C23×C3—68no—
538C23×C3—68no—
539C23×C3—91no—
540C23×C3—124no—
541C23×C3C2×D3214yes—
542C23×C3C2×D3214yes—
543C23×C3C22×C3⋊D311yescharacteristic
544C23×C3C22×C3⋊D311yescharacteristic
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—34no—
548C22×D3—41no—
549C22×D3—94no—
550C22×D3—91no—
551C22×D3—184no—
552C22×D3—182no—
553C22×D3—188no—
554C22×D3—188no—
555C22×D3—182no—
556C22×D3—361no—
557C22×D3—364no—
558C22×D3C22×C3⋊D311yescharacteristic
559C22×D3C22×C3⋊D311yescharacteristic
560C3×D4—44no—
561C3×D4—41no—
562C3×D4—48no—
563C3×D4—68no—
564C3×D4—68no—
565C3×D4—182no—
566C3×D4—361no—
567C2×C3×C4—24no—
568C2×C3×C4—34no—
569C2×C3×C4—34no—
570C2×C3×C4—91no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—182no—
574C2×C3×C4C2×D3214yes—
575C2×C3×C4C22×C3⋊D311yescharacteristic
576#67—22no—
577#67—22no—
578#67—68no—
579#67—916no—
580#67—124no—
581#67—188no—
582#67—182no—
583#67—182no—
584#67—188no—
585#67—188no—
586#67—182no—
587#67—368no—
588#67—368no—
589C2×Dic3—34no—
590C2×Dic3—34no—
591C2×Dic3—34no—
592C2×Dic3—68no—
593C2×Dic3—94no—
594C2×Dic3—94no—
595C2×Dic3—94no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—184no—
600C2×Dic3—184no—
601C2×Dic3—184no—
602C2×Dic3—188no—
603C2×Dic3—188no—
604C2×Dic3—364no—
605C2×Dic3C22×C3⋊D311yescharacteristic
606C2×Dic3C22×C3⋊D311yescharacteristic
607D12—94no—
608C4×D3—182no—
609C4×D3—188no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—364no—
613C4×D3—361no—
614C4×D3—361no—
615C4×D3—368no—
616Dic6—182no—
617Dic6—188no—
618C2×C32—24no—
619C2×C32—24no—
620C2×C32—24no—
621C2×C32—41no—
622C2×C32—41no—
623C2×C32—44no—
624C2×C32—44no—
625C2×C32—62no—
626C2×C32—62no—
627C2×C32—84no—
628C2×C32—84no—
629C2×C32C2×D3×D414yes—
630C2×C32C2×D3×D411yescharacteristic
631C2×C32C2×#23714yes—
632C2×C32#100414yes—
633C2×C32#100411yescharacteristic
634C2×C32D3×#4111yescharacteristic
635C3⋊D3—41no—
636C3⋊D3—62no—
637C3⋊D3—68no—
638C3⋊D3—128no—
639C3×D3—28no—
640C3×D3—28no—
641C3×D3—124no—
642C24—31no—
643C24—271no—
644#41—544no—
645C2×Q8—271no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—91no—
649C2×D4—91no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—544no—
655C2×D4D3×C3⋊D311yescharacteristic, complemented
656C22×C4—91no—
657C22×C4—271no—
658C22×C4—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C4⋊C4—91no—
663C4⋊C4—271no—
664C4⋊C4—271no—
665C4⋊C4—271no—
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4—31no—
669C22⋊C4—91no—
670C22⋊C4—91no—
671C22⋊C4—271no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C42—271no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—24no—
682C22×C3—24no—
683C22×C3—24no—
684C22×C3—24no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—24no—
692C22×C3—38no—
693C22×C3—38no—
694C22×C3—44no—
695C22×C3—44no—
696C22×C3—44no—
697C22×C3—44no—
698C22×C3—44no—
699C22×C3—44no—
700C22×C3—64no—
701C22×C3—64no—
702C22×C3—64no—
703C22×C3—64no—
704C22×C3—1216no—
705C22×C3—181no—
706C22×C3—181no—
707C22×C3—181no—
708C22×C3C22×D3214yes—
709C22×C3C23×C3⋊D311yescharacteristic
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—44no—
715C2×D3—64no—
716C2×D3—64no—
717C2×D3—64no—
718C2×D3—98no—
719C2×D3—92no—
720C2×D3—188no—
721C2×D3—184no—
722C2×D3—184no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—364no—
726C2×D3—364no—
727C2×D3—364no—
728C2×D3—3616no—
729C2×D3D4×C3⋊D312yes—
730C2×D3#383012yescomplemented
731C3×C4—28no—
732C3×C4—24no—
733C3×C4—21no—
734C3×C4—64no—
735C3×C4—64no—
736C3×C4—92no—
737C3×C4—181no—
738C3×C4—181no—
739Dic3—21no—
740Dic3—21no—
741Dic3—38no—
742Dic3—64no—
743Dic3—64no—
744Dic3—184no—
745Dic3—184no—
746Dic3—184no—
747Dic3—181no—
748Dic3—181no—
749Dic3—181no—
750Dic3—364no—
751Dic3—364no—
752Dic3—364no—
753C32—24no—
754C32#559114yescomplemented
755C32#561211yescharacteristic, complemented
756C23—31no—
757C23—31no—
758C23—62no—
759C23—62no—
760C23—91no—
761C23—121no—
762C23—271no—
763C23—542no—
764C23—542no—
765C23—1081no—
766C23C2×D3×C3⋊D311yescharacteristic
767C23C2×D3×C3⋊D311yescharacteristic
768Q8—542no—
769D4—41no—
770D4—62no—
771D4—62no—
772D4—182no—
773D4—274no—
774D4—361no—
775D4—542no—
776D4—542no—
777D4—542no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—91no—
781C2×C4—91no—
782C2×C4—91no—
783C2×C4—182no—
784C2×C4—271no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—542no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—1081no—
791C2×C4—1081no—
792C2×C4C2×D3×C3⋊D311yescharacteristic
793C2×C3—24no—
794C2×C3—24no—
795C2×C3—24no—
796C2×C3—44no—
797C2×C3—44no—
798C2×C3—41no—
799C2×C3—41no—
800C2×C3—68no—
801C2×C3—68no—
802C2×C3—84no—
803C2×C3—84no—
804C2×C3—361no—
805C2×C3D32×D414yes—
806C2×C3D3×#23714yes—
807C2×C3#6433014yes—
808C2×C3C2×D4×C3⋊D311yescharacteristic
809C2×C3C2×#383011yescharacteristic
810C2×C3#6436111yescharacteristic
811D3—22no—
812D3—22no—
813D3—124no—
814D3—188no—
815D3—182no—
816D3—368no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—32no—
824C22—32no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—124no—
830C22—181no—
831C22—181no—
832C22—181no—
833C22—272no—
834C22—541no—
835C22—541no—
836C22—1084no—
837C22C22×D3×C3⋊D311yescharacteristic
838C4—21no—
839C4—61no—
840C4—61no—
841C4—92no—
842C4—181no—
843C4—181no—
844C4—541no—
845C4—541no—
846C4—541no—
847C3—24no—
848C3#1059529414yescomplemented
849C3#1059606211yescharacteristic, complemented
850C2—41no—
851C2—41no—
852C2—62no—
853C2—62no—
854C2—361no—
855C2—542no—
856C2D3×D4×C3⋊D311yescharacteristic
857C2D3×#383011yescharacteristic
858C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#638C2semidirect
2. C2×#89028C2semidirect
3. #11723979C2semidirect
4. C3×#64148C2semidirect
5. C32×#937C2semidirect
6. #11723643C2semidirect
7. #11723628C2semidirect
8. #67×C3⋊Dic3C2semidirect
9. #11723615C2semidirect
10. D3×#3757C2semidirect
11. #11723591C2semidirect
12. #11723539C2semidirect
13. #11723491C2semidirect
14. #11723480C2semidirect
15. #11723462C2semidirect
20. C2×C33×D4C22semidirect
22. C2×#6312C22semidirect
23. C2×C4×C3⋊(C3⋊D3)C22semidirect
25. C2×C3×#638C22semidirect
26. C22×C3×C3⋊Dic3C22semidirect
28. C2×C32×#67C22semidirect
30. C2×#6293C22semidirect
33. C2×#6289C22semidirect
36. C2×D3×C3⋊Dic3C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
38. #88864C22semidirect
39. #88864C22semidirect
40. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
41. C3×#3757C22semidirect
42. C3×#3752C22semidirect
43. C3×#3750C22semidirect
44. C32×#217C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. #88807C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88804C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
62. #64148D3semidirect
75. C3×#937D3semidirect
117. #6291D4semidirect
132. C2×C32×D4C2×D3semidirect
133. C2×C32×D4C2×D3semidirect
144. C2×#638C2×D3semidirect
148. C22×C3⋊Dic3C2×D3semidirect
158. C2×C3×#67C2×D3semidirect
180. #3757C2×D3semidirect
184. #3752C2×D3semidirect
190. #3750C2×D3semidirect
193. C3×#217C2×D3semidirect
196. C3×(C2×D3)⋊C4C2×D3semidirect
225. C2×C32×D3#41semidirect
251. #937C3⋊D3semidirect
371. C2×C3×D4D32semidirect
372. C2×C3×D4C2×C3⋊D3semidirect
387. C2×#67C2×C3⋊D3semidirect
423. #217C2×C3⋊D3semidirect
432. (C2×D3)⋊C4C2×C3⋊D3semidirect
493. C2×C3×D3#237semidirect
532. C33#546semidirect
655. C2×D4D3×C3⋊D3semidirect
730. C2×D3#3830semidirect
754. C32#5591semidirect
755. C32#5612semidirect
848. C3#10595294semidirect
849. C3#10596062semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×#890282
#117239792
C3×#641482
C32×#9372
#117236432
#117236282
#67×C3⋊Dic32
#117236152
D3×#37572
#117235912
#117235392
#117234912
#117234802
#117234622
#105960623
#105952943