Finite Group Databasebeta

← #13168341

Subgroups — #13168341

Order 1728.

1036 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723666C211yesmaximal, characteristic, complemented
2#11723425C211yesmaximal, characteristic
3#11723409C211yesmaximal, characteristic, complemented
4#11723400C211yesmaximal, characteristic, complemented
5C3×D3×Dic3⋊C4C211yesmaximal, characteristic
6C3×#63851C211yesmaximal, characteristic
7C3×#63840C211yesmaximal, characteristic, complemented
8#11723035C211yesmaximal, characteristic, complemented
9#11723032C211yesmaximal, characteristic, complemented
10#11723017C211yesmaximal, characteristic, complemented
11#11723012C211yesmaximal, characteristic, complemented
12#11722978C211yesmaximal, characteristic
13#11722969C211yesmaximal, characteristic
14#11722914C211yesmaximal, characteristic
15#11722913C211yesmaximal, characteristic
16#10594812—31nomaximal
17#10594391—31nomaximal
18#10594342—31nomaximal
19C2×C3×#634C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6296C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88813C2211yescharacteristic
34#88807C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64133—31no—
55#64099—31no—
56#64098—31no—
57C3×#924—31no—
58C2×C3×Dic3⋊C4—31no—
59C3×#896—31no—
60C3×D3×C4⋊C4—31no—
61C3×#888—31no—
62C3×#888—31no—
63#63964—31no—
64#63964—31no—
65#63955—31no—
66#63955—31no—
67#63919—31no—
68#63899—31no—
69#63887—31no—
70#63878—31no—
71#63877—31no—
72D3×Dic3⋊C4D311yescharacteristic
73#63873—31no—
74#63869—31no—
75#63867—31no—
76#63856—31no—
77#63856—31no—
78#63856—31no—
79#63856—61no—
80#63855—31no—
81#63851—31no—
82#63851D311yescharacteristic
83#63847—31no—
84#63846—31no—
85#63846—31no—
86#63845—31no—
87#63845—31no—
88#63845—31no—
89#63845—31no—
90#63845—31no—
91#63845—61no—
92#63845—61no—
93#63841—31no—
94#63840—31no—
95#63840D311yescharacteristic, complemented
96#63839—31no—
97#63839—31no—
98#63839—31no—
99#63839—31no—
100#63839—31no—
101#63839—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—41no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×C4×D3—41no—
119#6296—41no—
120C3×#627—41no—
121C3×#627—41no—
122C3×D3×Dic3—41no—
123C3×D3×Dic3Q814yescomplemented
124#5729—91no—
125#5623—91no—
126#5500—91no—
127C22×C32×C4—31no—
128C2×#634C2×D311yescharacteristic
129C22×C3×Dic3—31no—
130C22×C3×Dic3—31no—
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3C2×D311yescharacteristic
135C2×C3×C4×D3C2×D311yescharacteristic
136C2×C3×Dic6—31no—
137C2×C3×Dic6—31no—
138C2×C3×Dic6—31no—
139C2×C3×Dic6—31no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6—61no—
143C2×#627—31no—
144C2×#627—31no—
145C2×#627—31no—
146C2×#627C2×D311yescharacteristic
147C2×#627C2×D311yescharacteristic
148C2×D3×Dic3C2×D311yescharacteristic
149C2×D3×Dic3C2×D311yescharacteristic
150C32×C4⋊C4—31no—
151C32×C4⋊C4—31no—
152#3757—31no—
153#3757—31no—
154C4⋊(C3⋊Dic3)—31no—
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)—61no—
160C4⋊(C3⋊Dic3)—61no—
161C4⋊(C3⋊Dic3)—61no—
162C4⋊(C3⋊Dic3)—121no—
163#3750—31no—
164#3750—31no—
165#3750—31no—
166#3750—31no—
167#3750—31no—
168#3750—31no—
169#3750C2×D311yescharacteristic
170#3750C2×D311yescharacteristic
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3—31no—
173C3×#217—31no—
174C3×#217—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×Dic3⋊C4—21no—
182C3×Dic3⋊C4—21no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
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⋊C4—61no—
194C3×Dic3⋊C4—61no—
195C3×Dic3⋊C4C2×D311yescharacteristic
196C3×Dic3⋊C4C2×D311yescharacteristic
197C3×Dic3⋊C4C2×D311yescharacteristic
198C3×Dic3⋊C4C2×D311yescharacteristic
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201#3724—31no—
202#3724—31no—
203#3724—31no—
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—61no—
212#3724—61no—
213#3724—61no—
214#3724—61no—
215#3724C2×D311yescharacteristic
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
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⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234Dic3⋊Dic3C2×D311yescharacteristic
235Dic3⋊Dic3C2×D311yescharacteristic
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—61no—
241(C2×D3)⋊Dic3—61no—
242(C2×D3)⋊Dic3C2×D311yescharacteristic
243(C2×D3)⋊Dic3C2×D311yescharacteristic
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—61no—
252Dic32—61no—
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)—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3C2×Q812yes—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3C2×Q812yes—
272C3×C4⋊Q8—91no—
273C3×C22⋊Q8—91no—
274C2×C3×C4⋊C4—91no—
275#946—91no—
276#946—91no—
277#944—91no—
278#944—91no—
279#944—91no—
280#944—91no—
281#926—91no—
282#926—91no—
283#924—31no—
284#924—91no—
285#924—91no—
286#924—91no—
287#924—91no—
288#924—181no—
289C2×Dic3⋊C4—31no—
290#896—31no—
291#896—91no—
292#892—91no—
293D3×C4⋊C4—31no—
294#890—91no—
295#890—91no—
296#890—91no—
297#890—91no—
298#890—91no—
299#890—181no—
300#889—91no—
301#889—91no—
302#889—91no—
303#889—91no—
304#889—91no—
305#889—91no—
306#889—181no—
307#888—31no—
308#888—31no—
309#888—91no—
310#888—91no—
311#888—91no—
312#888—91no—
313#888—91no—
314#878—91no—
315#878—91no—
316#877—91no—
317#877—91no—
318#872—91no—
319#870—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×C4—121no—
334C2×C32×C4C22×D311yescharacteristic
335C2×C32×C4C22×D311yescharacteristic
336C2×C32×C4C22×D311yescharacteristic
337C2×C3⋊Dic3—31no—
338C2×C3⋊Dic3—31no—
339C2×C3⋊Dic3—31no—
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—41no—
358C2×C3×Dic3—21no—
359C2×C3×Dic3—21no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—31no—
364C2×C3×Dic3—31no—
365C2×C3×Dic3—34no—
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—121no—
383C2×C3×Dic3C22×D311yescharacteristic
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
393C3×C4×D3—34no—
394C3×C4×D3—41no—
395C3×C4×D3—41no—
396C3×C4×D3—42no—
397C3×C4×D3—121no—
398C3×Dic6—121no—
399C3×Dic6—121no—
400C3×Dic6—121no—
401C3×Dic6—121no—
402C3×Dic6—121no—
403C3×Dic6—121no—
404C3×Dic6—122no—
405#627—41no—
406#627—41no—
407#627—121no—
408#627—121no—
409#627—121no—
410D3×Dic3—41no—
411D3×Dic3Dic614yescomplemented
412#544—271noSylow
413C2×C33C22×Q811yescharacteristic
414C2×C33H(5,𝔽2)11yescharacteristic
415C2×C332−1+411yescharacteristic
416C32×D3—22no—
417C2×C3×Q8—91no—
418C2×C3×Q8—91no—
419C2×C3×Q8—91no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—61no—
423C22×C3×C4—91no—
424C22×C3×C4—91no—
425C22×Dic3—31no—
426C22×Dic3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3D3211yescharacteristic
430C2×Dic6—31no—
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—61no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—91no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—61no—
445C3×C4⋊C4—61no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C42—91no—
456#217—31no—
457#217—31no—
458#217—91no—
459#217—91no—
460#217—91no—
461#217—91no—
462#217—181no—
463#217—181no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—91no—
467(C2×D3)⋊C4—91no—
468C4⋊Dic3—31no—
469C4⋊Dic3—31no—
470C4⋊Dic3—31no—
471C4⋊Dic3—31no—
472C4⋊Dic3—91no—
473C4⋊Dic3—91no—
474C4⋊Dic3—91no—
475C4⋊Dic3—91no—
476C4⋊Dic3—91no—
477C4⋊Dic3—91no—
478C4⋊Dic3—91no—
479C4⋊Dic3—91no—
480C4⋊Dic3—91no—
481C4⋊Dic3—91no—
482C4⋊Dic3—91no—
483C4⋊Dic3—181no—
484C4⋊Dic3—181no—
485C4⋊Dic3—181no—
486C4⋊Dic3—181no—
487C4⋊Dic3—181no—
488C4⋊Dic3—361no—
489Dic3⋊C4—31no—
490Dic3⋊C4—31no—
491Dic3⋊C4—31no—
492Dic3⋊C4—31no—
493Dic3⋊C4—31no—
494Dic3⋊C4—31no—
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—61no—
500Dic3⋊C4—61no—
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—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—181no—
524Dic3⋊C4—181no—
525Dic3⋊C4—181no—
526Dic3⋊C4—181no—
527Dic3⋊C4—181no—
528Dic3⋊C4—181no—
529Dic3⋊C4D3211yescharacteristic
530Dic3⋊C4D3211yescharacteristic
531C4×Dic3—31no—
532C4×Dic3—31no—
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—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—32no—
548C22×C32—41no—
549C22×C32—61no—
550C22×C32—61no—
551C22×C32C23×D311yescharacteristic
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C2×C3×D3—21no—
555C2×C3×D3—21no—
556C2×C3×D3—21no—
557C2×C3×D3—21no—
558C2×C3×D3—22no—
559C2×C3×D3—41no—
560C2×C3×D3—41no—
561C2×C3×D3C2×Dic612yes—
562C2×C3×D3D3×Q812yes—
563C32×C4—21no—
564C32×C4—22no—
565C32×C4—21no—
566C32×C4—21no—
567C32×C4—32no—
568C32×C4—41no—
569C32×C4—41no—
570C32×C4—42no—
571C32×C4—61no—
572C32×C4—61no—
573C32×C4—61no—
574C32×C4—61no—
575C3⋊Dic3—21no—
576C3⋊Dic3—21no—
577C3⋊Dic3—21no—
578C3⋊Dic3—21no—
579C3⋊Dic3—21no—
580C3⋊Dic3—61no—
581C3⋊Dic3—61no—
582C3⋊Dic3—61no—
583C3⋊Dic3—61no—
584C3⋊Dic3—61no—
585C3⋊Dic3—61no—
586C3⋊Dic3—121no—
587C3⋊Dic3—121no—
588C3⋊Dic3—121no—
589C3⋊Dic3—121no—
590C3⋊Dic3—121no—
591C3⋊Dic3—121no—
592C3⋊Dic3—241no—
593C3⋊Dic3—241no—
594C3⋊Dic3C2×Dic612yes—
595C3×Dic3—21no—
596C3×Dic3—21no—
597C3×Dic3—21no—
598C3×Dic3—21no—
599C3×Dic3—21no—
600C3×Dic3—21no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—22no—
604C3×Dic3—32no—
605C3×Dic3—32no—
606C3×Dic3—41no—
607C3×Dic3—41no—
608C3×Dic3—41no—
609C3×Dic3—41no—
610C3×Dic3—62no—
611C3×Dic3—61no—
612C3×Dic3—61no—
613C3×Dic3—61no—
614C3×Dic3—61no—
615C3×Dic3—61no—
616C3×Dic3—61no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—121no—
622C3×Dic3—121no—
623C3×Dic3—121no—
624C3×Dic3—121no—
625C3×Dic3—121no—
626C3×Dic3C2×Dic612yes—
627C3×Dic3D3×Q812yes—
628C4⋊Q8—91no—
629C4⋊Q8—271no—
630C4⋊Q8—271no—
631C4⋊Q8—271no—
632#125—271no—
633#125—271no—
634#125—271no—
635#125—271no—
636C22⋊Q8—91no—
637C22⋊Q8—271no—
638C22⋊Q8—271no—
639C22⋊Q8—271no—
640#117—271no—
641#117—271no—
642C2×C4⋊C4—91no—
643C33#54411yescharacteristic, complemented, Sylow
644C23×C3—31no—
645C23×C3—31no—
646C23×C3—61no—
647C22×D3C2×D3211yescharacteristic
648C3×Q8—361no—
649C3×Q8—361no—
650C3×Q8—361no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—31no—
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—41no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—94no—
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—121no—
678C2×C3×C4—121no—
679C2×C3×C4—122no—
680C2×C3×C4—361no—
681C2×C3×C4C2×D3211yescharacteristic
682C2×C3×C4C2×D3211yescharacteristic
683C2×C3×C4C2×D3211yescharacteristic
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—34no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—91no—
704C2×Dic3—91no—
705C2×Dic3—91no—
706C2×Dic3—91no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—121no—
710C2×Dic3—181no—
711C2×Dic3—181no—
712C2×Dic3—181no—
713C2×Dic3—181no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—361no—
717C2×Dic3—361no—
718C2×Dic3C2×D3211yescharacteristic
719C2×Dic3C2×D3211yescharacteristic
720C2×Dic3C2×D3211yescharacteristic
721C2×Dic3C2×D3211yescharacteristic
722C2×Dic3C2×D3211yescharacteristic
723C4×D3—34no—
724C4×D3—41no—
725C4×D3—121no—
726Dic6—121no—
727Dic6—121no—
728Dic6—121no—
729Dic6—121no—
730Dic6—121no—
731Dic6—121no—
732Dic6—122no—
733Dic6—361no—
734Dic6—361no—
735Dic6—361no—
736C2×C32—21no—
737C2×C32—21no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—41no—
746C2×C32—41no—
747C2×C32—41no—
748C2×C32—62no—
749C2×C32C22×Dic611yescharacteristic
750C2×C32#100411yescharacteristic
751C2×C32#100411yescharacteristic
752C2×C32#100411yescharacteristic
753C2×C32C2×D3×Q811yescharacteristic
754C2×C32C2×D3×Q811yescharacteristic
755C2×C32#100711yescharacteristic
756C2×C32#100711yescharacteristic
757C2×C32#101011yescharacteristic
758C3×D3—22no—
759C3×D3—22no—
760C3×D3—42no—
761C2×Q8—91no—
762C2×Q8—91no—
763C2×Q8—91no—
764C2×Q8—271no—
765C22×C4—31no—
766C22×C4—91no—
767C22×C4—91no—
768C4⋊C4—31no—
769C4⋊C4—31no—
770C4⋊C4—91no—
771C4⋊C4—91no—
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—
786C4⋊C4—271no—
787C4⋊C4—271no—
788C22⋊C4—91no—
789C22⋊C4—91no—
790C22⋊C4—271no—
791C22⋊C4—271no—
792C42—91no—
793C42—271no—
794C42—271no—
795C42—271no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—32no—
800C22×C3—32no—
801C22×C3—41no—
802C22×C3—62no—
803C22×C3—61no—
804C22×C3—61no—
805C22×C3—61no—
806C22×C3—61no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3C22×D3211yescharacteristic
810C22×C3C22×D3211yescharacteristic
811C22×C3C22×D3211yescharacteristic
812C2×D3—21no—
813C2×D3—21no—
814C2×D3D3×Dic612yes—
815C3×C4—22no—
816C3×C4—21no—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—32no—
820C3×C4—32no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—42no—
824C3×C4—62no—
825C3×C4—61no—
826C3×C4—61no—
827C3×C4—61no—
828C3×C4—61no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—61no—
832C3×C4—61no—
833C3×C4—92no—
834C3×C4—121no—
835C3×C4—121no—
836C3×C4—121no—
837C3×C4—121no—
838C3×C4—181no—
839C3×C4—181no—
840C3×C4—181no—
841C3×C4—181no—
842C3×C4—181no—
843Dic3—21no—
844Dic3—21no—
845Dic3—21no—
846Dic3—21no—
847Dic3—32no—
848Dic3—32no—
849Dic3—62no—
850Dic3—61no—
851Dic3—61no—
852Dic3—61no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—61no—
858Dic3—61no—
859Dic3—61no—
860Dic3—121no—
861Dic3—121no—
862Dic3—121no—
863Dic3—121no—
864Dic3—121no—
865Dic3—181no—
866Dic3—181no—
867Dic3—181no—
868Dic3—181no—
869Dic3—181no—
870Dic3—181no—
871Dic3—361no—
872Dic3—361no—
873Dic3—361no—
874Dic3—361no—
875Dic3—361no—
876Dic3—361no—
877Dic3—721no—
878Dic3—721no—
879Dic3D3×Dic612yes—
880C32—21no—
881C32—21no—
882C32—21no—
883C32—41no—
884C32#550011yescharacteristic, complemented
885C32#562311yescharacteristic, complemented
886C32#572911yescharacteristic, complemented
887C23—31no—
888Q8—361no—
889Q8—361no—
890Q8—361no—
891Q8—1081no—
892C2×C4—31no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—94no—
898C2×C4—91no—
899C2×C4—91no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—121no—
905C2×C4—271no—
906C2×C4—271no—
907C2×C4—361no—
908C2×C4D3311yescharacteristic
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—41no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—62no—
922C2×C3—62no—
923C2×C3—122no—
924C2×C3C2×D3×Dic611yescharacteristic
925C2×C3C2×D3×Dic611yescharacteristic
926C2×C3#6429711yescharacteristic
927C2×C3#6429711yescharacteristic
928C2×C3#6431311yescharacteristic
929C2×C3#6431311yescharacteristic
930C2×C3#6431611yescharacteristic
931C2×C3D32×Q811yescharacteristic
932C2×C3#6433011yescharacteristic
933D3—22no—
934C22—32no—
935C22—61no—
936C22—61no—
937C22C2×D3311yescharacteristic
938C4—21no—
939C4—32no—
940C4—61no—
941C4—61no—
942C4—61no—
943C4—61no—
944C4—92no—
945C4—181no—
946C4—181no—
947C4—181no—
948C4—181no—
949C4—181no—
950C4—541no—
951C4—541no—
952C3—21no—
953C3—21no—
954C3—21no—
955C3—41no—
956C3#1059434211yescharacteristic, complemented
957C3#1059439111yescharacteristic, complemented
958C3#1059481211yescharacteristic, complemented
959C2—62no—
960C2D32×Dic611yescharacteristic
961C2#1172439511yescharacteristic
962C2#1172441511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×D3C23
hypercenterC2×C4D33
hypocenterC33#544
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723666C2semidirect
3. #11723409C2semidirect
4. #11723400C2semidirect
7. C3×#63840C2semidirect
8. #11723035C2semidirect
9. #11723032C2semidirect
10. #11723017C2semidirect
11. #11723012C2semidirect
95. #63840D3semidirect
123. C3×D3×Dic3Q8semidirect
411. D3×Dic3Dic6semidirect
643. C33#544semidirect
884. C32#5500semidirect
885. C32#5623semidirect
886. C32#5729semidirect
956. C3#10594342semidirect
957. C3#10594391semidirect
958. C3#10594812semidirect

Maximal subgroups

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

subgroupindex
#117236662
#117234252
#117234092
#117234002
C3×D3×Dic3⋊C42
C3×#638512
C3×#638402
#117230352
#117230322
#117230172
#117230122
#117229782
#117229692
#117229142
#117229132
#105948123
#105943913
#105943423