Finite Group Databasebeta

← #13170732

Subgroups — #13170732

Order 1728.

1690 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88952C211yesmaximal, characteristic
2C2×D32×Dic3C211yesmaximal, characteristic, complemented
3#11723689C211yesmaximal, characteristic, complemented
4C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5#11723479C212yesmaximal, complemented
6C3×#63921C211yesmaximal, characteristic, complemented
7C3×#63891C212yesmaximal, complemented
8#11722989C212yesmaximal, complemented
9#11722987C212yesmaximal, complemented
10#11722908C211yesmaximal, characteristic, complemented
11#11722904C211yesmaximal, characteristic, complemented
12D3×#886—32nomaximal
13#10594260—31nomaximal
14C22×D3×C3⋊D3C2211yescharacteristic
15C22×C3×D32C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×#6294C2211yescharacteristic
18C2×#6294C2211yescharacteristic
19C2×#6291C2212yes—
20C2×Dic3×C3⋊D3C2211yescharacteristic
21C2×D3×C3⋊Dic3C2212yescomplemented
22C2×C3×#625C2212yes—
23C2×C3×#624C2211yescharacteristic
24C2×C3×D3×Dic3C2212yescomplemented
25#88952—24no—
26D32×Dic3—24no—
27#88859C2211yescharacteristic, complemented
28C3×C4⋊(C3⋊Dic3)C2212yescomplemented
29C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
30C32×(C2×D3)⋊C4C2212yescomplemented
31#88815C2212yescomplemented
32Dic3⋊(C3⋊Dic3)C2212yescomplemented
33#88804C2211yescharacteristic, complemented
34#88804C2212yescomplemented
35(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C2×#3811—31no—
40C2×D3×#67—32no—
41C22×D3×Dic3—32no—
42C2×C4×D32—31no—
43#64095—32no—
44C22⋊C4×C3⋊D3—31no—
45C3×#886—32no—
46C3×#883—32no—
47C3×D3×C22⋊C4—32no—
48#63974—31no—
49#63969—32no—
50#63966—32no—
51#63962—32no—
52#63921D311yescharacteristic, complemented
53D3×(C2×D3)⋊C4—32no—
54D3×(C2×D3)⋊C4—32no—
55D3×(C2×D3)⋊C4—61no—
56#63900—31no—
57#63891—32no—
58#63891D312yescomplemented
59#63890—32no—
60#63890—32no—
61#63890—32no—
62#63890—62no—
63D3×C4⋊Dic3—32no—
64D3×C4⋊Dic3—32no—
65#63883—31no—
66#63850—32no—
67C22×C3⋊(C3⋊D3)C2311yescharacteristic
68C22×C3×C3⋊D3C2311yescharacteristic
69C22×C32×D3C2311yescharacteristic
70C22×C32×D3C2312yes—
71C2×D3×C3⋊D3—22no—
72C2×D3×C3⋊D3—22no—
73C2×D3×C3⋊D3—22no—
74C2×C3×D32—22no—
75C2×C3×D32—22no—
76C2×C3×D32D414yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4×C3⋊D3—22no—
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2312yes—
85#6294—22no—
86#6294—22no—
87#6291—24no—
88Dic3×C3⋊D3—22no—
89D3×C3⋊Dic3—24no—
90C3×#625—24no—
91C3×#624—22no—
92C3×D3×Dic3—24no—
93D3×#123—92no—
94C2×#886—91no—
95C23×C3⋊D3—31no—
96C23×C3×D3—32no—
97C22×D32—32no—
98C22×D32—61no—
99C22×D32C2×D311yescharacteristic
100C2×#638—32no—
101C22×C3⋊Dic3—32no—
102C2×C4×C3⋊D3—31no—
103C2×C4×C3⋊D3C2×D311yescharacteristic
104C2×C3×#67—32no—
105C2×C3×#67—32no—
106C22×C3×Dic3—32no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—61no—
111#3811—64no—
112D3×#67—68no—
113C2×#626—32no—
114C2×#626—32no—
115C2×#626—62no—
116C2×#625C2×D312yes—
117C2×#624—31no—
118C2×#624—31no—
119C2×#624C2×D311yescharacteristic
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—32no—
125C2×D3×Dic3—68no—
126C2×D3×Dic3—61no—
127C2×D3×Dic3—62no—
128C2×D3×Dic3C2×D312yescomplemented
129C4×D32—64no—
130C32×C22⋊C4—32no—
131C32×C22⋊C4—31no—
132#3757—31no—
133#3752—31no—
134#3752—32no—
135#3752—31no—
136#3752—32no—
137#3752—62no—
138#3752—61no—
139#3752—121no—
140C4⋊(C3⋊Dic3)—32no—
141C4⋊(C3⋊Dic3)C2×D312yescomplemented
142C3×#217—32no—
143C3×#217—32no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—21no—
146C3×(C2×D3)⋊C4—32no—
147C3×(C2×D3)⋊C4—32no—
148C3×(C2×D3)⋊C4C2×D312yescomplemented
149C3×(C2×D3)⋊C4C2×D312yescomplemented
150C3×(C2×D3)⋊C4C2×D312yescomplemented
151C3×C4⋊Dic3—32no—
152C3×C4⋊Dic3—32no—
153C3×C4⋊Dic3—32no—
154C3×C4⋊Dic3—62no—
155C3×Dic3⋊C4—32no—
156#3724—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—62no—
162Dic3⋊Dic3C2×D312yescomplemented
163#3722—32no—
164#3722—32no—
165#3722—32no—
166#3722—62no—
167#3722—61no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—61no—
170(C2×D3)⋊Dic3C2×D312yescomplemented
171(C2×D3)⋊Dic3C2×D312yescomplemented
172C22×C33C2411yescharacteristic
173C2×C3⋊(C3⋊D3)—21no—
174C2×C3⋊(C3⋊D3)—21no—
175C2×C3⋊(C3⋊D3)—21no—
176C2×C3×C3⋊D3C2×D412yes—
177C2×C3×C3⋊D3#4112yes—
178C2×C3×C3⋊D3#4112yes—
179C2×C32×D3—22no—
180C2×C32×D3—22no—
181C2×C32×D3—21no—
182C2×C32×D3—21no—
183C2×C32×D3—21no—
184C2×C32×D3C2×D414yes—
185D3×C3⋊D3—44no—
186C3×D32—28no—
187C33×C4—21no—
188C3⋊(C3⋊Dic3)—21no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3—21no—
192C32×Dic3—21no—
193C32×Dic3—22no—
194C22×#67—91no—
195C23×Dic3—91no—
196C2×D3×D4—92no—
197C22×C4×D3—92no—
198C3×#123—92no—
199C2×C3×C22⋊C4—91no—
200#935—92no—
201#929—92no—
202C2×(C2×D3)⋊C4—91no—
203C2×(C2×D3)⋊C4—91no—
204C2×C4⋊Dic3—91no—
205C2×C4⋊Dic3—91no—
206#894—92no—
207#894—92no—
208D3×C4⋊C4—92no—
209D3×C4⋊C4—92no—
210#886—32no—
211#886—92no—
212#886—92no—
213#886—92no—
214#886—92no—
215#886—182no—
216#883—32no—
217#883—92no—
218D3×C22⋊C4—32no—
219D3×C22⋊C4—92no—
220D3×C22⋊C4—92no—
221D3×C22⋊C4—181no—
222C23×C32—32no—
223C23×C32—31no—
224C22×C3⋊D3—32no—
225C22×C3⋊D3—31no—
226C22×C3⋊D3—61no—
227C22×C3⋊D3—62no—
228C22×C3⋊D3—62no—
229C22×C3⋊D3—62no—
230C22×C3⋊D3—62no—
231C22×C3⋊D3—121no—
232C22×C3⋊D3C22×D311yescharacteristic
233C22×C3×D3—21no—
234C22×C3×D3—22no—
235C22×C3×D3—32no—
236C22×C3×D3—38no—
237C22×C3×D3—61no—
238C22×C3×D3—64no—
239C22×C3×D3—64no—
240C22×C3×D3C22×D312yes—
241C22×C3×D3C22×D312yes—
242C22×C3×D3C22×D312yes—
243C2×D32—22no—
244C2×D32—22no—
245C2×D32—64no—
246C2×D32—64no—
247C2×D32—64no—
248C2×D32—64no—
249C2×D32—122no—
250C2×D32—122no—
251C2×D32D1214yes—
252C2×C32×C4—22no—
253C2×C32×C4—21no—
254C2×C32×C4—31no—
255C2×C32×C4—32no—
256C2×C32×C4—41no—
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D312yes—
259#638—64no—
260C2×C3⋊Dic3—32no—
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—61no—
263C2×C3⋊Dic3—62no—
264C2×C3⋊Dic3—64no—
265C2×C3⋊Dic3—121no—
266C2×C3⋊Dic3C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D312yes—
268C2×C3⋊Dic3C22×D312yes—
269C4×C3⋊D3—22no—
270C4×C3⋊D3—62no—
271C3×#67—64no—
272C3×#67—64no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—64no—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D312yes—
287C3×C4×D3—64no—
288C3×C4×D3—64no—
289C3×C4×D3—64no—
290C3×C4×D3—122no—
291#626—64no—
292#626—64no—
293#626—124no—
294#625—24no—
295#624—22no—
296#624—62no—
297#624—62no—
298D3×Dic3—24no—
299D3×Dic3—64no—
300D3×Dic3—64no—
301D3×Dic3—64no—
302D3×Dic3—64no—
303D3×Dic3—64no—
304D3×Dic3—124no—
305D3×Dic3—122no—
306C2×#123—271noSylow
307C2×C33C22×D411yescharacteristic
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C3⋊(C3⋊D3)—41no—
311C3×C3⋊D3#12314yescomplemented
312C32×D3—24no—
313C32×D3—41no—
314C24×C3—91no—
315C23×D3—32no—
316C23×D3—92no—
317C23×D3—91no—
318C23×D3—181no—
319C2×C3×D4—92no—
320C22×C3×C4—91no—
321C22×C3×C4—92no—
322C22×C3×C4—91no—
323C2×#67—32no—
324C2×#67—32no—
325C2×#67—92no—
326C2×#67—92no—
327C2×#67—182no—
328C2×#67—184no—
329C22×Dic3—32no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C22×Dic3—92no—
333C22×Dic3—92no—
334C22×Dic3—91no—
335C22×Dic3—182no—
336C22×Dic3—184no—
337D3×D4—188no—
338C2×D12—92no—
339C2×C4×D3—32no—
340C2×C4×D3—32no—
341C2×C4×D3—32no—
342C2×C4×D3—61no—
343C2×C4×D3—92no—
344C2×C4×D3—92no—
345C2×C4×D3—92no—
346C2×C4×D3—92no—
347C2×C4×D3—181no—
348C2×C4×D3—188no—
349C3×C4⋊C4—92no—
350C3×C4⋊C4—92no—
351C3×C22⋊C4—32no—
352C3×C22⋊C4—32no—
353C3×C22⋊C4—32no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—62no—
356C3×C22⋊C4—92no—
357C3×C22⋊C4—92no—
358#217—32no—
359#217—32no—
360#217—92no—
361#217—181no—
362(C2×D3)⋊C4—32no—
363(C2×D3)⋊C4—32no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—92no—
366(C2×D3)⋊C4—92no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—92no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—92no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—181no—
373(C2×D3)⋊C4—182no—
374(C2×D3)⋊C4—181no—
375(C2×D3)⋊C4—182no—
376(C2×D3)⋊C4—361no—
377(C2×D3)⋊C4D3212yescomplemented
378(C2×D3)⋊C4D3211yescharacteristic, complemented
379C4⋊Dic3—32no—
380C4⋊Dic3—32no—
381C4⋊Dic3—32no—
382C4⋊Dic3—62no—
383C4⋊Dic3—92no—
384C4⋊Dic3—92no—
385C4⋊Dic3—92no—
386C4⋊Dic3—182no—
387Dic3⋊C4—32no—
388Dic3⋊C4—92no—
389Dic3⋊C4—92no—
390Dic3⋊C4—92no—
391C22×C32—22no—
392C22×C32—21no—
393C22×C32—34no—
394C22×C32—41no—
395C22×C32—61no—
396C22×C32—62no—
397C22×C32—62no—
398C22×C32—61no—
399C22×C32—61no—
400C22×C32C23×D311yescharacteristic
401C22×C32C23×D312yes—
402C2×C3⋊D3—61no—
403C2×C3⋊D3—62no—
404C2×C3⋊D3—61no—
405C2×C3⋊D3—62no—
406C2×C3⋊D3—61no—
407C2×C3⋊D3—62no—
408C2×C3⋊D3—62no—
409C2×C3⋊D3—122no—
410C2×C3⋊D3—122no—
411C2×C3⋊D3—121no—
412C2×C3⋊D3—121no—
413C2×C3⋊D3—122no—
414C2×C3⋊D3—122no—
415C2×C3⋊D3—124no—
416C2×C3⋊D3—241no—
417C2×C3⋊D3—241no—
418C2×C3⋊D3C2×D1212yes—
419C2×C3⋊D3#23712yes—
420C2×C3⋊D3#23712yes—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—24no—
430C2×C3×D3—34no—
431C2×C3×D3—34no—
432C2×C3×D3—34no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—42no—
436C2×C3×D3—42no—
437C2×C3×D3—62no—
438C2×C3×D3—62no—
439C2×C3×D3—62no—
440C2×C3×D3—616no—
441C2×C3×D3C2×D1214yes—
442C2×C3×D3D3×D414yes—
443D32—28no—
444D32—128no—
445D32—128no—
446C32×C4—21no—
447C32×C4—22no—
448C32×C4—41no—
449C32×C4—42no—
450C32×C4—61no—
451C32×C4—62no—
452C32×C4—81no—
453C3⋊Dic3—22no—
454C3⋊Dic3—22no—
455C3⋊Dic3—21no—
456C3⋊Dic3—61no—
457C3⋊Dic3—62no—
458C3⋊Dic3—122no—
459C3⋊Dic3—121no—
460C3⋊Dic3—241no—
461C3×Dic3—22no—
462C3×Dic3—22no—
463C3×Dic3—22no—
464C3×Dic3—41no—
465C3×Dic3—42no—
466C3×Dic3—62no—
467C3×Dic3—62no—
468C3×Dic3—62no—
469C3×Dic3—62no—
470C3×Dic3—62no—
471C3×Dic3—122no—
472C3×Dic3—122no—
473C3×Dic3—121no—
474C22×D4—271no—
475C23×C4—271no—
476#123—92no—
477#123—272no—
478#123—272no—
479#123—272no—
480C2×C4⋊C4—271no—
481C2×C4⋊C4—271no—
482C2×C22⋊C4—91no—
483C2×C22⋊C4—271no—
484C2×C22⋊C4—271no—
485C33C2×#12311yescharacteristic, complemented, Sylow
486C23×C3—32no—
487C23×C3—32no—
488C23×C3—32no—
489C23×C3—61no—
490C23×C3—62no—
491C23×C3—94no—
492C23×C3—91no—
493C23×C3—182no—
494C23×C3—182no—
495C22×D3—32no—
496C22×D3—38no—
497C22×D3—61no—
498C22×D3—64no—
499C22×D3—64no—
500C22×D3—92no—
501C22×D3—91no—
502C22×D3—181no—
503C22×D3—182no—
504C22×D3—182no—
505C22×D3—182no—
506C22×D3—182no—
507C22×D3—184no—
508C22×D3—184no—
509C22×D3—184no—
510C22×D3—184no—
511C22×D3—361no—
512C22×D3—362no—
513C22×D3—362no—
514C22×D3C2×D3211yescharacteristic
515C22×D3C2×D3212yes—
516C3×D4—184no—
517C2×C3×C4—22no—
518C2×C3×C4—21no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—41no—
523C2×C3×C4—62no—
524C2×C3×C4—61no—
525C2×C3×C4—92no—
526C2×C3×C4—92no—
527C2×C3×C4—91no—
528C2×C3×C4—182no—
529C2×C3×C4—182no—
530C2×C3×C4—184no—
531C2×C3×C4C2×D3211yescharacteristic
532C2×C3×C4C2×D3212yes—
533#67—64no—
534#67—64no—
535#67—184no—
536#67—184no—
537#67—364no—
538C2×Dic3—32no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—61no—
546C2×Dic3—64no—
547C2×Dic3—92no—
548C2×Dic3—91no—
549C2×Dic3—182no—
550C2×Dic3—181no—
551C2×Dic3—182no—
552C2×Dic3—182no—
553C2×Dic3—182no—
554C2×Dic3—184no—
555C2×Dic3—184no—
556C2×Dic3—361no—
557C2×Dic3—364no—
558C2×Dic3C2×D3212yes—
559C2×Dic3C2×D3211yescharacteristic
560D12—184no—
561C4×D3—64no—
562C4×D3—64no—
563C4×D3—64no—
564C4×D3—122no—
565C4×D3—184no—
566C4×D3—184no—
567C4×D3—184no—
568C4×D3—184no—
569C4×D3—362no—
570C2×C32—22no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—22no—
574C2×C32—22no—
575C2×C32—21no—
576C2×C32—41no—
577C2×C32—41no—
578C2×C32—41no—
579C2×C32—64no—
580C2×C32—121no—
581C2×C32C22×D1211yescharacteristic
582C2×C32C2×D3×D412yes—
583C2×C32C2×#23711yescharacteristic
584C2×C32C2×#23711yescharacteristic
585C2×C32D3×#4112yes—
586C2×C32D3×#4112yes—
587C3⋊D3—121no—
588C3⋊D3—122no—
589C3⋊D3—122no—
590C3⋊D3—242no—
591C3⋊D3—242no—
592C3⋊D3#88614yescomplemented
593C3×D3—24no—
594C3×D3—24no—
595C3×D3—38no—
596C3×D3—44no—
597C3×D3—42no—
598C3×D3—42no—
599C3×D3—64no—
600C24—91no—
601C24—271no—
602C2×D4—92no—
603C2×D4—272no—
604C2×D4—544no—
605C22×C4—91no—
606C22×C4—92no—
607C22×C4—91no—
608C22×C4—271no—
609C22×C4—271no—
610C22×C4—271no—
611C22×C4—272no—
612C22×C4—544no—
613C4⋊C4—92no—
614C4⋊C4—92no—
615C4⋊C4—272no—
616C4⋊C4—272no—
617C22⋊C4—32no—
618C22⋊C4—31no—
619C22⋊C4—92no—
620C22⋊C4—92no—
621C22⋊C4—272no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C22⋊C4—271no—
625C22×C3—22no—
626C22×C3—21no—
627C22×C3—34no—
628C22×C3—34no—
629C22×C3—41no—
630C22×C3—64no—
631C22×C3—62no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—62no—
639C22×C3—92no—
640C22×C3—92no—
641C22×C3—92no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—122no—
645C22×C3—122no—
646C22×C3—188no—
647C22×C3C22×D3212yes—
648C22×C3C22×D3211yescharacteristic
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—34no—
655C2×D3—34no—
656C2×D3—34no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—616no—
661C2×D3—182no—
662C2×D3—182no—
663C2×D3—181no—
664C2×D3—181no—
665C2×D3—182no—
666C2×D3—182no—
667C2×D3—181no—
668C2×D3—361no—
669C2×D3—361no—
670C2×D3—362no—
671C2×D3—362no—
672C2×D3—362no—
673C2×D3—362no—
674C2×D3—368no—
675C2×D3—364no—
676C2×D3—368no—
677C2×D3—721no—
678C2×D3—721no—
679C2×D3D3×D1214yes—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—41no—
683C3×C4—42no—
684C3×C4—62no—
685C3×C4—62no—
686C3×C4—62no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—122no—
690C3×C4—182no—
691C3×C4—182no—
692C3×C4—181no—
693Dic3—21no—
694Dic3—22no—
695Dic3—62no—
696Dic3—62no—
697Dic3—62no—
698Dic3—62no—
699Dic3—62no—
700Dic3—121no—
701Dic3—122no—
702Dic3—122no—
703Dic3—182no—
704Dic3—181no—
705Dic3—361no—
706Dic3—362no—
707Dic3—721no—
708C32—21no—
709C32—22no—
710C32—41no—
711C32C2×#88611yescharacteristic, complemented
712C32D3×#12312yescomplemented
713C23—32no—
714C23—31no—
715C23—94no—
716C23—91no—
717C23—182no—
718C23—182no—
719C23—271no—
720C23—542no—
721C23—542no—
722C23—542no—
723D4—184no—
724D4—544no—
725C2×C4—32no—
726C2×C4—31no—
727C2×C4—91no—
728C2×C4—92no—
729C2×C4—92no—
730C2×C4—182no—
731C2×C4—182no—
732C2×C4—184no—
733C2×C4—271no—
734C2×C4—542no—
735C2×C4—542no—
736C2×C4—542no—
737C2×C4—544no—
738C2×C4D3311yescharacteristic
739C2×C3—22no—
740C2×C3—21no—
741C2×C3—22no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—22no—
745C2×C3—41no—
746C2×C3—41no—
747C2×C3—41no—
748C2×C3—64no—
749C2×C3—64no—
750C2×C3—94no—
751C2×C3—124no—
752C2×C3—122no—
753C2×C3—122no—
754C2×C3C2×D3×D1212yes—
755C2×C3#6430611yescharacteristic
756C2×C3D32×D411yescharacteristic
757C2×C3D3×#23712yes—
758C2×C3D3×#23712yes—
759C2×C3#6431211yescharacteristic
760D3—24no—
761D3—38no—
762D3—41no—
763D3—64no—
764D3—362no—
765D3—361no—
766D3—362no—
767D3—722no—
768D3—722no—
769C22—34no—
770C22—62no—
771C22—62no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—92no—
776C22—92no—
777C22—92no—
778C22—188no—
779C22—541no—
780C22—541no—
781C22—541no—
782C22—1084no—
783C22C2×D3311yescharacteristic
784C4—21no—
785C4—62no—
786C4—61no—
787C4—182no—
788C4—182no—
789C4—181no—
790C4—541no—
791C3—21no—
792C3—22no—
793C3—41no—
794C3#1059426011yescharacteristic, complemented
795C3D3×#88612yescomplemented
796C2—64no—
797C2—94no—
798C2—121no—
799C2—1081no—
800C2#1172437311yescharacteristic
801C2D32×D1211yescharacteristic
802C2#1172440811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#88952C2
hypercenterC2×C4D33
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D32×Dic3C2semidirect
3. #11723689C2semidirect
4. C3⋊D3×(C2×D3)⋊C4C2semidirect
5. #11723479C2semidirect
6. C3×#63921C2semidirect
7. C3×#63891C2semidirect
8. #11722989C2semidirect
9. #11722987C2semidirect
10. #11722908C2semidirect
11. #11722904C2semidirect
21. C2×D3×C3⋊Dic3C22semidirect
24. C2×C3×D3×Dic3C22semidirect
27. #88859C22semidirect
28. C3×C4⋊(C3⋊Dic3)C22semidirect
29. C32×(C2×D3)⋊C4C22semidirect
30. C32×(C2×D3)⋊C4C22semidirect
31. #88815C22semidirect
32. Dic3⋊(C3⋊Dic3)C22semidirect
33. #88804C22semidirect
34. #88804C22semidirect
35. (C2×D3)⋊(C3⋊Dic3)C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
52. #63921D3semidirect
58. #63891D3semidirect
128. C2×D3×Dic3C2×D3semidirect
141. C4⋊(C3⋊Dic3)C2×D3semidirect
148. C3×(C2×D3)⋊C4C2×D3semidirect
149. C3×(C2×D3)⋊C4C2×D3semidirect
150. C3×(C2×D3)⋊C4C2×D3semidirect
162. Dic3⋊Dic3C2×D3semidirect
170. (C2×D3)⋊Dic3C2×D3semidirect
171. (C2×D3)⋊Dic3C2×D3semidirect
311. C3×C3⋊D3#123semidirect
377. (C2×D3)⋊C4D32semidirect
378. (C2×D3)⋊C4D32semidirect
485. C33C2×#123semidirect
592. C3⋊D3#886semidirect
711. C32C2×#886semidirect
712. C32D3×#123semidirect
794. C3#10594260semidirect
795. C3D3×#886semidirect

Maximal subgroups

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

subgroupindex
C2×#889522
C2×D32×Dic32
#117236892
C3⋊D3×(C2×D3)⋊C42
#117234792
C3×#639212
C3×#638912
#117229892
#117229872
#117229082
#117229042
D3×#8863
#105942603