Finite Group Databasebeta

← #13178042

Subgroups — #13178042

Order 1728.

2524 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3#11723994C211yesmaximal, characteristic, complemented
4C2×C32×#217C211yesmaximal, characteristic, complemented
5#11723641C211yesmaximal, characteristic, complemented
6#11723636C211yesmaximal, characteristic, complemented
7#11723632C211yesmaximal, characteristic, complemented
8#11723624C211yesmaximal, characteristic, complemented
9#11723623C211yesmaximal, characteristic, complemented
10#11723622C211yesmaximal, characteristic, complemented
11#11723621C211yesmaximal, characteristic, complemented
12C3⋊D3×#217C211yesmaximal, characteristic, complemented
13Dic3×#638C211yesmaximal, characteristic, complemented
14#11723605C211yesmaximal, characteristic, complemented
15#11723591C211yesmaximal, characteristic, complemented
16#10595961—31nomaximal
17#10595493—34nomaximal
18C24×C33C2211yescharacteristic
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×#6312C2211yescharacteristic, complemented
23C2×C3×#638—24no—
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic
26C2×C3×#638C2211yescharacteristic
27C2×C3×#638C2211yescharacteristic
28C22×C3×C3⋊Dic3C2211yescharacteristic
29C22×C32×Dic3C2211yescharacteristic, complemented
30C22×C32×Dic3C2211yescharacteristic, complemented
31C2×#6293C2211yescharacteristic, complemented
32C2×#6292C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic, complemented
35#89031—24no—
36C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38#88864C2211yescharacteristic
39#88864C2211yescharacteristic, complemented
40#88864C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic
42C32×#217C2211yescharacteristic
43C32×#217C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47#88806C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C22×#638D311yescharacteristic, complemented
56C2×#3828—31no—
57C22×C3×#67—34no—
58C2×#3804—34no—
59C2×C32×C22⋊C4—31no—
60#64162—31no—
61#64162—34no—
62#64162—64no—
63#64139—31no—
64#64138—31no—
65C4×#638—31no—
66#64094—31no—
67#64093—31no—
68#64093—31no—
69#64092—31no—
70#64091—31no—
71#64090—31no—
72C22⋊C4×C3⋊D3—31no—
73#64087—31no—
74C2×C3×#217D314yescomplemented
75#63978—34no—
76#63977—34no—
77Dic3×#67—34no—
78#63971—34no—
79#63969—34no—
80D3×#217—34no—
81#63964—34no—
82#63961—34no—
83#63959—34no—
84#63958—34no—
85#63952—34no—
86C23×C33—22no—
87C23×C33—22no—
88C23×C33—41no—
89C23×C33C2311yescharacteristic
90C23×C33C2311yescharacteristic
91C23×C33C2311yescharacteristic
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
93C22×C3×C3⋊D3—22no—
94C22×C3×C3⋊D3—22no—
95C22×C3×C3⋊D3—41no—
96C22×C3×C3⋊D3C2311yescharacteristic
97C22×C3×C3⋊D3C2311yescharacteristic
98#6312—22no—
99#6312—22no—
100#6312—41no—
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C3×#638—22no—
105C3×#638—22no—
106C3×#638—22no—
107C3×#638D414yescomplemented
108C2×C3×C3⋊Dic3—22no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C32×Dic3—22no—
112C2×C32×Dic3—41no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117#6293—22no—
118#6292—22no—
119#6292—41no—
120#6289—22no—
121Dic3×C3⋊D3—22no—
122Dic3×C3⋊D3—41no—
123#5806—91no—
124#5490—94no—
125C24×C32—24no—
126C24×C32C2×D314yes—
127C24×C32C2×D311yescharacteristic
128C23×C3⋊D3C2×D311yescharacteristic
129C23×C3×D3—34no—
130C22×C32×C4—31no—
131C22×C32×C4—31no—
132C2×#638—24no—
133C2×#638—31no—
134C2×#638—31no—
135C2×#638—34no—
136C2×#638—34no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—64no—
140C2×#638—64no—
141C2×#638—64no—
142C2×#638C2×D311yescharacteristic
143C2×#638C2×D311yescharacteristic
144C2×#638C2×D311yescharacteristic
145C2×#638C2×D311yescharacteristic
146C22×C3⋊Dic3C2×D311yescharacteristic
147#3828—64no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×#634—31no—
154C2×C3×#67—34no—
155C2×C3×#67—34no—
156C2×C3×#67—34no—
157C2×C3×#67—34no—
158C2×C3×#67—616no—
159C22×C3×Dic3—34no—
160C22×C3×Dic3C2×D314yescomplemented
161C22×C3×Dic3C2×D314yescomplemented
162C2×#627—34no—
163C2×#626—34no—
164C2×#626—34no—
165C2×#624—34no—
166#3804—616no—
167C2×D3×Dic3—34no—
168C2×D3×Dic3—34no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173#3757—31no—
174#3757—31no—
175#3757—31no—
176#3757—34no—
177#3757—34no—
178#3757—34no—
179#3757—64no—
180#3757—64no—
181#3757—64no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3752—31no—
187C4⋊(C3⋊Dic3)—31no—
188#3750—31no—
189#3750—31no—
190#3750—31no—
191C4×C3⋊Dic3—31no—
192C3×#217C2×D314yes—
193C3×#217C2×D314yes—
194C3×#217C2×D314yescomplemented
195C3×#217C2×D314yescomplemented
196#3724—34no—
197#3724—34no—
198Dic3⋊Dic3—34no—
199Dic3⋊Dic3—34no—
200#3722—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205Dic32—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33—21no—
213C22×C33—44no—
214C22×C33C2×D412yes—
215C22×C33#4112yescomplemented
216C22×C33C2411yescharacteristic
217C2×C3⋊(C3⋊D3)—21no—
218C2×C3⋊(C3⋊D3)—21no—
219C2×C3⋊(C3⋊D3)—21no—
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—21no—
222C2×C3×C3⋊D3—21no—
223C2×C3×C3⋊D3—21no—
224C2×C3×C3⋊D3—21no—
225C2×C3×C3⋊D3—44no—
226C2×C3×C3⋊D3C2×D412yes—
227C3⋊(C3⋊Dic3)—21no—
228C3⋊(C3⋊Dic3)—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3×C3⋊Dic3—21no—
231C3×C3⋊Dic3C2×D412yes—
232C32×Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C22×C3×D4—91no—
237C22×#67—34no—
238C2×#237—91no—
239C2×#235—94no—
240C2×C3×C22⋊C4—34no—
241#953—94no—
242#953—91no—
243#953—91no—
244#953—184no—
245C2×#217—91no—
246C2×#217C3⋊D311yescharacteristic, complemented
247#939—91no—
248#939—91no—
249#938—91no—
250#936—91no—
251#935—91no—
252#935—91no—
253D4×Dic3—91no—
254#930—94no—
255#929—94no—
256C4×#67—94no—
257C4×#67—91no—
258#924—91no—
259#885—94no—
260#884—94no—
261#884—94no—
262#883—94no—
263#882—94no—
264#67⋊C4—94no—
265D3×C22⋊C4—94no—
266#878—94no—
267C23×C32—22no—
268C23×C32—22no—
269C23×C32—24no—
270C23×C32—24no—
271C23×C32—24no—
272C23×C32—28no—
273C23×C32—28no—
274C23×C32—48no—
275C23×C32—48no—
276C23×C32—41no—
277C23×C32—44no—
278C23×C32—48no—
279C23×C32C22×D314yes—
280C23×C32C22×D314yes—
281C23×C32C22×D314yes—
282C23×C32C22×D311yescharacteristic
283C23×C32C22×D311yescharacteristic
284C23×C32C22×D311yescharacteristic
285C22×C3⋊D3—22no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3—31no—
288C22×C3⋊D3—34no—
289C22×C3⋊D3—41no—
290C22×C3⋊D3—64no—
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—34no—
294C22×C3×D3—34no—
295C22×C3×D3—68no—
296C22×C3×D3—68no—
297C22×C3×D3—124no—
298C2×C32×C4—31no—
299C2×C32×C4—31no—
300C2×C32×C4—31no—
301C2×C32×C4—31no—
302C2×C32×C4—62no—
303C2×C32×C4—121no—
304#638—22no—
305#638—22no—
306#638—22no—
307#638—62no—
308#638—62no—
309#638—68no—
310#638—68no—
311#638—128no—
312#638—128no—
313#638—121no—
314#638—124no—
315#638—128no—
316#638#6714yescomplemented
317C2×C3⋊Dic3—22no—
318C2×C3⋊Dic3—31no—
319C2×C3⋊Dic3—31no—
320C2×C3⋊Dic3—31no—
321C2×C3⋊Dic3—34no—
322C2×C3⋊Dic3—34no—
323C2×C3⋊Dic3—34no—
324C2×C3⋊Dic3—64no—
325C2×C3⋊Dic3—64no—
326C2×C3⋊Dic3—64no—
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C4⋊(C3⋊D3)—62no—
330C4⋊(C3⋊D3)—121no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—121no—
334#634—62no—
335C3×#67—316no—
336C3×#67—68no—
337C3×#67—68no—
338C3×#67—68no—
339C2×C3×Dic3—28no—
340C2×C3×Dic3—34no—
341C2×C3×Dic3—34no—
342C2×C3×Dic3—44no—
343C2×C3×Dic3—68no—
344C2×C3×Dic3C22×D314yes—
345C2×C3×Dic3C22×D314yes—
346C2×C3×Dic3C22×D314yes—
347C2×C3×Dic3C22×D314yes—
348#627—68no—
349#626—68no—
350#626—124no—
351#624—68no—
352D3×Dic3—68no—
353D3×Dic3—124no—
354#546—271noSylow
355C2×C33—22no—
356C2×C33—22no—
357C2×C33—41no—
358C2×C33C22×D411yescharacteristic
359C2×C33C2×#4111yescharacteristic
360C2×C33H(5,𝔽2)11yescharacteristic
361C3⋊(C3⋊D3)—41no—
362C3×C3⋊D3—22no—
363C3×C3⋊D3—41no—
364C24×C3—24no—
365C24×C3—91no—
366C24×C3D3214yes—
367C24×C3C2×C3⋊D311yescharacteristic
368C23×D3—34no—
369C2×C3×D4—91no—
370C2×C3×D4—91no—
371C2×C3×D4—91no—
372C2×C3×D4—91no—
373C2×C3×D4—184no—
374C22×C3×C4—34no—
375C22×C3×C4—34no—
376C22×C3×C4—91no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—616no—
382C2×#67—94no—
383C2×#67—94no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—94no—
387C2×#67—91no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—184no—
391C2×#67—184no—
392C2×#67—184no—
393C22×Dic3—34no—
394C22×Dic3—91no—
395C22×Dic3—91no—
396C22×Dic3C2×C3⋊D311yescharacteristic, complemented
397C22×Dic3C2×C3⋊D311yescharacteristic, complemented
398#237—184no—
399#235—1816no—
400C2×D12—94no—
401C2×D12—94no—
402C2×C4×D3—94no—
403C2×C4×D3—94no—
404C2×C4×D3—91no—
405C2×C4×D3—94no—
406C2×Dic6—94no—
407C2×Dic6—91no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412#217—94no—
413#217—94no—
414#217—94no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—91no—
421#217—91no—
422#217—184no—
423#217—184no—
424#217—184no—
425#217C2×C3⋊D311yescharacteristic
426#217C2×C3⋊D311yescharacteristic
427#217C2×C3⋊D311yescharacteristic, complemented
428#217C2×C3⋊D311yescharacteristic, complemented
429(C2×D3)⋊C4—94no—
430(C2×D3)⋊C4—94no—
431(C2×D3)⋊C4—94no—
432(C2×D3)⋊C4—94no—
433(C2×D3)⋊C4—94no—
434(C2×D3)⋊C4—91no—
435C4⋊Dic3—94no—
436C4⋊Dic3—91no—
437Dic3⋊C4—94no—
438Dic3⋊C4—94no—
439Dic3⋊C4—94no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442Dic3⋊C4—91no—
443C4×Dic3—94no—
444C4×Dic3—91no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—28no—
450C22×C32—21no—
451C22×C32—24no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—24no—
455C22×C32—28no—
456C22×C32—28no—
457C22×C32—24no—
458C22×C32—24no—
459C22×C32—24no—
460C22×C32—24no—
461C22×C32—24no—
462C22×C32—24no—
463C22×C32—44no—
464C22×C32—44no—
465C22×C32—44no—
466C22×C32—44no—
467C22×C32—44no—
468C22×C32—44no—
469C22×C32—44no—
470C22×C32—416no—
471C22×C32—432no—
472C22×C32#23518yescomplemented
473C22×C32D3×D418yes—
474C22×C32#23712yescomplemented
475C22×C32C2×#6712yes—
476C22×C32C23×D314yes—
477C22×C32C23×D311yescharacteristic
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—44no—
484C2×C3⋊D3—61no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—61no—
487C2×C3⋊D3—64no—
488C2×C3⋊D3—64no—
489C2×C3⋊D3—64no—
490C2×C3⋊D3—124no—
491C2×C3⋊D3—124no—
492C2×C3⋊D3—124no—
493C2×C3⋊D3C2×#6712yes—
494C2×C3×D3—38no—
495C2×C3×D3—64no—
496C2×C3×D3—64no—
497C2×C3×D3—64no—
498C2×C3×D3—64no—
499C2×C3×D3—64no—
500C2×C3×D3—1216no—
501C32×C4—61no—
502C32×C4—61no—
503C32×C4—61no—
504C32×C4—61no—
505C3⋊Dic3—21no—
506C3⋊Dic3—61no—
507C3⋊Dic3—61no—
508C3⋊Dic3—61no—
509C3⋊Dic3—64no—
510C3⋊Dic3—64no—
511C3⋊Dic3—64no—
512C3⋊Dic3—124no—
513C3⋊Dic3—124no—
514C3⋊Dic3—124no—
515C3⋊Dic3C2×#6712yes—
516C3×Dic3—24no—
517C3×Dic3—24no—
518C3×Dic3—24no—
519C3×Dic3—24no—
520C3×Dic3—38no—
521C3×Dic3—64no—
522C2×#41—271no—
523C22×D4—91no—
524#124—271no—
525#123—271no—
526#123—271no—
527C22⋊Q8—271no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—271no—
534C4×D4—271no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—271no—
537C33#54611yescharacteristic, complemented, Sylow
538C23×C3—28no—
539C23×C3—28no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—24no—
543C23×C3—24no—
544C23×C3—24no—
545C23×C3—48no—
546C23×C3—48no—
547C23×C3—44no—
548C23×C3—41no—
549C23×C3—48no—
550C23×C3—91no—
551C23×C3—91no—
552C23×C3—182no—
553C23×C3—182no—
554C23×C3—361no—
555C23×C3C2×D3214yes—
556C23×C3C2×D3214yes—
557C23×C3C2×D3214yes—
558C23×C3C22×C3⋊D311yescharacteristic
559C23×C3C22×C3⋊D311yescharacteristic
560C23×C3C22×C3⋊D311yescharacteristic
561C22×D3—34no—
562C22×D3—34no—
563C22×D3—68no—
564C22×D3—68no—
565C22×D3—94no—
566C22×D3—91no—
567C22×D3—124no—
568C22×D3—184no—
569C3×D4—94no—
570C3×D4—182no—
571C3×D4—182no—
572C3×D4—182no—
573C2×C3×C4—34no—
574C2×C3×C4—34no—
575C2×C3×C4—34no—
576C2×C3×C4—34no—
577C2×C3×C4—68no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—124no—
581C2×C3×C4—182no—
582#67—316no—
583#67—68no—
584#67—68no—
585#67—68no—
586#67—182no—
587#67—188no—
588#67—188no—
589#67—182no—
590#67—182no—
591#67—368no—
592#67—368no—
593#67—361no—
594#67—364no—
595#67—361no—
596#67—368no—
597C2×Dic3—22no—
598C2×Dic3—34no—
599C2×Dic3—34no—
600C2×Dic3—41no—
601C2×Dic3—68no—
602C2×Dic3—94no—
603C2×Dic3—94no—
604C2×Dic3—94no—
605C2×Dic3—91no—
606C2×Dic3—91no—
607C2×Dic3—91no—
608C2×Dic3—184no—
609C2×Dic3—184no—
610C2×Dic3—184no—
611C2×Dic3—182no—
612C2×Dic3—361no—
613C2×Dic3C22×C3⋊D311yescharacteristic
614C2×Dic3C22×C3⋊D311yescharacteristic
615C2×Dic3C22×C3⋊D311yescharacteristic
616C2×Dic3C22×C3⋊D311yescharacteristic
617D12—188no—
618D12—364no—
619C4×D3—182no—
620C4×D3—188no—
621C4×D3—188no—
622C4×D3—364no—
623Dic6—182no—
624Dic6—188no—
625C2×C32—22no—
626C2×C32—22no—
627C2×C32—24no—
628C2×C32—24no—
629C2×C32—24no—
630C2×C32—28no—
631C2×C32—28no—
632C2×C32—48no—
633C2×C32—48no—
634C2×C32—48no—
635C2×C32—44no—
636C2×C32—41no—
637C2×C32C2×#23514yes—
638C2×C32C2×D3×D414yes—
639C2×C32C2×#23711yescharacteristic
640C2×C32#100414yes—
641C2×C32#100411yescharacteristic
642C2×C32C22×#6711yescharacteristic
643C3⋊D3—22no—
644C3⋊D3—41no—
645C3⋊D3—121no—
646C3⋊D3—124no—
647C3⋊D3—244no—
648C3×D3—68no—
649C3×D3—124no—
650C24—91no—
651C24D3×C3⋊D311yescharacteristic
652#41—544no—
653C2×Q8—271no—
654C2×D4—91no—
655C2×D4—91no—
656C2×D4—91no—
657C2×D4—91no—
658C2×D4—184no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—271no—
663C2×D4—271no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—91no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—271no—
671C4⋊C4—271no—
672C4⋊C4—271no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—31no—
677C22⋊C4—31no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4—271no—
686C42—271no—
687C22×C3—24no—
688C22×C3—24no—
689C22×C3—24no—
690C22×C3—24no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—28no—
696C22×C3—24no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—24no—
703C22×C3—28no—
704C22×C3—28no—
705C22×C3—44no—
706C22×C3—44no—
707C22×C3—44no—
708C22×C3—44no—
709C22×C3—44no—
710C22×C3—44no—
711C22×C3—44no—
712C22×C3—416no—
713C22×C3—432no—
714C22×C3—92no—
715C22×C3—181no—
716C22×C3—181no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3—181no—
720C22×C3—364no—
721C22×C3#380418yescomplemented
722C22×C3D3×#6718yes—
723C22×C3#382812yescomplemented
724C22×C3D4×C3⋊D312yes—
725C22×C3C22×D3214yes—
726C22×C3C23×C3⋊D311yescharacteristic
727C2×D3—38no—
728C2×D3—64no—
729C2×D3—64no—
730C2×D3—64no—
731C2×D3—64no—
732C2×D3—64no—
733C2×D3—1216no—
734C2×D3—184no—
735C2×D3—184no—
736C2×D3—184no—
737C2×D3—181no—
738C2×D3—181no—
739C2×D3—181no—
740C2×D3—364no—
741C2×D3—364no—
742C2×D3—364no—
743C3×C4—64no—
744C3×C4—64no—
745C3×C4—64no—
746C3×C4—64no—
747C3×C4—92no—
748C3×C4—181no—
749Dic3—21no—
750Dic3—21no—
751Dic3—21no—
752Dic3—21no—
753Dic3—38no—
754Dic3—64no—
755Dic3—184no—
756Dic3—184no—
757Dic3—184no—
758Dic3—181no—
759Dic3—181no—
760Dic3—181no—
761Dic3—364no—
762Dic3—364no—
763Dic3—364no—
764C32—24no—
765C32#549014yescomplemented
766C32#580611yescharacteristic, complemented
767C23—22no—
768C23—22no—
769C23—41no—
770C23—91no—
771C23—91no—
772C23—182no—
773C23—182no—
774C23—271no—
775C23—361no—
776C23C2×D3×C3⋊D311yescharacteristic
777C23C2×D3×C3⋊D311yescharacteristic
778C23C2×D3×C3⋊D311yescharacteristic
779Q8—542no—
780D4—94no—
781D4—182no—
782D4—182no—
783D4—182no—
784D4—542no—
785D4—542no—
786D4—542no—
787D4—1081no—
788D4—1081no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—31no—
793C2×C4—62no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—121no—
797C2×C4—182no—
798C2×C4—271no—
799C2×C4—271no—
800C2×C4—271no—
801C2×C4—542no—
802C2×C4—542no—
803C2×C4—1081no—
804C2×C3—22no—
805C2×C3—22no—
806C2×C3—28no—
807C2×C3—28no—
808C2×C3—24no—
809C2×C3—24no—
810C2×C3—24no—
811C2×C3—48no—
812C2×C3—48no—
813C2×C3—48no—
814C2×C3—41no—
815C2×C3—44no—
816C2×C3—182no—
817C2×C3—361no—
818C2×C3C2×#380414yes—
819C2×C3C2×D3×#6714yes—
820C2×C3#6433014yes—
821C2×C3C2×#382811yescharacteristic
822C2×C3C2×D4×C3⋊D311yescharacteristic
823C2×C3#6436111yescharacteristic
824D3—68no—
825D3—124no—
826D3—361no—
827D3—364no—
828D3—724no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—44no—
837C22—92no—
838C22—181no—
839C22—181no—
840C22—181no—
841C22—181no—
842C22—181no—
843C22—364no—
844C22—541no—
845C22—541no—
846C22—541no—
847C22#8903112yescomplemented
848C22C3⋊D3×#6712yes—
849C22C22×D3×C3⋊D311yescharacteristic
850C4—61no—
851C4—61no—
852C4—61no—
853C4—61no—
854C4—92no—
855C4—181no—
856C4—541no—
857C4—541no—
858C4—541no—
859C3—24no—
860C3#1059549314yescomplemented
861C3#1059596111yescharacteristic, complemented
862C2—22no—
863C2—22no—
864C2—41no—
865C2—182no—
866C2—361no—
867C2—1081no—
868C2C2×#8903111yescharacteristic
869C2C2×C3⋊D3×#6711yescharacteristic
870C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC24×C33C22
hypercenterC24D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×C3×#638C2semidirect
2. C2×#89031C2semidirect
3. #11723994C2semidirect
4. C2×C32×#217C2semidirect
5. #11723641C2semidirect
6. #11723636C2semidirect
7. #11723632C2semidirect
8. #11723624C2semidirect
9. #11723623C2semidirect
10. #11723622C2semidirect
11. #11723621C2semidirect
12. C3⋊D3×#217C2semidirect
13. Dic3×#638C2semidirect
14. #11723605C2semidirect
15. #11723591C2semidirect
21. C2×#6312C22semidirect
22. C2×#6312C22semidirect
29. C22×C32×Dic3C22semidirect
30. C22×C32×Dic3C22semidirect
31. C2×#6293C22semidirect
32. C2×#6292C22semidirect
33. C2×#6292C22semidirect
34. C2×#6289C22semidirect
36. C2×Dic3×C3⋊D3C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
39. #88864C22semidirect
40. #88864C22semidirect
43. C32×#217C22semidirect
44. C32×#217C22semidirect
45. #88807C22semidirect
46. #88806C22semidirect
47. #88806C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88804C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. #88803C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
55. C22×#638D3semidirect
74. C2×C3×#217D3semidirect
107. C3×#638D4semidirect
160. C22×C3×Dic3C2×D3semidirect
161. C22×C3×Dic3C2×D3semidirect
194. C3×#217C2×D3semidirect
195. C3×#217C2×D3semidirect
215. C22×C33#41semidirect
246. C2×#217C3⋊D3semidirect
316. #638#67semidirect
396. C22×Dic3C2×C3⋊D3semidirect
397. C22×Dic3C2×C3⋊D3semidirect
427. #217C2×C3⋊D3semidirect
428. #217C2×C3⋊D3semidirect
472. C22×C32#235semidirect
474. C22×C32#237semidirect
537. C33#546semidirect
721. C22×C3#3804semidirect
723. C22×C3#3828semidirect
765. C32#5490semidirect
766. C32#5806semidirect
847. C22#89031semidirect
860. C3#10595493semidirect
861. C3#10595961semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C2×#890312
#117239942
C2×C32×#2172
#117236412
#117236362
#117236322
#117236242
#117236232
#117236222
#117236212
C3⋊D3×#2172
Dic3×#6382
#117236052
#117235912
#105959613
#105954933