Finite Group Databasebeta

← #13147940

Subgroups — #13147940

Order 1728.

944 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88663C211yesmaximal, characteristic, complemented
2C2×D9×Dic6C211yesmaximal, characteristic, complemented
3#11721724C211yesmaximal, characteristic, complemented
4C9×#885C211yesmaximal, characteristic, complemented
5C3×#63446C211yesmaximal, characteristic, complemented
6#611⋊Dic3C211yesmaximal, characteristic, complemented
7#11721270C211yesmaximal, characteristic, complemented
8#11721257C211yesmaximal, characteristic, complemented
9#11721042C211yesmaximal, characteristic, complemented
10#11721023C211yesmaximal, characteristic, complemented
11#11721012C211yesmaximal, characteristic, complemented
12Dic3×D36C211yesmaximal, characteristic, complemented
13#11720984C211yesmaximal, characteristic, complemented
14#11720982C211yesmaximal, characteristic, complemented
15#11720900C211yesmaximal, characteristic, complemented
16#10594076—31nomaximal
17#10589779—31nomaximal
18C22×C3⋊Dic9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C9×#67C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C9×Dic6C2211yescharacteristic
26C2×#6194C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28#88663—24no—
29C2×D3×Dic9C2211yescharacteristic
30C2×Dic3×D9C2211yescharacteristic
31C2×Dic3×D9C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C2×#6189C2211yescharacteristic
34C2×#6189C2211yescharacteristic
35D9×Dic6—24no—
36C3×C9×C22⋊C4C2211yescharacteristic
37#88551C2211yescharacteristic
38C4⋊(C3⋊Dic9)C2211yescharacteristic
39#88534C2211yescharacteristic
40#88534C2211yescharacteristic
41C9×#217C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C9×(C2×D3)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C4×C9×Dic3C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3805—31no—
56C2×D3×Dic6—31no—
57#64087—31no—
58C3×#885D311yescharacteristic
59C3×#884—31no—
60#67⋊Dic3—31no—
61#63970—31no—
62#63959—31no—
63#63913—31no—
64#63893—31no—
65Dic3×D12—31no—
66#63887—31no—
67#63885—31no—
68#63879—31no—
69#63837—31no—
70C2×Q8×D9—31no—
71C2×#3699—31no—
72C9×#124—31no—
73#63508—31no—
74#63500—31no—
75#63447—31no—
76#63447—31no—
77#63446—31no—
78#63446D311yescharacteristic, complemented
79#611⋊C4—31no—
80#611⋊C4—31no—
81#63440—31no—
82#63440—31no—
83#63440—61no—
84C4×D36—31no—
85C4×Dic18—31no—
86C23×C3×C9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3⋊Dic9—22no—
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97#6226—22no—
98C9×#67—22no—
99C3×#611—22no—
100C3×#611—22no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C3×D36—22no—
107C3×C4×D9—22no—
108C9×Dic6—22no—
109#6194—22no—
110#6194—22no—
111D3×Dic9—22no—
112Dic3×D9—22no—
113Dic3×D9—22no—
114Dic3×D9—22no—
115#6189—22no—
116#6189D414yescomplemented
117#5677—91no—
118#5598—91no—
119C22×C3⋊Dic3—31no—
120C2×#634—31no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67C2×D311yescharacteristic
124C2×C3×D12—31no—
125C2×C3×C4×D3—31no—
126C2×C3×Dic6C2×D311yescharacteristic
127C2×#627—31no—
128C2×#627—31no—
129C2×#625—31no—
130C2×#625—31no—
131#3805—64no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136D3×Dic6—64no—
137C32×C22⋊C4C2×D311yescharacteristic
138#3757—31no—
139C4⋊(C3⋊Dic3)—31no—
140#3750—31no—
141#3750—31no—
142C3×#217C2×D311yescharacteristic
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4C2×D311yescharacteristic
145C3×(C2×D3)⋊C4C2×D311yescharacteristic
146C3×Dic3⋊C4—31no—
147C3×C4×Dic3C2×D311yescharacteristic
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154Dic32—31no—
155Dic32—31no—
156C2×Q8×C9—31no—
157C2×D4×C9—31no—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611C2×D311yescharacteristic
161C2×#611C2×D311yescharacteristic
162C22×Dic9—31no—
163C22×Dic9—31no—
164C22×Dic9—61no—
165Q8×D9—64no—
166#3699—64no—
167C2×D36C2×D311yescharacteristic
168C2×C4×D9—31no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9C2×D311yescharacteristic
172C2×Dic18—31no—
173C2×Dic18—31no—
174C2×Dic18—31no—
175C2×Dic18—61no—
176C9×C22⋊C4—21no—
177C9×C22⋊C4—31no—
178C9×C22⋊C4—31no—
179C9×C22⋊C4—31no—
180C9×C22⋊C4C2×D311yescharacteristic
181C42×C9—31no—
182#3676—31no—
183#3676—31no—
184#3676—61no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4C2×D311yescharacteristic
189C4⋊Dic9—31no—
190C4⋊Dic9—31no—
191C4⋊Dic9—61no—
192Dic9⋊C4—31no—
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—61no—
196Dic9⋊C4—61no—
197Dic9⋊C4C2×D311yescharacteristic
198C4×Dic9—31no—
199C4×Dic9—31no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9C2411yescharacteristic
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9#4112yescomplemented
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9—21no—
218C3⋊Dic9C2×D412yes—
219C9×Dic3—21no—
220C9×Dic3—21no—
221C9×Dic3C2×D412yes—
222C3×Dic9—21no—
223C3×Dic9C2×D412yes—
224C2×D3×Q8—91no—
225C2×#237—91no—
226C2×#237—91no—
227C22×Dic6—91no—
228C3×#124—31no—
229C3×#121—91no—
230#946—91no—
231#939—91no—
232#939—91no—
233#938—91no—
234#936—91no—
235D4×Dic3—91no—
236D4×Dic3—91no—
237C4×#67—91no—
238#897—91no—
239#887—91no—
240#885—91no—
241#885—91no—
242#885—91no—
243#885D911yescharacteristic, complemented
244#884—31no—
245#884—91no—
246#67⋊C4—91no—
247#67⋊C4—91no—
248#878—91no—
249#878—91no—
250#878—91no—
251#878—91no—
252#878—181no—
253C4×D12—91no—
254C4×Dic6—91no—
255C23×C32C22×D311yescharacteristic
256C22×C3×D3—31no—
257C22×C3×D3—31no—
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—62no—
266#634—62no—
267C3×#67—22no—
268C3×#67—62no—
269C3×#67—62no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C3×D12—62no—
276C3×C4×D3—62no—
277C3×Dic6—22no—
278#627—34no—
279#627—62no—
280#625—62no—
281#625—62no—
282D3×Dic3—62no—
283D3×Dic3—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C23×C9—21no—
287C23×C9—31no—
288C23×C9C22×D311yescharacteristic
289C22×D9C22×D311yescharacteristic
290C22×D9C22×D311yescharacteristic
291Q8×C9—62no—
292D4×C9—62no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9C22×D311yescharacteristic
299C2×C4×C9C22×D311yescharacteristic
300#611—22no—
301#611—22no—
302#611—62no—
303#611—62no—
304C2×Dic9—31no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9—61no—
312C2×Dic9—62no—
313C2×Dic9—62no—
314C2×Dic9—122no—
315C2×Dic9C22×D311yescharacteristic
316C2×Dic9C22×D311yescharacteristic
317D36—22no—
318C4×D9—22no—
319C4×D9—62no—
320C4×D9—62no—
321C4×D9—62no—
322Dic18—34no—
323Dic18—62no—
324Dic18—62no—
325Dic18—122no—
326#548—271noSylow
327C2×C3×C9—41no—
328C2×C3×C9C22×D411yescharacteristic
329C2×C3×C9C2×#4111yescharacteristic
330C2×C3×C92−1+411yescharacteristic
331D3×C9—41no—
332C3×D9—22no—
333C3×D9—41no—
334C2×C3×Q8—31no—
335C2×C3×D4—31no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C22×C3×C4—91no—
340C2×#67—31no—
341C2×#67—31no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67C2×D911yescharacteristic
347C22×Dic3—91no—
348C22×Dic3—91no—
349C22×Dic3—91no—
350C22×Dic3—91no—
351C22×Dic3—91no—
352C22×Dic3—91no—
353C22×Dic3—181no—
354D3×Q8—184no—
355#237—184no—
356#237—184no—
357C2×D12—31no—
358C2×C4×D3—31no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×Dic6—91no—
364C2×Dic6—91no—
365C2×Dic6—91no—
366C2×Dic6—91no—
367C2×Dic6—91no—
368C2×Dic6—91no—
369C2×Dic6—181no—
370C2×Dic6—184no—
371C2×Dic6C2×D911yescharacteristic
372C3×C4⋊C4—91no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4C2×D911yescharacteristic
379C3×C22⋊C4D3211yescharacteristic
380C3×C42—31no—
381#217—91no—
382#217—91no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—91no—
387#217—181no—
388#217C2×D911yescharacteristic
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4C2×D911yescharacteristic
395(C2×D3)⋊C4C2×D911yescharacteristic
396C4⋊Dic3—91no—
397C4⋊Dic3—91no—
398C4⋊Dic3—91no—
399C4⋊Dic3—91no—
400C4⋊Dic3—181no—
401Dic3⋊C4—31no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—181no—
409Dic3⋊C4—181no—
410C4×Dic3—91no—
411C4×Dic3—91no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3C2×D911yescharacteristic
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32C23×D311yescharacteristic
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—32no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C32×C4—21no—
429C32×C4—21no—
430C3⋊Dic3—32no—
431C3⋊Dic3—61no—
432C3⋊Dic3—61no—
433C3⋊Dic3—61no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—32no—
437C3×Dic3—61no—
438C3×Dic3D3×D412yes—
439C22×C9—22no—
440C22×C9—21no—
441C22×C9—21no—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—41no—
445C22×C9—41no—
446C22×C9—61no—
447C22×C9—61no—
448C22×C9—61no—
449C22×C9C23×D311yescharacteristic
450C2×D9—21no—
451C2×D9—21no—
452C2×D9—21no—
453C2×D9—21no—
454C2×D9—21no—
455C2×D9#23712yescomplemented
456C4×C9—21no—
457C4×C9—21no—
458C4×C9—32no—
459C4×C9—41no—
460C4×C9—41no—
461C4×C9—61no—
462C4×C9—61no—
463Dic9—21no—
464Dic9—32no—
465Dic9—62no—
466Dic9—61no—
467Dic9—61no—
468Dic9—61no—
469Dic9—121no—
470Dic9—121no—
471Dic9—121no—
472Dic9D3×D412yes—
473C2×#41—271no—
474C22×Q8—271no—
475#124—31no—
476#124—271no—
477#124—271no—
478C22⋊Q8—271no—
479C22⋊Q8—271no—
480C22⋊Q8—271no—
481#121—91no—
482#121—271no—
483#121—271no—
484C4×Q8—271no—
485C4×D4—271no—
486C4×D4—271no—
487C4×D4—271no—
488C3×C9#54811yescharacteristic, complemented, Sylow
489C23×C3—21no—
490C23×C3—31no—
491C23×C3—91no—
492C23×C3—91no—
493C23×C3C22×D911yescharacteristic
494C23×C3C2×D3211yescharacteristic
495C22×D3—31no—
496C22×D3—31no—
497C22×D3C22×D911yescharacteristic
498C3×Q8—62no—
499C3×D4—62no—
500C3×D4—182no—
501C3×D4—182no—
502C3×D4—182no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—182no—
511C2×C3×C4C22×D911yescharacteristic
512C2×C3×C4C22×D911yescharacteristic
513C2×C3×C4C2×D3211yescharacteristic
514C2×C3×C4C2×D3211yescharacteristic
515#67—22no—
516#67—62no—
517#67—62no—
518#67—182no—
519#67—182no—
520#67—182no—
521#67—182no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—91no—
525C2×Dic3—91no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—181no—
533C2×Dic3—181no—
534C2×Dic3—181no—
535C2×Dic3—181no—
536C2×Dic3—182no—
537C2×Dic3—182no—
538C2×Dic3—182no—
539C2×Dic3—182no—
540C2×Dic3—182no—
541C2×Dic3—182no—
542C2×Dic3—362no—
543C2×Dic3C22×D911yescharacteristic
544C2×Dic3C22×D911yescharacteristic
545C2×Dic3C22×D911yescharacteristic
546D12—62no—
547C4×D3—62no—
548C4×D3—182no—
549C4×D3—182no—
550C4×D3—182no—
551C4×D3—182no—
552Dic6—22no—
553Dic6—94no—
554Dic6—94no—
555Dic6—182no—
556Dic6—182no—
557Dic6—182no—
558Dic6—182no—
559Dic6—362no—
560C2×C32—41no—
561C2×C32C2×D3×D411yescharacteristic
562C2×C32D3×#4111yescharacteristic
563C2×C32#101011yescharacteristic
564C3×D3—41no—
565C3×D3—62no—
566C3×D3—121no—
567C2×C9—21no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—42no—
571C2×C9—41no—
572C2×C9—121no—
573C2×C9C2×D3×D411yescharacteristic
574C2×C9C2×#23711yescharacteristic
575C2×C9#101011yescharacteristic
576D9—22no—
577D9—41no—
578#41—544no—
579C2×Q8—31no—
580C2×Q8—271no—
581C2×Q8—271no—
582C2×Q8—271no—
583C2×Q8—544no—
584C2×D4—31no—
585C2×D4—91no—
586C2×D4—91no—
587C2×D4—91no—
588C2×D4—271no—
589C2×D4—271no—
590C22×C4—91no—
591C22×C4—271no—
592C22×C4—271no—
593C22×C4—271no—
594C22×C4—271no—
595C22×C4—271no—
596C4⋊C4—91no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C4⋊C4—271no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C22⋊C4—31no—
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—91no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4D3×D911yescharacteristic
612C42—31no—
613C42—271no—
614C42—271no—
615C22×C3—22no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—92no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3—181no—
633C22×C3—181no—
634C22×C3C23×D911yescharacteristic
635C22×C3C22×D3211yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—32no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—32no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—92no—
655C3×C4—181no—
656Dic3—21no—
657Dic3—21no—
658Dic3—32no—
659Dic3—61no—
660Dic3—92no—
661Dic3—92no—
662Dic3—182no—
663Dic3—181no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—181no—
668Dic3—181no—
669Dic3—361no—
670Dic3—361no—
671Dic3—361no—
672Dic3D4×D912yes—
673C32#567711yescharacteristic
674C9—21no—
675C9#559811yescharacteristic, complemented
676C23—31no—
677C23—91no—
678C23—91no—
679C23C2×D3×D911yescharacteristic
680Q8—62no—
681Q8—274no—
682Q8—542no—
683Q8—542no—
684D4—62no—
685D4—182no—
686D4—182no—
687D4—182no—
688D4—542no—
689D4—542no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—91no—
694C2×C4—91no—
695C2×C4—182no—
696C2×C4—271no—
697C2×C4—271no—
698C2×C4—271no—
699C2×C4—271no—
700C2×C4—542no—
701C2×C4—542no—
702C2×C4—542no—
703C2×C4—542no—
704C2×C4—542no—
705C2×C4C2×D3×D911yescharacteristic
706C2×C4C2×D3×D911yescharacteristic
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—42no—
711C2×C3—41no—
712C2×C3—41no—
713C2×C3—121no—
714C2×C3—182no—
715C2×C3—361no—
716C2×C3C2×D4×D911yescharacteristic
717C2×C3#41×D911yescharacteristic
718C2×C3#6371611yescharacteristic
719C2×C3#6429811yescharacteristic
720C2×C3D32×D411yescharacteristic
721C2×C3D3×#23711yescharacteristic
722D3—41no—
723D3—62no—
724D3—121no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22—92no—
732C22—181no—
733C22—181no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22C22×D3×D911yescharacteristic
738C4—21no—
739C4—21no—
740C4—32no—
741C4—61no—
742C4—61no—
743C4—92no—
744C4—181no—
745C4—272no—
746C4—541no—
747C4—541no—
748C4—541no—
749C3—21no—
750C3#1058977911yescharacteristic, complemented
751C3#1059407611yescharacteristic
752C2—41no—
753C2—121no—
754C2—182no—
755C2—361no—
756C2#1172246511yescharacteristic
757C2D3×D4×D911yescharacteristic
758C2D9×#23711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#548
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#88663C2semidirect
2. C2×D9×Dic6C2semidirect
3. #11721724C2semidirect
4. C9×#885C2semidirect
5. C3×#63446C2semidirect
6. #611⋊Dic3C2semidirect
7. #11721270C2semidirect
8. #11721257C2semidirect
9. #11721042C2semidirect
10. #11721023C2semidirect
11. #11721012C2semidirect
12. Dic3×D36C2semidirect
13. #11720984C2semidirect
14. #11720982C2semidirect
15. #11720900C2semidirect
78. #63446D3semidirect
116. #6189D4semidirect
212. C2×C3×D9#41semidirect
243. #885D9semidirect
455. C2×D9#237semidirect
488. C3×C9#548semidirect
675. C9#5598semidirect
750. C3#10589779semidirect

Maximal subgroups

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

subgroupindex
C2×#886632
C2×D9×Dic62
#117217242
C9×#8852
C3×#634462
#611⋊Dic32
#117212702
#117212572
#117210422
#117210232
#117210122
Dic3×D362
#117209842
#117209822
#117209002
#105940763
#105897793