Finite Group Databasebeta

← #13170750

Subgroups — #13170750

Order 1728.

1602 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88957C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic
3#11723689C211yesmaximal, characteristic, complemented
4C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic
5#11723485C212yesmaximal, complemented
6C3×#63893C212yesmaximal, complemented
7C3×#63883C211yesmaximal, characteristic, complemented
8#11722973C212yesmaximal, complemented
9#11722971C212yesmaximal, complemented
10#11722908C211yesmaximal, characteristic, complemented
11#11722904C211yesmaximal, characteristic
12D3×#897—32nomaximal
13#10594067—31nomaximal
14C22×D3×C3⋊D3C2211yescharacteristic
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×#6294C2211yescharacteristic
17C2×#6294C2211yescharacteristic
18C2×#6293C2212yescomplemented
19C2×#6289C2212yes—
20C2×Dic3×C3⋊D3C2211yescharacteristic
21C2×C3×#627C2212yescomplemented
22C2×C3×#624C2211yescharacteristic
23C2×C3×#624C2211yescharacteristic
24C2×C3×D3×Dic3C2212yes—
25#88957—24no—
26D3×#624—24no—
27#88859C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2212yescomplemented
29C32×(C2×D3)⋊C4C2211yescharacteristic
30C32×Dic3⋊C4C2212yescomplemented
31#88815C2212yescomplemented
32Dic3⋊(C3⋊Dic3)C2212yescomplemented
33#88804C2211yescharacteristic
34#88804C2212yes—
35(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×Dic3⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yes—
39C22×#624—31no—
40C2×C4×D32—32no—
41C2×#3797—31no—
42C2×D3×Dic6—32no—
43#64106—32no—
44C22⋊C4×C3⋊D3—31no—
45C3×#897—32no—
46C3×D3×C4⋊C4—32no—
47C3×#878—32no—
48#63974—31no—
49#63964—32no—
50D3×(C2×D3)⋊C4—32no—
51D3×(C2×D3)⋊C4—32no—
52D3×(C2×D3)⋊C4—61no—
53#63900—31no—
54#63895—32no—
55#63895—32no—
56#63895—32no—
57#63895—62no—
58#63893—32no—
59#63893D312yescomplemented
60D3×C4⋊Dic3—32no—
61D3×C4⋊Dic3—32no—
62#63888—32no—
63#63883—31no—
64#63883D311yescharacteristic, complemented
65#63871—32no—
66#63857—32no—
67C22×C3⋊(C3⋊D3)C2311yescharacteristic
68C22×C3×C3⋊D3C2311yescharacteristic
69C22×C32×D3C2311yescharacteristic
70C2×D3×C3⋊D3—22no—
71C2×D3×C3⋊D3—22no—
72C2×D3×C3⋊D3Q814yescomplemented
73C2×C33×C4C2311yescharacteristic
74C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
75C2×C3×C3⋊Dic3C2312yes—
76C2×C3×C3⋊Dic3C2312yes—
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C3×C4×C3⋊D3—22no—
79C2×C32×Dic3C2312yes—
80C2×C32×Dic3C2311yescharacteristic
81C2×C32×Dic3C2312yes—
82#6294—22no—
83#6294—22no—
84#6293—24no—
85#6289—24no—
86Dic3×C3⋊D3—22no—
87C3×#627—24no—
88C3×#624—22no—
89C3×#624D414yes—
90C3×D3×Dic3—24no—
91D3×C22⋊Q8—92no—
92C2×#897—91no—
93C23×C3⋊D3—31no—
94C22×D32—32no—
95C22×D32—61no—
96C2×C4×C3⋊D3—31no—
97C2×C4×C3⋊D3—32no—
98C2×C4×C3⋊D3C2×D311yescharacteristic
99C2×#634—32no—
100C22×C3×Dic3—32no—
101C2×C3×C4×D3—32no—
102C2×C3×C4×D3—32no—
103C2×C3×C4×D3—32no—
104C2×C3×C4×D3—32no—
105C2×C3×C4×D3—61no—
106C2×C3×Dic6—32no—
107C2×C3×Dic6—32no—
108C2×#627—32no—
109C2×#627—32no—
110C2×#627—62no—
111C2×#627C2×D312yescomplemented
112C2×#624—31no—
113C2×#624—31no—
114C2×#624—32no—
115C2×#624—32no—
116C2×#624—64no—
117C2×#624—62no—
118C2×#624C2×D311yescharacteristic
119C2×#624C2×D311yescharacteristic
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—61no—
124C2×D3×Dic3C2×D312yes—
125C4×D32—68no—
126#3797—64no—
127D3×Dic6—68no—
128C32×C4⋊C4—32no—
129C32×C22⋊C4—31no—
130#3757—31no—
131#3752—31no—
132#3752—32no—
133#3752—31no—
134#3752—32no—
135#3752—62no—
136#3752—61no—
137#3752—121no—
138C4⋊(C3⋊Dic3)—32no—
139C4⋊(C3⋊Dic3)C2×D312yescomplemented
140C3×#217—32no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—32no—
143C3×(C2×D3)⋊C4C2×D312yes—
144C3×C4⋊Dic3—32no—
145C3×C4⋊Dic3—32no—
146C3×C4⋊Dic3—32no—
147C3×C4⋊Dic3—32no—
148C3×C4⋊Dic3—62no—
149C3×Dic3⋊C4—22no—
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4C2×D312yescomplemented
153C3×Dic3⋊C4C2×D312yescomplemented
154#3724—32no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—62no—
160Dic3⋊Dic3C2×D312yescomplemented
161Dic3⋊Dic3C2×D312yescomplemented
162#3722—32no—
163#3722—32no—
164#3722—32no—
165#3722—62no—
166#3722—61no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—61no—
169(C2×D3)⋊Dic3C2×D312yes—
170C22×C33C2411yescharacteristic
171C2×C3⋊(C3⋊D3)—21no—
172C2×C3⋊(C3⋊D3)—21no—
173C2×C3⋊(C3⋊D3)C2×Q812yescomplemented
174C2×C3×C3⋊D3C2×D412yes—
175C2×C3×C3⋊D3C2×Q812yes—
176C2×C3×C3⋊D3#4112yes—
177C2×C32×D3—21no—
178C2×C32×D3—21no—
179C2×C32×D3C2×Q812yescomplemented
180D3×C3⋊D3—28no—
181C33×C4—21no—
182C3⋊(C3⋊Dic3)—21no—
183C3×C3⋊Dic3—22no—
184C3×C3⋊Dic3—22no—
185C3×C3⋊Dic3—21no—
186C32×Dic3—21no—
187C32×Dic3—22no—
188C32×Dic3C2×D414yes—
189C2×D3×Q8—92no—
190C22×C4×D3—91no—
191C22×C4×D3—92no—
192C22×Dic6—91no—
193C3×C22⋊Q8—92no—
194C2×C3×C4⋊C4—91no—
195#946—92no—
196C2×(C2×D3)⋊C4—91no—
197C2×(C2×D3)⋊C4—91no—
198C2×C4⋊Dic3—91no—
199C2×C4⋊Dic3—91no—
200#924—92no—
201#897—32no—
202#897—92no—
203#897—92no—
204#897—92no—
205#897—92no—
206#897—182no—
207#896—92no—
208#896—92no—
209D3×C4⋊C4—32no—
210D3×C4⋊C4—92no—
211D3×C4⋊C4—92no—
212D3×C22⋊C4—92no—
213D3×C22⋊C4—92no—
214D3×C22⋊C4—181no—
215#878—32no—
216#878—92no—
217C23×C32—31no—
218C22×C3⋊D3—32no—
219C22×C3⋊D3—31no—
220C22×C3⋊D3—34no—
221C22×C3⋊D3—61no—
222C22×C3⋊D3—62no—
223C22×C3⋊D3—62no—
224C22×C3⋊D3—62no—
225C22×C3⋊D3—121no—
226C22×C3⋊D3C22×D311yescharacteristic
227C22×C3×D3—21no—
228C22×C3×D3—32no—
229C22×C3×D3—61no—
230C22×C3×D3C22×D312yes—
231C2×D32—38no—
232C2×D32—64no—
233C2×D32—64no—
234C2×D32—64no—
235C2×D32—122no—
236C2×D32—122no—
237C2×C32×C4—22no—
238C2×C32×C4—21no—
239C2×C32×C4—32no—
240C2×C32×C4—31no—
241C2×C32×C4—32no—
242C2×C32×C4—41no—
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D312yes—
245C2×C3⋊Dic3—32no—
246C2×C3⋊Dic3—31no—
247C2×C3⋊Dic3—61no—
248C2×C3⋊Dic3—62no—
249C2×C3⋊Dic3—121no—
250C2×C3⋊Dic3C22×D312yes—
251C2×C3⋊Dic3C22×D312yes—
252C2×C3⋊Dic3C22×D311yescharacteristic
253C4×C3⋊D3—22no—
254C4×C3⋊D3—64no—
255C4×C3⋊D3—62no—
256#634—64no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—22no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—32no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—61no—
266C2×C3×Dic3—62no—
267C2×C3×Dic3—62no—
268C2×C3×Dic3—64no—
269C2×C3×Dic3C22×D312yes—
270C2×C3×Dic3C22×D312yes—
271C2×C3×Dic3C22×D312yes—
272C2×C3×Dic3C22×D312yes—
273C2×C3×Dic3C22×D312yes—
274C3×C4×D3—38no—
275C3×C4×D3—64no—
276C3×C4×D3—64no—
277C3×C4×D3—64no—
278C3×C4×D3—122no—
279C3×Dic6—64no—
280C3×Dic6—64no—
281#627—24no—
282#627—64no—
283#627—64no—
284#627—124no—
285#624—22no—
286#624—62no—
287#624—62no—
288#624—64no—
289#624—64no—
290#624—124no—
291#624D1214yes—
292D3×Dic3—24no—
293D3×Dic3—64no—
294D3×Dic3—64no—
295D3×Dic3—64no—
296D3×Dic3—122no—
297C2×C22⋊Q8—271noSylow
298C2×C33C22×D411yescharacteristic
299C2×C33C22×Q811yescharacteristic
300C2×C33C2×#4111yescharacteristic
301C3⋊(C3⋊D3)—22no—
302C3×C3⋊D3C22⋊Q814yescomplemented
303C32×D3—22no—
304C23×D3—92no—
305C23×D3—91no—
306C23×D3—181no—
307C2×C3×Q8—92no—
308C22×C3×C4—91no—
309C22×C3×C4—91no—
310C22×C3×C4—92no—
311C22×C3×C4—91no—
312C22×Dic3—32no—
313C22×Dic3—91no—
314C22×Dic3—91no—
315C22×Dic3—91no—
316D3×Q8—188no—
317C2×C4×D3—32no—
318C2×C4×D3—32no—
319C2×C4×D3—32no—
320C2×C4×D3—32no—
321C2×C4×D3—61no—
322C2×C4×D3—92no—
323C2×C4×D3—92no—
324C2×C4×D3—92no—
325C2×C4×D3—92no—
326C2×C4×D3—92no—
327C2×C4×D3—92no—
328C2×C4×D3—182no—
329C2×C4×D3—181no—
330C2×C4×D3—188no—
331C2×C4×D3—184no—
332C2×Dic6—32no—
333C2×Dic6—32no—
334C2×Dic6—92no—
335C2×Dic6—92no—
336C2×Dic6—92no—
337C2×Dic6—182no—
338C2×Dic6—184no—
339C3×C4⋊C4—32no—
340C3×C4⋊C4—32no—
341C3×C4⋊C4—62no—
342C3×C4⋊C4—92no—
343C3×C4⋊C4—92no—
344C3×C4⋊C4—92no—
345C3×C22⋊C4—32no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—92no—
348#217—32no—
349#217—92no—
350#217—181no—
351(C2×D3)⋊C4—32no—
352(C2×D3)⋊C4—92no—
353(C2×D3)⋊C4—92no—
354(C2×D3)⋊C4—92no—
355(C2×D3)⋊C4—91no—
356(C2×D3)⋊C4—92no—
357(C2×D3)⋊C4—91no—
358(C2×D3)⋊C4—92no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—181no—
361(C2×D3)⋊C4—182no—
362(C2×D3)⋊C4—181no—
363(C2×D3)⋊C4—182no—
364(C2×D3)⋊C4—361no—
365(C2×D3)⋊C4D3211yescharacteristic
366C4⋊Dic3—32no—
367C4⋊Dic3—32no—
368C4⋊Dic3—32no—
369C4⋊Dic3—32no—
370C4⋊Dic3—62no—
371C4⋊Dic3—92no—
372C4⋊Dic3—92no—
373C4⋊Dic3—92no—
374C4⋊Dic3—182no—
375Dic3⋊C4—32no—
376Dic3⋊C4—32no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4D3212yescomplemented
381C22×C32—22no—
382C22×C32—21no—
383C22×C32—32no—
384C22×C32—41no—
385C22×C32—61no—
386C22×C32—61no—
387C22×C32C23×D311yescharacteristic
388C22×C32C23×D312yes—
389C2×C3⋊D3—34no—
390C2×C3⋊D3—32no—
391C2×C3⋊D3—62no—
392C2×C3⋊D3—64no—
393C2×C3⋊D3—61no—
394C2×C3⋊D3—62no—
395C2×C3⋊D3—61no—
396C2×C3⋊D3—62no—
397C2×C3⋊D3—68no—
398C2×C3⋊D3—122no—
399C2×C3⋊D3—122no—
400C2×C3⋊D3—121no—
401C2×C3⋊D3—121no—
402C2×C3⋊D3—122no—
403C2×C3⋊D3—241no—
404C2×C3⋊D3—241no—
405C2×C3⋊D3C2×D1212yes—
406C2×C3⋊D3#23712yes—
407C2×C3⋊D3D3×Q812yes—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—34no—
412C2×C3×D3—34no—
413C2×C3×D3—34no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—62no—
417C2×C3×D3—62no—
418C2×C3×D3—62no—
419C2×C3×D3D3×Q814yescomplemented
420D32—616no—
421D32—128no—
422C32×C4—21no—
423C32×C4—22no—
424C32×C4—34no—
425C32×C4—41no—
426C32×C4—42no—
427C32×C4—61no—
428C32×C4—62no—
429C32×C4—81no—
430C3⋊Dic3—22no—
431C3⋊Dic3—22no—
432C3⋊Dic3—21no—
433C3⋊Dic3—61no—
434C3⋊Dic3—62no—
435C3⋊Dic3—121no—
436C3⋊Dic3—122no—
437C3⋊Dic3—241no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—24no—
442C3×Dic3—41no—
443C3×Dic3—42no—
444C3×Dic3—62no—
445C3×Dic3—62no—
446C3×Dic3—62no—
447C3×Dic3—62no—
448C3×Dic3—62no—
449C3×Dic3—122no—
450C3×Dic3—122no—
451C3×Dic3—121no—
452C3×Dic3C2×D1214yes—
453C3×Dic3D3×D414yes—
454C22×Q8—271no—
455C23×C4—271no—
456C22⋊Q8—92no—
457C22⋊Q8—272no—
458C22⋊Q8—272no—
459C22⋊Q8—272no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—271no—
462C2×C4⋊C4—271no—
463C2×C22⋊C4—271no—
464C2×C22⋊C4—271no—
465C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
466C23×C3—32no—
467C23×C3—61no—
468C23×C3—91no—
469C22×D3—32no—
470C22×D3—61no—
471C22×D3—98no—
472C22×D3—91no—
473C22×D3—92no—
474C22×D3—94no—
475C22×D3—184no—
476C22×D3—182no—
477C22×D3—181no—
478C22×D3—182no—
479C22×D3—182no—
480C22×D3—184no—
481C22×D3—184no—
482C22×D3—361no—
483C22×D3—362no—
484C22×D3—362no—
485C22×D3C2×D3211yescharacteristic
486C3×Q8—184no—
487C2×C3×C4—22no—
488C2×C3×C4—21no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—41no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—61no—
498C2×C3×C4—94no—
499C2×C3×C4—92no—
500C2×C3×C4—92no—
501C2×C3×C4—91no—
502C2×C3×C4—182no—
503C2×C3×C4—184no—
504C2×C3×C4—182no—
505C2×C3×C4C2×D3212yes—
506C2×C3×C4C2×D3211yescharacteristic
507C2×Dic3—32no—
508C2×Dic3—32no—
509C2×Dic3—32no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—62no—
513C2×Dic3—62no—
514C2×Dic3—61no—
515C2×Dic3—64no—
516C2×Dic3—92no—
517C2×Dic3—91no—
518C2×Dic3—182no—
519C2×Dic3—181no—
520C2×Dic3—182no—
521C2×Dic3—182no—
522C2×Dic3—182no—
523C2×Dic3—361no—
524C2×Dic3C2×D3212yes—
525C2×Dic3C2×D3211yescharacteristic
526C2×Dic3C2×D3212yes—
527C4×D3—38no—
528C4×D3—64no—
529C4×D3—64no—
530C4×D3—64no—
531C4×D3—122no—
532C4×D3—184no—
533C4×D3—184no—
534C4×D3—184no—
535C4×D3—184no—
536C4×D3—184no—
537C4×D3—184no—
538C4×D3—364no—
539C4×D3—362no—
540Dic6—64no—
541Dic6—64no—
542Dic6—184no—
543Dic6—184no—
544Dic6—184no—
545Dic6—364no—
546C2×C32—21no—
547C2×C32—22no—
548C2×C32—21no—
549C2×C32—22no—
550C2×C32—21no—
551C2×C32—22no—
552C2×C32—41no—
553C2×C32—41no—
554C2×C32—41no—
555C2×C32—62no—
556C2×C32C22×D1211yescharacteristic
557C2×C32C2×D3×D412yes—
558C2×C32C2×#23711yescharacteristic
559C2×C32C2×D3×Q812yes—
560C2×C32C2×D3×Q811yescharacteristic
561C2×C32D3×#4112yes—
562C3⋊D3—62no—
563C3⋊D3—64no—
564C3⋊D3—122no—
565C3⋊D3—124no—
566C3⋊D3—242no—
567C3⋊D3#89714yescomplemented
568C3×D3—24no—
569C3×D3—38no—
570C3×D3—42no—
571C3×D3—64no—
572C24—271no—
573C2×Q8—92no—
574C2×Q8—272no—
575C2×Q8—544no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—92no—
579C22×C4—91no—
580C22×C4—272no—
581C22×C4—271no—
582C22×C4—271no—
583C22×C4—271no—
584C22×C4—544no—
585C4⋊C4—32no—
586C4⋊C4—92no—
587C4⋊C4—92no—
588C4⋊C4—92no—
589C4⋊C4—272no—
590C4⋊C4—272no—
591C22⋊C4—31no—
592C22⋊C4—92no—
593C22⋊C4—271no—
594C22⋊C4—272no—
595C22⋊C4—271no—
596C22⋊C4—271no—
597C22×C3—22no—
598C22×C3—21no—
599C22×C3—34no—
600C22×C3—41no—
601C22×C3—62no—
602C22×C3—62no—
603C22×C3—62no—
604C22×C3—92no—
605C22×C3—92no—
606C22×C3—92no—
607C22×C3—121no—
608C22×C3—121no—
609C22×C3C22×D3211yescharacteristic
610C22×C3C22×D3212yes—
611C2×D3—21no—
612C2×D3—21no—
613C2×D3—34no—
614C2×D3—34no—
615C2×D3—34no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—92no—
620C2×D3—94no—
621C2×D3—182no—
622C2×D3—184no—
623C2×D3—188no—
624C2×D3—1816no—
625C2×D3—182no—
626C2×D3—181no—
627C2×D3—182no—
628C2×D3—181no—
629C2×D3—362no—
630C2×D3—368no—
631C2×D3—362no—
632C2×D3—361no—
633C2×D3—361no—
634C2×D3—362no—
635C2×D3—721no—
636C2×D3—721no—
637C2×D3#379712yescomplemented
638C3×C4—22no—
639C3×C4—21no—
640C3×C4—34no—
641C3×C4—34no—
642C3×C4—41no—
643C3×C4—42no—
644C3×C4—64no—
645C3×C4—62no—
646C3×C4—62no—
647C3×C4—62no—
648C3×C4—81no—
649C3×C4—121no—
650C3×C4—122no—
651C3×C4—182no—
652C3×C4—182no—
653C3×C4—181no—
654Dic3—21no—
655Dic3—22no—
656Dic3—62no—
657Dic3—62no—
658Dic3—62no—
659Dic3—62no—
660Dic3—62no—
661Dic3—122no—
662Dic3—121no—
663Dic3—122no—
664Dic3—182no—
665Dic3—181no—
666Dic3—362no—
667Dic3—361no—
668Dic3—721no—
669Dic3D3×D1214yes—
670C32—21no—
671C32—22no—
672C32—41no—
673C32C2×#89711yescharacteristic, complemented
674C32D3×C22⋊Q812yescomplemented
675C23—31no—
676C23—91no—
677C23—274no—
678C23—271no—
679C23—542no—
680C23—542no—
681Q8—184no—
682Q8—544no—
683C2×C4—32no—
684C2×C4—31no—
685C2×C4—32no—
686C2×C4—94no—
687C2×C4—92no—
688C2×C4—91no—
689C2×C4—92no—
690C2×C4—182no—
691C2×C4—184no—
692C2×C4—182no—
693C2×C4—271no—
694C2×C4—544no—
695C2×C4—542no—
696C2×C4—542no—
697C2×C4—542no—
698C2×C4D3311yescharacteristic
699C2×C3—21no—
700C2×C3—22no—
701C2×C3—22no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—22no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—64no—
709C2×C3—94no—
710C2×C3—122no—
711C2×C3C2×#379711yescharacteristic
712C2×C3C2×D3×D1212yes—
713C2×C3D32×D411yescharacteristic
714C2×C3D3×#23712yes—
715C2×C3#6431211yescharacteristic
716C2×C3D32×Q812yes—
717D3—22no—
718D3—38no—
719D3—64no—
720D3—182no—
721D3—184no—
722D3—362no—
723D3—364no—
724D3—722no—
725C22—32no—
726C22—61no—
727C22—61no—
728C22—92no—
729C22—92no—
730C22—92no—
731C22—272no—
732C22—548no—
733C22—541no—
734C22—541no—
735C22C2×D3311yescharacteristic
736C4—21no—
737C4—34no—
738C4—61no—
739C4—62no—
740C4—182no—
741C4—182no—
742C4—181no—
743C4—541no—
744C3—21no—
745C3—22no—
746C3—41no—
747C3#1059406711yescharacteristic, complemented
748C3D3×#89712yescomplemented
749C2—62no—
750C2—94no—
751C2—542no—
752C2D3×#379711yescharacteristic
753C2D32×D1211yescharacteristic
754C2#1172440811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×D3×C3⋊D3C22
hypercenterC2×C4D33
hypocenterC33C2×C22⋊Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88957C2semidirect
3. #11723689C2semidirect
5. #11723485C2semidirect
6. C3×#63893C2semidirect
7. C3×#63883C2semidirect
8. #11722973C2semidirect
9. #11722971C2semidirect
10. #11722908C2semidirect
18. C2×#6293C22semidirect
21. C2×C3×#627C22semidirect
28. C3×C4⋊(C3⋊Dic3)C22semidirect
30. C32×Dic3⋊C4C22semidirect
31. #88815C22semidirect
32. Dic3⋊(C3⋊Dic3)C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×Dic3⋊Dic3C22semidirect
59. #63893D3semidirect
64. #63883D3semidirect
72. C2×D3×C3⋊D3Q8semidirect
111. C2×#627C2×D3semidirect
139. C4⋊(C3⋊Dic3)C2×D3semidirect
152. C3×Dic3⋊C4C2×D3semidirect
153. C3×Dic3⋊C4C2×D3semidirect
160. Dic3⋊Dic3C2×D3semidirect
161. Dic3⋊Dic3C2×D3semidirect
173. C2×C3⋊(C3⋊D3)C2×Q8semidirect
179. C2×C32×D3C2×Q8semidirect
302. C3×C3⋊D3C22⋊Q8semidirect
380. Dic3⋊C4D32semidirect
419. C2×C3×D3D3×Q8semidirect
465. C33C2×C22⋊Q8semidirect
567. C3⋊D3#897semidirect
637. C2×D3#3797semidirect
673. C32C2×#897semidirect
674. C32D3×C22⋊Q8semidirect
747. C3#10594067semidirect
748. C3D3×#897semidirect

Maximal subgroups

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

subgroupindex
C2×#889572
C2×D3×#6242
#117236892
C3⋊D3×(C2×D3)⋊C42
#117234852
C3×#638932
C3×#638832
#117229732
#117229712
#117229082
#117229042
D3×#8973
#105940673