Finite Group Databasebeta

← #13177403

Subgroups — #13177403

Order 1728.

2236 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3#11723980C211yesmaximal, characteristic, complemented
4C3×#64148C211yesmaximal, characteristic, complemented
5#11723637C211yesmaximal, characteristic, complemented
6#11723635C211yesmaximal, characteristic, complemented
7#11723633C211yesmaximal, characteristic, complemented
8#11723618C211yesmaximal, characteristic, complemented
9Dic3×#638C211yesmaximal, characteristic, complemented
10#11723600C211yesmaximal, characteristic, complemented
11C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic, complemented
12#11723510C211yesmaximal, characteristic, complemented
13#11723506C211yesmaximal, characteristic, complemented
14#11723393C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596303—31nomaximal
17#10595155—34nomaximal
18C2×C33×D4C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C22×C3×C3⋊Dic3C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic
28C22×C32×Dic3C2211yescharacteristic
29C32×#237—24no—
30C2×C32×C4×D3C2211yescharacteristic
31C2×C32×Dic6C2211yescharacteristic
32C2×#6293C2211yescharacteristic
33C2×#6292C2211yescharacteristic
34C2×#6291C2211yescharacteristic
35C2×#6290C2211yescharacteristic
36C2×#6289C2211yescharacteristic
37#89031—24no—
38C2×Dic3×C3⋊D3C2211yescharacteristic
39#88864C2211yescharacteristic
40#88859C2211yescharacteristic
41#88857C2211yescharacteristic
42C3×#3757C2211yescharacteristic
43C3×#3752C2211yescharacteristic
44C3×#3750C2211yescharacteristic
45#88807C2211yescharacteristic
46#88806C2211yescharacteristic
47#88804C2211yescharacteristic
48#88803C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53Dic3×C3⋊Dic3C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×C32×#41—31no—
56C2×#3828—31no—
57C2×C3×#237D314yescomplemented
58C2×#3804—34no—
59#64156—31no—
60#64153—31no—
61#64149—31no—
62#64148—31no—
63#64148—31no—
64#64148—31no—
65#64148—34no—
66#64148—64no—
67#64148D311yescharacteristic, complemented
68#64145—31no—
69C4×#638—31no—
70C4×#638—31no—
71C4×#638—31no—
72C4×#638—31no—
73C2×C4×C3⋊Dic3—31no—
74C3×#939—34no—
75#63980—34no—
76#63979—34no—
77#63978—34no—
78Dic3×#67—34no—
79#63959—34no—
80C2×Dic32—34no—
81#63952—34no—
82#63907—34no—
83#63904—34no—
84#63879—34no—
85#63839—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C33×D4—22no—
92C2×C33×C4C2311yescharacteristic
93#6312—22no—
94#6312—22no—
95C2×C3⋊(C3⋊Dic3)—22no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C3×#638—22no—
100C3×#638—22no—
101C2×C3×C3⋊Dic3—22no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C32×#67—22no—
106C32×#67—22no—
107C2×C32×Dic3—22no—
108C2×C32×Dic3D414yescomplemented
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C32×C4×D3—22no—
113C32×Dic6—22no—
114#6293—22no—
115#6292—22no—
116#6291—22no—
117#6290—22no—
118#6289—22no—
119Dic3×C3⋊D3—22no—
120#5832—94no—
121#5596—91no—
122C32×#41—64no—
123C2×C32×Q8—31no—
124C2×C32×D4—24no—
125C2×C32×D4—31no—
126C2×C32×D4—31no—
127C2×C32×D4C2×D314yes—
128C2×C32×D4C2×D311yescharacteristic
129C22×C32×C4—31no—
130C22×C32×C4—31no—
131C22×C32×C4—31no—
132C2×#638—31no—
133C2×#638—31no—
134C2×#638—34no—
135C2×#638—34no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—64no—
139C2×#638—64no—
140C2×#638C2×D311yescharacteristic
141C2×#638C2×D311yescharacteristic
142C22×C3⋊Dic3—31no—
143C22×C3⋊Dic3—34no—
144C22×C3⋊Dic3—64no—
145C22×C3⋊Dic3C2×D311yescharacteristic
146#3828—64no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×#634—31no—
151C2×C3×#67—34no—
152C2×C3×#67—34no—
153C2×C3×#67C2×D314yes—
154C2×C3×#67C2×D314yes—
155C22×C3×Dic3—34no—
156C22×C3×Dic3C2×D314yes—
157C22×C3×Dic3C2×D314yes—
158C3×#237—216no—
159C2×C3×C4×D3C2×D314yes—
160C2×C3×Dic6C2×D314yes—
161C2×#627—34no—
162C2×#626—34no—
163C2×#626—34no—
164C2×#625—34no—
165C2×#624—34no—
166#3804—616no—
167C2×D3×Dic3—34no—
168#3757—31no—
169#3757—34no—
170#3757—31no—
171#3757—31no—
172#3757—64no—
173#3757C2×D311yescharacteristic
174#3752—31no—
175#3752—31no—
176#3752—34no—
177#3752—31no—
178#3752—64no—
179#3752C2×D311yescharacteristic
180#3750—31no—
181#3750—34no—
182#3750—31no—
183#3750—31no—
184#3750—64no—
185#3750C2×D311yescharacteristic
186C4×C3⋊Dic3—31no—
187C4×C3⋊Dic3—31no—
188C4×C3⋊Dic3—31no—
189C4×C3⋊Dic3—31no—
190C3×#217—34no—
191C3×(C2×D3)⋊C4—34no—
192C3×Dic3⋊C4—34no—
193#3724—34no—
194Dic3⋊Dic3—34no—
195#3722—34no—
196(C2×D3)⋊Dic3—34no—
197(C2×D3)⋊Dic3—34no—
198(C2×D3)⋊Dic3—34no—
199Dic32—34no—
200Dic32—34no—
201Dic32—34no—
202Dic32—34no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33—21no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33C2×D412yes—
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3—21no—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3—21no—
219C33×C4—21no—
220C3⋊(C3⋊Dic3)—21no—
221C3⋊(C3⋊Dic3)—21no—
222C3⋊(C3⋊Dic3)#4112yescomplemented
223C3×C3⋊Dic3—21no—
224C3×C3⋊Dic3—21no—
225C3×C3⋊Dic3#4112yescomplemented
226C32×Dic3—21no—
227C32×Dic3C2×D412yes—
228C32×Dic3C2×D412yes—
229C2×C3×#41—34no—
230C2×#237—91no—
231C2×#237C3⋊D311yescharacteristic, complemented
232C2×#235—94no—
233C3×#121—91no—
234#947—94no—
235#944—94no—
236#940—94no—
237#940—91no—
238#939—34no—
239#939—94no—
240#939—94no—
241#939—94no—
242#939—91no—
243#939—91no—
244#939—184no—
245#936—94no—
246D4×Dic3—91no—
247#930—91no—
248C4×#67—94no—
249C4×#67—94no—
250C4×#67—94no—
251C4×#67—94no—
252C2×C4×Dic3—94no—
253C2×C4×Dic3—91no—
254#893—91no—
255#888—91no—
256#885—91no—
257#885—91no—
258#67⋊C4—91no—
259#67⋊C4—91no—
260C23×C32—24no—
261C23×C32—24no—
262C23×C32—31no—
263C23×C32C22×D314yes—
264C23×C32C22×D314yes—
265C23×C32C22×D311yescharacteristic
266C23×C32C22×D311yescharacteristic
267C22×C3⋊D3—31no—
268C22×C3⋊D3—34no—
269C22×C3⋊D3—64no—
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3×D3—34no—
272C22×C3×D3C22×D314yes—
273C32×Q8—62no—
274C32×D4—22no—
275C32×D4—28no—
276C32×D4—48no—
277C32×D4—62no—
278C32×D4—62no—
279C2×C32×C4—24no—
280C2×C32×C4—34no—
281C2×C32×C4—31no—
282C2×C32×C4—31no—
283C2×C32×C4—31no—
284C2×C32×C4—62no—
285C2×C32×C4—62no—
286C2×C32×C4C22×D314yes—
287C2×C32×C4C22×D311yescharacteristic
288#638—22no—
289#638—22no—
290#638—62no—
291#638—62no—
292#638—62no—
293#638—62no—
294#638—68no—
295#638—68no—
296#638—128no—
297#638—128no—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—31no—
300C2×C3⋊Dic3—31no—
301C2×C3⋊Dic3—31no—
302C2×C3⋊Dic3—34no—
303C2×C3⋊Dic3—34no—
304C2×C3⋊Dic3—34no—
305C2×C3⋊Dic3—64no—
306C2×C3⋊Dic3—64no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3—62no—
309C2×C3⋊Dic3—68no—
310C2×C3⋊Dic3—128no—
311C2×C3⋊Dic3C22×D311yescharacteristic
312C2×C3⋊Dic3C22×D311yescharacteristic
313C2×C3⋊Dic3C22×D311yescharacteristic
314C4⋊(C3⋊D3)—62no—
315C4×C3⋊D3—62no—
316C4×C3⋊D3—62no—
317#634—62no—
318C3×#67—28no—
319C3×#67—28no—
320C3×#67—68no—
321C3×#67—68no—
322C2×C3×Dic3—28no—
323C2×C3×Dic3—34no—
324C2×C3×Dic3—34no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3—68no—
327C2×C3×Dic3#67116yescomplemented
328C2×C3×Dic3C22×D314yes—
329C2×C3×Dic3C22×D314yes—
330C2×C3×Dic3C22×D314yes—
331C3×C4×D3—28no—
332C3×Dic6—28no—
333#627—68no—
334#626—68no—
335#626—68no—
336#625—68no—
337#624—68no—
338D3×Dic3—68no—
339#532—271noSylow
340C2×C33—22no—
341C2×C33—41no—
342C2×C33C22×D411yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C2×C33C2×#4111yescharacteristic
345C3⋊(C3⋊D3)—41no—
346C3×C3⋊D3—41no—
347C32×D3—41no—
348C3×#41—616no—
349C2×C3×Q8—34no—
350C2×C3×D4—24no—
351C2×C3×D4—34no—
352C2×C3×D4—34no—
353C2×C3×D4—91no—
354C2×C3×D4—91no—
355C2×C3×D4D3214yes—
356C2×C3×D4C2×C3⋊D311yescharacteristic
357C22×C3×C4—34no—
358C22×C3×C4—34no—
359C22×C3×C4—34no—
360C22×C3×C4—91no—
361C2×#67—34no—
362C2×#67—34no—
363C2×#67—94no—
364C2×#67—94no—
365C2×#67—94no—
366C2×#67—94no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—91no—
370C2×#67—91no—
371C2×#67—184no—
372C2×#67—184no—
373C2×#67C2×C3⋊D311yescharacteristic
374C2×#67C2×C3⋊D311yescharacteristic
375C22×Dic3—34no—
376C22×Dic3—94no—
377C22×Dic3—91no—
378C22×Dic3—91no—
379C22×Dic3—184no—
380C22×Dic3C2×C3⋊D311yescharacteristic
381C22×Dic3C2×C3⋊D311yescharacteristic
382#237—24no—
383#237—184no—
384#235—1816no—
385C2×D12—94no—
386C2×D12—91no—
387C2×C4×D3—94no—
388C2×C4×D3—94no—
389C2×C4×D3—91no—
390C2×C4×D3C2×C3⋊D311yescharacteristic
391C2×Dic6—94no—
392C2×Dic6—91no—
393C2×Dic6C2×C3⋊D311yescharacteristic
394C3×C4⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397#217—34no—
398#217—94no—
399#217—94no—
400#217—94no—
401#217—91no—
402#217—91no—
403#217—184no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—94no—
406(C2×D3)⋊C4—94no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—94no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—184no—
413C4⋊Dic3—91no—
414Dic3⋊C4—34no—
415Dic3⋊C4—94no—
416Dic3⋊C4—94no—
417Dic3⋊C4—94no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—184no—
421C4×Dic3—94no—
422C4×Dic3—94no—
423C4×Dic3—94no—
424C4×Dic3—94no—
425C4×Dic3—91no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—91no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—24no—
435C22×C32—28no—
436C22×C32—24no—
437C22×C32—24no—
438C22×C32—24no—
439C22×C32—24no—
440C22×C32—24no—
441C22×C32—44no—
442C22×C32—44no—
443C22×C32—44no—
444C22×C32—44no—
445C22×C32—44no—
446C22×C32—61no—
447C22×C32—61no—
448C22×C32—61no—
449C22×C32D3×D412yes—
450C22×C32C2×#6718yes—
451C22×C32C23×D314yes—
452C22×C32C23×D311yescharacteristic
453C2×C3⋊D3—21no—
454C2×C3⋊D3—21no—
455C2×C3⋊D3—21no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3⋊D3—61no—
459C2×C3⋊D3—64no—
460C2×C3⋊D3—64no—
461C2×C3⋊D3—64no—
462C2×C3⋊D3—124no—
463C2×C3⋊D3—124no—
464C2×C3⋊D3—124no—
465C2×C3×D3—24no—
466C2×C3×D3—24no—
467C2×C3×D3—24no—
468C2×C3×D3—64no—
469C2×C3×D3—64no—
470C2×C3×D3—64no—
471C32×C4—21no—
472C32×C4—24no—
473C32×C4—32no—
474C32×C4—32no—
475C32×C4—44no—
476C32×C4—61no—
477C3⋊Dic3—21no—
478C3⋊Dic3—21no—
479C3⋊Dic3—32no—
480C3⋊Dic3—38no—
481C3⋊Dic3—68no—
482C3⋊Dic3—61no—
483C3⋊Dic3—61no—
484C3⋊Dic3—64no—
485C3⋊Dic3—64no—
486C3⋊Dic3—124no—
487C3⋊Dic3—124no—
488C3⋊Dic3#23712yescomplemented
489C3×Dic3—24no—
490C3×Dic3—38no—
491C3×Dic3—64no—
492C3×Dic3—64no—
493C3×Dic3C2×#6718yes—
494C3×Dic3C2×#6718yes—
495C2×#41—31no—
496C2×#41—271no—
497C4⋊Q8—271no—
498#127—271no—
499#124—271no—
500#124—271no—
501#121—91no—
502#121—271no—
503#121—271no—
504#121—271no—
505C4×D4—271no—
506C4×D4—271no—
507C4×D4—271no—
508C4×D4—271no—
509C2×C42—271no—
510C33#53211yescharacteristic, complemented, Sylow
511C23×C3—24no—
512C23×C3—24no—
513C23×C3—34no—
514C23×C3—91no—
515C23×C3C2×D3214yes—
516C23×C3C2×D3214yes—
517C23×C3C22×C3⋊D311yescharacteristic
518C23×C3C22×C3⋊D311yescharacteristic
519C22×D3—34no—
520C22×D3—94no—
521C22×D3—91no—
522C22×D3—184no—
523C22×D3C22×C3⋊D311yescharacteristic
524C3×Q8—68no—
525C3×D4—28no—
526C3×D4—22no—
527C3×D4—48no—
528C3×D4—68no—
529C3×D4—68no—
530C3×D4—182no—
531C3×D4—182no—
532C2×C3×C4—24no—
533C2×C3×C4—34no—
534C2×C3×C4—34no—
535C2×C3×C4—316no—
536C2×C3×C4—34no—
537C2×C3×C4—68no—
538C2×C3×C4—68no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—91no—
542C2×C3×C4—182no—
543C2×C3×C4C2×D3214yes—
544C2×C3×C4C22×C3⋊D311yescharacteristic
545#67—22no—
546#67—22no—
547#67—68no—
548#67—68no—
549#67—188no—
550#67—182no—
551#67—188no—
552#67—182no—
553#67—188no—
554#67—188no—
555#67—182no—
556#67—182no—
557#67—368no—
558#67—368no—
559C2×Dic3—22no—
560C2×Dic3—34no—
561C2×Dic3—34no—
562C2×Dic3—34no—
563C2×Dic3—68no—
564C2×Dic3—94no—
565C2×Dic3—91no—
566C2×Dic3—94no—
567C2×Dic3—94no—
568C2×Dic3—91no—
569C2×Dic3—91no—
570C2×Dic3—184no—
571C2×Dic3—184no—
572C2×Dic3—184no—
573C2×Dic3—182no—
574C2×Dic3—188no—
575C2×Dic3—182no—
576C2×Dic3—368no—
577C2×Dic3#63814yescomplemented
578C2×Dic3C22×C3⋊D311yescharacteristic
579C2×Dic3C22×C3⋊D311yescharacteristic
580C2×Dic3C22×C3⋊D311yescharacteristic
581D12—188no—
582D12—182no—
583C4×D3—22no—
584C4×D3—188no—
585C4×D3—188no—
586C4×D3—182no—
587Dic6—22no—
588Dic6—188no—
589Dic6—182no—
590C2×C32—22no—
591C2×C32—24no—
592C2×C32—24no—
593C2×C32—24no—
594C2×C32—28no—
595C2×C32—48no—
596C2×C32—41no—
597C2×C32—44no—
598C2×C32—84no—
599C2×C32—121no—
600C2×C32C2×D3×D411yescharacteristic
601C2×C32C2×#23711yescharacteristic
602C2×C32D3×#4114yes—
603C2×C32D3×#4114yes—
604C2×C32D3×#4111yescharacteristic
605C2×C32C22×#6714yes—
606C3⋊D3—41no—
607C3⋊D3—121no—
608C3⋊D3—124no—
609C3⋊D3—244no—
610C3×D3—44no—
611C3×D3—124no—
612#41—64no—
613#41—544no—
614C2×Q8—31no—
615C2×Q8—271no—
616C2×D4—31no—
617C2×D4—31no—
618C2×D4—91no—
619C2×D4—91no—
620C2×D4—271no—
621C2×D4—271no—
622C2×D4—271no—
623C2×D4—271no—
624C2×D4—271no—
625C2×D4D3×C3⋊D311yescharacteristic
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—91no—
630C22×C4—271no—
631C22×C4—271no—
632C22×C4—271no—
633C4⋊C4—91no—
634C4⋊C4—271no—
635C4⋊C4—271no—
636C4⋊C4—271no—
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C42—271no—
646C42—271no—
647C42—271no—
648C42—271no—
649C22×C3—24no—
650C22×C3—24no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—24no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—24no—
660C22×C3—28no—
661C22×C3—44no—
662C22×C3—44no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3—44no—
666C22×C3—64no—
667C22×C3—64no—
668C22×C3—64no—
669C22×C3—181no—
670C22×C3—181no—
671C22×C3—181no—
672C22×C3D3×#6718yes—
673C22×C3C2×#63812yes—
674C22×C3C22×D3214yes—
675C22×C3C23×C3⋊D311yescharacteristic
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—64no—
680C2×D3—64no—
681C2×D3—64no—
682C2×D3—184no—
683C2×D3—184no—
684C2×D3—184no—
685C2×D3—181no—
686C2×D3—181no—
687C2×D3—181no—
688C2×D3—364no—
689C2×D3—364no—
690C2×D3—364no—
691C3×C4—24no—
692C3×C4—21no—
693C3×C4—38no—
694C3×C4—38no—
695C3×C4—44no—
696C3×C4—64no—
697C3×C4—92no—
698C3×C4—181no—
699C3×C4—181no—
700Dic3—21no—
701Dic3—38no—
702Dic3—64no—
703Dic3—64no—
704Dic3—98no—
705Dic3—92no—
706Dic3—188no—
707Dic3—184no—
708Dic3—184no—
709Dic3—181no—
710Dic3—181no—
711Dic3—364no—
712Dic3—364no—
713Dic3C2×#63812yes—
714Dic3C2×#63812yes—
715C32—24no—
716C32#559611yescharacteristic, complemented
717C32#583214yescomplemented
718C23—31no—
719C23—91no—
720C23—271no—
721C23C2×D3×C3⋊D311yescharacteristic
722C23C2×D3×C3⋊D311yescharacteristic
723Q8—62no—
724Q8—542no—
725D4—22no—
726D4—62no—
727D4—62no—
728D4—182no—
729D4—182no—
730D4—542no—
731D4—542no—
732D4—542no—
733D4—542no—
734D4—542no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—34no—
738C2×C4—31no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—91no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—182no—
745C2×C4—271no—
746C2×C4—271no—
747C2×C4—271no—
748C2×C4—542no—
749C2×C4—542no—
750C2×C4—542no—
751C2×C4C2×D3×C3⋊D311yescharacteristic
752C2×C3—28no—
753C2×C3—22no—
754C2×C3—24no—
755C2×C3—24no—
756C2×C3—24no—
757C2×C3—48no—
758C2×C3—44no—
759C2×C3—41no—
760C2×C3—84no—
761C2×C3—124no—
762C2×C3—361no—
763C2×C3D3×#23714yes—
764C2×C3#6431214yes—
765C2×C3C2×D3×#6714yes—
766C2×C3#41×C3⋊D311yescharacteristic
767C2×C3#41×C3⋊D311yescharacteristic
768C2×C3C22×#63811yescharacteristic
769D3—41no—
770D3—124no—
771D3—364no—
772D3—361no—
773D3—724no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—181no—
783C22—181no—
784C22—181no—
785C22—541no—
786C22—541no—
787C22—541no—
788C22D3×#63812yes—
789C22C22×D3×C3⋊D311yescharacteristic
790C4—21no—
791C4—32no—
792C4—32no—
793C4—61no—
794C4—92no—
795C4—181no—
796C4—181no—
797C4—272no—
798C4—541no—
799C4—541no—
800C3—24no—
801C3#1059515514yescomplemented
802C3#1059630311yescharacteristic, complemented
803C2—22no—
804C2—41no—
805C2—121no—
806C2—361no—
807C2—1081no—
808C2C3⋊D3×#23711yescharacteristic
809C2#1172458611yescharacteristic
810C2C2×D3×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#532
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C2×#89031C2semidirect
3. #11723980C2semidirect
4. C3×#64148C2semidirect
5. #11723637C2semidirect
6. #11723635C2semidirect
7. #11723633C2semidirect
8. #11723618C2semidirect
9. Dic3×#638C2semidirect
10. #11723600C2semidirect
11. C2×Dic3×C3⋊Dic3C2semidirect
12. #11723510C2semidirect
13. #11723506C2semidirect
14. #11723393C2semidirect
15. #11723392C2semidirect
57. C2×C3×#237D3semidirect
67. #64148D3semidirect
108. C2×C32×Dic3D4semidirect
222. C3⋊(C3⋊Dic3)#41semidirect
225. C3×C3⋊Dic3#41semidirect
231. C2×#237C3⋊D3semidirect
327. C2×C3×Dic3#67semidirect
488. C3⋊Dic3#237semidirect
510. C33#532semidirect
577. C2×Dic3#638semidirect
716. C32#5596semidirect
717. C32#5832semidirect
801. C3#10595155semidirect
802. C3#10596303semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×#890312
#117239802
C3×#641482
#117236372
#117236352
#117236332
#117236182
Dic3×#6382
#117236002
C2×Dic3×C3⋊Dic32
#117235102
#117235062
#117233932
#117233922
#105963033
#105951553