Finite Group Databasebeta

← #13178284

Subgroups — #13178284

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×#89049C211yesmaximal, characteristic
2C2×C4×#1113C211yesmaximal, characteristic, complemented
3C3×#64092C212yesmaximal, complemented
4C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
5#11723724C212yesmaximal, complemented
6#11723723C211yesmaximal, characteristic, complemented
7#11723700C211yesmaximal, characteristic, complemented
8#11723694C212yesmaximal, complemented
9#11723690C212yesmaximal, complemented
10#11723689C211yesmaximal, characteristic, complemented
11#11723682C211yesmaximal, characteristic, complemented
12#10594260—31nomaximal
13D3×#883—32nomaximal
14C23×C3×C3⋊D3C2211yescharacteristic
15C22×#1113C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2212yescomplemented
20#89049—24no—
21C2×#6295C2212yes—
22C2×#6294C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C2×#6294C2212yescomplemented
26C4×#1113—24no—
27C33×C22⋊C4C2211yescharacteristic, complemented
28C3×#3757C2211yescharacteristic, complemented
29C3×#3757C2212yescomplemented
30C3×#3752C2211yescharacteristic, complemented
31C3×#3752C2211yescharacteristic, complemented
32C3×#3752C2212yescomplemented
33C3×C4⋊(C3⋊Dic3)C2212yescomplemented
34C3×#3750C2212yescomplemented
35#88815C2212yescomplemented
36#88815C2212yescomplemented
37#88814C2212yescomplemented
38#88814C2212yescomplemented
39C2×#3811—31no—
40C2×D3×#67—32no—
41C2×C4×D32—31no—
42C2×C4×D32—32no—
43#64092D312yescomplemented
44C22⋊C4×C3⋊D3D311yescharacteristic, complemented
45C3×#883—32no—
46C3×#883—32no—
47C3×#883—62no—
48C3×D3×C22⋊C4—32no—
49C3×D3×C22⋊C4—61no—
50#63975—32no—
51#63974—31no—
52#63969—32no—
53#63969—32no—
54D3×#217—32no—
55#63921—31no—
56D3×(C2×D3)⋊C4—32no—
57#63905—32no—
58#63900—31no—
59#63891—32no—
60#63890—32no—
61D3×C4⋊Dic3—32no—
62#63883—31no—
63D3×Dic3⋊C4—32no—
64#63854—32no—
65#63853—32no—
66#63850—32no—
67C23×C33C2311yescharacteristic
68C22×C3×C3⋊D3—22no—
69C22×C3×C3⋊D3—22no—
70C22×C3×C3⋊D3—22no—
71C22×C3×C3⋊D3C2311yescharacteristic
72C22×C3×C3⋊D3C2312yes—
73C22×C3×C3⋊D3C2311yescharacteristic
74C2×#1113—22no—
75C2×#1113—22no—
76C2×#1113D414yes—
77C2×C33×C4C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C3×#638—24no—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4×C3⋊D3—22no—
86C3×C4×C3⋊D3—24no—
87C3×C4×C3⋊D3—22no—
88#6295—24no—
89#6294—22no—
90#6294—24no—
91#6294—22no—
92#6294—22no—
93D3×#123—92no—
94C2×#883—91no—
95C23×C3⋊D3C2×D311yescharacteristic
96C23×C3×D3—32no—
97C23×C3×D3—61no—
98C22×D32—32no—
99C22×D32—31no—
100C2×#638C2×D312yes—
101C2×C4×C3⋊D3C2×D311yescharacteristic
102C2×C4×C3⋊D3C2×D311yescharacteristic
103C2×C4×C3⋊D3C2×D312yescomplemented
104C2×C3×#67—32no—
105C2×C3×#67—32no—
106C2×C3×#67—62no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—61no—
112C2×C3×C4×D3—61no—
113C2×C3×C4×D3—62no—
114#3811—64no—
115D3×#67—68no—
116C2×#626—32no—
117C2×#626—32no—
118C2×#625—32no—
119C2×#624—32no—
120C2×#624—31no—
121C2×#624—31no—
122C2×#624—31no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—32no—
125C2×D3×Dic3—32no—
126C2×D3×Dic3—32no—
127C2×D3×Dic3—32no—
128C4×D32—64no—
129C4×D32—68no—
130C32×C22⋊C4—21no—
131C32×C22⋊C4—22no—
132C32×C22⋊C4—41no—
133C32×C22⋊C4C2×D312yescomplemented
134C32×C22⋊C4C2×D311yescharacteristic, complemented
135#3757C2×D311yescharacteristic, complemented
136#3757C2×D312yescomplemented
137#3752C2×D311yescharacteristic, complemented
138#3752C2×D311yescharacteristic, complemented
139#3752C2×D312yescomplemented
140C4⋊(C3⋊Dic3)C2×D312yescomplemented
141#3750C2×D312yescomplemented
142C3×#217—32no—
143C3×#217—32no—
144C3×#217—32no—
145C3×#217—61no—
146C3×#217—62no—
147C3×(C2×D3)⋊C4—32no—
148C3×(C2×D3)⋊C4—32no—
149C3×(C2×D3)⋊C4—32no—
150C3×(C2×D3)⋊C4—32no—
151C3×(C2×D3)⋊C4—61no—
152C3×(C2×D3)⋊C4—61no—
153C3×(C2×D3)⋊C4—62no—
154C3×C4⋊Dic3—32no—
155C3×C4⋊Dic3—32no—
156C3×C4⋊Dic3—62no—
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—32no—
159C3×Dic3⋊C4—62no—
160#3724—32no—
161#3724—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166#3722—32no—
167#3722—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172C22×C33—21no—
173C22×C33—21no—
174C22×C33—21no—
175C22×C33C2411yescharacteristic
176C2×C3×C3⋊D3—22no—
177C2×C3×C3⋊D3—22no—
178C2×C3×C3⋊D3—21no—
179C2×C3×C3⋊D3—21no—
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—44no—
182C2×C3×C3⋊D3C2×D414yes—
183C2×C3×C3⋊D3C2×D412yes—
184C2×C3×C3⋊D3#4112yes—
185C2×C3×C3⋊D3#4112yes—
186#1113—28no—
187C33×C4—21no—
188C33×C4—21no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—22no—
193C3×C3⋊Dic3—21no—
194C22×#67—91no—
195C2×D3×D4—92no—
196C22×C4×D3—92no—
197C22×C4×D3—91no—
198C3×#123—92no—
199C2×C3×C22⋊C4—91no—
200C2×#217—91no—
201#935—92no—
202#929—92no—
203C2×(C2×D3)⋊C4—91no—
204C2×C4⋊Dic3—91no—
205C2×Dic3⋊C4—91no—
206#894—92no—
207#894—92no—
208D3×C4⋊C4—92no—
209D3×C4⋊C4—92no—
210#886—92no—
211#883—32no—
212#883—32no—
213#883—62no—
214#883—92no—
215#883—92no—
216#883—92no—
217#883—92no—
218D3×C22⋊C4—32no—
219D3×C22⋊C4—61no—
220D3×C22⋊C4—92no—
221D3×C22⋊C4—92no—
222C23×C32—21no—
223C23×C32—22no—
224C23×C32—41no—
225C23×C32C22×D312yes—
226C23×C32C22×D311yescharacteristic
227C22×C3⋊D3—22no—
228C22×C3⋊D3—22no—
229C22×C3⋊D3—22no—
230C22×C3⋊D3C22×D311yescharacteristic
231C22×C3⋊D3C22×D312yes—
232C22×C3⋊D3C22×D311yescharacteristic
233C22×C3×D3—32no—
234C22×C3×D3—32no—
235C22×C3×D3—32no—
236C22×C3×D3—32no—
237C22×C3×D3—61no—
238C22×C3×D3—61no—
239C22×C3×D3—62no—
240C22×C3×D3—64no—
241C22×C3×D3—64no—
242C22×C3×D3—64no—
243C22×C3×D3—64no—
244C22×C3×D3—122no—
245C22×C3×D3—122no—
246C2×D32—38no—
247C2×D32—34no—
248C2×D32—64no—
249C2×D32—64no—
250C2×D32—62no—
251C2×D32—62no—
252C2×C32×C4—22no—
253C2×C32×C4—22no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—41no—
257C2×C32×C4—41no—
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D312yes—
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D312yes—
262#638—24no—
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D312yes—
265C2×C3⋊Dic3C22×D312yes—
266C2×C3⋊Dic3C22×D312yes—
267C2×C3⋊Dic3C22×D311yescharacteristic
268C4×C3⋊D3—22no—
269C4×C3⋊D3—24no—
270C4×C3⋊D3—22no—
271C3×#67—64no—
272C3×#67—64no—
273C3×#67—124no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C3×C4×D3—64no—
288C3×C4×D3—64no—
289C3×C4×D3—64no—
290C3×C4×D3—64no—
291C3×C4×D3—122no—
292C3×C4×D3—124no—
293C3×C4×D3—122no—
294#626—64no—
295#626—64no—
296#625—64no—
297#624—62no—
298#624—64no—
299#624—62no—
300#624—62no—
301D3×Dic3—64no—
302D3×Dic3—64no—
303D3×Dic3—64no—
304D3×Dic3—64no—
305D3×Dic3—64no—
306C2×#123—271noSylow
307C2×C33—41no—
308C2×C33C22×D411yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C3×C3⋊D3—24no—
312C3×C3⋊D3—41no—
313C3×C3⋊D3#12314yescomplemented
314C24×C3—91no—
315C23×D3—32no—
316C23×D3—61no—
317C23×D3—92no—
318C23×D3—91no—
319C2×C3×D4—92no—
320C22×C3×C4—91no—
321C22×C3×C4—91no—
322C22×C3×C4—92no—
323C2×#67—32no—
324C2×#67—32no—
325C2×#67—62no—
326C2×#67—92no—
327C2×#67—92no—
328C2×#67—184no—
329C22×Dic3—92no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C22×Dic3—91no—
333D3×D4—188no—
334C2×D12—92no—
335C2×C4×D3—32no—
336C2×C4×D3—32no—
337C2×C4×D3—32no—
338C2×C4×D3—32no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—62no—
342C2×C4×D3—92no—
343C2×C4×D3—92no—
344C2×C4×D3—92no—
345C2×C4×D3—92no—
346C2×C4×D3—92no—
347C2×C4×D3—188no—
348C2×C4×D3—184no—
349C3×C4⋊C4—92no—
350C3×C4⋊C4—92no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—22no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—92no—
355C3×C22⋊C4—91no—
356C3×C22⋊C4—92no—
357C3×C22⋊C4—91no—
358C3×C22⋊C4—91no—
359C3×C22⋊C4D3212yescomplemented
360C3×C22⋊C4D3211yescharacteristic, complemented
361#217—32no—
362#217—32no—
363#217—32no—
364#217—61no—
365#217—62no—
366#217—92no—
367#217—92no—
368(C2×D3)⋊C4—32no—
369(C2×D3)⋊C4—32no—
370(C2×D3)⋊C4—32no—
371(C2×D3)⋊C4—32no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—62no—
375(C2×D3)⋊C4—92no—
376(C2×D3)⋊C4—92no—
377(C2×D3)⋊C4—92no—
378(C2×D3)⋊C4—92no—
379C4⋊Dic3—32no—
380C4⋊Dic3—32no—
381C4⋊Dic3—62no—
382C4⋊Dic3—92no—
383C4⋊Dic3—92no—
384Dic3⋊C4—32no—
385Dic3⋊C4—32no—
386Dic3⋊C4—62no—
387Dic3⋊C4—92no—
388Dic3⋊C4—92no—
389Dic3⋊C4—92no—
390Dic3⋊C4—92no—
391C22×C32—21no—
392C22×C32—22no—
393C22×C32—21no—
394C22×C32—22no—
395C22×C32—21no—
396C22×C32—22no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—21no—
400C22×C32—41no—
401C22×C32—42no—
402C22×C32—42no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—42no—
406C22×C32—42no—
407C22×C32—81no—
408C22×C32—81no—
409C22×C32C23×D311yescharacteristic
410C22×C32C23×D312yes—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—22no—
413C2×C3⋊D3—22no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—44no—
417C2×C3⋊D3#23512yes—
418C2×C3⋊D3D3×D414yes—
419C2×C3⋊D3D3×D412yes—
420C2×C3⋊D3#23712yes—
421C2×C3×D3—34no—
422C2×C3×D3—34no—
423C2×C3×D3—34no—
424C2×C3×D3—34no—
425C2×C3×D3—34no—
426C2×C3×D3—62no—
427C2×C3×D3—62no—
428C2×C3×D3—62no—
429C2×C3×D3—64no—
430C2×C3×D3—62no—
431C2×C3×D3—62no—
432C2×C3×D3—62no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—62no—
438C2×C3×D3—122no—
439C2×C3×D3—122no—
440C2×C3×D3—121no—
441C2×C3×D3—121no—
442C2×C3×D3—128no—
443C2×C3×D3—128no—
444D32—616no—
445D32—68no—
446C32×C4—22no—
447C32×C4—21no—
448C32×C4—21no—
449C32×C4—22no—
450C32×C4—42no—
451C32×C4—41no—
452C32×C4—41no—
453C32×C4—42no—
454C32×C4—81no—
455C32×C4—81no—
456C3⋊Dic3—22no—
457C3⋊Dic3—21no—
458C3⋊Dic3—22no—
459C3⋊Dic3—21no—
460C3⋊Dic3—22no—
461C3×Dic3—62no—
462C3×Dic3—62no—
463C3×Dic3—62no—
464C3×Dic3—62no—
465C3×Dic3—62no—
466C3×Dic3—62no—
467C3×Dic3—62no—
468C3×Dic3—62no—
469C3×Dic3—122no—
470C3×Dic3—121no—
471C3×Dic3—121no—
472C3×Dic3—122no—
473C3×Dic3—122no—
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—21no—
487C23×C3—22no—
488C23×C3—41no—
489C23×C3—91no—
490C23×C3—92no—
491C23×C3—91no—
492C23×C3—182no—
493C23×C3—182no—
494C23×C3—182no—
495C23×C3C2×D3211yescharacteristic
496C23×C3C2×D3212yes—
497C22×D3—32no—
498C22×D3—32no—
499C22×D3—32no—
500C22×D3—32no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—62no—
504C22×D3—64no—
505C22×D3—64no—
506C22×D3—64no—
507C22×D3—64no—
508C22×D3—98no—
509C22×D3—94no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—184no—
513C22×D3—184no—
514C22×D3—182no—
515C22×D3—182no—
516C3×D4—184no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—91no—
524C2×C3×C4—92no—
525C2×C3×C4—92no—
526C2×C3×C4—91no—
527C2×C3×C4—92no—
528C2×C3×C4—182no—
529C2×C3×C4—184no—
530C2×C3×C4—182no—
531C2×C3×C4C2×D3211yescharacteristic
532C2×C3×C4C2×D3212yes—
533C2×C3×C4C2×D3211yescharacteristic
534C2×C3×C4C2×D3212yes—
535#67—64no—
536#67—64no—
537#67—124no—
538#67—184no—
539#67—184no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—32no—
548C2×Dic3—62no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—182no—
554C2×Dic3—184no—
555C2×Dic3—182no—
556C2×Dic3—182no—
557D12—184no—
558C4×D3—64no—
559C4×D3—64no—
560C4×D3—64no—
561C4×D3—64no—
562C4×D3—122no—
563C4×D3—124no—
564C4×D3—122no—
565C4×D3—184no—
566C4×D3—184no—
567C4×D3—184no—
568C4×D3—184no—
569C4×D3—184no—
570C2×C32—22no—
571C2×C32—21no—
572C2×C32—22no—
573C2×C32—21no—
574C2×C32—22no—
575C2×C32—21no—
576C2×C32—41no—
577C2×C32—41no—
578C2×C32—41no—
579C2×C32—41no—
580C2×C32—42no—
581C2×C32—42no—
582C2×C32—82no—
583C2×C32—82no—
584C2×C32C2×#23511yescharacteristic
585C2×C32C2×D3×D412yes—
586C2×C32C2×D3×D411yescharacteristic
587C2×C32C2×#23711yescharacteristic
588C2×C32D3×#4112yes—
589C2×C32D3×#4112yes—
590C3⋊D3—24no—
591C3⋊D3—41no—
592C3⋊D3#88314yescomplemented
593C3×D3—38no—
594C3×D3—64no—
595C3×D3—64no—
596C3×D3—64no—
597C3×D3—124no—
598C3×D3—122no—
599C3×D3—122no—
600C24—91no—
601C24—271no—
602C2×D4—92no—
603C2×D4—272no—
604C2×D4—544no—
605C22×C4—91no—
606C22×C4—91no—
607C22×C4—92no—
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—91no—
618C22⋊C4—92no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—92no—
622C22⋊C4—272no—
623C22⋊C4—272no—
624C22⋊C4#111311yescharacteristic, complemented
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—41no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—92no—
644C22×C3—92no—
645C22×C3—92no—
646C22×C3—94no—
647C22×C3—182no—
648C22×C3—182no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—364no—
653C22×C3C22×D3212yes—
654C22×C3C22×D3211yescharacteristic
655C2×D3—34no—
656C2×D3—34no—
657C2×D3—34no—
658C2×D3—34no—
659C2×D3—34no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—64no—
664C2×D3—62no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—122no—
675C2×D3—122no—
676C2×D3—128no—
677C2×D3—128no—
678C2×D3—1816no—
679C2×D3—188no—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—22no—
683C3×C4—21no—
684C3×C4—42no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—42no—
688C3×C4—81no—
689C3×C4—81no—
690C3×C4—182no—
691C3×C4—182no—
692C3×C4—181no—
693C3×C4—182no—
694C3×C4—181no—
695Dic3—62no—
696Dic3—62no—
697Dic3—62no—
698Dic3—62no—
699Dic3—62no—
700Dic3—62no—
701Dic3—62no—
702Dic3—62no—
703Dic3—122no—
704Dic3—121no—
705Dic3—121no—
706Dic3—122no—
707Dic3—122no—
708C32—22no—
709C32—21no—
710C32—41no—
711C32C2×#88311yescharacteristic, complemented
712C32D3×#12312yescomplemented
713C23—91no—
714C23—92no—
715C23—91no—
716C23—182no—
717C23—182no—
718C23—182no—
719C23—274no—
720C23—542no—
721C23—542no—
722C23C2×#111311yescharacteristic
723D4—184no—
724D4—544no—
725C2×C4—92no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—92no—
729C2×C4—92no—
730C2×C4—182no—
731C2×C4—184no—
732C2×C4—182no—
733C2×C4—542no—
734C2×C4—544no—
735C2×C4—542no—
736C2×C4—542no—
737C2×C4C2×#111311yescharacteristic
738C2×C4C2×#111311yescharacteristic
739C2×C3—22no—
740C2×C3—21no—
741C2×C3—22no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—22no—
745C2×C3—42no—
746C2×C3—42no—
747C2×C3—41no—
748C2×C3—41no—
749C2×C3—41no—
750C2×C3—41no—
751C2×C3—82no—
752C2×C3—82no—
753C2×C3—94no—
754C2×C3—184no—
755C2×C3—361no—
756C2×C3D3×#23512yes—
757C2×C3#6430611yescharacteristic
758C2×C3D32×D412yes—
759C2×C3D32×D411yescharacteristic
760C2×C3D3×#23712yes—
761C2×C3#6431211yescharacteristic
762D3—38no—
763D3—64no—
764D3—64no—
765D3—64no—
766D3—124no—
767D3—122no—
768D3—122no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—92no—
773C22—92no—
774C22—92no—
775C22—94no—
776C22—182no—
777C22—182no—
778C22—181no—
779C22—181no—
780C22—181no—
781C22—364no—
782C22—548no—
783C22C22×#111311yescharacteristic
784C4—21no—
785C4—21no—
786C4—182no—
787C4—181no—
788C4—182no—
789C4—182no—
790C4—181no—
791C3—21no—
792C3—22no—
793C3—41no—
794C3D3×#88312yescomplemented
795C3#1059426011yescharacteristic, complemented
796C2—41no—
797C2—94no—
798C2—184no—
799C2—361no—
800C2#1172461811yescharacteristic
801C2D4×#111311yescharacteristic
802C2#1172462211yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC2×#89049C2
hypercenterC22⋊C4#1113
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1113C2semidirect
3. C3×#64092C2semidirect
4. C3×C22⋊C4×C3⋊D3C2semidirect
5. #11723724C2semidirect
6. #11723723C2semidirect
7. #11723700C2semidirect
8. #11723694C2semidirect
9. #11723690C2semidirect
10. #11723689C2semidirect
11. #11723682C2semidirect
19. C2×C3×C4×C3⋊D3C22semidirect
25. C2×#6294C22semidirect
27. C33×C22⋊C4C22semidirect
28. C3×#3757C22semidirect
29. C3×#3757C22semidirect
30. C3×#3752C22semidirect
31. C3×#3752C22semidirect
32. C3×#3752C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C3×#3750C22semidirect
35. #88815C22semidirect
36. #88815C22semidirect
37. #88814C22semidirect
38. #88814C22semidirect
43. #64092D3semidirect
44. C22⋊C4×C3⋊D3D3semidirect
103. C2×C4×C3⋊D3C2×D3semidirect
133. C32×C22⋊C4C2×D3semidirect
134. C32×C22⋊C4C2×D3semidirect
135. #3757C2×D3semidirect
136. #3757C2×D3semidirect
137. #3752C2×D3semidirect
138. #3752C2×D3semidirect
139. #3752C2×D3semidirect
140. C4⋊(C3⋊Dic3)C2×D3semidirect
141. #3750C2×D3semidirect
313. C3×C3⋊D3#123semidirect
359. C3×C22⋊C4D32semidirect
360. C3×C22⋊C4D32semidirect
485. C33C2×#123semidirect
592. C3⋊D3#883semidirect
624. C22⋊C4#1113semidirect
711. C32C2×#883semidirect
712. C32D3×#123semidirect
794. C3D3×#883semidirect
795. C3#10594260semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×C4×#11132
C3×#640922
C3×C22⋊C4×C3⋊D32
#117237242
#117237232
#117237002
#117236942
#117236902
#117236892
#117236822
#105942603
D3×#8833