Finite Group Databasebeta

← #13148977

Subgroups — #13148977

Order 1728.

954 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×#88640C211yesmaximal, characteristic, complemented
2C2×#88635C211yesmaximal, characteristic, complemented
3#11721750C211yesmaximal, characteristic, complemented
4C9×#896C211yesmaximal, characteristic, complemented
5C3×C4⋊C4×D9C211yesmaximal, characteristic, complemented
6#11721039C211yesmaximal, characteristic, complemented
7#11721033C211yesmaximal, characteristic, complemented
8#11721031C211yesmaximal, characteristic, complemented
9#11721030C211yesmaximal, characteristic, complemented
10#11721002C211yesmaximal, characteristic, complemented
11#11720995C211yesmaximal, characteristic, complemented
12#11720980C211yesmaximal, characteristic, complemented
13#11720958C211yesmaximal, characteristic, complemented
14#11720938C211yesmaximal, characteristic, complemented
15#11720903C211yesmaximal, characteristic, complemented
16#10594516—31nomaximal
17#10589733—31nomaximal
18C2×C4⋊(C3⋊D9)C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×D3×C9C2211yescharacteristic
21C2×C3×C4×D9C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×C9×Dic6C2211yescharacteristic
25C2×#6195C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33C2×#6189C2211yescharacteristic
34#88640—24no—
35#88635—24no—
36C3×C9×C4⋊C4C2211yescharacteristic
37#88536C2211yescharacteristic
38#88536C2211yescharacteristic
39#88536C2211yescharacteristic
40#88534C2211yescharacteristic
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C9×Dic3⋊C4C2211yescharacteristic
44C9×Dic3⋊C4C2211yescharacteristic
45C3×C4⋊Dic9C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49#88445C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic
52#88442C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3799—31no—
56C2×#3798—31no—
57#64103—31no—
58C3×#896D311yescharacteristic
59C3×D3×C4⋊C4—31no—
60#63910—31no—
61#63906—31no—
62#63905—31no—
63#63904—31no—
64#63904—31no—
65#63895—31no—
66#63883—31no—
67#63854—31no—
68#63850—31no—
69#63839—31no—
70C2×#3701—31no—
71C2×#3697—31no—
72C9×C22⋊Q8—31no—
73#63506—31no—
74C4×#611—31no—
75#63459—31no—
76#63456—31no—
77#63456—31no—
78#63456—61no—
79#63455—31no—
80C4⋊C4×D9—31no—
81C4⋊C4×D9D311yescharacteristic, complemented
82#63446—31no—
83#63446—31no—
84#63445—31no—
85#63445—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4⋊(C3⋊D9)—22no—
96C4×C3⋊D9—22no—
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C4×D3×C9—22no—
104C3×C4×D9—22no—
105C3×C4×D9—22no—
106C3×C4×D9—22no—
107C9×Dic6—22no—
108#6195—22no—
109#6195—22no—
110#6194—22no—
111#6192—22no—
112#6192D414yescomplemented
113(C3⋊D9)⋊C4—22no—
114(C3⋊D9)⋊C4—22no—
115(C3⋊D9)⋊C4—22no—
116#6189—22no—
117#5631—91no—
118#5507—91no—
119C2×C4⋊(C3⋊D3)—31no—
120C2×C4×C3⋊D3—31no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×C3×Dic6C2×D311yescharacteristic
126C2×#627—31no—
127C2×#626—31no—
128C2×#626—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#625—31no—
132C2×#624—31no—
133C2×#624—31no—
134C2×#624—31no—
135#3799—64no—
136#3798—64no—
137C32×C4⋊C4C2×D311yescharacteristic
138#3752—31no—
139#3752—31no—
140#3752—31no—
141#3750—31no—
142C3×(C2×D3)⋊C4C2×D311yescharacteristic
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×C4⋊Dic3—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4C2×D311yescharacteristic
148C3×Dic3⋊C4C2×D311yescharacteristic
149#3724—31no—
150Dic3⋊Dic3—31no—
151Dic3⋊Dic3—31no—
152#3722—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C2×Q8×C9—31no—
157C22×C4×C9—31no—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611—31no—
161#3701—64no—
162#3697—64no—
163C2×D36—31no—
164C2×D36—31no—
165C2×D36—31no—
166C2×D36—61no—
167C2×C4×D9—31no—
168C2×C4×D9—31no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9—61no—
172C2×C4×D9C2×D311yescharacteristic
173C2×C4×D9C2×D311yescharacteristic
174C2×C4×D9C2×D311yescharacteristic
175C2×Dic18—31no—
176C9×C4⋊C4—21no—
177C9×C4⋊C4—31no—
178C9×C4⋊C4—31no—
179C9×C4⋊C4C2×D311yescharacteristic
180C9×C22⋊C4—31no—
181C9×C22⋊C4—31no—
182#3676—31no—
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—61no—
189(C2×D9)⋊C4—61no—
190(C2×D9)⋊C4—61no—
191C4⋊Dic9—31no—
192C4⋊Dic9C2×D311yescharacteristic
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—61no—
197Dic9⋊C4C2×D311yescharacteristic
198Dic9⋊C4C2×D311yescharacteristic
199C4×Dic9—31no—
200C22×C3×C9C2411yescharacteristic
201C2×C3⋊D9—21no—
202C2×C3⋊D9—21no—
203C2×C3⋊D9—21no—
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9C2×D412yes—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9C2×D412yes—
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3×C4×C9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9—21no—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3C2×D412yes—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9#4112yescomplemented
224C2×#239—91no—
225C2×#235—91no—
226C2×#235—91no—
227C2×#235—91no—
228C3×C22⋊Q8—31no—
229C2×C3×C4⋊C4—91no—
230#944—91no—
231#930—91no—
232#929—91no—
233#929—91no—
234C4×#67—91no—
235C4×#67—91no—
236#897—91no—
237#896—91no—
238#896D911yescharacteristic, complemented
239#895—91no—
240#894—91no—
241#894—91no—
242#894—91no—
243#894—91no—
244#894—181no—
245#893—91no—
246#893—91no—
247D3×C4⋊C4—31no—
248D3×C4⋊C4—91no—
249D3×C4⋊C4—91no—
250#888—91no—
251#884—91no—
252#884—91no—
253#883—91no—
254#883—91no—
255C22×C3⋊D3—31no—
256C22×C3⋊D3—31no—
257C22×C3×D3—31no—
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C4⋊(C3⋊D3)—62no—
265C4×C3⋊D3—62no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C22×D311yescharacteristic
272C3×C4×D3—22no—
273C3×C4×D3—62no—
274C3×C4×D3—62no—
275C3×C4×D3—62no—
276C3×Dic6—22no—
277#627—62no—
278#626—34no—
279#626—62no—
280#626—62no—
281#626—62no—
282#625—62no—
283#624—62no—
284#624—62no—
285#624—62no—
286C23×C9—31no—
287C22×D9—31no—
288C22×D9—31no—
289C22×D9—61no—
290C22×D9—61no—
291C22×D9C22×D311yescharacteristic
292Q8×C9—62no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—21no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—62no—
300C2×C4×C9C22×D311yescharacteristic
301C2×C4×C9C22×D311yescharacteristic
302C2×C4×C9C22×D311yescharacteristic
303#611—62no—
304#611—62no—
305#611—62no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9C22×D311yescharacteristic
311C2×Dic9C22×D311yescharacteristic
312C2×Dic9C22×D311yescharacteristic
313D36—34no—
314D36—62no—
315D36—62no—
316D36—122no—
317C4×D9—22no—
318C4×D9—22no—
319C4×D9—22no—
320C4×D9—62no—
321C4×D9—62no—
322C4×D9—62no—
323C4×D9—62no—
324C4×D9—122no—
325Dic18—62no—
326#547—271noSylow
327C2×C3×C9C22×D411yescharacteristic
328C2×C3×C9C2×#4111yescharacteristic
329C2×C3×C92−1+411yescharacteristic
330C3⋊D9—22no—
331C3⋊D9—41no—
332D3×C9—41no—
333C3×D9—22no—
334C2×C3×Q8—31no—
335C22×C3×C4—31no—
336C22×C3×C4—91no—
337C22×C3×C4—91no—
338C22×C3×C4—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345#239—184no—
346#235—184no—
347#235—184no—
348#235—184no—
349C2×D12—91no—
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—91no—
353C2×D12—91no—
354C2×D12—91no—
355C2×D12—181no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×C4×D3—91no—
365C2×C4×D3—91no—
366C2×C4×D3—91no—
367C2×C4×D3—181no—
368C2×C4×D3C2×D911yescharacteristic
369C2×Dic6—91no—
370C2×Dic6—91no—
371C2×Dic6C2×D911yescharacteristic
372C3×C4⋊C4—21no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—91no—
376C3×C4⋊C4—91no—
377C3×C4⋊C4—91no—
378C3×C4⋊C4C2×D911yescharacteristic
379C3×C4⋊C4D3211yescharacteristic
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382#217—91no—
383#217—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—181no—
395(C2×D3)⋊C4—181no—
396(C2×D3)⋊C4—181no—
397(C2×D3)⋊C4C2×D911yescharacteristic
398(C2×D3)⋊C4C2×D911yescharacteristic
399C4⋊Dic3—31no—
400C4⋊Dic3—91no—
401C4⋊Dic3—91no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—181no—
411Dic3⋊C4C2×D911yescharacteristic
412Dic3⋊C4C2×D911yescharacteristic
413C4×Dic3—91no—
414C4×Dic3—91no—
415C22×C32C23×D311yescharacteristic
416C2×C3⋊D3—32no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—32no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—21no—
431C3⋊Dic3—61no—
432C3⋊Dic3—61no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—32no—
436C3×Dic3—61no—
437C3×Dic3—61no—
438C3×Dic3D3×D412yes—
439C22×C9—21no—
440C22×C9—61no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9C23×D311yescharacteristic
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—32no—
447C2×D9—62no—
448C2×D9—61no—
449C2×D9—61no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—61no—
453C2×D9—121no—
454C2×D9—121no—
455C2×D9—121no—
456C2×D9—121no—
457C2×D9—121no—
458C2×D9D3×D412yes—
459C4×C9—21no—
460C4×C9—21no—
461C4×C9—21no—
462C4×C9—32no—
463C4×C9—41no—
464C4×C9—41no—
465C4×C9—41no—
466C4×C9—61no—
467C4×C9—61no—
468Dic9—21no—
469Dic9—21no—
470Dic9—61no—
471Dic9—61no—
472Dic9—121no—
473Dic9—121no—
474Dic9#23512yescomplemented
475C2×#41—271no—
476C2×#41—271no—
477C4⋊Q8—271no—
478#123—271no—
479#123—271no—
480#123—271no—
481#123—271no—
482C22⋊Q8—31no—
483C22⋊Q8—271no—
484#121—271no—
485#121—271no—
486C4×D4—271no—
487C4×D4—271no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—271no—
490C3×C9#54711yescharacteristic, complemented, Sylow
491C23×C3—31no—
492C23×C3—91no—
493C22×D3—31no—
494C22×D3—91no—
495C22×D3—91no—
496C22×D3—91no—
497C22×D3—91no—
498C22×D3—181no—
499C22×D3—181no—
500C22×D3C22×D911yescharacteristic
501C3×Q8—62no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—62no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—182no—
513C2×C3×C4—182no—
514C2×C3×C4—182no—
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C22×D911yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521#67—94no—
522#67—182no—
523#67—182no—
524#67—182no—
525#67—182no—
526#67—182no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—181no—
535C2×Dic3—181no—
536C2×Dic3C22×D911yescharacteristic
537C2×Dic3C22×D911yescharacteristic
538C2×Dic3C22×D911yescharacteristic
539D12—94no—
540D12—182no—
541D12—182no—
542D12—182no—
543D12—182no—
544D12—182no—
545D12—362no—
546C4×D3—22no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—62no—
550C4×D3—182no—
551C4×D3—182no—
552C4×D3—182no—
553C4×D3—182no—
554C4×D3—182no—
555C4×D3—182no—
556C4×D3—182no—
557C4×D3—182no—
558C4×D3—362no—
559Dic6—22no—
560Dic6—182no—
561Dic6—182no—
562C2×C32C2×D3×D411yescharacteristic
563C2×C32#100711yescharacteristic
564C2×C32D3×#4111yescharacteristic
565C3⋊D3—62no—
566C3⋊D3—121no—
567C3×D3—41no—
568C3×D3—62no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9—21no—
572C2×C9—121no—
573C2×C9C2×#23511yescharacteristic
574C2×C9C2×D3×D411yescharacteristic
575C2×C9#100711yescharacteristic
576D9—22no—
577D9—62no—
578D9—122no—
579D9—121no—
580D9—241no—
581#41—544no—
582#41—544no—
583C2×Q8—31no—
584C2×Q8—271no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C2×D4—271no—
590C2×D4—271no—
591C22×C4—31no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C22×C4—271no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—91no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C4⋊C4—271no—
608C4⋊C4D3×D911yescharacteristic
609C22⋊C4—31no—
610C22⋊C4—31no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C42—271no—
618C22×C3—21no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—92no—
623C22×C3—181no—
624C22×C3—181no—
625C22×C3C23×D911yescharacteristic
626C22×C3C22×D3211yescharacteristic
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—32no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—92no—
634C2×D3—92no—
635C2×D3—182no—
636C2×D3—181no—
637C2×D3—181no—
638C2×D3—181no—
639C2×D3—181no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—361no—
647C2×D3—361no—
648C2×D3—361no—
649C2×D3—361no—
650C2×D3—361no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—32no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—92no—
664C3×C4—181no—
665C3×C4—181no—
666Dic3—21no—
667Dic3—21no—
668Dic3—32no—
669Dic3—61no—
670Dic3—61no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675Dic3—361no—
676Dic3—361no—
677Dic3D4×D912yes—
678C32#563111yescharacteristic
679C9—21no—
680C9#550711yescharacteristic, complemented
681C23—31no—
682C23—91no—
683C23—271no—
684C23—271no—
685Q8—62no—
686Q8—542no—
687D4—274no—
688D4—542no—
689D4—542no—
690D4—542no—
691D4—542no—
692D4—542no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—62no—
697C2×C4—91no—
698C2×C4—91no—
699C2×C4—91no—
700C2×C4—182no—
701C2×C4—182no—
702C2×C4—182no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—542no—
706C2×C4—542no—
707C2×C4—542no—
708C2×C4—542no—
709C2×C4C2×D3×D911yescharacteristic
710C2×C4C2×D3×D911yescharacteristic
711C2×C4C2×D3×D911yescharacteristic
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—121no—
716C2×C3—182no—
717C2×C3C2×D4×D911yescharacteristic
718C2×C3#6371311yescharacteristic
719C2×C3#41×D911yescharacteristic
720C2×C3D3×#23511yescharacteristic
721C2×C3D32×D411yescharacteristic
722C2×C3#6431611yescharacteristic
723D3—41no—
724D3—62no—
725D3—182no—
726D3—182no—
727D3—362no—
728D3—361no—
729D3—361no—
730D3—721no—
731C22—61no—
732C22—61no—
733C22—61no—
734C22—92no—
735C22—181no—
736C22—181no—
737C22—272no—
738C22—541no—
739C22—541no—
740C22—541no—
741C22—541no—
742C22—541no—
743C22C22×D3×D911yescharacteristic
744C4—21no—
745C4—21no—
746C4—21no—
747C4—32no—
748C4—61no—
749C4—61no—
750C4—92no—
751C4—181no—
752C4—181no—
753C4—541no—
754C4—541no—
755C3—21no—
756C3#1058973311yescharacteristic, complemented
757C3#1059451611yescharacteristic
758C2—121no—
759C2—182no—
760C2—542no—
761C2—1081no—
762C2D9×#23511yescharacteristic
763C2D3×D4×D911yescharacteristic
764C2#1172250911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#547
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#88640C2semidirect
2. C2×#88635C2semidirect
3. #11721750C2semidirect
4. C9×#896C2semidirect
5. C3×C4⋊C4×D9C2semidirect
6. #11721039C2semidirect
7. #11721033C2semidirect
8. #11721031C2semidirect
9. #11721030C2semidirect
10. #11721002C2semidirect
11. #11720995C2semidirect
12. #11720980C2semidirect
13. #11720958C2semidirect
14. #11720938C2semidirect
15. #11720903C2semidirect
81. C4⋊C4×D9D3semidirect
112. #6192D4semidirect
223. C3×Dic9#41semidirect
238. #896D9semidirect
474. Dic9#235semidirect
490. C3×C9#547semidirect
680. C9#5507semidirect
756. C3#10589733semidirect

Maximal subgroups

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

subgroupindex
C2×#886402
C2×#886352
#117217502
C9×#8962
C3×C4⋊C4×D92
#117210392
#117210332
#117210312
#117210302
#117210022
#117209952
#117209802
#117209582
#117209382
#117209032
#105945163
#105897333