Finite Group Databasebeta

← #13167922

Subgroups — #13167922

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723668C211yesmaximal, characteristic, complemented
2#11723459C211yesmaximal, characteristic
3#11723402C211yesmaximal, characteristic, complemented
4#11723394C211yesmaximal, characteristic, complemented
5C3×#63896C211yesmaximal, characteristic
6C3×#63893C211yesmaximal, characteristic
7C3×#63838C211yesmaximal, characteristic, complemented
8#11723032C211yesmaximal, characteristic, complemented
9#11723016C211yesmaximal, characteristic, complemented
10#11722975C211yesmaximal, characteristic
11#11722969C211yesmaximal, characteristic
12#11722943C211yesmaximal, characteristic, complemented
13#11722940C211yesmaximal, characteristic, complemented
14#11722916C211yesmaximal, characteristic
15D3×Dic32C211yesmaximal, characteristic
16#10594386—31nomaximal
17#10594385—31nomaximal
18#10594030—31nomaximal
19C2×C3×#634C2211yescharacteristic
20C2×#6293C2211yescharacteristic
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26#88857C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C32×(C2×D3)⋊C4C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88813C2211yescharacteristic
35#88813C2211yescharacteristic
36#88807C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40#88806C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64098—31no—
55#64097—31no—
56#64086—31no—
57C3×#897—31no—
58C3×#896—31no—
59C3×#887—31no—
60C3×#887—31no—
61C3×#878—31no—
62C3×#878—31no—
63#63964—31no—
64#63964—31no—
65#63957—31no—
66C2×Dic32—31no—
67#63896—31no—
68#63896D311yescharacteristic
69#63893D311yescharacteristic
70#63887—31no—
71#63877—31no—
72#63877—31no—
73#63877—31no—
74#63877—31no—
75#63877—61no—
76C4×D3×Dic3—31no—
77C4×D3×Dic3—31no—
78#63873—31no—
79#63870—31no—
80#63856—31no—
81#63851—31no—
82#63847—31no—
83#63847—31no—
84#63847—31no—
85#63847—31no—
86#63847—61no—
87#63844—31no—
88#63844—31no—
89#63843—31no—
90#63843—31no—
91Dic3×Dic6—31no—
92Dic3×Dic6—31no—
93#63839—31no—
94#63839—31no—
95#63839—31no—
96#63839—31no—
97#63839—61no—
98#63838—31no—
99#63838D311yescharacteristic, complemented
100#63837—31no—
101#63837—31no—
102C22×C32×D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×#634—22no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6293—22no—
119D3×C3⋊Dic3Q814yescomplemented
120C3×#627—22no—
121C3×#627—22no—
122C3×D3×Dic3—22no—
123C3×D3×Dic3—22no—
124#5622—91no—
125#5622—91no—
126#5578—91no—
127C22×C3⋊Dic3—31no—
128C2×#634—31no—
129C2×#634C2×D311yescharacteristic
130C22×C3×Dic3—31no—
131C22×C3×Dic3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×C3×Dic6—31no—
138C2×C3×Dic6—31no—
139C2×C3×Dic6—31no—
140C2×C3×Dic6—61no—
141C2×#627—31no—
142C2×#627—31no—
143C2×#627—61no—
144C2×#627C2×D311yescharacteristic
145C2×#627C2×D311yescharacteristic
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C2×D3×Dic3—61no—
149C2×D3×Dic3C2×D311yescharacteristic
150C2×D3×Dic3C2×D311yescharacteristic
151C32×C4⋊C4—31no—
152C32×C4⋊C4—31no—
153C32×C22⋊C4—31no—
154#3757—31no—
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)C2×D311yescharacteristic
157#3750—31no—
158#3750—31no—
159#3750—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750—61no—
166#3750—61no—
167#3750—61no—
168#3750—121no—
169C4×C3⋊Dic3—31no—
170C4×C3⋊Dic3—31no—
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3C2×D311yescharacteristic
173C3×#217—31no—
174C3×#217—31no—
175C3×(C2×D3)⋊C4—21no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4C2×D311yescharacteristic
179C3×(C2×D3)⋊C4C2×D311yescharacteristic
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—61no—
185C3×Dic3⋊C4—21no—
186C3×Dic3⋊C4—21no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4C2×D311yescharacteristic
194C3×Dic3⋊C4C2×D311yescharacteristic
195C3×Dic3⋊C4C2×D311yescharacteristic
196C3×Dic3⋊C4C2×D311yescharacteristic
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—61no—
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—61no—
215#3724—61no—
216#3724—61no—
217#3724—61no—
218#3724C2×D311yescharacteristic
219#3724C2×D311yescharacteristic
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—61no—
235(C2×D3)⋊Dic3C2×D311yescharacteristic
236(C2×D3)⋊Dic3C2×D311yescharacteristic
237Dic32—31no—
238Dic32—31no—
239Dic32—31no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—61no—
250Dic32—61no—
251Dic32—61no—
252Dic32C2×D311yescharacteristic
253Dic32C2×D311yescharacteristic
254C22×C33C2411yescharacteristic
255C2×C32×D3—21no—
256C2×C32×D3—21no—
257C2×C32×D3C2×Q812yes—
258C33×C4—21no—
259C3⋊(C3⋊Dic3)—21no—
260C3⋊(C3⋊Dic3)C2×Q812yes—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3C2×Q812yes—
266C3×C3⋊Dic3#4112yes—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3#4112yes—
272C3×C22⋊Q8—91no—
273C3×C22⋊Q8—91no—
274C3×C4×Q8—91no—
275#946—91no—
276Q8×Dic3—91no—
277Q8×Dic3—91no—
278#944—91no—
279#944—91no—
280#944—91no—
281#924—91no—
282#924—91no—
283C2×C4×Dic3—91no—
284C2×C4×Dic3—91no—
285#897—31no—
286#896—31no—
287#896—91no—
288#889—91no—
289#889—91no—
290#889—91no—
291#889—91no—
292#889—91no—
293#889—91no—
294#889—181no—
295#888—91no—
296#888—91no—
297#888—91no—
298#888—181no—
299#887—31no—
300#887—31no—
301#887—91no—
302#887—91no—
303#887—91no—
304#887—91no—
305#878—31no—
306#878—31no—
307#878—91no—
308#878—91no—
309#877—91no—
310#877—91no—
311#877—91no—
312#877—91no—
313#877—181no—
314#872—91no—
315#872—91no—
316C42×D3—91no—
317C4×Dic6—91no—
318C4×Dic6—91no—
319C4×Dic6—91no—
320C23×C32—31no—
321C22×C3×D3—21no—
322C22×C3×D3C22×D311yescharacteristic
323C22×C3×D3C22×D311yescharacteristic
324C2×C32×C4—21no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—31no—
328C2×C32×C4—31no—
329C2×C32×C4—31no—
330C2×C32×C4—31no—
331C2×C32×C4—31no—
332C2×C32×C4—41no—
333C2×C32×C4C22×D311yescharacteristic
334C2×C32×C4C22×D311yescharacteristic
335C2×C32×C4C22×D311yescharacteristic
336C2×C3⋊Dic3—31no—
337C2×C3⋊Dic3—31no—
338C2×C3⋊Dic3—31no—
339C2×C3⋊Dic3—34no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—61no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—121no—
350C2×C3⋊Dic3—121no—
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357#634—22no—
358#634—62no—
359C2×C3×Dic3—21no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—31no—
365C2×C3×Dic3—31no—
366C2×C3×Dic3—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—62no—
383C2×C3×Dic3—62no—
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C3×C4×D3—62no—
395C3×C4×D3—62no—
396C3×Dic6—62no—
397C3×Dic6—62no—
398C3×Dic6—62no—
399C3×Dic6—62no—
400C3×Dic6—62no—
401C3×Dic6—62no—
402C3×Dic6—122no—
403#627—22no—
404#627—22no—
405#627—62no—
406#627—62no—
407#627—122no—
408D3×Dic3—22no—
409D3×Dic3—22no—
410D3×Dic3—34no—
411D3×Dic3—34no—
412D3×Dic3—64no—
413#533—271noSylow
414C2×C33C22×Q811yescharacteristic
415C2×C33C2×#4111yescharacteristic
416C2×C33C2×#4111yescharacteristic
417C32×D3—22no—
418C2×C3×Q8—91no—
419C2×C3×Q8—91no—
420C2×C3×Q8—91no—
421C22×C3×C4—91no—
422C22×C3×C4—91no—
423C22×Dic3—31no—
424C22×Dic3—31no—
425C22×Dic3—91no—
426C22×Dic3—91no—
427C22×Dic3—181no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—91no—
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6—61no—
438C2×Dic6—91no—
439C2×Dic6—91no—
440C2×Dic6—91no—
441C2×Dic6—181no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—61no—
447C3×C4⋊C4—61no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C22⋊C4—31no—
454C3×C22⋊C4—31no—
455C3×C22⋊C4—61no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4—91no—
458C3×C42—91no—
459C3×C42—91no—
460C3×C42—91no—
461#217—31no—
462#217—31no—
463#217—91no—
464#217—91no—
465#217—181no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4D3211yescharacteristic
470C4⋊Dic3—31no—
471C4⋊Dic3—31no—
472C4⋊Dic3—31no—
473C4⋊Dic3—31no—
474C4⋊Dic3—61no—
475C4⋊Dic3—91no—
476C4⋊Dic3—91no—
477C4⋊Dic3—91no—
478C4⋊Dic3—91no—
479C4⋊Dic3—91no—
480C4⋊Dic3—181no—
481Dic3⋊C4—31no—
482Dic3⋊C4—31no—
483Dic3⋊C4—31no—
484Dic3⋊C4—31no—
485Dic3⋊C4—31no—
486Dic3⋊C4—31no—
487Dic3⋊C4—91no—
488Dic3⋊C4—91no—
489Dic3⋊C4—91no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494Dic3⋊C4—91no—
495Dic3⋊C4—91no—
496Dic3⋊C4—91no—
497Dic3⋊C4—91no—
498Dic3⋊C4—91no—
499Dic3⋊C4—91no—
500Dic3⋊C4—91no—
501Dic3⋊C4—91no—
502Dic3⋊C4—91no—
503Dic3⋊C4—91no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—181no—
510Dic3⋊C4—181no—
511Dic3⋊C4—181no—
512Dic3⋊C4—181no—
513Dic3⋊C4—181no—
514Dic3⋊C4—181no—
515Dic3⋊C4—181no—
516Dic3⋊C4—181no—
517Dic3⋊C4—361no—
518Dic3⋊C4D3211yescharacteristic
519Dic3⋊C4D3211yescharacteristic
520C4×Dic3—31no—
521C4×Dic3—31no—
522C4×Dic3—31no—
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—31no—
526C4×Dic3—61no—
527C4×Dic3—91no—
528C4×Dic3—91no—
529C4×Dic3—91no—
530C4×Dic3—91no—
531C4×Dic3—91no—
532C4×Dic3—91no—
533C4×Dic3—91no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—181no—
543C4×Dic3—181no—
544C4×Dic3—181no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—32no—
549C22×C32—41no—
550C22×C32—61no—
551C22×C32—61no—
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C22×C32C23×D311yescharacteristic
555C2×C3×D3—21no—
556C2×C3×D3—21no—
557C2×C3×D3—21no—
558C2×C3×D3—21no—
559C2×C3×D3—22no—
560C2×C3×D3—41no—
561C2×C3×D3—41no—
562C2×C3×D3D3×Q812yes—
563C2×C3×D3D3×Q812yes—
564C32×C4—21no—
565C32×C4—21no—
566C32×C4—21no—
567C32×C4—32no—
568C32×C4—41no—
569C32×C4—41no—
570C32×C4—41no—
571C32×C4—61no—
572C32×C4—61no—
573C32×C4—61no—
574C32×C4—61no—
575C32×C4—81no—
576C3⋊Dic3—21no—
577C3⋊Dic3—21no—
578C3⋊Dic3—21no—
579C3⋊Dic3—21no—
580C3⋊Dic3—32no—
581C3⋊Dic3—32no—
582C3⋊Dic3—32no—
583C3⋊Dic3—62no—
584C3⋊Dic3—62no—
585C3⋊Dic3—62no—
586C3⋊Dic3—61no—
587C3⋊Dic3—61no—
588C3⋊Dic3—61no—
589C3⋊Dic3—122no—
590C3⋊Dic3—121no—
591C3⋊Dic3—121no—
592C3⋊Dic3—121no—
593C3⋊Dic3—241no—
594C3⋊Dic3#23712yes—
595C3⋊Dic3D3×Q812yes—
596C3×Dic3—21no—
597C3×Dic3—21no—
598C3×Dic3—21no—
599C3×Dic3—21no—
600C3×Dic3—21no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—21no—
604C3×Dic3—22no—
605C3×Dic3—32no—
606C3×Dic3—32no—
607C3×Dic3—32no—
608C3×Dic3—32no—
609C3×Dic3—41no—
610C3×Dic3—41no—
611C3×Dic3—41no—
612C3×Dic3—41no—
613C3×Dic3—62no—
614C3×Dic3—62no—
615C3×Dic3—61no—
616C3×Dic3—61no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—121no—
624C3×Dic3—121no—
625C3×Dic3—121no—
626C3×Dic3—121no—
627C3×Dic3#23512yes—
628C3×Dic3#23712yes—
629C4⋊Q8—271no—
630C4⋊Q8—271no—
631#125—271no—
632#125—271no—
633C22⋊Q8—91no—
634C22⋊Q8—91no—
635C22⋊Q8—271no—
636C22⋊Q8—271no—
637C4×Q8—91no—
638C4×Q8—271no—
639C4×Q8—271no—
640C4×Q8—271no—
641#117—271no—
642#117—271no—
643C2×C42—271no—
644C33#53311yescharacteristic, complemented, Sylow
645C23×C3—31no—
646C23×C3—31no—
647C23×C3—61no—
648C22×D3C2×D3211yescharacteristic
649C3×Q8—182no—
650C3×Q8—182no—
651C3×Q8—182no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—31no—
656C2×C3×C4—31no—
657C2×C3×C4—31no—
658C2×C3×C4—31no—
659C2×C3×C4—31no—
660C2×C3×C4—31no—
661C2×C3×C4—31no—
662C2×C3×C4—31no—
663C2×C3×C4—31no—
664C2×C3×C4—31no—
665C2×C3×C4—41no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—91no—
672C2×C3×C4—91no—
673C2×C3×C4—91no—
674C2×C3×C4—91no—
675C2×C3×C4—91no—
676C2×C3×C4—91no—
677C2×C3×C4—182no—
678C2×C3×C4—182no—
679C2×C3×C4C2×D3211yescharacteristic
680C2×C3×C4C2×D3211yescharacteristic
681C2×C3×C4C2×D3211yescharacteristic
682C2×Dic3—31no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—62no—
701C2×Dic3—62no—
702C2×Dic3—94no—
703C2×Dic3—94no—
704C2×Dic3—91no—
705C2×Dic3—91no—
706C2×Dic3—91no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—91no—
710C2×Dic3—184no—
711C2×Dic3—181no—
712C2×Dic3—181no—
713C2×Dic3—181no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—181no—
717C2×Dic3—361no—
718C2×Dic3—361no—
719C2×Dic3C2×D3211yescharacteristic
720C2×Dic3C2×D3211yescharacteristic
721C2×Dic3C2×D3211yescharacteristic
722C2×Dic3C2×D3211yescharacteristic
723C2×Dic3C2×D3211yescharacteristic
724C4×D3—62no—
725C4×D3—62no—
726C4×D3—94no—
727Dic6—62no—
728Dic6—62no—
729Dic6—62no—
730Dic6—62no—
731Dic6—62no—
732Dic6—62no—
733Dic6—122no—
734Dic6—182no—
735Dic6—182no—
736Dic6—182no—
737Dic6—362no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—41no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32—62no—
751C2×C32C2×#23511yescharacteristic
752C2×C32C2×#23711yescharacteristic
753C2×C32C2×#23711yescharacteristic
754C2×C32C2×D3×Q811yescharacteristic
755C2×C32C2×D3×Q811yescharacteristic
756C2×C32C2×D3×Q811yescharacteristic
757C2×C32D3×#4111yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32D3×#4111yescharacteristic
760C3×D3—22no—
761C3×D3—22no—
762C3×D3—42no—
763C2×Q8—91no—
764C2×Q8—91no—
765C2×Q8—91no—
766C2×Q8—271no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—271no—
770C4⋊C4—31no—
771C4⋊C4—31no—
772C4⋊C4—91no—
773C4⋊C4—91no—
774C4⋊C4—91no—
775C4⋊C4—91no—
776C4⋊C4—91no—
777C4⋊C4—271no—
778C4⋊C4—271no—
779C4⋊C4—271no—
780C4⋊C4—271no—
781C4⋊C4—271no—
782C4⋊C4—271no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C4⋊C4—271no—
786C22⋊C4—31no—
787C22⋊C4—91no—
788C22⋊C4—91no—
789C22⋊C4—271no—
790C42—91no—
791C42—91no—
792C42—91no—
793C42—271no—
794C42—271no—
795C42—271no—
796C42—271no—
797C42—271no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—32no—
802C22×C3—32no—
803C22×C3—41no—
804C22×C3—62no—
805C22×C3—61no—
806C22×C3—61no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3C22×D3211yescharacteristic
812C22×C3C22×D3211yescharacteristic
813C22×C3C22×D3211yescharacteristic
814C2×D3—21no—
815C2×D3—21no—
816C2×D3#379712yes—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—32no—
821C3×C4—32no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—41no—
825C3×C4—62no—
826C3×C4—61no—
827C3×C4—61no—
828C3×C4—61no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—61no—
832C3×C4—61no—
833C3×C4—61no—
834C3×C4—81no—
835C3×C4—92no—
836C3×C4—92no—
837C3×C4—121no—
838C3×C4—121no—
839C3×C4—121no—
840C3×C4—121no—
841C3×C4—181no—
842C3×C4—181no—
843C3×C4—181no—
844C3×C4—181no—
845Dic3—21no—
846Dic3—21no—
847Dic3—21no—
848Dic3—21no—
849Dic3—32no—
850Dic3—32no—
851Dic3—32no—
852Dic3—32no—
853Dic3—62no—
854Dic3—62no—
855Dic3—61no—
856Dic3—61no—
857Dic3—61no—
858Dic3—61no—
859Dic3—61no—
860Dic3—61no—
861Dic3—61no—
862Dic3—61no—
863Dic3—92no—
864Dic3—92no—
865Dic3—92no—
866Dic3—121no—
867Dic3—121no—
868Dic3—121no—
869Dic3—121no—
870Dic3—182no—
871Dic3—182no—
872Dic3—182no—
873Dic3—181no—
874Dic3—181no—
875Dic3—181no—
876Dic3—362no—
877Dic3—361no—
878Dic3—361no—
879Dic3—361no—
880Dic3—721no—
881Dic3#379512yes—
882C32—21no—
883C32—21no—
884C32—21no—
885C32—41no—
886C32#557811yescharacteristic, complemented
887C32#562211yescharacteristic, complemented
888C32#562211yescharacteristic, complemented
889C23—31no—
890Q8—182no—
891Q8—182no—
892Q8—182no—
893Q8—542no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—31no—
898C2×C4—31no—
899C2×C4—91no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—182no—
906C2×C4—182no—
907C2×C4—274no—
908C2×C4—271no—
909C2×C4—271no—
910C2×C4D3311yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—41no—
921C2×C3—41no—
922C2×C3—41no—
923C2×C3—62no—
924C2×C3—62no—
925C2×C3—122no—
926C2×C3C2×#379511yescharacteristic
927C2×C3C2×#379711yescharacteristic
928C2×C3D3×#23511yescharacteristic
929C2×C3D3×#23711yescharacteristic
930C2×C3D3×#23711yescharacteristic
931C2×C3D3×#23711yescharacteristic
932C2×C3#6431211yescharacteristic
933C2×C3D32×Q811yescharacteristic
934C2×C3D32×Q811yescharacteristic
935D3—22no—
936C22—32no—
937C22—61no—
938C22—61no—
939C22C2×D3311yescharacteristic
940C4—21no—
941C4—32no—
942C4—61no—
943C4—61no—
944C4—61no—
945C4—61no—
946C4—92no—
947C4—92no—
948C4—181no—
949C4—181no—
950C4—181no—
951C4—181no—
952C4—272no—
953C4—541no—
954C3—21no—
955C3—21no—
956C3—21no—
957C3—41no—
958C3#1059403011yescharacteristic, complemented
959C3#1059438511yescharacteristic, complemented
960C3#1059438611yescharacteristic, complemented
961C2—62no—
962C2D3×#379511yescharacteristic
963C2D3×#379711yescharacteristic
964C2#1172440811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×D3C23
hypercenterC2×C4D33
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723668C2semidirect
3. #11723402C2semidirect
4. #11723394C2semidirect
7. C3×#63838C2semidirect
8. #11723032C2semidirect
9. #11723016C2semidirect
12. #11722943C2semidirect
13. #11722940C2semidirect
99. #63838D3semidirect
119. D3×C3⋊Dic3Q8semidirect
644. C33#533semidirect
886. C32#5578semidirect
887. C32#5622semidirect
888. C32#5622semidirect
958. C3#10594030semidirect
959. C3#10594385semidirect
960. C3#10594386semidirect

Maximal subgroups

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

subgroupindex
#117236682
#117234592
#117234022
#117233942
C3×#638962
C3×#638932
C3×#638382
#117230322
#117230162
#117229752
#117229692
#117229432
#117229402
#117229162
D3×Dic322
#105943863
#105943853
#105940303