Finite Group Databasebeta

← #13175503

Subgroups — #13175503

Order 1728.

2064 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89029C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723927C211yesmaximal, characteristic, complemented
4C3×#64095C211yesmaximal, characteristic, complemented
5C32×#67⋊C4C211yesmaximal, characteristic, complemented
6#11723632C211yesmaximal, characteristic, complemented
7C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8#11723534C211yesmaximal, characteristic, complemented
9#11723514C211yesmaximal, characteristic, complemented
10#11723485C211yesmaximal, characteristic, complemented
11#11723483C211yesmaximal, characteristic, complemented
12#11723480C211yesmaximal, characteristic, complemented
13#11723479C211yesmaximal, characteristic, complemented
14D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
15#11723471C211yesmaximal, characteristic, complemented
16#10596026—31nomaximal
17#10594077—34nomaximal
18C2×#6312C2211yescharacteristic
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×#6293C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×#6289C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic
32#89029—24no—
33#89028—24no—
34C2×D3×C3⋊Dic3C2211yescharacteristic
35C2×D3×C3⋊Dic3C2211yescharacteristic
36C33×C22⋊C4C2211yescharacteristic
37#88859C2211yescharacteristic
38#88859C2211yescharacteristic
39C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
40C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
41C3×#3752C2211yescharacteristic
42C3×#3752C2211yescharacteristic
43C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
44C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×C4×Dic3C2211yescharacteristic
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic
49Dic3⋊(C3⋊Dic3)C2211yescharacteristic
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic
51Dic3⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3⋊(C3⋊Dic3)C2211yescharacteristic
53#88804C2211yescharacteristic
54#88803C2211yescharacteristic
55C2×#3830—31no—
56C2×#3830—31no—
57C2×#3805—34no—
58C2×#3804—34no—
59C32×C4×D4—31no—
60#64139—31no—
61#64139—31no—
62C2×C4⋊(C3⋊Dic3)—31no—
63C2×C4⋊(C3⋊Dic3)—31no—
64#64106—31no—
65#64106—31no—
66#64095—31no—
67#64095—31no—
68#64095—31no—
69#64095—34no—
70#64095—64no—
71#64095D311yescharacteristic, complemented
72C4×C4⋊(C3⋊D3)—31no—
73#64078—31no—
74C3×#886—34no—
75C3×#67⋊C4D314yescomplemented
76#63978—34no—
77C2×Dic3⋊Dic3—34no—
78#63918—34no—
79#63906—34no—
80#63895—34no—
81#63893—34no—
82#63891—34no—
83#63890—34no—
84D3×C4⋊Dic3—34no—
85#63880—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92#6312—22no—
93C2×C3⋊(C3⋊Dic3)—22no—
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C3×#638—22no—
98C2×C3×C3⋊Dic3—22no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C32×#67D414yescomplemented
103C2×C32×Dic3—22no—
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C32×C4×D3—22no—
108#6293—22no—
109#6293—22no—
110#6292—22no—
111#6291—22no—
112#6290—22no—
113#6289—22no—
114Dic3×C3⋊D3—22no—
115D3×C3⋊Dic3—22no—
116D3×C3⋊Dic3—22no—
117#5655—91no—
118#5555—94no—
119C2×C32×D4—31no—
120C22×C32×C4—31no—
121C22×C32×C4—31no—
122C2×#638—31no—
123C2×#638—34no—
124C2×#638—31no—
125C2×#638—31no—
126C2×#638—64no—
127C2×#638C2×D311yescharacteristic
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—34no—
130C22×C3⋊Dic3—31no—
131C22×C3⋊Dic3—31no—
132C22×C3⋊Dic3—64no—
133C22×C3⋊Dic3C2×D311yescharacteristic
134#3830—64no—
135#3830—64no—
136C2×C4⋊(C3⋊D3)—31no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—31no—
139C2×#634—31no—
140C2×#634—31no—
141C2×C3×#67—34no—
142C2×C3×#67C2×D314yes—
143C22×C3×Dic3—34no—
144C22×C3×Dic3C2×D314yes—
145C2×C3×C4×D3C2×D314yes—
146C2×#627—34no—
147C2×#627—34no—
148C2×#626—34no—
149C2×#626—34no—
150C2×#625—34no—
151C2×#624—34no—
152#3805—616no—
153#3804—616no—
154C2×D3×Dic3—34no—
155C2×D3×Dic3—34no—
156C2×D3×Dic3—34no—
157C32×C4⋊C4—31no—
158C32×C22⋊C4—24no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4C2×D314yes—
161C32×C22⋊C4C2×D311yescharacteristic
162C32×C42—31no—
163#3752—31no—
164#3752—31no—
165#3752—31no—
166#3752—34no—
167#3752—34no—
168#3752—31no—
169#3752—64no—
170#3752—64no—
171#3752C2×D311yescharacteristic
172#3752C2×D311yescharacteristic
173C4⋊(C3⋊Dic3)—31no—
174C4⋊(C3⋊Dic3)—31no—
175C4⋊(C3⋊Dic3)—34no—
176C4⋊(C3⋊Dic3)—34no—
177C4⋊(C3⋊Dic3)—31no—
178C4⋊(C3⋊Dic3)—31no—
179C4⋊(C3⋊Dic3)—31no—
180C4⋊(C3⋊Dic3)—31no—
181C4⋊(C3⋊Dic3)—31no—
182C4⋊(C3⋊Dic3)—64no—
183C4⋊(C3⋊Dic3)—64no—
184C4⋊(C3⋊Dic3)C2×D311yescharacteristic
185C4⋊(C3⋊Dic3)C2×D311yescharacteristic
186C3×(C2×D3)⋊C4—34no—
187C3×(C2×D3)⋊C4—34no—
188C3×(C2×D3)⋊C4C2×D314yes—
189C3×C4⋊Dic3—34no—
190C3×C4⋊Dic3—34no—
191C3×Dic3⋊C4C2×D314yes—
192C3×C4×Dic3C2×D314yes—
193Dic3⋊Dic3—34no—
194Dic3⋊Dic3—34no—
195Dic3⋊Dic3—34no—
196Dic3⋊Dic3—34no—
197Dic3⋊Dic3—34no—
198#3722—34no—
199(C2×D3)⋊Dic3—34no—
200C22×C33—21no—
201C22×C33—21no—
202C22×C33C2×D412yes—
203C22×C33C2411yescharacteristic
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3⋊(C3⋊D3)—21no—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C3×C3⋊D3—21no—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3C2×D412yes—
213C33×C4—21no—
214C33×C4—21no—
215C3⋊(C3⋊Dic3)—21no—
216C3⋊(C3⋊Dic3)—21no—
217C3⋊(C3⋊Dic3)—21no—
218C3×C3⋊Dic3—21no—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3—21no—
221C32×Dic3—21no—
222C32×Dic3C2×D412yes—
223C32×Dic3#4112yescomplemented
224C2×#237—94no—
225C2×#237—94no—
226C2×#237—91no—
227C2×#235—91no—
228C3×#123—91no—
229C3×C4×D4—34no—
230#939—91no—
231#930—94no—
232#930—94no—
233C2×C4⋊Dic3—94no—
234C2×C4⋊Dic3—94no—
235C2×Dic3⋊C4—91no—
236#897—94no—
237#897—94no—
238#896—91no—
239#894—91no—
240D3×C4⋊C4—91no—
241#888—91no—
242#886—34no—
243#886—94no—
244#886—94no—
245#886—94no—
246#886—91no—
247#886—184no—
248#884—91no—
249#883—91no—
250#67⋊C4—91no—
251#67⋊C4C3⋊D311yescharacteristic, complemented
252#878—91no—
253C4×D12—94no—
254#869—94no—
255C23×C32—24no—
256C23×C32—31no—
257C23×C32C22×D314yes—
258C23×C32C22×D311yescharacteristic
259C22×C3⋊D3—31no—
260C22×C3⋊D3—34no—
261C22×C3⋊D3—64no—
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3×D3—34no—
264C22×C3×D3C22×D314yes—
265C32×D4—34no—
266C2×C32×C4—24no—
267C2×C32×C4—24no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4—31no—
271C2×C32×C4—62no—
272C2×C32×C4—62no—
273C2×C32×C4C22×D314yes—
274C2×C32×C4C22×D314yes—
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277#638—22no—
278#638—62no—
279#638—62no—
280#638—62no—
281#638—68no—
282#638—128no—
283C2×C3⋊Dic3—22no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—34no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—34no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3—64no—
293C2×C3⋊Dic3—62no—
294C2×C3⋊Dic3—62no—
295C2×C3⋊Dic3—62no—
296C2×C3⋊Dic3—68no—
297C2×C3⋊Dic3—128no—
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C4⋊(C3⋊D3)—62no—
302C4×C3⋊D3—62no—
303C4×C3⋊D3—62no—
304#634—62no—
305#634—62no—
306C3×#67—68no—
307C3×#67D12116yescomplemented
308C2×C3×Dic3—28no—
309C2×C3×Dic3—34no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—68no—
313C2×C3×Dic3C22×D314yes—
314C2×C3×Dic3C22×D314yes—
315C2×C3×Dic3C22×D314yes—
316C3×C4×D3—28no—
317#627—68no—
318#627—68no—
319#626—68no—
320#626—68no—
321#625—68no—
322#624—68no—
323D3×Dic3—68no—
324D3×Dic3—68no—
325D3×Dic3—68no—
326#547—271noSylow
327C2×C33—22no—
328C2×C33C22×D411yescharacteristic
329C2×C33C2×#4111yescharacteristic
330C2×C332−1+411yescharacteristic
331C3⋊(C3⋊D3)—41no—
332C3×C3⋊D3—41no—
333C32×D3—22no—
334C2×C3×D4—34no—
335C2×C3×D4—91no—
336C22×C3×C4—34no—
337C22×C3×C4—34no—
338C22×C3×C4—91no—
339C2×#67—34no—
340C2×#67—94no—
341C2×#67—94no—
342C2×#67—94no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—184no—
347C2×#67C2×C3⋊D311yescharacteristic
348C22×Dic3—34no—
349C22×Dic3—94no—
350C22×Dic3—94no—
351C22×Dic3—94no—
352C22×Dic3—91no—
353C22×Dic3—91no—
354C22×Dic3—184no—
355C22×Dic3C2×C3⋊D311yescharacteristic
356#237—1816no—
357#237—1816no—
358#237—184no—
359#235—184no—
360C2×D12—94no—
361C2×D12—91no—
362C2×C4×D3—94no—
363C2×C4×D3—94no—
364C2×C4×D3—91no—
365C2×C4×D3—91no—
366C2×C4×D3—91no—
367C2×C4×D3C2×C3⋊D311yescharacteristic
368C2×Dic6—94no—
369C2×Dic6—94no—
370C2×Dic6—91no—
371C2×Dic6—91no—
372C3×C4⋊C4—34no—
373C3×C4⋊C4—91no—
374C3×C4⋊C4—91no—
375C3×C22⋊C4—24no—
376C3×C22⋊C4—34no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4D3214yes—
380C3×C22⋊C4C2×C3⋊D311yescharacteristic
381C3×C42—34no—
382#217—91no—
383(C2×D3)⋊C4—34no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—94no—
388(C2×D3)⋊C4—94no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—184no—
393(C2×D3)⋊C4—184no—
394(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
395C4⋊Dic3—34no—
396C4⋊Dic3—34no—
397C4⋊Dic3—94no—
398C4⋊Dic3—94no—
399C4⋊Dic3—94no—
400C4⋊Dic3—94no—
401C4⋊Dic3—94no—
402C4⋊Dic3—94no—
403C4⋊Dic3—94no—
404C4⋊Dic3—91no—
405C4⋊Dic3—91no—
406C4⋊Dic3—184no—
407C4⋊Dic3—184no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4C2×C3⋊D311yescharacteristic
414C4×Dic3C2×C3⋊D311yescharacteristic
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—24no—
418C22×C32—28no—
419C22×C32—24no—
420C22×C32—24no—
421C22×C32—32no—
422C22×C32—44no—
423C22×C32—44no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32C2×D1218yes—
427C22×C32D3×D412yes—
428C22×C32C23×D314yes—
429C22×C32C23×D311yescharacteristic
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3⋊D3—64no—
437C2×C3⋊D3—64no—
438C2×C3⋊D3—64no—
439C2×C3⋊D3—124no—
440C2×C3⋊D3—124no—
441C2×C3⋊D3—124no—
442C2×C3×D3—24no—
443C2×C3×D3—24no—
444C2×C3×D3—64no—
445C2×C3×D3—64no—
446C2×C3×D3—64no—
447C2×C3×D3C2×D1218yes—
448C32×C4—21no—
449C32×C4—21no—
450C32×C4—24no—
451C32×C4—24no—
452C32×C4—32no—
453C32×C4—32no—
454C32×C4—44no—
455C32×C4—44no—
456C32×C4—61no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—61no—
461C3⋊Dic3—61no—
462C3⋊Dic3—61no—
463C3⋊Dic3—64no—
464C3⋊Dic3—64no—
465C3⋊Dic3—64no—
466C3⋊Dic3—124no—
467C3⋊Dic3—124no—
468C3⋊Dic3—124no—
469C3×Dic3—24no—
470C3×Dic3—64no—
471C3×Dic3—64no—
472C3×Dic3—64no—
473C3×Dic3C2×D1218yes—
474C3×Dic3#23718yescomplemented
475C2×#41—271no—
476C2×#41—271no—
477C4⋊Q8—271no—
478#123—91no—
479#123—271no—
480#123—271no—
481#123—271no—
482C22⋊Q8—271no—
483C22⋊Q8—271no—
484#121—271no—
485#121—271no—
486C4×D4—31no—
487C4×D4—271no—
488C2×C4⋊C4—271no—
489C2×C4⋊C4—271no—
490C33#54711yescharacteristic, complemented, Sylow
491C23×C3—24no—
492C23×C3—34no—
493C23×C3—91no—
494C23×C3C2×D3214yes—
495C23×C3C22×C3⋊D311yescharacteristic
496C22×D3—34no—
497C22×D3—94no—
498C22×D3—91no—
499C22×D3—184no—
500C22×D3C22×C3⋊D311yescharacteristic
501C3×D4—316no—
502C3×D4—182no—
503C2×C3×C4—24no—
504C2×C3×C4—24no—
505C2×C3×C4—34no—
506C2×C3×C4—34no—
507C2×C3×C4—34no—
508C2×C3×C4—68no—
509C2×C3×C4—68no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—182no—
514C2×C3×C4C2×D3214yes—
515C2×C3×C4C2×D3214yes—
516C2×C3×C4C22×C3⋊D311yescharacteristic
517C2×C3×C4C22×C3⋊D311yescharacteristic
518#67—68no—
519#67—188no—
520#67—188no—
521#67—188no—
522#67—182no—
523#67—182no—
524#67—182no—
525#67—368no—
526#67C4⋊(C3⋊D3)14yescomplemented
527C2×Dic3—22no—
528C2×Dic3—34no—
529C2×Dic3—34no—
530C2×Dic3—34no—
531C2×Dic3—68no—
532C2×Dic3—94no—
533C2×Dic3—94no—
534C2×Dic3—94no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—184no—
539C2×Dic3—184no—
540C2×Dic3—184no—
541C2×Dic3—188no—
542C2×Dic3—188no—
543C2×Dic3—188no—
544C2×Dic3—182no—
545C2×Dic3—182no—
546C2×Dic3—368no—
547C2×Dic3C22×C3⋊D311yescharacteristic
548C2×Dic3C22×C3⋊D311yescharacteristic
549C2×Dic3C22×C3⋊D311yescharacteristic
550D12—188no—
551D12—182no—
552C4×D3—22no—
553C4×D3—188no—
554C4×D3—188no—
555C4×D3—182no—
556C4×D3—182no—
557C4×D3—182no—
558Dic6—188no—
559Dic6—188no—
560Dic6—182no—
561Dic6—182no—
562C2×C32—22no—
563C2×C32—24no—
564C2×C32—24no—
565C2×C32—24no—
566C2×C32—28no—
567C2×C32—48no—
568C2×C32—62no—
569C2×C32C22×D1214yes—
570C2×C32C2×D3×D411yescharacteristic
571C2×C32C2×#23714yes—
572C2×C32D3×#4111yescharacteristic
573C2×C32#101014yes—
574C2×C32#101011yescharacteristic
575C3⋊D3—41no—
576C3⋊D3—121no—
577C3⋊D3—124no—
578C3⋊D3—244no—
579C3×D3—28no—
580C3×D3—124no—
581#41—544no—
582#41—544no—
583C2×Q8—271no—
584C2×Q8—271no—
585C2×D4—31no—
586C2×D4—91no—
587C2×D4—271no—
588C2×D4—271no—
589C2×D4—271no—
590C2×D4—271no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—91no—
594C22×C4—271no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C22×C4—271no—
599C4⋊C4—31no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C4⋊C4—271no—
608C4⋊C4—271no—
609C22⋊C4—31no—
610C22⋊C4—91no—
611C22⋊C4—91no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4D3×C3⋊D311yescharacteristic
617C42—31no—
618C22×C3—24no—
619C22×C3—24no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—24no—
623C22×C3—28no—
624C22×C3—38no—
625C22×C3—44no—
626C22×C3—44no—
627C22×C3—64no—
628C22×C3—64no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3D3×D1218yes—
633C22×C3C2×C4⋊(C3⋊D3)12yes—
634C22×C3C22×D3214yes—
635C22×C3C23×C3⋊D311yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—64no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—184no—
642C2×D3—184no—
643C2×D3—184no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—364no—
648C2×D3—364no—
649C2×D3—364no—
650C2×D3C2×C4⋊(C3⋊D3)12yes—
651C3×C4—24no—
652C3×C4—24no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—38no—
656C3×C4—38no—
657C3×C4—44no—
658C3×C4—44no—
659C3×C4—64no—
660C3×C4—181no—
661C3×C4—181no—
662C3×C4—181no—
663Dic3—21no—
664Dic3—64no—
665Dic3—64no—
666Dic3—64no—
667Dic3—184no—
668Dic3—184no—
669Dic3—184no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—364no—
674Dic3—364no—
675Dic3—364no—
676Dic3C2×C4⋊(C3⋊D3)12yes—
677Dic3#383012yescomplemented
678C32—24no—
679C32#555514yescomplemented
680C32#565511yescharacteristic, complemented
681C23—31no—
682C23—91no—
683C23—271no—
684C23C2×D3×C3⋊D311yescharacteristic
685Q8—542no—
686Q8—542no—
687D4—34no—
688D4—182no—
689D4—542no—
690D4—542no—
691D4—542no—
692D4—542no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—91no—
699C2×C4—91no—
700C2×C4—91no—
701C2×C4—182no—
702C2×C4—271no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—542no—
706C2×C4—542no—
707C2×C4—542no—
708C2×C4—542no—
709C2×C4—542no—
710C2×C4C2×D3×C3⋊D311yescharacteristic
711C2×C4C2×D3×C3⋊D311yescharacteristic
712C2×C3—28no—
713C2×C3—22no—
714C2×C3—24no—
715C2×C3—24no—
716C2×C3—24no—
717C2×C3—48no—
718C2×C3—68no—
719C2×C3—361no—
720C2×C3C2×D3×D1214yes—
721C2×C3#6430914yes—
722C2×C3D3×#23714yes—
723C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
724C2×C3C2×#383011yescharacteristic
725C2×C3#6436711yescharacteristic
726D3—22no—
727D3—124no—
728D3—364no—
729D3—361no—
730D3—724no—
731C22—21no—
732C22—21no—
733C22—32no—
734C22—61no—
735C22—61no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—541no—
740C22—541no—
741C22—541no—
742C22D3×C4⋊(C3⋊D3)12yes—
743C22C22×D3×C3⋊D311yescharacteristic
744C4—21no—
745C4—21no—
746C4—32no—
747C4—32no—
748C4—61no—
749C4—181no—
750C4—181no—
751C4—181no—
752C4—541no—
753C4—541no—
754C4—541no—
755C3—24no—
756C3#1059407714yescomplemented
757C3#1059602611yescharacteristic, complemented
758C2—22no—
759C2—62no—
760C2—361no—
761C2—1081no—
762C2C2×D3×C4⋊(C3⋊D3)11yescharacteristic
763C2#1172458211yescharacteristic
764C2D3×#383011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#547
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89029C2semidirect
2. C2×#89028C2semidirect
3. #11723927C2semidirect
4. C3×#64095C2semidirect
5. C32×#67⋊C4C2semidirect
6. #11723632C2semidirect
7. C2×Dic3⋊(C3⋊Dic3)C2semidirect
8. #11723534C2semidirect
9. #11723514C2semidirect
10. #11723485C2semidirect
11. #11723483C2semidirect
12. #11723480C2semidirect
13. #11723479C2semidirect
14. D3×C4⋊(C3⋊Dic3)C2semidirect
15. #11723471C2semidirect
71. #64095D3semidirect
75. C3×#67⋊C4D3semidirect
102. C32×#67D4semidirect
223. C32×Dic3#41semidirect
251. #67⋊C4C3⋊D3semidirect
307. C3×#67D12semidirect
474. C3×Dic3#237semidirect
490. C33#547semidirect
526. #67C4⋊(C3⋊D3)semidirect
677. Dic3#3830semidirect
679. C32#5555semidirect
680. C32#5655semidirect
756. C3#10594077semidirect
757. C3#10596026semidirect

Maximal subgroups

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

subgroupindex
C2×#890292
C2×#890282
#117239272
C3×#640952
C32×#67⋊C42
#117236322
C2×Dic3⋊(C3⋊Dic3)2
#117235342
#117235142
#117234852
#117234832
#117234802
#117234792
D3×C4⋊(C3⋊Dic3)2
#117234712
#105960263
#105940773