Finite Group Databasebeta

← #13168338

Subgroups — #13168338

Order 1728.

1072 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723669C211yesmaximal, characteristic, complemented
2#11723426C211yesmaximal, characteristic
3#11723395C211yesmaximal, characteristic, complemented
4#11723395C211yesmaximal, characteristic, complemented
5C3×D3×Dic3⋊C4C211yesmaximal, characteristic
6C3×#63851C211yesmaximal, characteristic
7C3×#63845C211yesmaximal, characteristic, complemented
8#11723034C211yesmaximal, characteristic, complemented
9#11723033C211yesmaximal, characteristic, complemented
10#11723015C211yesmaximal, characteristic, complemented
11#11723013C211yesmaximal, characteristic, complemented
12#11722975C211yesmaximal, characteristic
13#11722971C211yesmaximal, characteristic
14#11722914C211yesmaximal, characteristic
15#11722913C211yesmaximal, characteristic
16#10594812—31nomaximal
17#10594390—31nomaximal
18#10594344—31nomaximal
19C2×#6308C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×#6293C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C32×Dic3⋊C4C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88813C2211yescharacteristic
35#88807C2211yescharacteristic
36#88807C2211yescharacteristic
37#88807C2211yescharacteristic
38#88807C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
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#64097—31no—
56#64097—31no—
57C3×#924—31no—
58C2×C3×Dic3⋊C4—31no—
59C3×#896—31no—
60C3×D3×C4⋊C4—31no—
61C3×#890—31no—
62C3×#889—31no—
63#63964—31no—
64#63964—31no—
65#63955—31no—
66#63955—31no—
67#63918—31no—
68#63896—31no—
69#63893—31no—
70#63878—31no—
71#63877—31no—
72D3×Dic3⋊C4D311yescharacteristic
73#63872—31no—
74#63870—31no—
75#63866—31no—
76#63857—31no—
77#63857—31no—
78#63857—31no—
79#63857—61no—
80#63855—31no—
81#63851—31no—
82#63851D311yescharacteristic
83#63847—31no—
84#63846—31no—
85#63846—31no—
86#63846—31no—
87#63846—31no—
88#63845—31no—
89#63845—31no—
90#63845D311yescharacteristic, complemented
91#63841—31no—
92#63840—31no—
93#63840—31no—
94#63840—31no—
95#63840—31no—
96#63840—31no—
97#63840—61no—
98#63840—61no—
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
106#6308—41no—
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×C4×D3—41no—
119#6293—41no—
120#6293—41no—
121C3×#627—41no—
122C3×D3×Dic3—41no—
123C3×D3×Dic3Q814yescomplemented
124#5689—91no—
125#5623—91no—
126#5500—91no—
127C22×C32×C4—31no—
128C2×#634—31no—
129C2×#634—31no—
130C2×#634—31no—
131C2×#634—31no—
132C2×#634—31no—
133C2×#634—61no—
134C2×#634—61no—
135C2×#634—61no—
136C2×#634—121no—
137C22×C3×Dic3—31no—
138C22×C3×Dic3—31no—
139C2×C3×C4×D3—21no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3C2×D311yescharacteristic
143C2×C3×C4×D3C2×D311yescharacteristic
144C2×C3×Dic6—31no—
145C2×C3×Dic6—31no—
146C2×#627—31no—
147C2×#627—31no—
148C2×#627—31no—
149C2×#627—31no—
150C2×#627—61no—
151C2×#627—61no—
152C2×#627C2×D311yescharacteristic
153C2×D3×Dic3C2×D311yescharacteristic
154C2×D3×Dic3C2×D311yescharacteristic
155C32×C4⋊C4—31no—
156C32×C4⋊C4—31no—
157#3757—31no—
158#3757—31no—
159C4⋊(C3⋊Dic3)—31no—
160C4⋊(C3⋊Dic3)—31no—
161C4⋊(C3⋊Dic3)C2×D311yescharacteristic
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750—31no—
166#3750C2×D311yescharacteristic
167#3750C2×D311yescharacteristic
168C4×C3⋊Dic3—31no—
169C4×C3⋊Dic3—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—61no—
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—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—61no—
196C3×Dic3⋊C4—61no—
197C3×Dic3⋊C4C2×D311yescharacteristic
198C3×Dic3⋊C4C2×D311yescharacteristic
199C3×Dic3⋊C4C2×D311yescharacteristic
200C3×Dic3⋊C4C2×D311yescharacteristic
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203#3724—31no—
204#3724—31no—
205#3724—31no—
206#3724C2×D311yescharacteristic
207#3724C2×D311yescharacteristic
208Dic3⋊Dic3—31no—
209Dic3⋊Dic3—31no—
210Dic3⋊Dic3—31no—
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
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—61no—
227Dic3⋊Dic3—61no—
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×#125—91no—
273C3×C22⋊Q8—91no—
274C2×C3×C4⋊C4—91no—
275#944—91no—
276#944—91no—
277#926—91no—
278#926—91no—
279#924—31no—
280#924—91no—
281#924—91no—
282#924—91no—
283#924—91no—
284#924—181no—
285C2×Dic3⋊C4—31no—
286#897—91no—
287#897—91no—
288#896—31no—
289#896—91no—
290#892—91no—
291D3×C4⋊C4—31no—
292#890—31no—
293#890—91no—
294#890—91no—
295#890—91no—
296#890—91no—
297#889—31no—
298#889—91no—
299#889—91no—
300#889—91no—
301#889—91no—
302#889—91no—
303#888—91no—
304#888—91no—
305#888—91no—
306#888—91no—
307#888—91no—
308#888—91no—
309#888—91no—
310#888—91no—
311#888—91no—
312#888—181no—
313#888—181no—
314#878—91no—
315#878—91no—
316#877—91no—
317#877—91no—
318#872—91no—
319#869—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—121no—
358#634—121no—
359#634—121no—
360#634—121no—
361#634—121no—
362#634—122no—
363#634—122no—
364#634—122no—
365#634—124no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—34no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—121no—
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C3×C4×D3—34no—
402C3×C4×D3—41no—
403C3×C4×D3—41no—
404C3×C4×D3—42no—
405C3×C4×D3—121no—
406C3×Dic6—121no—
407C3×Dic6—121no—
408#627—41no—
409#627—121no—
410#627—121no—
411#627—121no—
412#627—121no—
413#627—122no—
414#627—122no—
415D3×Dic3—41no—
416D3×Dic3Dic614yescomplemented
417#544—271noSylow
418C2×C33C22×Q811yescharacteristic
419C2×C33H(5,𝔽2)11yescharacteristic
420C2×C332−1+411yescharacteristic
421C32×D3—22no—
422C2×C3×Q8—91no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—61no—
426C22×C3×C4—91no—
427C22×C3×C4—91no—
428C22×Dic3—31no—
429C22×Dic3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3D3211yescharacteristic
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—91no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—91no—
440C2×Dic6—91no—
441C2×Dic6—91no—
442C2×Dic6—91no—
443C2×Dic6—91no—
444C2×Dic6—181no—
445C2×Dic6—181no—
446C2×Dic6—181no—
447C2×Dic6—181no—
448C2×Dic6—181no—
449C2×Dic6—361no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4—31no—
453C3×C4⋊C4—31no—
454C3×C4⋊C4—61no—
455C3×C4⋊C4—61no—
456C3×C4⋊C4—91no—
457C3×C4⋊C4—91no—
458C3×C4⋊C4—91no—
459C3×C4⋊C4—91no—
460C3×C4⋊C4—91no—
461C3×C4⋊C4—91no—
462C3×C4⋊C4—91no—
463C3×C4⋊C4—91no—
464C3×C4⋊C4—91no—
465C3×C22⋊C4—91no—
466C3×C22⋊C4—91no—
467C3×C42—91no—
468#217—31no—
469#217—31no—
470#217—91no—
471#217—91no—
472#217—91no—
473#217—91no—
474#217—181no—
475#217—181no—
476(C2×D3)⋊C4—31no—
477(C2×D3)⋊C4—31no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480C4⋊Dic3—31no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—61no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—91no—
497C4⋊Dic3—91no—
498C4⋊Dic3—181no—
499C4⋊Dic3—181no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—31no—
511Dic3⋊C4—31no—
512Dic3⋊C4—61no—
513Dic3⋊C4—61no—
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—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—91no—
527Dic3⋊C4—91no—
528Dic3⋊C4—91no—
529Dic3⋊C4—91no—
530Dic3⋊C4—181no—
531Dic3⋊C4—181no—
532Dic3⋊C4—181no—
533Dic3⋊C4—181no—
534Dic3⋊C4D3211yescharacteristic
535Dic3⋊C4D3211yescharacteristic
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C4×Dic3—91no—
545C4×Dic3—91no—
546C4×Dic3—91no—
547C4×Dic3—181no—
548C4×Dic3—181no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32—32no—
553C22×C32—41no—
554C22×C32—61no—
555C22×C32—61no—
556C22×C32C23×D311yescharacteristic
557C22×C32C23×D311yescharacteristic
558C22×C32C23×D311yescharacteristic
559C2×C3×D3—21no—
560C2×C3×D3—21no—
561C2×C3×D3—21no—
562C2×C3×D3—21no—
563C2×C3×D3—22no—
564C2×C3×D3—41no—
565C2×C3×D3—41no—
566C2×C3×D3C2×Dic612yes—
567C2×C3×D3D3×Q812yes—
568C32×C4—21no—
569C32×C4—22no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—32no—
573C32×C4—41no—
574C32×C4—41no—
575C32×C4—42no—
576C32×C4—61no—
577C32×C4—61no—
578C32×C4—61no—
579C32×C4—61no—
580C3⋊Dic3—21no—
581C3⋊Dic3—21no—
582C3⋊Dic3—21no—
583C3⋊Dic3—21no—
584C3⋊Dic3—21no—
585C3⋊Dic3—61no—
586C3⋊Dic3—61no—
587C3⋊Dic3—62no—
588C3⋊Dic3—62no—
589C3⋊Dic3—61no—
590C3⋊Dic3—61no—
591C3⋊Dic3—61no—
592C3⋊Dic3—61no—
593C3⋊Dic3—121no—
594C3⋊Dic3—121no—
595C3⋊Dic3—121no—
596C3⋊Dic3—121no—
597C3⋊Dic3—122no—
598C3⋊Dic3—122no—
599C3⋊Dic3C2×Dic612yes—
600C3×Dic3—22no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—21no—
604C3×Dic3—21no—
605C3×Dic3—21no—
606C3×Dic3—21no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—22no—
610C3×Dic3—32no—
611C3×Dic3—32no—
612C3×Dic3—41no—
613C3×Dic3—41no—
614C3×Dic3—41no—
615C3×Dic3—62no—
616C3×Dic3—62no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—121no—
628C3×Dic3—121no—
629C3×Dic3—121no—
630C3×Dic3—121no—
631C3×Dic3C2×Dic612yes—
632C3×Dic3D3×Q812yes—
633C4⋊Q8—271no—
634C4⋊Q8—271no—
635C4⋊Q8—271no—
636C4⋊Q8—271no—
637#125—91no—
638#125—271no—
639#125—271no—
640#125—271no—
641C22⋊Q8—91no—
642C22⋊Q8—271no—
643C22⋊Q8—271no—
644C22⋊Q8—271no—
645#117—271no—
646#117—271no—
647C2×C4⋊C4—91no—
648C33#54411yescharacteristic, complemented, Sylow
649C23×C3—31no—
650C23×C3—31no—
651C23×C3—61no—
652C22×D3C2×D3211yescharacteristic
653C3×Q8—361no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
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—31no—
666C2×C3×C4—31no—
667C2×C3×C4—41no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—94no—
674C2×C3×C4—91no—
675C2×C3×C4—91no—
676C2×C3×C4—91no—
677C2×C3×C4—91no—
678C2×C3×C4—91no—
679C2×C3×C4—91no—
680C2×C3×C4—121no—
681C2×C3×C4—121no—
682C2×C3×C4—122no—
683C2×C3×C4—361no—
684C2×C3×C4C2×D3211yescharacteristic
685C2×C3×C4C2×D3211yescharacteristic
686C2×C3×C4C2×D3211yescharacteristic
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—34no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—91no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—91no—
710C2×Dic3—91no—
711C2×Dic3—91no—
712C2×Dic3—121no—
713C2×Dic3—181no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—181no—
717C2×Dic3—181no—
718C2×Dic3—181no—
719C2×Dic3—361no—
720C2×Dic3—361no—
721C2×Dic3C2×D3211yescharacteristic
722C2×Dic3C2×D3211yescharacteristic
723C2×Dic3C2×D3211yescharacteristic
724C2×Dic3C2×D3211yescharacteristic
725C2×Dic3C2×D3211yescharacteristic
726C4×D3—34no—
727C4×D3—41no—
728C4×D3—121no—
729Dic6—121no—
730Dic6—121no—
731Dic6—361no—
732Dic6—361no—
733Dic6—361no—
734Dic6—361no—
735Dic6—361no—
736Dic6—361no—
737Dic6—362no—
738Dic6—362no—
739Dic6—361no—
740Dic6—361no—
741Dic6—361no—
742Dic6—362no—
743Dic6—362no—
744Dic6—362no—
745Dic6—364no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—41no—
756C2×C32—41no—
757C2×C32—41no—
758C2×C32—62no—
759C2×C32C22×Dic611yescharacteristic
760C2×C32#100411yescharacteristic
761C2×C32#100411yescharacteristic
762C2×C32C2×D3×Q811yescharacteristic
763C2×C32C2×D3×Q811yescharacteristic
764C2×C32#100711yescharacteristic
765C2×C32#100911yescharacteristic
766C2×C32#101011yescharacteristic
767C2×C32#101011yescharacteristic
768C3×D3—22no—
769C3×D3—22no—
770C3×D3—42no—
771C2×Q8—91no—
772C2×Q8—271no—
773C2×Q8—271no—
774C2×Q8—271no—
775C22×C4—31no—
776C22×C4—91no—
777C22×C4—91no—
778C4⋊C4—31no—
779C4⋊C4—31no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—91no—
784C4⋊C4—91no—
785C4⋊C4—91no—
786C4⋊C4—91no—
787C4⋊C4—91no—
788C4⋊C4—91no—
789C4⋊C4—271no—
790C4⋊C4—271no—
791C4⋊C4—271no—
792C4⋊C4—271no—
793C4⋊C4—271no—
794C4⋊C4—271no—
795C4⋊C4—271no—
796C4⋊C4—271no—
797C4⋊C4—271no—
798C22⋊C4—91no—
799C22⋊C4—91no—
800C22⋊C4—271no—
801C22⋊C4—271no—
802C42—91no—
803C42—271no—
804C42—271no—
805C42—271no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—32no—
810C22×C3—32no—
811C22×C3—41no—
812C22×C3—62no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3C22×D3211yescharacteristic
820C22×C3C22×D3211yescharacteristic
821C22×C3C22×D3211yescharacteristic
822C2×D3—21no—
823C2×D3—21no—
824C2×D3D3×Dic612yes—
825C3×C4—22no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—32no—
830C3×C4—32no—
831C3×C4—41no—
832C3×C4—41no—
833C3×C4—42no—
834C3×C4—62no—
835C3×C4—62no—
836C3×C4—61no—
837C3×C4—61no—
838C3×C4—61no—
839C3×C4—61no—
840C3×C4—61no—
841C3×C4—61no—
842C3×C4—61no—
843C3×C4—61no—
844C3×C4—92no—
845C3×C4—121no—
846C3×C4—121no—
847C3×C4—121no—
848C3×C4—181no—
849C3×C4—181no—
850C3×C4—181no—
851C3×C4—181no—
852C3×C4—181no—
853Dic3—21no—
854Dic3—21no—
855Dic3—21no—
856Dic3—21no—
857Dic3—32no—
858Dic3—32no—
859Dic3—62no—
860Dic3—62no—
861Dic3—61no—
862Dic3—61no—
863Dic3—61no—
864Dic3—61no—
865Dic3—61no—
866Dic3—61no—
867Dic3—61no—
868Dic3—61no—
869Dic3—61no—
870Dic3—61no—
871Dic3—121no—
872Dic3—121no—
873Dic3—121no—
874Dic3—121no—
875Dic3—182no—
876Dic3—182no—
877Dic3—181no—
878Dic3—181no—
879Dic3—181no—
880Dic3—181no—
881Dic3—181no—
882Dic3—181no—
883Dic3—361no—
884Dic3—361no—
885Dic3—361no—
886Dic3—361no—
887Dic3—362no—
888Dic3—362no—
889Dic3D3×Dic612yes—
890C32—21no—
891C32—21no—
892C32—21no—
893C32—41no—
894C32#550011yescharacteristic, complemented
895C32#562311yescharacteristic, complemented
896C32#568911yescharacteristic, complemented
897C23—31no—
898Q8—361no—
899Q8—1081no—
900Q8—1081no—
901Q8—1081no—
902C2×C4—31no—
903C2×C4—31no—
904C2×C4—31no—
905C2×C4—31no—
906C2×C4—31no—
907C2×C4—94no—
908C2×C4—91no—
909C2×C4—91no—
910C2×C4—91no—
911C2×C4—91no—
912C2×C4—91no—
913C2×C4—91no—
914C2×C4—121no—
915C2×C4—271no—
916C2×C4—271no—
917C2×C4—361no—
918C2×C4D3311yescharacteristic
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—41no—
929C2×C3—41no—
930C2×C3—41no—
931C2×C3—62no—
932C2×C3—62no—
933C2×C3—122no—
934C2×C3C2×D3×Dic611yescharacteristic
935C2×C3C2×D3×Dic611yescharacteristic
936C2×C3#6429711yescharacteristic
937C2×C3#6429811yescharacteristic
938C2×C3#6431411yescharacteristic
939C2×C3#6431411yescharacteristic
940C2×C3#6431511yescharacteristic
941C2×C3D32×Q811yescharacteristic
942C2×C3#6433011yescharacteristic
943D3—22no—
944C22—32no—
945C22—61no—
946C22—61no—
947C22C2×D3311yescharacteristic
948C4—21no—
949C4—32no—
950C4—61no—
951C4—61no—
952C4—61no—
953C4—61no—
954C4—92no—
955C4—181no—
956C4—181no—
957C4—181no—
958C4—181no—
959C4—181no—
960C4—541no—
961C4—541no—
962C3—21no—
963C3—21no—
964C3—21no—
965C3—41no—
966C3#1059434411yescharacteristic, complemented
967C3#1059439011yescharacteristic, complemented
968C3#1059481211yescharacteristic, complemented
969C2—62no—
970C2D32×Dic611yescharacteristic
971C2#1172439611yescharacteristic
972C2#1172441911yescharacteristic
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. #11723669C2semidirect
3. #11723395C2semidirect
4. #11723395C2semidirect
7. C3×#63845C2semidirect
8. #11723034C2semidirect
9. #11723033C2semidirect
10. #11723015C2semidirect
11. #11723013C2semidirect
90. #63845D3semidirect
123. C3×D3×Dic3Q8semidirect
416. D3×Dic3Dic6semidirect
648. C33#544semidirect
894. C32#5500semidirect
895. C32#5623semidirect
896. C32#5689semidirect
966. C3#10594344semidirect
967. C3#10594390semidirect
968. C3#10594812semidirect

Maximal subgroups

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

subgroupindex
#117236692
#117234262
#117233952
C3×D3×Dic3⋊C42
C3×#638512
C3×#638452
#117230342
#117230332
#117230152
#117230132
#117229752
#117229712
#117229142
#117229132
#105948123
#105943903
#105943443