Finite Group Databasebeta

← #13175505

Subgroups — #13175505

Order 1728.

2128 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89031C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723922C211yesmaximal, characteristic, complemented
4C3×#64095C211yesmaximal, characteristic, complemented
5C32×#886C211yesmaximal, characteristic, complemented
6#11723637C211yesmaximal, characteristic, complemented
7C2×#88806C211yesmaximal, characteristic, complemented
8#11723536C211yesmaximal, characteristic, complemented
9#11723527C211yesmaximal, characteristic, complemented
10#11723508C211yesmaximal, characteristic, complemented
11#11723504C211yesmaximal, characteristic, complemented
12#11723503C211yesmaximal, characteristic, complemented
13#11723502C211yesmaximal, characteristic, complemented
14#11723500C211yesmaximal, characteristic, complemented
15#11723422C211yesmaximal, characteristic, complemented
16#10596126—31nomaximal
17#10594083—34nomaximal
18C2×#6312C2211yescharacteristic
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×#6293C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×#6289C2211yescharacteristic
31C2×#6289C2211yescharacteristic
32#89031—24no—
33C2×Dic3×C3⋊D3C2211yescharacteristic
34#89028—24no—
35C2×D3×C3⋊Dic3C2211yescharacteristic
36C33×C22⋊C4C2211yescharacteristic
37#88859C2211yescharacteristic
38#88857C2211yescharacteristic
39C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C3×#3752C2211yescharacteristic
42C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
43C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×C4⋊Dic3C2211yescharacteristic
47C32×C4⋊Dic3C2211yescharacteristic
48#88806C2211yescharacteristic
49#88806C2211yescharacteristic
50#88806C2211yescharacteristic
51#88806C2211yescharacteristic
52#88806C2211yescharacteristic
53#88803C2211yescharacteristic
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
55C2×#3830—31no—
56C2×#3828—31no—
57C2×#3804—34no—
58C2×#3804—34no—
59C32×#123—31no—
60#64148—31no—
61C2×#3750—31no—
62#64105—31no—
63#64103—31no—
64C4⋊C4×C3⋊D3—31no—
65#64097—31no—
66#64095D311yescharacteristic, complemented
67#64093—31no—
68#64092—31no—
69#64090—31no—
70#64090—31no—
71#64090—34no—
72#64090—64no—
73#64087—31no—
74C3×#886—34no—
75C3×#886D314yescomplemented
76#63980—34no—
77C2×#3724—34no—
78#63919—34no—
79#63912—34no—
80#63902—34no—
81#63900—34no—
82#63899—34no—
83#63899—34no—
84#63854—34no—
85#63854—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92#6312D414yescomplemented
93C2×C3⋊(C3⋊Dic3)—22no—
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C4×C3⋊(C3⋊D3)—22no—
98C3×#638—22no—
99C2×C3×C3⋊Dic3—22no—
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C32×#67—22no—
104C2×C32×Dic3—22no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108#6293—22no—
109#6293—22no—
110#6292—22no—
111#6291—22no—
112#6290—22no—
113#6289—22no—
114#6289—22no—
115Dic3×C3⋊D3—22no—
116D3×C3⋊Dic3—22no—
117#5655—94no—
118#5655—91no—
119C2×C32×D4—31no—
120C22×C32×C4—31no—
121C2×#638—31no—
122C2×#638—34no—
123C2×#638—31no—
124C2×#638—31no—
125C2×#638—64no—
126C2×#638C2×D311yescharacteristic
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—34no—
129C22×C3⋊Dic3—31no—
130C22×C3⋊Dic3—64no—
131C22×C3⋊Dic3C2×D311yescharacteristic
132#3830—64no—
133#3828—64no—
134C2×C4⋊(C3⋊D3)—31no—
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—34no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—64no—
141C2×#634—31no—
142C2×#634—31no—
143C2×C3×#67—34no—
144C2×C3×#67C2×D314yes—
145C22×C3×Dic3—34no—
146C22×C3×Dic3C2×D314yes—
147C2×#627—34no—
148C2×#627—34no—
149C2×#626—34no—
150C2×#626—34no—
151C2×#625—34no—
152C2×#624—34no—
153C2×#624—34no—
154#3804—616no—
155#3804—616no—
156C2×D3×Dic3—34no—
157C2×D3×Dic3—34no—
158C32×C4⋊C4—31no—
159C32×C4⋊C4—31no—
160C32×C22⋊C4—24no—
161C32×C22⋊C4—31no—
162C32×C22⋊C4—31no—
163C32×C22⋊C4C2×D314yes—
164C32×C22⋊C4C2×D311yescharacteristic
165#3757—31no—
166#3752—31no—
167#3752—31no—
168#3752—34no—
169#3752—64no—
170#3752C2×D311yescharacteristic
171#3752C2×D311yescharacteristic
172C4⋊(C3⋊Dic3)C2×D311yescharacteristic
173C4⋊(C3⋊Dic3)C2×D311yescharacteristic
174#3750—31no—
175#3750—34no—
176#3750—31no—
177#3750—31no—
178#3750—31no—
179#3750—31no—
180#3750—31no—
181#3750—64no—
182C4×C3⋊Dic3—31no—
183C4×C3⋊Dic3—34no—
184C4×C3⋊Dic3—64no—
185C3×(C2×D3)⋊C4—34no—
186C3×(C2×D3)⋊C4—34no—
187C3×(C2×D3)⋊C4C2×D314yes—
188C3×(C2×D3)⋊C4C2×D314yes—
189C3×C4⋊Dic3—34no—
190C3×C4⋊Dic3—34no—
191C3×C4⋊Dic3C2×D314yes—
192C3×C4⋊Dic3C2×D314yes—
193#3724—34no—
194#3724—34no—
195#3724—34no—
196#3724—34no—
197#3724—34no—
198(C2×D3)⋊Dic3—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)C2×D412yes—
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×D3—21no—
213C33×C4—21no—
214C33×C4—21no—
215C3⋊(C3⋊Dic3)—21no—
216C3⋊(C3⋊Dic3)C2×D412yes—
217C3⋊(C3⋊Dic3)#4112yescomplemented
218C3×C3⋊Dic3—21no—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3—21no—
221C32×Dic3—21no—
222C32×Dic3—21no—
223C32×Dic3—21no—
224C2×#237—94no—
225C2×#237—91no—
226C2×#235—94no—
227C2×#235—91no—
228C3×#123—34no—
229C3×#123—91no—
230#939—94no—
231#939—91no—
232C2×Dic3⋊C4—94no—
233C2×Dic3⋊C4—91no—
234#896—94no—
235#896—91no—
236#894—94no—
237#894—91no—
238D3×C4⋊C4—94no—
239D3×C4⋊C4—91no—
240#888—94no—
241#888—91no—
242#886—34no—
243#886C3⋊D311yescharacteristic, complemented
244#884—94no—
245#884—91no—
246#883—94no—
247#883—91no—
248#67⋊C4—94no—
249#67⋊C4—94no—
250#67⋊C4—91no—
251#67⋊C4—91no—
252#67⋊C4—184no—
253#878—94no—
254#878—91no—
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—62no—
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×C4C22×D314yes—
273C2×C32×C4C22×D314yes—
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276#638—22no—
277#638—34no—
278#638—316no—
279#638—616no—
280#638—62no—
281#638—62no—
282C2×C3⋊Dic3—22no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—34no—
287C2×C3⋊Dic3—34no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—64no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3—62no—
293C2×C3⋊Dic3—62no—
294C2×C3⋊Dic3—68no—
295C2×C3⋊Dic3—128no—
296C2×C3⋊Dic3C22×D311yescharacteristic
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C4⋊(C3⋊D3)—62no—
300C4×C3⋊D3—62no—
301C4×C3⋊D3—62no—
302C4×C3⋊D3—62no—
303C4×C3⋊D3—62no—
304C4×C3⋊D3—68no—
305C4×C3⋊D3—128no—
306#634—62no—
307#634—62no—
308C3×#67—28no—
309C3×#67—68no—
310C2×C3×Dic3—28no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—34no—
313C2×C3×Dic3—34no—
314C2×C3×Dic3—68no—
315C2×C3×Dic3C22×D314yes—
316C2×C3×Dic3C22×D314yes—
317C2×C3×Dic3C22×D314yes—
318#627—68no—
319#627—68no—
320#626—68no—
321#626—68no—
322#625—68no—
323#624—68no—
324#624—68no—
325D3×Dic3—68no—
326D3×Dic3—68no—
327#547—271noSylow
328C2×C33—22no—
329C2×C33C22×D411yescharacteristic
330C2×C33C2×#4111yescharacteristic
331C2×C332−1+411yescharacteristic
332C3⋊(C3⋊D3)—22no—
333C3×C3⋊D3—41no—
334C32×D3—41no—
335C2×C3×D4—34no—
336C2×C3×D4—91no—
337C22×C3×C4—34no—
338C22×C3×C4—91no—
339C2×#67—34no—
340C2×#67—94no—
341C2×#67—94no—
342C2×#67—91no—
343C2×#67—94no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—184no—
347C2×#67C2×C3⋊D311yescharacteristic
348C22×Dic3—34no—
349C22×Dic3—94no—
350C22×Dic3—94no—
351C22×Dic3—91no—
352C22×Dic3—91no—
353C22×Dic3—184no—
354C22×Dic3C2×C3⋊D311yescharacteristic
355#237—184no—
356#237—1816no—
357#235—184no—
358#235—1816no—
359C2×D12—94no—
360C2×D12—91no—
361C2×C4×D3—94no—
362C2×C4×D3—94no—
363C2×C4×D3—94no—
364C2×C4×D3—91no—
365C2×C4×D3—94no—
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×C4×D3—91no—
369C2×C4×D3—184no—
370C2×Dic6—94no—
371C2×Dic6—94no—
372C2×Dic6—91no—
373C2×Dic6—91no—
374C3×C4⋊C4—34no—
375C3×C4⋊C4—34no—
376C3×C4⋊C4—91no—
377C3×C4⋊C4—91no—
378C3×C22⋊C4—24no—
379C3×C22⋊C4—34no—
380C3×C22⋊C4—34no—
381C3×C22⋊C4—91no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4D3214yes—
384C3×C22⋊C4C2×C3⋊D311yescharacteristic
385#217—94no—
386#217—91no—
387(C2×D3)⋊C4—34no—
388(C2×D3)⋊C4—34no—
389(C2×D3)⋊C4—94no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—94no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—184no—
394(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
395(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
396C4⋊Dic3—34no—
397C4⋊Dic3—34no—
398C4⋊Dic3C2×C3⋊D311yescharacteristic
399C4⋊Dic3C2×C3⋊D311yescharacteristic
400Dic3⋊C4—94no—
401Dic3⋊C4—94no—
402Dic3⋊C4—94no—
403Dic3⋊C4—94no—
404Dic3⋊C4—94no—
405Dic3⋊C4—94no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—184no—
413C4×Dic3—94no—
414C4×Dic3—91no—
415C4×Dic3—184no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—24no—
419C22×C32—28no—
420C22×C32—24no—
421C22×C32—24no—
422C22×C32—44no—
423C22×C32—44no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32—61no—
427C22×C32D3×D418yes—
428C22×C32D3×D412yes—
429C22×C32C23×D314yes—
430C22×C32C23×D311yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—32no—
435C2×C3⋊D3—38no—
436C2×C3⋊D3—68no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—64no—
440C2×C3⋊D3—64no—
441C2×C3⋊D3—124no—
442C2×C3⋊D3—124no—
443C2×C3×D3—24no—
444C2×C3×D3—24no—
445C2×C3×D3—24no—
446C2×C3×D3—64no—
447C2×C3×D3—64no—
448C2×C3×D3—64no—
449C32×C4—21no—
450C32×C4—21no—
451C32×C4—24no—
452C32×C4—24no—
453C32×C4—44no—
454C32×C4—44no—
455C32×C4—61no—
456C32×C4—61no—
457C32×C4—61no—
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—32no—
462C3⋊Dic3—32no—
463C3⋊Dic3—38no—
464C3⋊Dic3—38no—
465C3⋊Dic3—68no—
466C3⋊Dic3—68no—
467C3⋊Dic3—61no—
468C3⋊Dic3—64no—
469C3⋊Dic3—124no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3—24no—
473C3×Dic3—64no—
474C3×Dic3—64no—
475C3×Dic3—64no—
476C2×#41—271no—
477C2×#41—271no—
478C4⋊Q8—271no—
479#123—31no—
480#123—91no—
481#123—271no—
482#123—271no—
483C22⋊Q8—271no—
484C22⋊Q8—271no—
485#121—271no—
486#121—271no—
487C4×D4—271no—
488C4×D4—271no—
489C2×C4⋊C4—271no—
490C2×C4⋊C4—271no—
491C33#54711yescharacteristic, complemented, Sylow
492C23×C3—24no—
493C23×C3—34no—
494C23×C3—91no—
495C23×C3C2×D3214yes—
496C23×C3C22×C3⋊D311yescharacteristic
497C22×D3—34no—
498C22×D3—94no—
499C22×D3—91no—
500C22×D3—184no—
501C22×D3C22×C3⋊D311yescharacteristic
502C3×D4—68no—
503C3×D4—182no—
504C2×C3×C4—24no—
505C2×C3×C4—24no—
506C2×C3×C4—34no—
507C2×C3×C4—34no—
508C2×C3×C4—34no—
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—22no—
519#67—68no—
520#67—916no—
521#67—94no—
522#67—1816no—
523#67—182no—
524#67—188no—
525#67—182no—
526#67—188no—
527C2×Dic3—22no—
528C2×Dic3—34no—
529C2×Dic3—34no—
530C2×Dic3—34no—
531C2×Dic3—68no—
532C2×Dic3—94no—
533C2×Dic3—94no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—94no—
537C2×Dic3—91no—
538C2×Dic3—184no—
539C2×Dic3—184no—
540C2×Dic3—184no—
541C2×Dic3—182no—
542C2×Dic3—188no—
543C2×Dic3—182no—
544C2×Dic3—188no—
545C2×Dic3—368no—
546C2×Dic3C22×C3⋊D311yescharacteristic
547C2×Dic3C22×C3⋊D311yescharacteristic
548C2×Dic3C22×C3⋊D311yescharacteristic
549D12—188no—
550D12—182no—
551C4×D3—182no—
552C4×D3—182no—
553C4×D3—188no—
554C4×D3—188no—
555C4×D3—182no—
556C4×D3—188no—
557C4×D3—188no—
558C4×D3—182no—
559C4×D3—368no—
560Dic6—182no—
561Dic6—182no—
562Dic6—188no—
563Dic6—188no—
564C2×C32—22no—
565C2×C32—24no—
566C2×C32—24no—
567C2×C32—24no—
568C2×C32—28no—
569C2×C32—48no—
570C2×C32—121no—
571C2×C32C2×D3×D414yes—
572C2×C32C2×D3×D411yescharacteristic
573C2×C32D3×#4114yes—
574C2×C32D3×#4111yescharacteristic
575C2×C32#101014yes—
576C2×C32#101011yescharacteristic
577C3⋊D3—41no—
578C3⋊D3—62no—
579C3⋊D3—68no—
580C3⋊D3—128no—
581C3×D3—44no—
582C3×D3—124no—
583#41—544no—
584#41—544no—
585C2×Q8—271no—
586C2×Q8—271no—
587C2×D4—31no—
588C2×D4—91no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C2×D4—271no—
593C22×C4—31no—
594C22×C4—91no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C22×C4—271no—
599C22×C4—271no—
600C22×C4—271no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C4⋊C4—271no—
608C4⋊C4—271no—
609C4⋊C4—271no—
610C4⋊C4—271no—
611C22⋊C4—31no—
612C22⋊C4—31no—
613C22⋊C4—91no—
614C22⋊C4—91no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C22⋊C4D3×C3⋊D311yescharacteristic
619C42—271no—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—24no—
625C22×C3—28no—
626C22×C3—44no—
627C22×C3—44no—
628C22×C3—64no—
629C22×C3—64no—
630C22×C3—64no—
631C22×C3—181no—
632C22×C3—181no—
633C22×C3—181no—
634C22×C3#380218yes—
635C22×C3D4×C3⋊D312yes—
636C22×C3C22×D3214yes—
637C22×C3C23×C3⋊D311yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—64no—
642C2×D3—64no—
643C2×D3—64no—
644C2×D3—98no—
645C2×D3—92no—
646C2×D3—188no—
647C2×D3—184no—
648C2×D3—184no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—364no—
652C2×D3—364no—
653C3×C4—24no—
654C3×C4—24no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—44no—
658C3×C4—44no—
659C3×C4—64no—
660C3×C4—64no—
661C3×C4—64no—
662C3×C4—181no—
663C3×C4—181no—
664C3×C4—181no—
665Dic3—21no—
666Dic3—21no—
667Dic3—21no—
668Dic3—64no—
669Dic3—64no—
670Dic3—64no—
671Dic3—98no—
672Dic3—98no—
673Dic3—92no—
674Dic3—92no—
675Dic3—188no—
676Dic3—188no—
677Dic3—184no—
678Dic3—181no—
679Dic3—364no—
680C32—24no—
681C32#565514yescomplemented
682C32#565511yescharacteristic, complemented
683C23—31no—
684C23—91no—
685C23—271no—
686C23C2×D3×C3⋊D311yescharacteristic
687Q8—542no—
688Q8—542no—
689D4—62no—
690D4—182no—
691D4—274no—
692D4—542no—
693D4—542no—
694D4—542no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—62no—
699C2×C4—91no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—182no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—542no—
707C2×C4—542no—
708C2×C4—542no—
709C2×C4—542no—
710C2×C4—542no—
711C2×C4—542no—
712C2×C4C2×D3×C3⋊D311yescharacteristic
713C2×C4C2×D3×C3⋊D311yescharacteristic
714C2×C3—22no—
715C2×C3—28no—
716C2×C3—24no—
717C2×C3—24no—
718C2×C3—24no—
719C2×C3—48no—
720C2×C3—124no—
721C2×C3—361no—
722C2×C3C2×#380214yes—
723C2×C3#6430914yes—
724C2×C3#6431214yes—
725C2×C3C2×D4×C3⋊D311yescharacteristic
726C2×C3#41×C3⋊D311yescharacteristic
727C2×C3#6436711yescharacteristic
728D3—41no—
729D3—124no—
730D3—182no—
731D3—188no—
732D3—368no—
733C22—21no—
734C22—21no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—181no—
739C22—181no—
740C22—181no—
741C22—272no—
742C22—541no—
743C22—541no—
744C22#8902612yes—
745C22C22×D3×C3⋊D311yescharacteristic
746C4—21no—
747C4—21no—
748C4—61no—
749C4—61no—
750C4—61no—
751C4—181no—
752C4—181no—
753C4—181no—
754C4—272no—
755C4—272no—
756C4—541no—
757C3—24no—
758C3#1059408314yescomplemented
759C3#1059612611yescharacteristic, complemented
760C2—22no—
761C2—121no—
762C2—361no—
763C2—542no—
764C2C2×#8902611yescharacteristic
765C2#1172458211yescharacteristic
766C2#1172458611yescharacteristic
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×#89031C2semidirect
2. C2×#89028C2semidirect
3. #11723922C2semidirect
4. C3×#64095C2semidirect
5. C32×#886C2semidirect
6. #11723637C2semidirect
7. C2×#88806C2semidirect
8. #11723536C2semidirect
9. #11723527C2semidirect
10. #11723508C2semidirect
11. #11723504C2semidirect
12. #11723503C2semidirect
13. #11723502C2semidirect
14. #11723500C2semidirect
15. #11723422C2semidirect
66. #64095D3semidirect
75. C3×#886D3semidirect
92. #6312D4semidirect
217. C3⋊(C3⋊Dic3)#41semidirect
243. #886C3⋊D3semidirect
491. C33#547semidirect
681. C32#5655semidirect
682. C32#5655semidirect
758. C3#10594083semidirect
759. C3#10596126semidirect

Maximal subgroups

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

subgroupindex
C2×#890312
C2×#890282
#117239222
C3×#640952
C32×#8862
#117236372
C2×#888062
#117235362
#117235272
#117235082
#117235042
#117235032
#117235022
#117235002
#117234222
#105961263
#105940833