Finite Group Databasebeta

← #13172210

Subgroups — #13172210

Order 1728.

1146 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723721C211yesmaximal, characteristic
2#11723641C211yesmaximal, characteristic
3#11723640C211yesmaximal, characteristic
4#11723594C211yesmaximal, characteristic
5C3×#63964C211yesmaximal, characteristic
6C3×#63955C211yesmaximal, characteristic
7C2×C3×Dic32C211yesmaximal, characteristic
8#11723036C211yesmaximal, characteristic, complemented
9#11723033C211yesmaximal, characteristic, complemented
10#11723012C211yesmaximal, characteristic, complemented
11#11723011C211yesmaximal, characteristic, complemented
12#11722944C211yesmaximal, characteristic, complemented
13#11722942C211yesmaximal, characteristic, complemented
14#11722942C211yesmaximal, characteristic, complemented
15Dic3×#627C211yesmaximal, characteristic, complemented
16#10595049—31nomaximal
17#10594808—31nomaximal
18#10594029—31nomaximal
19C22×C3×C3⋊Dic3C2211yescharacteristic
20C22×C32×Dic3C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C2×#6296C2211yescharacteristic
23C2×#6293C2211yescharacteristic
24C2×#6293C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic
26#88864C2211yescharacteristic
27C3×#3757C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C32×#217C2211yescharacteristic
30#88815C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88807C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic32C2211yescharacteristic
49C3×Dic32C2211yescharacteristic
50C3×Dic32C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64135—31no—
55#64133—31no—
56#64087—31no—
57C3×#926—31no—
58C3×#924—31no—
59C2×C3×C4×Dic3—31no—
60C2×C3×C4×Dic3—31no—
61C3×#878—31no—
62C3×#877—31no—
63#63982—31no—
64#63964—31no—
65#63964—31no—
66#63964—31no—
67#63964—31no—
68#63964—31no—
69#63964—31no—
70#63964—61no—
71#63964—61no—
72#63964D311yescharacteristic
73#63955—31no—
74#63955—31no—
75#63955—61no—
76#63955D311yescharacteristic
77C2×Dic32D311yescharacteristic
78#63918—31no—
79#63918—31no—
80#63918—31no—
81C4×#627—31no—
82C4×#627—31no—
83C4×#627—31no—
84C4×#627—31no—
85#63869—31no—
86#63869—31no—
87#63867—31no—
88#63867—31no—
89#63866—31no—
90#63846—31no—
91#63845—31no—
92#63844—31no—
93#63844—31no—
94Dic3×Dic6—31no—
95Dic3×Dic6—31no—
96#63840—31no—
97#63839—31no—
98#63837—31no—
99#63837—31no—
100#63837—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3×C3⋊Dic3—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3—22no—
113C2×C32×Dic3Q814yescomplemented
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120#6296—22no—
121#6293—22no—
122#6293—22no—
123C3×#627—22no—
124#5622—91no—
125#5517—91no—
126#5470—91no—
127C22×C32×C4—31no—
128C22×C32×C4—31no—
129C22×C3⋊Dic3C2×D311yescharacteristic
130C2×#634—31no—
131C2×#634—31no—
132C22×C3×Dic3—21no—
133C22×C3×Dic3—21no—
134C22×C3×Dic3—31no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3—61no—
137C22×C3×Dic3C2×D311yescharacteristic
138C22×C3×Dic3C2×D311yescharacteristic
139C22×C3×Dic3C2×D311yescharacteristic
140C22×C3×Dic3C2×D311yescharacteristic
141C2×C3×Dic6—31no—
142C2×C3×Dic6—31no—
143C2×#627—31no—
144C2×#627—31no—
145C2×#627—31no—
146C2×#627—31no—
147C2×#627—31no—
148C2×#627—31no—
149C2×#627—31no—
150C2×#627—61no—
151C2×#627—61no—
152C2×#627C2×D311yescharacteristic
153C32×C22⋊C4—31no—
154#3757—31no—
155#3757—31no—
156#3757—31no—
157#3757—61no—
158#3757—61no—
159#3757—61no—
160#3757—121no—
161#3757C2×D311yescharacteristic
162#3757C2×D311yescharacteristic
163C4⋊(C3⋊Dic3)—31no—
164C4⋊(C3⋊Dic3)—31no—
165C4⋊(C3⋊Dic3)—31no—
166C4⋊(C3⋊Dic3)—31no—
167#3750—31no—
168#3750—31no—
169#3750—31no—
170#3750—31no—
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3—31no—
173C3×#217—21no—
174C3×#217—31no—
175C3×#217—31no—
176C3×#217—31no—
177C3×#217—31no—
178C3×#217—61no—
179C3×#217—61no—
180C3×#217C2×D311yescharacteristic
181C3×#217C2×D311yescharacteristic
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—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×C4×Dic3—31no—
193C3×C4×Dic3—31no—
194C3×C4×Dic3—31no—
195C3×C4×Dic3—31no—
196C3×C4×Dic3—31no—
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—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#3724C2×D311yescharacteristic
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—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—61no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3—61no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3C2×D311yescharacteristic
239Dic3⋊Dic3C2×D311yescharacteristic
240Dic3⋊Dic3C2×D311yescharacteristic
241Dic3⋊Dic3C2×D311yescharacteristic
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—61no—
247Dic32—61no—
248Dic32C2×D311yescharacteristic
249Dic32C2×D311yescharacteristic
250Dic32C2×D311yescharacteristic
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253Dic32C2×D311yescharacteristic
254C22×C33—21no—
255C22×C33—21no—
256C22×C33C2×Q812yes—
257C22×C33C2411yescharacteristic
258C3⋊(C3⋊Dic3)—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#4112yes—
266C32×Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3C2×Q812yes—
270C32×Dic3C2×Q812yes—
271C32×Dic3#4112yes—
272C3×C22⋊Q8—91no—
273C3×#117—91no—
274C2×C3×C42—91no—
275Q8×Dic3—91no—
276#944—91no—
277#926—31no—
278#926—91no—
279#926—91no—
280#926—181no—
281#924—31no—
282#924—91no—
283#924—91no—
284#924—91no—
285#924—91no—
286#924—181no—
287C2×C4×Dic3—31no—
288C2×C4×Dic3—31no—
289#890—91no—
290#890—91no—
291#889—91no—
292#889—91no—
293#888—91no—
294#888—91no—
295#888—91no—
296#887—91no—
297#887—91no—
298#887—91no—
299#878—31no—
300#878—91no—
301#878—91no—
302#878—91no—
303#878—91no—
304#878—91no—
305#878—181no—
306#877—31no—
307#877—91no—
308#870—91no—
309#870—91no—
310#869—91no—
311#869—91no—
312C4×Dic6—91no—
313C4×Dic6—91no—
314C4×Dic6—91no—
315C4×Dic6—91no—
316C4×Dic6—91no—
317C4×Dic6—91no—
318C4×Dic6—91no—
319C4×Dic6—91no—
320C23×C32—21no—
321C23×C32—21no—
322C23×C32—21no—
323C23×C32—41no—
324C23×C32C22×D311yescharacteristic
325C23×C32C22×D311yescharacteristic
326C23×C32C22×D311yescharacteristic
327C2×C32×C4—34no—
328C2×C32×C4—31no—
329C2×C32×C4—31no—
330C2×C32×C4—31no—
331C2×C32×C4—31no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—62no—
335C2×C3⋊Dic3—22no—
336C2×C3⋊Dic3—31no—
337C2×C3⋊Dic3—31no—
338C2×C3⋊Dic3—31no—
339C2×C3⋊Dic3—31no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—61no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—61no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—121no—
349C2×C3⋊Dic3—121no—
350C2×C3⋊Dic3C22×D311yescharacteristic
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356#634—62no—
357#634—62no—
358C2×C3×Dic3—22no—
359C2×C3×Dic3—22no—
360C2×C3×Dic3—24no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
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—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—42no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—62no—
387C2×C3×Dic3—62no—
388C2×C3×Dic3—122no—
389C2×C3×Dic3Dic614yescomplemented
390C2×C3×Dic3Dic614yescomplemented
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
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C3×Dic6—62no—
404C3×Dic6—62no—
405#627—22no—
406#627—62no—
407#627—62no—
408#627—62no—
409#627—62no—
410#627—62no—
411#627—62no—
412#627—62no—
413#627—122no—
414#627—122no—
415#533—271noSylow
416C2×C33—22no—
417C2×C33C22×Q811yescharacteristic
418C2×C33C2×#4111yescharacteristic
419C2×C33C2×#4111yescharacteristic
420C2×C3×Q8—91no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—61no—
426C22×C3×C4—61no—
427C22×C3×C4—91no—
428C22×Dic3—31no—
429C22×Dic3—31no—
430C22×Dic3—61no—
431C22×Dic3D3211yescharacteristic
432C22×Dic3D3211yescharacteristic
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—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C22⋊C4—31no—
452C3×C22⋊C4—31no—
453C3×C22⋊C4—61no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C42—91no—
457C3×C42—91no—
458C3×C42—91no—
459C3×C42—91no—
460C3×C42—91no—
461C3×C42—91no—
462#217—31no—
463#217—31no—
464#217—31no—
465#217—31no—
466#217—61no—
467#217—61no—
468#217—91no—
469#217—91no—
470#217—91no—
471#217—181no—
472#217—181no—
473#217—181no—
474#217—361no—
475#217D3211yescharacteristic
476C4⋊Dic3—31no—
477C4⋊Dic3—31no—
478C4⋊Dic3—31no—
479C4⋊Dic3—31no—
480C4⋊Dic3—91no—
481C4⋊Dic3—91no—
482C4⋊Dic3—91no—
483C4⋊Dic3—91no—
484C4⋊Dic3—91no—
485C4⋊Dic3—91no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—181no—
494C4⋊Dic3—181no—
495C4⋊Dic3—181no—
496C4⋊Dic3—181no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
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—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—31no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C4×Dic3—91no—
545C4×Dic3—181no—
546C4×Dic3—181no—
547C22×C32—21no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32—21no—
554C22×C32—21no—
555C22×C32—21no—
556C22×C32—22no—
557C22×C32—22no—
558C22×C32—22no—
559C22×C32—41no—
560C22×C32—42no—
561C22×C32—41no—
562C22×C32—41no—
563C22×C32—41no—
564C22×C32—41no—
565C22×C32—41no—
566C22×C32—41no—
567C22×C32—81no—
568C22×C32—81no—
569C22×C32C2×Dic612yes—
570C22×C32C2×Dic612yes—
571C22×C32D3×Q812yes—
572C22×C32C23×D311yescharacteristic
573C22×C32C23×D311yescharacteristic
574C22×C32C23×D311yescharacteristic
575C32×C4—32no—
576C32×C4—32no—
577C32×C4—32no—
578C32×C4—61no—
579C32×C4—61no—
580C32×C4—61no—
581C3⋊Dic3—21no—
582C3⋊Dic3—21no—
583C3⋊Dic3—21no—
584C3⋊Dic3—21no—
585C3⋊Dic3—21no—
586C3⋊Dic3—61no—
587C3⋊Dic3—61no—
588C3⋊Dic3—61no—
589C3⋊Dic3—61no—
590C3⋊Dic3—61no—
591C3⋊Dic3—61no—
592C3⋊Dic3—121no—
593C3⋊Dic3—121no—
594C3⋊Dic3—121no—
595C3⋊Dic3—121no—
596C3⋊Dic3—121no—
597C3⋊Dic3—121no—
598C3⋊Dic3—241no—
599C3⋊Dic3—241no—
600C3⋊Dic3#23512yes—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—21no—
604C3×Dic3—21no—
605C3×Dic3—21no—
606C3×Dic3—21no—
607C3×Dic3—22no—
608C3×Dic3—22no—
609C3×Dic3—22no—
610C3×Dic3—32no—
611C3×Dic3—32no—
612C3×Dic3—41no—
613C3×Dic3—41no—
614C3×Dic3—41no—
615C3×Dic3—62no—
616C3×Dic3—61no—
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—121no—
627C3×Dic3—121no—
628C3×Dic3—121no—
629C3×Dic3—121no—
630C3×Dic3—121no—
631C3×Dic3C2×Dic612yes—
632C3×Dic3C2×Dic612yes—
633C3×Dic3C2×Dic612yes—
634C3×Dic3C2×Dic612yes—
635C3×Dic3#23512yes—
636C3×Dic3#23712yes—
637C4⋊Q8—271no—
638C4⋊Q8—271no—
639#125—271no—
640#125—271no—
641C22⋊Q8—91no—
642C22⋊Q8—271no—
643C22⋊Q8—271no—
644C22⋊Q8—271no—
645C4×Q8—271no—
646C4×Q8—271no—
647C4×Q8—271no—
648C4×Q8—271no—
649#117—91no—
650#117—271no—
651C2×C42—91no—
652C33#53311yescharacteristic, complemented, Sylow
653C23×C3—21no—
654C23×C3—21no—
655C23×C3—21no—
656C23×C3—41no—
657C23×C3C2×D3211yescharacteristic
658C23×C3C2×D3211yescharacteristic
659C23×C3C2×D3211yescharacteristic
660C3×Q8—182no—
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—34no—
668C2×C3×C4—34no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—64no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—62no—
683C2×C3×C4—62no—
684C2×C3×C4—91no—
685C2×C3×C4—91no—
686C2×C3×C4—91no—
687C2×C3×C4—91no—
688C2×C3×C4—91no—
689C2×C3×C4—91no—
690C2×C3×C4—122no—
691C2×C3×C4—182no—
692C2×Dic3—22no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—31no—
703C2×Dic3—31no—
704C2×Dic3—31no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—62no—
712C2×Dic3—62no—
713C2×Dic3—91no—
714C2×Dic3—91no—
715C2×Dic3—91no—
716C2×Dic3—91no—
717C2×Dic3—91no—
718C2×Dic3—91no—
719C2×Dic3—122no—
720C2×Dic3—181no—
721C2×Dic3—181no—
722C2×Dic3—181no—
723C2×Dic3—181no—
724C2×Dic3—181no—
725C2×Dic3—181no—
726C2×Dic3—361no—
727C2×Dic3—361no—
728C2×Dic3#62714yescomplemented
729C2×Dic3C2×D3211yescharacteristic
730C2×Dic3C2×D3211yescharacteristic
731C2×Dic3C2×D3211yescharacteristic
732C2×Dic3C2×D3211yescharacteristic
733C2×Dic3C2×D3211yescharacteristic
734C2×Dic3C2×D3211yescharacteristic
735Dic6—62no—
736Dic6—62no—
737Dic6—182no—
738Dic6—182no—
739Dic6—182no—
740Dic6—182no—
741Dic6—182no—
742Dic6—182no—
743Dic6—182no—
744Dic6—182no—
745Dic6—182no—
746Dic6—362no—
747Dic6—362no—
748C2×C32—22no—
749C2×C32—22no—
750C2×C32—22no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—21no—
758C2×C32—21no—
759C2×C32—21no—
760C2×C32—41no—
761C2×C32—41no—
762C2×C32—41no—
763C2×C32—42no—
764C2×C32—42no—
765C2×C32—42no—
766C2×C32—82no—
767C2×C32C22×Dic611yescharacteristic
768C2×C32C22×Dic611yescharacteristic
769C2×C32C2×#23511yescharacteristic
770C2×C32C2×#23511yescharacteristic
771C2×C32C2×#23711yescharacteristic
772C2×C32C2×D3×Q811yescharacteristic
773C2×C32D3×#4111yescharacteristic
774C2×C32D3×#4111yescharacteristic
775C2×C32D3×#4111yescharacteristic
776C2×Q8—91no—
777C2×Q8—271no—
778C2×Q8—271no—
779C2×Q8—271no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—91no—
783C4⋊C4—91no—
784C4⋊C4—91no—
785C4⋊C4—91no—
786C4⋊C4—91no—
787C4⋊C4—91no—
788C4⋊C4—271no—
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—
798C4⋊C4—271no—
799C22⋊C4—31no—
800C22⋊C4—91no—
801C22⋊C4—91no—
802C22⋊C4—271no—
803C42—91no—
804C42—91no—
805C42—91no—
806C42—91no—
807C42—91no—
808C42—91no—
809C42—271no—
810C42—271no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—42no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3D3×Dic612yes—
834C22×C3D3×Dic612yes—
835C22×C3C2×#62712yes—
836C22×C3C22×D3211yescharacteristic
837C22×C3C22×D3211yescharacteristic
838C22×C3C22×D3211yescharacteristic
839C3×C4—32no—
840C3×C4—32no—
841C3×C4—32no—
842C3×C4—32no—
843C3×C4—32no—
844C3×C4—32no—
845C3×C4—62no—
846C3×C4—62no—
847C3×C4—62no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—92no—
855C3×C4—121no—
856C3×C4—121no—
857C3×C4—121no—
858C3×C4—181no—
859C3×C4—181no—
860C3×C4—181no—
861C3×C4—181no—
862C3×C4—181no—
863Dic3—21no—
864Dic3—21no—
865Dic3—21no—
866Dic3—32no—
867Dic3—32no—
868Dic3—62no—
869Dic3—61no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—61no—
878Dic3—61no—
879Dic3—121no—
880Dic3—121no—
881Dic3—121no—
882Dic3—121no—
883Dic3—121no—
884Dic3—181no—
885Dic3—181no—
886Dic3—181no—
887Dic3—181no—
888Dic3—181no—
889Dic3—181no—
890Dic3—361no—
891Dic3—361no—
892Dic3—361no—
893Dic3—361no—
894Dic3—361no—
895Dic3—361no—
896Dic3—721no—
897Dic3—721no—
898Dic3#380412yes—
899Dic3C2×#62712yes—
900Dic3C2×#62712yes—
901C32—21no—
902C32—21no—
903C32—21no—
904C32—41no—
905C32#547011yescharacteristic, complemented
906C32#551711yescharacteristic, complemented
907C32#562211yescharacteristic, complemented
908C23D3311yescharacteristic
909Q8—182no—
910Q8—542no—
911Q8—542no—
912Q8—542no—
913C2×C4—31no—
914C2×C4—31no—
915C2×C4—31no—
916C2×C4—34no—
917C2×C4—31no—
918C2×C4—31no—
919C2×C4—31no—
920C2×C4—62no—
921C2×C4—91no—
922C2×C4—91no—
923C2×C4—91no—
924C2×C4—91no—
925C2×C4—91no—
926C2×C4—91no—
927C2×C4—182no—
928C2×C4—271no—
929C2×C4—271no—
930C2×C3—22no—
931C2×C3—22no—
932C2×C3—22no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—42no—
943C2×C3—42no—
944C2×C3—42no—
945C2×C3—41no—
946C2×C3—41no—
947C2×C3—41no—
948C2×C3—82no—
949C2×C3C2×D3×Dic611yescharacteristic
950C2×C3C2×D3×Dic611yescharacteristic
951C2×C3D3×#23511yescharacteristic
952C2×C3D3×#23511yescharacteristic
953C2×C3D3×#23511yescharacteristic
954C2×C3D3×#23711yescharacteristic
955C2×C3#6431211yescharacteristic
956C2×C3C2×#380411yescharacteristic
957C2×C3C22×#62711yescharacteristic
958C22—21no—
959C22—21no—
960C22D3×#62712yes—
961C22C2×D3311yescharacteristic
962C4—32no—
963C4—32no—
964C4—32no—
965C4—61no—
966C4—61no—
967C4—61no—
968C4—92no—
969C4—181no—
970C4—181no—
971C4—181no—
972C4—181no—
973C4—181no—
974C4—541no—
975C4—541no—
976C3—21no—
977C3—21no—
978C3—21no—
979C3—41no—
980C3#1059402911yescharacteristic, complemented
981C3#1059480811yescharacteristic, complemented
982C3#1059504911yescharacteristic, complemented
983C2—22no—
984C2D3×#380411yescharacteristic
985C2#1172441011yescharacteristic
986C2C2×D3×#62711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
Fitting, prime radicalC23×C33C23
hypercenterC23D33
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
8. #11723036C2semidirect
9. #11723033C2semidirect
10. #11723012C2semidirect
11. #11723011C2semidirect
12. #11722944C2semidirect
13. #11722942C2semidirect
14. #11722942C2semidirect
15. Dic3×#627C2semidirect
113. C2×C32×Dic3Q8semidirect
389. C2×C3×Dic3Dic6semidirect
390. C2×C3×Dic3Dic6semidirect
652. C33#533semidirect
728. C2×Dic3#627semidirect
905. C32#5470semidirect
906. C32#5517semidirect
907. C32#5622semidirect
980. C3#10594029semidirect
981. C3#10594808semidirect
982. C3#10595049semidirect

Maximal subgroups

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

subgroupindex
#117237212
#117236412
#117236402
#117235942
C3×#639642
C3×#639552
C2×C3×Dic322
#117230362
#117230332
#117230122
#117230112
#117229442
#117229422
Dic3×#6272
#105950493
#105948083
#105940293