Finite Group Databasebeta

← #10800525

Subgroups — #10800525

Order 768.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5586C211yesmaximal, characteristic
2C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
3#73817C211yesmaximal, characteristic, complemented
4C3×#1898C211yesmaximal, characteristic, complemented
5#71670C211yesmaximal, characteristic, complemented
6#71543C211yesmaximal, characteristic, complemented
7#70030C212yesmaximal, complemented
8Dic3×#99C212yesmaximal, complemented
9#69496C211yesmaximal, characteristic, complemented
10#68955C212yesmaximal, complemented
11#68952C212yesmaximal, complemented
12#21420—31nomaximal, Sylow
13C24×Dic3C2211yescharacteristic
14C22×#237C411yescharacteristic, complemented
15C2×C3×#120C2211yescharacteristic
16C22×C3×C22⋊C4C2211yescharacteristic
17C2×#953C2211yescharacteristic
18C22×#217C2211yescharacteristic
19C2×#939C411yescharacteristic, complemented
20C2×#939C2211yescharacteristic
21C2×#935C411yescharacteristic, complemented
22C2×D4×Dic3C411yescharacteristic, complemented
23C2×D4×Dic3C2211yescharacteristic
24C22×C4×Dic3—21no—
25#5586—21no—
26#5586—21no—
27#5586—21no—
28#5586—21no—
29#5586—21no—
30#5586—21no—
31#5586—21no—
32#5586—21no—
33C2×#886C411yescharacteristic, complemented
34C2×#67⋊C4C411yescharacteristic, complemented
35C2×#67⋊C4C2211yescharacteristic
36C2×#878C411yescharacteristic, complemented
37C2×#878C2211yescharacteristic
38C2×#877—21no—
39C2×#877C411yescharacteristic, complemented
40C2×C3×#99C2212yes—
41C3×#379C2211yescharacteristic
42#5247C2211yescharacteristic
43C2×#834C2212yes—
44C2×C3⋊#95—21no—
45C2×#806C2212yes—
46C2×#806C2212yes—
47#4943—21no—
48#4942—21no—
49#4942C2212yes—
50Dic3×C22⋊C4—21no—
51Dic3×C22⋊C4—21no—
52Dic3×C22⋊C4—21no—
53Dic3×C22⋊C4C2212yes—
54Dic3×C22⋊C4C2212yes—
55Dic3×C22⋊C4C2212yes—
56C3×#342C2212yes—
57#4527C2212yes—
58#4527C2212yes—
59#4526C2212yes—
60C2×#525—31no—
61#2280—31no—
62C2×C4×C22⋊C4—31no—
63#1996—32no—
64#1964—32no—
65#1898—31no—
66#1898—31no—
67#1898—31no—
68#1898D311yescharacteristic, complemented
69C4×#99—32no—
70C4×#99—32no—
71C25×C3C2311yescharacteristic
72C22×C3×D4C2×C411yescharacteristic
73C22×C3×D4C2×C411yescharacteristic
74C22×C3×D4C2311yescharacteristic
75C23×C3×C4—21no—
76C22×#67C2×C411yescharacteristic
77C22×#67C2×C411yescharacteristic
78C22×#67C2×C411yescharacteristic, complemented
79C22×#67C2311yescharacteristic
80C23×Dic3—21no—
81C23×Dic3—44no—
82C23×Dic3C2×C411yescharacteristic
83C23×Dic3C2×C411yescharacteristic
84C23×Dic3C2×C411yescharacteristic
85C23×Dic3C2×C411yescharacteristic
86C23×Dic3C2×C411yescharacteristic, complemented
87C23×Dic3D411yescharacteristic
88C23×Dic3D411yescharacteristic
89C23×Dic3D411yescharacteristic
90C23×Dic3D411yescharacteristic
91C23×Dic3D411yescharacteristic
92C23×Dic3D411yescharacteristic
93C23×Dic3D411yescharacteristic
94C23×Dic3D411yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C2×#237—21no—
98C2×#237—21no—
99C2×#237—21no—
100C2×#237—21no—
101C2×#237—44no—
102C22×C4×D3C2×C411yescharacteristic, complemented
103C22×Dic6C2×C411yescharacteristic, complemented
104C3×#120—21no—
105C3×#120—21no—
106C3×#120—21no—
107C3×#120—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4C2×C411yescharacteristic
113C2×C3×C22⋊C4C2×C411yescharacteristic
114C2×C3×C22⋊C4C2312yes—
115C2×C3×C22⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4C2312yes—
117#953—21no—
118#953—21no—
119#953—21no—
120#953—21no—
121C2×#217—21no—
122C2×#217—24no—
123C2×#217—21no—
124C2×#217—21no—
125C2×#217C2×C411yescharacteristic
126C2×#217C2×C411yescharacteristic
127C2×#217C2×C411yescharacteristic, complemented
128C2×#217C2×C411yescharacteristic, complemented
129C2×#217C2312yes—
130C2×#217C2311yescharacteristic
131C2×#217C2312yes—
132#939—21no—
133#939—21no—
134#939—21no—
135#939—21no—
136#939—21no—
137#939—21no—
138#939—21no—
139#939—21no—
140#935—21no—
141#935—21no—
142#935—21no—
143#935—21no—
144D4×Dic3—21no—
145D4×Dic3—21no—
146D4×Dic3—21no—
147D4×Dic3—21no—
148D4×Dic3—21no—
149D4×Dic3—21no—
150D4×Dic3—21no—
151D4×Dic3—21no—
152C2×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
153C2×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
154C2×C4⋊Dic3C2×C411yescharacteristic, complemented
155C2×C4⋊Dic3C2×C411yescharacteristic, complemented
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4C2×C411yescharacteristic, complemented
158C2×Dic3⋊C4C2×C411yescharacteristic, complemented
159C2×Dic3⋊C4C2×C411yescharacteristic, complemented
160C2×Dic3⋊C4C2×C411yescharacteristic, complemented
161C2×C4×Dic3—22no—
162C2×C4×Dic3—22no—
163C2×C4×Dic3—22no—
164C2×C4×Dic3—44no—
165C2×C4×Dic3C2×C411yescharacteristic, complemented
166C2×C4×Dic3C2×C411yescharacteristic, complemented
167#886—21no—
168#886—21no—
169#886—21no—
170#886—21no—
171#67⋊C4—21no—
172#67⋊C4—21no—
173#67⋊C4—21no—
174#67⋊C4—21no—
175#67⋊C4—21no—
176#67⋊C4—21no—
177#67⋊C4—21no—
178#67⋊C4—21no—
179#878—21no—
180#878—21no—
181#878—21no—
182#878—21no—
183#878—21no—
184#878—21no—
185#878—21no—
186#878—21no—
187#877—21no—
188#877—21no—
189#877—21no—
190#877—21no—
191#877—44no—
192C3×#99—24no—
193#834—24no—
194C3⋊#95—22no—
195C3⋊#95—22no—
196C3⋊#95—22no—
197C3⋊#95—22no—
198#806—24no—
199#806—24no—
200C22×#41—31no—
201C24×C4—31no—
202#525—61no—
203#525—61no—
204#525—61no—
205#525—61no—
206#525—61no—
207#525—61no—
208#525—61no—
209#525—61no—
210C2×#123—31no—
211C2×#123—31no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8—31no—
214C2×#121—31no—
215C2×#121—31no—
216C2×#120—31no—
217C2×#120C2×D311yescharacteristic
218C2×C4×D4—31no—
219C2×C4×D4—31no—
220C2×C4×D4—31no—
221C2×C4×D4—31no—
222C2×#117—31no—
223C2×#117—61no—
224C22×C22⋊C4—31no—
225C22×C22⋊C4C2×D311yescharacteristic
226C22×C42—61no—
227C2×#99—32no—
228C2×#99—32no—
229C2×#99—32no—
230C2×#99C2×D312yes—
231#381—61no—
232#380—32no—
233#380—61no—
234#379—31no—
235#379C2×D311yescharacteristic
236C4×C22⋊C4—32no—
237C4×C22⋊C4—32no—
238C4×C22⋊C4—32no—
239C4×C22⋊C4—61no—
240C4×C22⋊C4—61no—
241C4×C22⋊C4—61no—
242C2×#95—61no—
243#342—32no—
244#342—32no—
245#342—32no—
246#342C2×D312yes—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—42no—
250C24×C3—42no—
251C24×C3C22×C411yescharacteristic
252C24×C3C22×C411yescharacteristic
253C24×C3C22×C411yescharacteristic
254C24×C3C2×D411yescharacteristic
255C24×C3C2×D411yescharacteristic
256C24×C3C2×D411yescharacteristic
257C24×C3C2×D411yescharacteristic
258C24×C3C2411yescharacteristic
259C23×D3C22×C411yescharacteristic
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—22no—
267C2×C3×D4—22no—
268C2×C3×D4—42no—
269C2×C3×D4—42no—
270C22×C3×C4—24no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4C22×C411yescharacteristic
276C22×C3×C4C22×C411yescharacteristic
277C22×C3×C4C22×C411yescharacteristic
278C2×#67—21no—
279C2×#67—21no—
280C2×#67—21no—
281C2×#67—21no—
282C2×#67—21no—
283C2×#67—21no—
284C2×#67—22no—
285C2×#67—22no—
286C2×#67—21no—
287C2×#67—21no—
288C2×#67—42no—
289C2×#67—42no—
290C2×#67—42no—
291C22×Dic3—24no—
292C22×Dic3—24no—
293C22×Dic3—24no—
294C22×Dic3—24no—
295C22×Dic3—22no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—22no—
299C22×Dic3—42no—
300C22×Dic3—42no—
301C22×Dic3—42no—
302C22×Dic3—42no—
303C22×Dic3—42no—
304C22×Dic3—42no—
305C22×Dic3—42no—
306C22×Dic3—42no—
307C22×Dic3—42no—
308C22×Dic3—42no—
309C22×Dic3—42no—
310C22×Dic3—42no—
311C22×Dic3—42no—
312C22×Dic3—42no—
313C22×Dic3C22⋊C411yescharacteristic
314C22×Dic3C22⋊C411yescharacteristic
315C22×Dic3C22⋊C411yescharacteristic
316C22×Dic3C22⋊C411yescharacteristic
317C22×Dic3C22⋊C411yescharacteristic
318C22×Dic3C22⋊C411yescharacteristic
319C22×Dic3C22⋊C411yescharacteristic
320C22×Dic3C22⋊C411yescharacteristic
321C22×Dic3C22⋊C411yescharacteristic
322C22×Dic3C22⋊C411yescharacteristic
323C22×Dic3C22⋊C411yescharacteristic
324C22×Dic3C22⋊C411yescharacteristic
325C22×Dic3C22⋊C411yescharacteristic
326C22×Dic3C22⋊C411yescharacteristic
327C22×Dic3C22⋊C411yescharacteristic
328C22×Dic3C22⋊C411yescharacteristic
329C22×Dic3C22×C411yescharacteristic
330C22×Dic3C22×C411yescharacteristic
331C22×Dic3C22×C411yescharacteristic
332C22×Dic3C22×C411yescharacteristic
333C22×Dic3C22×C411yescharacteristic
334C22×Dic3C22×C411yescharacteristic
335C22×Dic3C22×C411yescharacteristic
336C22×Dic3C2×D411yescharacteristic
337C22×Dic3C2×D411yescharacteristic
338C22×Dic3C2×D411yescharacteristic
339C22×Dic3C2×D411yescharacteristic
340C22×Dic3C2×D411yescharacteristic
341C22×Dic3C2×D411yescharacteristic
342C22×Dic3C2×D411yescharacteristic
343C22×Dic3C2×D411yescharacteristic
344#237—44no—
345#237—44no—
346#237—44no—
347#237—44no—
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×C4×D3—42no—
351C2×Dic6—21no—
352C2×Dic6—21no—
353C2×Dic6—42no—
354C3×C22⋊C4—24no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—22no—
362C3×C22⋊C4—22no—
363C3×C22⋊C4—22no—
364C3×C22⋊C4—42no—
365C3×C22⋊C4—42no—
366C3×C22⋊C4#4114yescomplemented
367#217—24no—
368#217—21no—
369#217—21no—
370#217—21no—
371#217—21no—
372#217—21no—
373#217—21no—
374#217—22no—
375#217—21no—
376#217—21no—
377#217—21no—
378#217—21no—
379#217—22no—
380#217—22no—
381#217—42no—
382#217—42no—
383#217#4114yescomplemented
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—44no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3—44no—
406C4×Dic3—44no—
407C4×Dic3—44no—
408C25C22×D311yescharacteristic
409C2×#41—61no—
410C2×#41—61no—
411C2×#41—61no—
412C2×#41—61no—
413C2×#41—124no—
414C22×Q8—31no—
415C22×D4—31no—
416C22×D4—31no—
417C22×D4—31no—
418C22×D4—31no—
419C22×D4C4×D311yescharacteristic
420C22×D4C4×D311yescharacteristic
421C22×D4C22×D311yescharacteristic
422C23×C4—21no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—31no—
428C23×C4—31no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—31no—
432C23×C4—31no—
433C23×C4—31no—
434C23×C4—31no—
435C23×C4—31no—
436C23×C4—31no—
437C23×C4—31no—
438C23×C4—31no—
439C23×C4—61no—
440C23×C4—124no—
441#123—61no—
442#123—61no—
443#123—61no—
444#123—61no—
445#123—61no—
446#123—61no—
447#123—61no—
448#123—61no—
449C22⋊Q8—61no—
450C22⋊Q8—61no—
451C22⋊Q8—61no—
452C22⋊Q8—61no—
453C22⋊Q8—61no—
454C22⋊Q8—61no—
455C22⋊Q8—61no—
456C22⋊Q8—61no—
457#121—61no—
458#121—61no—
459#121—61no—
460#121—61no—
461#121—61no—
462#121—61no—
463#121—61no—
464#121—61no—
465#120—21no—
466#120—21no—
467#120—21no—
468#120—21no—
469#120—61no—
470#120—61no—
471#120—61no—
472#120—61no—
473C4×D4—61no—
474C4×D4—61no—
475C4×D4—61no—
476C4×D4—61no—
477C4×D4—61no—
478C4×D4—61no—
479C4×D4—61no—
480C4×D4—61no—
481C4×D4—61no—
482C4×D4—61no—
483C4×D4—61no—
484C4×D4—61no—
485C4×D4—61no—
486C4×D4—61no—
487C4×D4—61no—
488C4×D4—61no—
489#117—61no—
490#117—61no—
491#117—61no—
492#117—61no—
493#117—124no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—62no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—32no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—31no—
513C2×C22⋊C4—32no—
514C2×C22⋊C4—64no—
515C2×C22⋊C4—61no—
516C2×C22⋊C4—61no—
517C2×C22⋊C4—61no—
518C2×C22⋊C4C4×D311yescharacteristic
519C2×C22⋊C4C4×D311yescharacteristic
520C2×C22⋊C4C22×D312yes—
521C2×C22⋊C4C22×D311yescharacteristic
522C2×C22⋊C4C22×D312yes—
523C2×C42—31no—
524C2×C42—31no—
525C2×C42—62no—
526C2×C42—62no—
527C2×C42—62no—
528C2×C42—124no—
529#99—24no—
530#99—64no—
531#99—64no—
532#99—64no—
533#95—62no—
534#95—62no—
535#95—62no—
536#95—62no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—21no—
552C23×C3—22no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—48no—
562C23×C3—48no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3C2×C22⋊C411yescharacteristic
566C23×C3C2×C22⋊C411yescharacteristic
567C23×C3C2×C22⋊C411yescharacteristic
568C23×C3C2×C22⋊C411yescharacteristic
569C23×C3C23×C411yescharacteristic
570C23×C3C22×D411yescharacteristic
571C23×C3C22×D411yescharacteristic
572C23×C3C2×#4112yes—
573C23×C3C2×#4112yes—
574C22×D3—21no—
575C22×D3—22no—
576C22×D3—41no—
577C22×D3—41no—
578C3×D4—42no—
579C3×D4—42no—
580C3×D4—41no—
581C3×D4—41no—
582C3×D4—42no—
583C3×D4—42no—
584C3×D4—42no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—24no—
590C2×C3×C4—42no—
591C2×C3×C4—48no—
592C2×C3×C4—42no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—42no—
596C2×C3×C4—42no—
597C2×C3×C4—42no—
598#67—42no—
599#67—42no—
600#67—42no—
601#67—41no—
602#67—41no—
603#67—42no—
604#67—42no—
605#67—42no—
606#67—42no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—22no—
626C2×Dic3—24no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—42no—
640C2×Dic3—42no—
641C2×Dic3—48no—
642C2×Dic3—42no—
643C2×Dic3—42no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—42no—
647C2×Dic3—42no—
648C2×Dic3—42no—
649C2×Dic3#9914yescomplemented
650C2×Dic3C2×C22⋊C411yescharacteristic
651C2×Dic3C2×C22⋊C411yescharacteristic
652C2×Dic3C2×C22⋊C411yescharacteristic
653C2×Dic3C2×C22⋊C411yescharacteristic
654C2×Dic3C2×C22⋊C411yescharacteristic
655C2×Dic3C2×C22⋊C411yescharacteristic
656C2×Dic3C2×C22⋊C411yescharacteristic
657C2×Dic3C2×C22⋊C411yescharacteristic
658C4×D3—42no—
659C4×D3—42no—
660Dic6—42no—
661Dic6—42no—
662C24—22no—
663C24—22no—
664C24—31no—
665C24—42no—
666C24—42no—
667C24C2×C4×D311yescharacteristic
668C24C2×C4×D311yescharacteristic
669C24C2×C4×D311yescharacteristic
670C24D3×D411yescharacteristic
671C24D3×D411yescharacteristic
672C24D3×D411yescharacteristic
673C24D3×D411yescharacteristic
674C24C23×D311yescharacteristic
675#41—124no—
676#41—124no—
677#41—124no—
678#41—124no—
679C2×Q8—61no—
680C2×Q8—61no—
681C2×Q8—122no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—61no—
697C2×D4—61no—
698C2×D4—61no—
699C2×D4—61no—
700C2×D4—62no—
701C2×D4—62no—
702C2×D4—122no—
703C2×D4—122no—
704C2×D4—122no—
705C22×C4—24no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—31no—
731C22×C4—31no—
732C22×C4—31no—
733C22×C4—31no—
734C22×C4—31no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—61no—
742C22×C4—61no—
743C22×C4—64no—
744C22×C4—64no—
745C22×C4—64no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—64no—
749C22×C4—62no—
750C22×C4—62no—
751C22×C4—122no—
752C22×C4—122no—
753C22×C4—122no—
754C22×C4—122no—
755C22×C4—122no—
756C22×C4—122no—
757C22×C4—122no—
758C22×C4—122no—
759C22×C4—122no—
760C22×C4—122no—
761C22×C4—122no—
762C22×C4—122no—
763C22×C4—122no—
764C22×C4—122no—
765C22×C4—122no—
766C22×C4C2×C4×D311yescharacteristic
767C22×C4C2×C4×D311yescharacteristic
768C22×C4C2×C4×D311yescharacteristic
769C4⋊C4—61no—
770C4⋊C4—61no—
771C4⋊C4—61no—
772C4⋊C4—61no—
773C4⋊C4—61no—
774C4⋊C4—61no—
775C4⋊C4—61no—
776C4⋊C4—61no—
777C4⋊C4—61no—
778C4⋊C4—61no—
779C4⋊C4—61no—
780C4⋊C4—61no—
781C4⋊C4—124no—
782C22⋊C4—24no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—22no—
790C22⋊C4—22no—
791C22⋊C4—22no—
792C22⋊C4—34no—
793C22⋊C4—42no—
794C22⋊C4—42no—
795C22⋊C4—61no—
796C22⋊C4—61no—
797C22⋊C4—61no—
798C22⋊C4—61no—
799C22⋊C4—61no—
800C22⋊C4—61no—
801C22⋊C4—61no—
802C22⋊C4—61no—
803C22⋊C4—64no—
804C22⋊C4—61no—
805C22⋊C4—61no—
806C22⋊C4—61no—
807C22⋊C4—61no—
808C22⋊C4—61no—
809C22⋊C4—61no—
810C22⋊C4—62no—
811C22⋊C4—62no—
812C22⋊C4—62no—
813C22⋊C4—122no—
814C22⋊C4—122no—
815C22⋊C4#23714yescomplemented
816C42—61no—
817C42—61no—
818C42—61no—
819C42—61no—
820C42—124no—
821C42—124no—
822C42—124no—
823C22×C3—24no—
824C22×C3—24no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—44no—
844C22×C3—44no—
845C22×C3—44no—
846C22×C3—44no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—82no—
853C22×C3C2×#9912yes—
854C22×C3#41012yes—
855C22×C3C22×C22⋊C411yescharacteristic
856C22×C3C4×#4112yes—
857C22×C3#52511yescharacteristic
858C22×C3#52511yescharacteristic
859C22×C3#53212yes—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—82no—
864C3×C4—44no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—41no—
868C3×C4—82no—
869Dic3—21no—
870Dic3—21no—
871Dic3—21no—
872Dic3—21no—
873Dic3—21no—
874Dic3—21no—
875Dic3—44no—
876Dic3—41no—
877Dic3—41no—
878Dic3—41no—
879Dic3—82no—
880Dic3C2×#9912yes—
881Dic3C2×#9912yes—
882C23—21no—
883C23—22no—
884C23—22no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—21no—
894C23—22no—
895C23—22no—
896C23—21no—
897C23—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—48no—
907C23—48no—
908C23—41no—
909C23—41no—
910C23—61no—
911C23—62no—
912C23—121no—
913C23—121no—
914C23D3×C22⋊C411yescharacteristic
915C23D3×C22⋊C411yescharacteristic
916C23D3×C22⋊C411yescharacteristic
917C23D3×C22⋊C411yescharacteristic
918C23C22×C4×D311yescharacteristic
919C23C2×D3×D411yescharacteristic
920C23C2×D3×D411yescharacteristic
921C23C2×#23712yes—
922C23D3×#4112yes—
923Q8—122no—
924Q8—122no—
925D4—42no—
926D4—42no—
927D4—41no—
928D4—42no—
929D4—42no—
930D4—41no—
931D4—42no—
932D4—122no—
933D4—122no—
934D4—122no—
935D4—122no—
936D4—121no—
937D4—122no—
938D4—122no—
939D4—121no—
940D4—122no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—31no—
947C2×C4—31no—
948C2×C4—34no—
949C2×C4—31no—
950C2×C4—31no—
951C2×C4—31no—
952C2×C4—31no—
953C2×C4—31no—
954C2×C4—31no—
955C2×C4—42no—
956C2×C4—48no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—64no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—62no—
983C2×C4—122no—
984C2×C4—122no—
985C2×C4—122no—
986C2×C4—121no—
987C2×C4—121no—
988C2×C4—121no—
989C2×C4—121no—
990C2×C4—121no—
991C2×C4—121no—
992C2×C4—121no—
993C2×C4—121no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—122no—
999C2×C4—122no—
1000C2×C4—128no—
1001C2×C4—122no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—122no—
1005C2×C4—122no—
1006C2×C4—122no—
1007C2×C3—21no—
1008C2×C3—22no—
1009C2×C3—21no—
1010C2×C3—22no—
1011C2×C3—22no—
1012C2×C3—22no—
1013C2×C3—41no—
1014C2×C3—41no—
1015C2×C3—81no—
1016C2×C3#229711yescharacteristic
1017C2×C3C22×#9911yescharacteristic
1018C2×C3C2×#41011yescharacteristic
1019D3—81no—
1020C22—24no—
1021C22—24no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—21no—
1038C22—42no—
1039C22—42no—
1040C22—44no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—42no—
1045C22—42no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—82no—
1050C22—121no—
1051C22—121no—
1052C22—121no—
1053C22—242no—
1054C22#474012yes—
1055C22D3×#9912yes—
1056C22C2×D3×C22⋊C411yescharacteristic
1057C22C4×#23712yes—
1058C22#558611yescharacteristic
1059C22#559612yes—
1060C22#565611yescharacteristic
1061C4—32no—
1062C4—32no—
1063C4—44no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—61no—
1068C4—61no—
1069C4—61no—
1070C4—61no—
1071C4—61no—
1072C4—61no—
1073C4—82no—
1074C4—124no—
1075C4—121no—
1076C4—121no—
1077C4—121no—
1078C4—242no—
1079C3#2142011yescharacteristic, complemented, Sylow
1080C2—21no—
1081C2—22no—
1082C2—21no—
1083C2—22no—
1084C2—22no—
1085C2—22no—
1086C2—41no—
1087C2—41no—
1088C2—81no—
1089C2—241no—
1090C2#7465811yescharacteristic
1091C2C2×#474011yescharacteristic
1092C2C2×D3×#9911yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1898C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5586C2
cosocleC24×C3C24
hypercenter#1898D3
hypocenterC3#21420
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ #1898

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×C22⋊C4C2semidirect
3. #73817C2semidirect
4. C3×#1898C2semidirect
5. #71670C2semidirect
6. #71543C2semidirect
7. #70030C2semidirect
8. Dic3×#99C2semidirect
9. #69496C2semidirect
10. #68955C2semidirect
11. #68952C2semidirect
14. C22×#237C4semidirect
19. C2×#939C4semidirect
21. C2×#935C4semidirect
22. C2×D4×Dic3C4semidirect
33. C2×#886C4semidirect
34. C2×#67⋊C4C4semidirect
36. C2×#878C4semidirect
39. C2×#877C4semidirect
68. #1898D3semidirect
78. C22×#67C2×C4semidirect
86. C23×Dic3C2×C4semidirect
102. C22×C4×D3C2×C4semidirect
103. C22×Dic6C2×C4semidirect
127. C2×#217C2×C4semidirect
128. C2×#217C2×C4semidirect
152. C2×(C2×D3)⋊C4C2×C4semidirect
153. C2×(C2×D3)⋊C4C2×C4semidirect
154. C2×C4⋊Dic3C2×C4semidirect
155. C2×C4⋊Dic3C2×C4semidirect
157. C2×Dic3⋊C4C2×C4semidirect
158. C2×Dic3⋊C4C2×C4semidirect
159. C2×Dic3⋊C4C2×C4semidirect
160. C2×Dic3⋊C4C2×C4semidirect
165. C2×C4×Dic3C2×C4semidirect
166. C2×C4×Dic3C2×C4semidirect
366. C3×C22⋊C4#41semidirect
383. #217#41semidirect
649. C2×Dic3#99semidirect
815. C22⋊C4#237semidirect
1079. C3#21420semidirect

Maximal subgroups

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

subgroupindex
C2×#55862
C2×Dic3×C22⋊C42
#738172
C3×#18982
#716702
#715432
#700302
Dic3×#992
#694962
#689552
#689522
#214203