Finite Group Databasebeta

← #13168331

Subgroups — #13168331

Order 1728.

1306 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Dic6C211yesmaximal, characteristic
2#11723668C211yesmaximal, characteristic, complemented
3#11723424C211yesmaximal, characteristic
4Dic3×#634C211yesmaximal, characteristic, complemented
5Dic6×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63855C211yesmaximal, characteristic
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11722941C212yesmaximal, complemented
9#11722940C212yesmaximal, complemented
10#11722914C212yesmaximal
11#11722913C212yesmaximal
12#10595347—31nomaximal
13#10594818—31nomaximal
14#10593885—31nomaximal
15C2×C3×#634C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×C3×#627C2212yes—
19C2×C3×D3×Dic3C2212yes—
20C3×D3×Dic6C418yescomplemented
21C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25#88815C2212yes—
26#88813C2212yes—
27#88807C2212yes—
28Dic3⋊(C3⋊Dic3)C2212yes—
29(C2×D3)⋊(C3⋊Dic3)C2212yes—
30Dic3×C3⋊Dic3C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2211yescharacteristic
35C3×Dic3⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C3×Dic32C2212yes—
39C2×C3×D3×Q8—31no—
40C22×C3×Dic6—31no—
41C2×D3×Dic6D311yescharacteristic
42Q8×C3⋊Dic3—31no—
43#64135—31no—
44C4×#634—31no—
45C3×Q8×Dic3—31no—
46C3×#926—31no—
47C3×#872—31no—
48C3×C4×Dic6—31no—
49#63955—32no—
50#63955—32no—
51#63878—32no—
52#63877—32no—
53#63855—32no—
54#63855D311yescharacteristic
55#63844—31no—
56#63843—31no—
57#63843—32no—
58#63843—32no—
59#63843—32no—
60Dic3×Dic6—31no—
61Dic3×Dic6—31no—
62Dic3×Dic6—31no—
63Dic3×Dic6—31no—
64Dic3×Dic6—31no—
65Dic3×Dic6—32no—
66Dic3×Dic6—61no—
67Dic3×Dic6—61no—
68Dic3×Dic6D311yescharacteristic, complemented
69#63841—31no—
70#63841—31no—
71#63841—32no—
72#63841—61no—
73#63838—32no—
74#63837—32no—
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C3×#634C2×C414yes—
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3C2×C414yes—
88C32×Dic6C2×C414yes—
89C3×#627C2×C418yes—
90C3×D3×Dic3C2×C418yes—
91#5812—91no—
92#5572—91no—
93#5516—91no—
94C2×C32×Q8—31no—
95C22×C32×C4—31no—
96C2×#634C2×D311yescharacteristic
97C22×C3×Dic3—32no—
98C3×D3×Q8—38no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3C2×D311yescharacteristic
102C2×C3×C4×D3C2×D311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6—31no—
105C2×C3×Dic6—31no—
106C2×C3×Dic6—32no—
107C2×C3×Dic6—32no—
108C2×C3×Dic6—38no—
109C2×C3×Dic6—61no—
110C2×C3×Dic6C2×D311yescharacteristic
111C2×C3×Dic6C2×D311yescharacteristic
112C2×#627C2×D312yes—
113C2×D3×Dic3C2×D312yes—
114D3×Dic6Dic318yescomplemented
115C32×C42—31no—
116#3757—32no—
117C4⋊(C3⋊Dic3)—31no—
118C4⋊(C3⋊Dic3)—31no—
119C4⋊(C3⋊Dic3)—31no—
120C4⋊(C3⋊Dic3)—32no—
121C4⋊(C3⋊Dic3)—61no—
122C4⋊(C3⋊Dic3)—61no—
123C4⋊(C3⋊Dic3)—61no—
124C4⋊(C3⋊Dic3)—121no—
125C4⋊(C3⋊Dic3)C2×D311yescharacteristic
126#3750—32no—
127C4×C3⋊Dic3—32no—
128C4×C3⋊Dic3—32no—
129C4×C3⋊Dic3—32no—
130C4×C3⋊Dic3C2×D311yescharacteristic
131C3×#217—31no—
132C3×#217—31no—
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—32no—
140C3×C4⋊Dic3—61no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4—32no—
144C3×C4×Dic3—21no—
145C3×C4×Dic3—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—32no—
148C3×C4×Dic3—32no—
149C3×C4×Dic3—61no—
150C3×C4×Dic3C2×D311yescharacteristic
151C3×C4×Dic3C2×D311yescharacteristic
152#3724—32no—
153Dic3⋊Dic3—32no—
154Dic3⋊Dic3—32no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—62no—
160Dic3⋊Dic3—62no—
161Dic3⋊Dic3C2×D311yescharacteristic
162Dic3⋊Dic3C2×D312yes—
163Dic3⋊Dic3C2×D311yescharacteristic
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—62no—
167(C2×D3)⋊Dic3C2×D311yescharacteristic
168(C2×D3)⋊Dic3C2×D311yescharacteristic
169Dic32—32no—
170Dic32—32no—
171Dic32—32no—
172Dic32—32no—
173Dic32—32no—
174Dic32—32no—
175Dic32—32no—
176Dic32—32no—
177Dic32—32no—
178Dic32—62no—
179Dic32—62no—
180Dic32—62no—
181Dic32C2×D312yes—
182C22×C33C2411yescharacteristic
183C2×C32×D3—21no—
184C2×C32×D3—21no—
185C2×C32×D3C22×C412yes—
186C33×C4C22×C412yes—
187C3⋊(C3⋊Dic3)—22no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3C22×C414yes—
192C32×Dic3—21no—
193C32×Dic3—21no—
194C32×Dic3C22×C414yes—
195C32×Dic3C22×C412yes—
196C22×C3×Q8—91no—
197C2×D3×Q8—31no—
198C22×Dic6—31no—
199C3×C4×Q8—91no—
200C3×#117—91no—
201Q8×Dic3—31no—
202Q8×Dic3—91no—
203Q8×Dic3—92no—
204Q8×Dic3—91no—
205Q8×Dic3—91no—
206Q8×Dic3—92no—
207Q8×Dic3—91no—
208Q8×Dic3—181no—
209#926—31no—
210#926—92no—
211#926—92no—
212#926—91no—
213#926—91no—
214#926—181no—
215#892—92no—
216#892—91no—
217#887—92no—
218#887—91no—
219#887—92no—
220#887—92no—
221#877—92no—
222#877—92no—
223#872—31no—
224#872—92no—
225C4×Dic6—31no—
226C4×Dic6—92no—
227C4×Dic6—91no—
228C4×Dic6—91no—
229C4×Dic6—91no—
230C4×Dic6—91no—
231C4×Dic6—181no—
232C23×C32—31no—
233C22×C3×D3—21no—
234C22×C3×D3C22×D311yescharacteristic
235C22×C3×D3C22×D311yescharacteristic
236C32×Q8—34no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—32no—
241C2×C32×C4—31no—
242C2×C32×C4—34no—
243C2×C32×C4—31no—
244C2×C32×C4—31no—
245C2×C32×C4—41no—
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C3⋊Dic3—32no—
250C2×C3⋊Dic3—32no—
251C2×C3⋊Dic3—32no—
252C2×C3⋊Dic3—62no—
253C2×C3⋊Dic3—62no—
254C2×C3⋊Dic3—62no—
255C2×C3⋊Dic3—122no—
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D312yes—
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D312yes—
260#634C2×Dic314yes—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—38no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3—62no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D312yes—
286C3×C4×D3—24no—
287C3×C4×D3—38no—
288C3×C4×D3C4×D314yes—
289C3×C4×D3C2×Dic314yes—
290C3×Dic6—24no—
291C3×Dic6—34no—
292C3×Dic6—34no—
293C3×Dic6—38no—
294C3×Dic6—38no—
295C3×Dic6—64no—
296C3×Dic6C4×D314yes—
297C3×Dic6C2×Dic314yes—
298#627C2×Dic318yes—
299D3×Dic3C2×Dic318yes—
300#519—271noSylow
301C2×C33C23×C411yescharacteristic
302C2×C332−1+411yescharacteristic
303C2×C332−1+411yescharacteristic
304C32×D3—22no—
305C2×C3×Q8—31no—
306C2×C3×Q8—31no—
307C2×C3×Q8—61no—
308C2×C3×Q8—92no—
309C2×C3×Q8—98no—
310C2×C3×Q8—91no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—92no—
315C22×Dic3—32no—
316D3×Q8—38no—
317C2×C4×D3—32no—
318C2×C4×D3D3211yescharacteristic
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—32no—
322C2×Dic6—32no—
323C2×Dic6—38no—
324C2×Dic6—61no—
325C2×Dic6D3211yescharacteristic
326C3×C4⋊C4—91no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4—92no—
329C3×C4⋊C4—91no—
330C3×C22⋊C4—91no—
331C3×C22⋊C4—91no—
332C3×C42—31no—
333C3×C42—31no—
334C3×C42—61no—
335C3×C42—92no—
336C3×C42—91no—
337#217—31no—
338#217—31no—
339#217—92no—
340#217—92no—
341#217—182no—
342(C2×D3)⋊C4—31no—
343(C2×D3)⋊C4—31no—
344(C2×D3)⋊C4—92no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—32no—
350C4⋊Dic3—61no—
351C4⋊Dic3—92no—
352C4⋊Dic3—92no—
353C4⋊Dic3—92no—
354C4⋊Dic3—91no—
355C4⋊Dic3—91no—
356C4⋊Dic3—91no—
357C4⋊Dic3—92no—
358C4⋊Dic3—182no—
359C4⋊Dic3—181no—
360C4⋊Dic3—181no—
361C4⋊Dic3—181no—
362C4⋊Dic3—361no—
363Dic3⋊C4—32no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—92no—
367Dic3⋊C4—92no—
368Dic3⋊C4—92no—
369Dic3⋊C4—92no—
370Dic3⋊C4—92no—
371Dic3⋊C4—182no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—32no—
375C4×Dic3—32no—
376C4×Dic3—61no—
377C4×Dic3—92no—
378C4×Dic3—92no—
379C4×Dic3—92no—
380C4×Dic3—92no—
381C4×Dic3—92no—
382C4×Dic3—92no—
383C4×Dic3—92no—
384C4×Dic3—92no—
385C4×Dic3—92no—
386C4×Dic3—92no—
387C4×Dic3—92no—
388C4×Dic3—92no—
389C4×Dic3—182no—
390C4×Dic3—182no—
391C4×Dic3—182no—
392C4×Dic3D3211yescharacteristic
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—32no—
397C22×C32—41no—
398C22×C32—61no—
399C22×C32—61no—
400C22×C32C23×D311yescharacteristic
401C22×C32C23×D311yescharacteristic
402C22×C32C23×D311yescharacteristic
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3C2×C4×D312yes—
411C2×C3×D3C22×Dic312yes—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—22no—
415C32×C4—32no—
416C32×C4—34no—
417C32×C4—42no—
418C32×C4—61no—
419C32×C4—61no—
420C32×C4C2×C4×D312yes—
421C32×C4C2×C4×D312yes—
422C32×C4C22×Dic312yes—
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3⋊Dic3—22no—
426C3⋊Dic3—62no—
427C3⋊Dic3—62no—
428C3⋊Dic3—62no—
429C3⋊Dic3—122no—
430C3⋊Dic3—122no—
431C3⋊Dic3—122no—
432C3⋊Dic3—242no—
433C3⋊Dic3C22×Dic314yes—
434C3×Dic3—22no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—24no—
440C3×Dic3—22no—
441C3×Dic3—34no—
442C3×Dic3—34no—
443C3×Dic3—41no—
444C3×Dic3—64no—
445C3×Dic3—62no—
446C3×Dic3—61no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C3×Dic3—62no—
450C3×Dic3—62no—
451C3×Dic3—61no—
452C3×Dic3—122no—
453C3×Dic3—121no—
454C3×Dic3C2×C4×D312yes—
455C3×Dic3C2×C4×D314yes—
456C3×Dic3C22×Dic314yes—
457C3×Dic3C22×Dic312yes—
458C22×Q8—91no—
459C4×Q8—91no—
460C4×Q8—271no—
461C4×Q8—272no—
462C4×Q8—271no—
463C4×Q8—271no—
464C4×Q8—272no—
465#117—91no—
466#117—272no—
467#117—272no—
468#117—271no—
469C33#51911yescharacteristic, complemented, Sylow
470C23×C3—31no—
471C23×C3—31no—
472C23×C3—61no—
473C22×D3C2×D3211yescharacteristic
474C3×Q8—34no—
475C3×Q8—34no—
476C3×Q8—64no—
477C3×Q8—98no—
478C3×Q8—94no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—32no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—32no—
486C2×C3×C4—34no—
487C2×C3×C4—34no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—41no—
493C2×C3×C4—64no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—62no—
497C2×C3×C4—61no—
498C2×C3×C4—98no—
499C2×C3×C4—92no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—92no—
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505C2×C3×C4C2×D3211yescharacteristic
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—38no—
509C2×Dic3—31no—
510C2×Dic3—32no—
511C2×Dic3—31no—
512C2×Dic3—32no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—61no—
516C2×Dic3—62no—
517C2×Dic3—61no—
518C2×Dic3—62no—
519C2×Dic3—92no—
520C2×Dic3—92no—
521C2×Dic3—92no—
522C2×Dic3—182no—
523C2×Dic3—182no—
524C2×Dic3—182no—
525C2×Dic3—362no—
526C2×Dic3C2×D3211yescharacteristic
527C2×Dic3C2×D3211yescharacteristic
528C2×Dic3C2×D3212yes—
529C2×Dic3C2×D3211yescharacteristic
530C4×D3—38no—
531C4×D3D3×Dic314yes—
532Dic6—34no—
533Dic6—34no—
534Dic6—38no—
535Dic6—38no—
536Dic6—64no—
537Dic6D3×Dic314yes—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32—21no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—41no—
548C2×C32—41no—
549C2×C32—41no—
550C2×C32—62no—
551C2×C32C22×C4×D311yescharacteristic
552C2×C32C22×C4×D311yescharacteristic
553C2×C32#100711yescharacteristic
554C2×C32#100711yescharacteristic
555C2×C32#100711yescharacteristic
556C2×C32#101011yescharacteristic
557C2×C32#101011yescharacteristic
558C2×C32#101011yescharacteristic
559C2×C32C23×Dic311yescharacteristic
560C3×D3—22no—
561C3×D3—22no—
562C3×D3—42no—
563C2×Q8—31no—
564C2×Q8—92no—
565C2×Q8—98no—
566C2×Q8—91no—
567C22×C4—31no—
568C22×C4—92no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—92no—
572C4⋊C4—91no—
573C4⋊C4—272no—
574C4⋊C4—272no—
575C4⋊C4—272no—
576C4⋊C4—271no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—272no—
580C42—31no—
581C42—92no—
582C42—91no—
583C42—272no—
584C42—272no—
585C42—272no—
586C42—272no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—32no—
591C22×C3—32no—
592C22×C3—41no—
593C22×C3—62no—
594C22×C3—61no—
595C22×C3—61no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3—121no—
599C22×C3—121no—
600C22×C3C22×D3211yescharacteristic
601C22×C3C22×D3211yescharacteristic
602C22×C3C22×D3211yescharacteristic
603C2×D3—21no—
604C2×D3—21no—
605C2×D3C2×D3×Dic312yes—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—22no—
609C3×C4—32no—
610C3×C4—34no—
611C3×C4—32no—
612C3×C4—34no—
613C3×C4—42no—
614C3×C4—62no—
615C3×C4—64no—
616C3×C4—62no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—61no—
620C3×C4—61no—
621C3×C4—94no—
622C3×C4—121no—
623C3×C4—182no—
624C3×C4—181no—
625C3×C4—181no—
626C3×C4C4×D3212yes—
627C3×C4C2×D3×Dic312yes—
628C3×C4C2×D3×Dic312yes—
629Dic3—21no—
630Dic3—21no—
631Dic3—34no—
632Dic3—34no—
633Dic3—64no—
634Dic3—62no—
635Dic3—61no—
636Dic3—61no—
637Dic3—61no—
638Dic3—61no—
639Dic3—62no—
640Dic3—62no—
641Dic3—121no—
642Dic3—122no—
643Dic3—182no—
644Dic3—182no—
645Dic3—182no—
646Dic3—362no—
647Dic3—362no—
648Dic3—362no—
649Dic3—722no—
650Dic3C2×D3×Dic312yes—
651Dic3C2×D3×Dic314yes—
652C32—21no—
653C32—21no—
654C32—21no—
655C32—41no—
656C32#551611yescharacteristic, complemented
657C32#557211yescharacteristic, complemented
658C32#581211yescharacteristic, complemented
659C23—31no—
660Q8—34no—
661Q8—98no—
662Q8—94no—
663C2×C4—32no—
664C2×C4—31no—
665C2×C4—34no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—98no—
669C2×C4—92no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—92no—
673C2×C4—272no—
674C2×C4D3311yescharacteristic
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—41no—
685C2×C3—41no—
686C2×C3—41no—
687C2×C3—62no—
688C2×C3—62no—
689C2×C3—122no—
690C2×C3#6429711yescharacteristic
691C2×C3#6429711yescharacteristic
692C2×C3#6429711yescharacteristic
693C2×C3#6429811yescharacteristic
694C2×C3C2×C4×D3211yescharacteristic
695C2×C3#6431511yescharacteristic
696C2×C3#6431611yescharacteristic
697C2×C3C22×D3×Dic311yescharacteristic
698C2×C3C22×D3×Dic311yescharacteristic
699D3—22no—
700C22—32no—
701C22—61no—
702C22—61no—
703C22C2×D3311yescharacteristic
704C4—32no—
705C4—34no—
706C4—61no—
707C4—61no—
708C4—94no—
709C4—181no—
710C4—181no—
711C4—182no—
712C4—542no—
713C4D32×Dic312yes—
714C3—21no—
715C3—21no—
716C3—21no—
717C3—41no—
718C3#1059388511yescharacteristic, complemented
719C3#1059481811yescharacteristic, complemented
720C3#1059534711yescharacteristic, complemented
721C2—62no—
722C2#1172439511yescharacteristic
723C2#1172439611yescharacteristic
724C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC22×C32×D3C23
hypercenterC2×C4D33
hypocenterC33#519
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723668C2semidirect
4. Dic3×#634C2semidirect
5. Dic6×C3⋊Dic3C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11722941C2semidirect
9. #11722940C2semidirect
20. C3×D3×Dic6C4semidirect
68. Dic3×Dic6D3semidirect
114. D3×Dic6Dic3semidirect
469. C33#519semidirect
656. C32#5516semidirect
657. C32#5572semidirect
658. C32#5812semidirect
718. C3#10593885semidirect
719. C3#10594818semidirect
720. C3#10595347semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Dic62
#117236682
#117234242
Dic3×#6342
Dic6×C3⋊Dic32
C3×#638552
C3×Dic3×Dic62
#117229412
#117229402
#117229142
#117229132
#105953473
#105948183
#105938853