Finite Group Databasebeta

← #11664134

Subgroups — #11664134

Order 768.

2074 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5827C211yesmaximal, characteristic, complemented
2#85970C211yesmaximal, characteristic, complemented
3C3×#3007C211yesmaximal, characteristic, complemented
4#84080C211yesmaximal, characteristic
5#83971C212yesmaximal, complemented
6#83965C212yesmaximal, complemented
7C2×#5044C211yesmaximal, characteristic, complemented
8#80218C214yesmaximal, complemented
9#80216C214yesmaximal, complemented
10#80175C212yesmaximal, complemented
11#80172C212yesmaximal, complemented
12#80134C212yesmaximal, complemented
13#80133C212yesmaximal, complemented
14#78872C212yesmaximal, complemented
15#78868C212yesmaximal, complemented
16#78622C211yesmaximal, characteristic, complemented
17#78621C211yesmaximal, characteristic, complemented
18#60589—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C2×C3×#137C2212yes—
21C2×C3×C22⋊Q8C2211yescharacteristic
22#5827—21no—
23#5827—21no—
24#5827—22no—
25#5827C2212yes—
26#5827C2212yes—
27#5827C2214yes—
28C2×#950C2212yes—
29#5816C2211yescharacteristic, complemented
30#5812C2211yescharacteristic, complemented
31C2×Q8×Dic3C2212yes—
32C2×D4×Dic3—22no—
33C2×D4×Dic3C2212yes—
34#5791C2211yescharacteristic
35C2×#926—21no—
36C2×#926C2211yescharacteristic
37C22×C4⋊Dic3—21no—
38C22×C4⋊Dic3C2211yescharacteristic
39#5643C2212yescomplemented
40#5642—21no—
41#5641—21no—
42#5639—21no—
43#5635—21no—
44#5625C2212yescomplemented
45#5624C2212yes—
46#5622C2212yes—
47#5513—22no—
48#5504C2211yescharacteristic, complemented
49#5500C2211yescharacteristic, complemented
50#5495—22no—
51C3×#452C2214yes—
52C3×#451C2212yes—
53C3×#450C2212yes—
54C3×#417C2212yes—
55C3×#407C2211yescharacteristic
56#5239C2212yes—
57#5238C2212yes—
58#5233C2212yes—
59#5228C2211yescharacteristic
60#5227C2211yescharacteristic
61C2×#835C2212yescomplemented
62#5218C2211yescharacteristic
63#5217C2211yescharacteristic
64C2×#830C2211yescharacteristic
65#5185C2214yescomplemented
66#5184C2214yescomplemented
67#5182C2214yescomplemented
68Dic3×Q16C2214yescomplemented
69#5165C2214yescomplemented
70#5164C2214yescomplemented
71#5162C2214yescomplemented
72Dic3×SD16C2214yescomplemented
73#5133C2212yescomplemented
74#5122C2212yescomplemented
75#5121C2212yescomplemented
76#5119C2212yescomplemented
77#5044C2212yes—
78#5044C2212yes—
79#5044C2214yescomplemented
80C2×#807C2212yescomplemented
81#4817C2214yescomplemented
82#4799C2214yescomplemented
83#4793C2214yescomplemented
84#4790C2214yescomplemented
85#4763C2214yescomplemented
86#4759C2214yescomplemented
87#4757C2214yescomplemented
88#4756C2214yescomplemented
89#4736C2212yescomplemented
90#4735C2212yes—
91#4722C2212yes—
92#4721C2212yescomplemented
93#4720C2214yescomplemented
94#4719C2212yes—
95#4718C2212yes—
96#3495—31no—
97C2×#520—31no—
98#3124—34no—
99#3120—34no—
100#3117—32no—
101#3110—32no—
102#3105—32no—
103#3104—32no—
104#3092—31no—
105C2×#484—31no—
106#3083—32no—
107#3046—32no—
108#3007D311yescharacteristic, complemented
109#3002—31no—
110#2951—32no—
111#2947—32no—
112#2924—31no—
113C2×C3×#41—28no—
114C2×C3×#41—21no—
115C2×C3×#41—21no—
116C2×C3×#41C2312yes—
117C2×C3×#41C2312yes—
118C22×C3×Q8C2311yescharacteristic
119C22×C3×Q8C2311yescharacteristic
120C22×C3×D4—21no—
121C22×C3×D4C2311yescharacteristic
122C23×C3×C4—21no—
123C23×C3×C4C2311yescharacteristic
124C23×Dic3—21no—
125C23×Dic3—22no—
126C2×#235C2311yescharacteristic
127C3×#137—28no—
128C2×C3×Q16C2314yes—
129C2×C3×SD16C2314yes—
130C2×C3×M16C2312yes—
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8—21no—
133C3×C22⋊Q8C2312yes—
134C3×C22⋊Q8C2312yes—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4—21no—
138#953—21no—
139C2×#217—22no—
140C2×#217D412yes—
141#950—28no—
142#947C2312yes—
143#946—21no—
144#946—21no—
145Q8×Dic3—21no—
146Q8×Dic3—21no—
147Q8×Dic3—22no—
148Q8×Dic3—22no—
149Q8×Dic3C2312yes—
150Q8×Dic3C2312yes—
151Q8×Dic3C2314yes—
152Q8×Dic3C2314yes—
153#944C2312yes—
154C2×#216C2312yes—
155C2×#215C2312yes—
156D4×Dic3—24no—
157D4×Dic3—24no—
158D4×Dic3—24no—
159D4×Dic3—24no—
160D4×Dic3—22no—
161D4×Dic3—22no—
162D4×Dic3C2314yes—
163D4×Dic3C2314yes—
164C2×#214C2312yes—
165C2×#213C2312yes—
166#930C2311yescharacteristic
167#930C2311yescharacteristic
168#929—21no—
169#929—22no—
170C4×#67—21no—
171C4×#67—21no—
172C4×#67—22no—
173#926—22no—
174#926—24no—
175#926—22no—
176#926—22no—
177#926D411yescharacteristic
178#926D411yescharacteristic
179#926D412yes—
180#926C2311yescharacteristic
181#926C2311yescharacteristic
182#926C2312yes—
183#926C2311yescharacteristic
184C2×C4⋊Dic3—21no—
185C2×C4⋊Dic3—21no—
186C2×C4⋊Dic3—21no—
187C2×C4⋊Dic3—22no—
188C2×C4⋊Dic3—22no—
189C2×C4⋊Dic3—24no—
190C2×C4⋊Dic3—22no—
191C2×C4⋊Dic3D411yescharacteristic
192C2×C4⋊Dic3D411yescharacteristic
193C2×C4⋊Dic3C2312yes—
194C2×C4⋊Dic3C2312yes—
195C2×C4⋊Dic3C2312yes—
196#924—22no—
197#924C2311yescharacteristic
198#924C2311yescharacteristic
199C2×C4×Dic3—22no—
200C2×C4×Dic3C2312yes—
201C22×C3⋊C8C2312yes—
202#898—22no—
203#898—22no—
204#897—22no—
205#893C2312yes—
206#892—21no—
207#892—22no—
208D3×C4⋊C4—21no—
209#890—21no—
210#890—22no—
211#890C2312yes—
212#889—22no—
213#889—22no—
214#888—21no—
215#888C2312yes—
216#887—22no—
217#887C2312yes—
218#886—22no—
219#885—22no—
220#883—22no—
221#67⋊C4—22no—
222#879—22no—
223#879—22no—
224#878—22no—
225#877—22no—
226C3×#103C2314yes—
227C3×#102C2314yes—
228C3×C22⋊C8C2312yes—
229C3×C22⋊C8C2312yes—
230#835C2314yes—
231#835C2314yes—
232#835C2312yes—
233#835C2312yes—
234#832C2312yes—
235#832C2312yes—
236#830C2311yescharacteristic
237#830C2311yescharacteristic
238#830C2312yes—
239#821C2314yes—
240#818C2314yes—
241#817C2314yes—
242#816C2314yes—
243#815C2314yes—
244Dic3⋊C8C2314yes—
245Dic3⋊C8C2314yes—
246C8×Dic3C2314yes—
247#807C2314yes—
248#807C2314yes—
249C22×#41C2×D311yescharacteristic
250C2×#137C2×D312yes—
251C2×#135—32no—
252#556—61no—
253#554—61no—
254#552—62no—
255#552—61no—
256#552—61no—
257#551—62no—
258#544—31no—
259#542—32no—
260#541—32no—
261#536—31no—
262#533—32no—
263#529—32no—
264#525—31no—
265C2×C22⋊Q8C2×D311yescharacteristic
266#520—32no—
267#520—34no—
268#520—32no—
269#520—31no—
270#520—61no—
271#520—62no—
272#520—61no—
273#519—31no—
274C2×C4×Q8—32no—
275C2×C4×D4—32no—
276C2×C4×D4—62no—
277C2×#117—31no—
278C2×#117—61no—
279C22×C4⋊C4—31no—
280C22×C4⋊C4—61no—
281#484—32no—
282#484—32no—
283#484—34no—
284#484—32no—
285#483—32no—
286#481—32no—
287#480—32no—
288#479—34no—
289#478—34no—
290#477—34no—
291#474—34no—
292#464—34no—
293#463—34no—
294#462—34no—
295#461—34no—
296#452—32no—
297#452C2×D314yes—
298#451—31no—
299#451C2×D312yes—
300#450—31no—
301#450C2×D312yes—
302#449—32no—
303#448—31no—
304#447—31no—
305#441—34no—
306#440—34no—
307#440—34no—
308#440—34no—
309C4×Q16—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313#433—34no—
314#432—32no—
315#431—32no—
316#428—32no—
317C2×#107—32no—
318#424—32no—
319#417—32no—
320#417C2×D312yes—
321#416—32no—
322C2×#103—32no—
323#407C2×D311yescharacteristic
324C2×C22⋊C8—31no—
325#405—32no—
326C24×C3—21no—
327C24×C3C2×D411yescharacteristic
328C3×#41—28no—
329C3×#41—28no—
330C3×#41—24no—
331C3×#41—24no—
332C3×#41—24no—
333C3×#41#4118yes—
334C2×C3×Q8—24no—
335C2×C3×Q8—21no—
336C2×C3×Q8—21no—
337C2×C3×Q8—24no—
338C2×C3×Q8C2412yes—
339C2×C3×Q8C2412yes—
340C2×C3×D4—28no—
341C2×C3×D4—22no—
342C2×C3×D4—22no—
343C2×C3×D4—24no—
344C2×C3×D4—21no—
345C2×C3×D4C2412yes—
346C22×C3×C4—28no—
347C22×C3×C4—21no—
348C22×C3×C4—22no—
349C22×C3×C4—22no—
350C22×C3×C4—24no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4C2×D411yescharacteristic
354C22×C3×C4C2×D411yescharacteristic
355C22×C3×C4C2×D411yescharacteristic
356C22×C3×C4C2411yescharacteristic
357C22×C3×C4C2411yescharacteristic
358C22×C3×C4C2411yescharacteristic
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—21no—
362C22×Dic3—22no—
363C22×Dic3—22no—
364C22×Dic3—22no—
365C22×Dic3—24no—
366C22×Dic3—24no—
367C22×Dic3—84no—
368C22×Dic3—82no—
369C22×Dic3C2×D412yes—
370C22×Dic3C2×D412yes—
371#235—24no—
372C2×D12C2411yescharacteristic
373C2×C4×D3—21no—
374C2×C4×D3—22no—
375C2×Dic6—22no—
376C2×Dic6C2411yescharacteristic
377C3×Q16—28no—
378C3×SD16—28no—
379C3×M16—24no—
380C2×C3×C8C2414yes—
381C3×C4⋊C4—22no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4C2412yes—
385C3×C22⋊C4—22no—
386C3×C22⋊C4—22no—
387#217—21no—
388#217—21no—
389#217—21no—
390#217—24no—
391#217—24no—
392#217C2×D412yes—
393#217C2×D412yes—
394#217C2×D412yes—
395#217C2×D412yes—
396#216—24no—
397#215—24no—
398#214—24no—
399#213—24no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—22no—
404(C2×D3)⋊C4—22no—
405C4⋊Dic3—22no—
406C4⋊Dic3—22no—
407C4⋊Dic3—22no—
408C4⋊Dic3—22no—
409C4⋊Dic3—22no—
410C4⋊Dic3—22no—
411C4⋊Dic3—24no—
412C4⋊Dic3—24no—
413C4⋊Dic3C2×D411yescharacteristic
414C4⋊Dic3C2×D412yes—
415C4⋊Dic3C2×D412yes—
416C4⋊Dic3C2×D411yescharacteristic
417C4⋊Dic3C2×D411yescharacteristic
418C4⋊Dic3C2×D411yescharacteristic
419C4⋊Dic3C2414yes—
420C4⋊Dic3C2411yescharacteristic
421C4⋊Dic3C2411yescharacteristic
422Dic3⋊C4—21no—
423Dic3⋊C4—21no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—22no—
429C4×Dic3—21no—
430C4×Dic3—22no—
431C4×Dic3—22no—
432C4×Dic3—22no—
433C4×Dic3—24no—
434C4×Dic3—24no—
435C4×Dic3C2×D412yes—
436C4×Dic3C2×D412yes—
437C4×Dic3C2412yes—
438C4×Dic3C2412yes—
439C2×C3⋊C8—24no—
440C2×C3⋊C8C2412yes—
441C2×C3⋊C8C2412yes—
442C2×#41—28no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—31no—
446C2×#41C22×D312yes—
447C2×#41C22×D312yes—
448C22×Q8C22×D311yescharacteristic
449C22×Q8C22×D311yescharacteristic
450C22×D4—21no—
451C22×D4C22×D311yescharacteristic
452C23×C4—21no—
453C23×C4—62no—
454C23×C4—61no—
455C23×C4C22×D311yescharacteristic
456#137—28no—
457#135—68no—
458C2×Q16—32no—
459C2×Q16C22×D314yes—
460C2×SD16—32no—
461C2×SD16—32no—
462C2×SD16C22×D314yes—
463C2×D8—32no—
464C2×M16C22×D312yes—
465C22×C8—32no—
466C4⋊Q8—32no—
467C4⋊Q8—32no—
468C4⋊Q8—61no—
469#126—62no—
470#126—62no—
471#126—62no—
472#126—62no—
473#125—32no—
474#125—62no—
475#125—62no—
476#125—62no—
477#125—61no—
478#124—32no—
479#124—62no—
480#123—62no—
481#123—62no—
482#123—62no—
483#123—61no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—31no—
487C22⋊Q8—31no—
488C22⋊Q8—62no—
489C22⋊Q8—62no—
490C22⋊Q8—62no—
491C22⋊Q8—61no—
492C22⋊Q8—61no—
493C22⋊Q8C22×D312yes—
494C22⋊Q8C22×D312yes—
495#121—31no—
496#121—31no—
497#120—61no—
498C4×Q8—34no—
499C4×Q8—34no—
500C4×Q8—32no—
501C4×Q8—32no—
502C4×Q8—32no—
503C4×Q8—62no—
504C4×Q8—62no—
505C4×Q8—62no—
506C4×Q8—61no—
507C4×Q8—61no—
508C4×D4—34no—
509C4×D4—34no—
510C4×D4—32no—
511C4×D4—62no—
512C4×D4—62no—
513C4×D4—62no—
514C4×D4—62no—
515C4×D4—64no—
516C4×D4—64no—
517C4×D4—64no—
518C4×D4—64no—
519C4×D4—61no—
520C4×D4—61no—
521#117—31no—
522#117—32no—
523#117—31no—
524#117—31no—
525#117—31no—
526#117—32no—
527#117—31no—
528#117—62no—
529#117—62no—
530#117—62no—
531#117—61no—
532#117—62no—
533#117—62no—
534#117—64no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—32no—
540C2×C4⋊C4—32no—
541C2×C4⋊C4—61no—
542C2×C4⋊C4—62no—
543C2×C4⋊C4—64no—
544C2×C4⋊C4—62no—
545C2×C4⋊C4—62no—
546C2×C4⋊C4—61no—
547C2×C4⋊C4—61no—
548C2×C4⋊C4—61no—
549C2×C4⋊C4C22×D311yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—32no—
552C2×C22⋊C4—62no—
553C2×C42—32no—
554C2×C42—62no—
555#107—34no—
556#107—34no—
557#107—34no—
558#106—34no—
559C4⋊C8—34no—
560C4⋊C8—34no—
561#103—34no—
562#103—34no—
563#103—32no—
564#103—32no—
565#103—34no—
566#103C22×D314yes—
567#102—32no—
568#102—32no—
569#102—34no—
570#102C22×D314yes—
571C22⋊C8—31no—
572C22⋊C8—31no—
573C22⋊C8—32no—
574C22⋊C8C22×D312yes—
575C22⋊C8C22×D312yes—
576#97—34no—
577C4×C8—34no—
578C23×C3—24no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—41no—
583C23×C3—42no—
584C23×C3—42no—
585C23×C3C22×D411yescharacteristic
586C23×C3C22×D411yescharacteristic
587C23×C3C22×D411yescharacteristic
588C22×D3—21no—
589C3×Q8—24no—
590C3×Q8—22no—
591C3×Q8—24no—
592C3×Q8—42no—
593C3×Q8C2×#4114yes—
594C3×D4—28no—
595C3×D4—24no—
596C3×D4—28no—
597C3×D4—22no—
598C3×D4C2×#4114yes—
599C2×C3×C4—24no—
600C2×C3×C4—28no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—28no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—42no—
611C2×C3×C4—81no—
612C2×C3×C4C22×D411yescharacteristic
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C22×D411yescharacteristic
615C2×C3×C4C2×#4114yes—
616C2×C3×C4C2511yescharacteristic
617#67—42no—
618#67—42no—
619#67—81no—
620C2×Dic3—24no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—24no—
625C2×Dic3—42no—
626C2×Dic3—44no—
627C2×Dic3—84no—
628C2×Dic3—84no—
629C2×Dic3—82no—
630C2×Dic3—82no—
631C2×Dic3C22×D412yes—
632C2×Dic3C22×D412yes—
633C2×Dic3C22×D412yes—
634C2×Dic3C22×D412yes—
635D12—22no—
636C4×D3—42no—
637C4×D3—82no—
638Dic6—22no—
639Dic6—82no—
640C3×C8—24no—
641C3⋊C8—22no—
642C3⋊C8—22no—
643C24—21no—
644C24D3×D411yescharacteristic
645#41—28no—
646#41—28no—
647#41—24no—
648#41—24no—
649#41—24no—
650#41—64no—
651#41#23718yes—
652C2×Q8—24no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—24no—
656C2×Q8—31no—
657C2×Q8—62no—
658C2×Q8C23×D312yes—
659C2×Q8C23×D312yes—
660C2×D4—28no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—31no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4C23×D312yes—
670C22×C4—28no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—24no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—32no—
678C22×C4—32no—
679C22×C4—62no—
680C22×C4—64no—
681C22×C4—64no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—61no—
686C22×C4—244no—
687C22×C4—242no—
688C22×C4D3×D411yescharacteristic
689C22×C4D3×D411yescharacteristic
690C22×C4D3×D411yescharacteristic
691C22×C4C23×D311yescharacteristic
692C22×C4C23×D311yescharacteristic
693C22×C4C23×D311yescharacteristic
694Q16—28no—
695Q16—64no—
696SD16—28no—
697SD16—64no—
698SD16—64no—
699D8—64no—
700M16—24no—
701C2×C8—32no—
702C2×C8—32no—
703C2×C8—64no—
704C2×C8C23×D314yes—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—21no—
708C4⋊C4—31no—
709C4⋊C4—32no—
710C4⋊C4—31no—
711C4⋊C4—31no—
712C4⋊C4—31no—
713C4⋊C4—32no—
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—34no—
717C4⋊C4—64no—
718C4⋊C4—64no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—62no—
722C4⋊C4—62no—
723C4⋊C4—62no—
724C4⋊C4—62no—
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4—62no—
728C4⋊C4—62no—
729C4⋊C4—62no—
730C4⋊C4—61no—
731C4⋊C4—61no—
732C4⋊C4C23×D312yes—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—32no—
736C22⋊C4—32no—
737C22⋊C4—32no—
738C22⋊C4—32no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—62no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C22⋊C4—61no—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—61no—
748C22⋊C4—61no—
749C42—32no—
750C42—32no—
751C42—32no—
752C42—32no—
753C42—64no—
754C42—64no—
755C42—62no—
756C42—62no—
757C42—62no—
758C42—61no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—24no—
766C22×C3—21no—
767C22×C3—44no—
768C22×C3—48no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3#52512yes—
772C22×C3#57812yes—
773C22×C3C23×D411yescharacteristic
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C3×C4—21no—
778C3×C4—24no—
779C3×C4—21no—
780C3×C4—42no—
781C3×C4—42no—
782C3×C4#52512yes—
783C3×C4C22×#4112yes—
784Dic3—22no—
785Dic3—22no—
786Dic3—22no—
787Dic3—22no—
788Dic3—41no—
789Dic3—44no—
790Dic3—41no—
791Dic3—41no—
792C23—24no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—61no—
800C23C2×D3×D411yescharacteristic
801C23C2×D3×D411yescharacteristic
802C23C2×D3×D411yescharacteristic
803Q8—24no—
804Q8—22no—
805Q8—24no—
806Q8—42no—
807Q8—62no—
808Q8—242no—
809Q8C2×#23714yes—
810D4—28no—
811D4—24no—
812D4—28no—
813D4—22no—
814D4—62no—
815D4—122no—
816D4—122no—
817D4—241no—
818D4C2×#23714yes—
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—28no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—32no—
834C2×C4—42no—
835C2×C4—64no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—64no—
839C2×C4—61no—
840C2×C4—81no—
841C2×C4—122no—
842C2×C4—124no—
843C2×C4—122no—
844C2×C4—242no—
845C2×C4—244no—
846C2×C4—244no—
847C2×C4—242no—
848C2×C4—242no—
849C2×C4C2×D3×D411yescharacteristic
850C2×C4C2×D3×D411yescharacteristic
851C2×C4C2×D3×D411yescharacteristic
852C2×C4C2×#23714yes—
853C2×C4C24×D311yescharacteristic
854C8—24no—
855C8—62no—
856C8—62no—
857C2×C3—22no—
858C2×C3—22no—
859C2×C3—41no—
860C2×C3—44no—
861C2×C3C2×#52511yescharacteristic
862C2×C3C2×#57811yescharacteristic
863C2×C3#358511yescharacteristic
864D3—81no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—24no—
871C22—21no—
872C22—21no—
873C22—44no—
874C22—48no—
875C22—42no—
876C22—42no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22#558612yes—
881C22#577912yes—
882C22C22×D3×D411yescharacteristic
883C4—21no—
884C4—24no—
885C4—21no—
886C4—42no—
887C4—42no—
888C4—62no—
889C4—62no—
890C4—62no—
891C4—62no—
892C4—121no—
893C4—121no—
894C4—124no—
895C4—121no—
896C4#558612yes—
897C4C22×#23712yes—
898C3#6058911yescharacteristic, complemented, Sylow
899C2—22no—
900C2—22no—
901C2—41no—
902C2—44no—
903C2—241no—
904C2C2×#558611yescharacteristic
905C2C2×#577911yescharacteristic
906C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3007C2
socleC22×C3C23×D4
prime radical#84080C2
hypercenter#3007D3
hypocenterC3#60589
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. C2×#5827C2semidirect
2. #85970C2semidirect
3. C3×#3007C2semidirect
5. #83971C2semidirect
6. #83965C2semidirect
7. C2×#5044C2semidirect
8. #80218C2semidirect
9. #80216C2semidirect
10. #80175C2semidirect
11. #80172C2semidirect
12. #80134C2semidirect
13. #80133C2semidirect
14. #78872C2semidirect
15. #78868C2semidirect
16. #78622C2semidirect
17. #78621C2semidirect
29. #5816C22semidirect
30. #5812C22semidirect
39. #5643C22semidirect
44. #5625C22semidirect
48. #5504C22semidirect
49. #5500C22semidirect
61. C2×#835C22semidirect
65. #5185C22semidirect
66. #5184C22semidirect
67. #5182C22semidirect
68. Dic3×Q16C22semidirect
69. #5165C22semidirect
70. #5164C22semidirect
71. #5162C22semidirect
72. Dic3×SD16C22semidirect
73. #5133C22semidirect
74. #5122C22semidirect
75. #5121C22semidirect
76. #5119C22semidirect
79. #5044C22semidirect
80. C2×#807C22semidirect
81. #4817C22semidirect
82. #4799C22semidirect
83. #4793C22semidirect
84. #4790C22semidirect
85. #4763C22semidirect
86. #4759C22semidirect
87. #4757C22semidirect
88. #4756C22semidirect
89. #4736C22semidirect
92. #4721C22semidirect
93. #4720C22semidirect
108. #3007D3semidirect
898. C3#60589semidirect

Maximal subgroups

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

subgroupindex
C2×#58272
#859702
C3×#30072
#840802
#839712
#839652
C2×#50442
#802182
#802162
#801752
#801722
#801342
#801332
#788722
#788682
#786222
#786212
#605893