Finite Group Databasebeta

← #11664171

Subgroups — #11664171

Order 768.

2074 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×H(5,𝔽2)C211yesmaximal, characteristic
2#85830C211yesmaximal, characteristic, complemented
3#84105C212yesmaximal
4#82575C214yesmaximal, complemented
5#82573C212yesmaximal, complemented
6#82571C212yesmaximal, complemented
7#82545C214yesmaximal, complemented
8#82543C212yesmaximal, complemented
9#82535C212yesmaximal, complemented
10#82534C212yesmaximal, complemented
11#82533C211yesmaximal, characteristic, complemented
12#82515C211yesmaximal, characteristic, complemented
13#82507C211yesmaximal, characteristic, complemented
14#82315C212yesmaximal, complemented
15#82314C212yesmaximal, complemented
16C2×#5019C211yesmaximal, characteristic, complemented
17#82296C211yesmaximal, characteristic, complemented
18#60591—31nomaximal, Sylow
19C2×C3×H(5,𝔽2)C2211yescharacteristic
20C3×#520—21no—
21C3×#520C2211yescharacteristic
22C3×#520C2212yes—
23C3×#520C2211yescharacteristic
24C3×#518—22no—
25C3×#518—21no—
26C3×#518C2211yescharacteristic
27C3×#518C2212yes—
28C3×C4×#41—21no—
29C3×C4×#41C2211yescharacteristic
30C3×C4×#41C2212yes—
31C3×C4×#41C2211yescharacteristic
32C2×C3×C4×D4—22no—
33C2×C3×C4×D4—21no—
34C2×C3×C4×D4C2211yescharacteristic
35C2×C3×C4×D4C2212yes—
36#5825C2212yes—
37C2×#951C2212yes—
38C22×#214C2212yes—
39#5567—21no—
40#5567—21no—
41#5542—21no—
42#5542—21no—
43#5541—22no—
44#5541—22no—
45#5518C2214yescomplemented
46#5516C2212yescomplemented
47#5470C2211yescharacteristic, complemented
48#5470C2212yescomplemented
49#5470C2212yescomplemented
50C2×#869C2211yescharacteristic, complemented
51#5239C2214yes—
52#5239C2214yes—
53#5234C2212yes—
54#5233C2212yes—
55#5218C2214yes—
56#5218C2214yes—
57#5215C2212yes—
58#5031C2212yescomplemented
59#5031C2212yescomplemented
60#5030C2214yescomplemented
61C4×#216C2214yescomplemented
62#5022C2212yescomplemented
63#5021C2211yescharacteristic, complemented
64#5020C2211yescharacteristic, complemented
65#5019C2212yescomplemented
66#5019C2212yescomplemented
67#5019C2212yescomplemented
68#5019C2212yescomplemented
69#5019C2214yescomplemented
70#5018C2214yescomplemented
71#5018C2214yescomplemented
72#5018C2214yescomplemented
73C4×#214C2214yescomplemented
74C4×#214C2214yescomplemented
75C4×#214C2214yescomplemented
76#5009C2212yescomplemented
77#5009C2214yescomplemented
78#5008C2211yescharacteristic, complemented
79#5008C2212yescomplemented
80#5007C2211yescharacteristic, complemented
81#5007C2212yescomplemented
82#5004C2212yescomplemented
83#5000C2214yescomplemented
84#4998C2212yescomplemented
85#4997C2212yescomplemented
86#4996C2214yescomplemented
87#4996C2214yescomplemented
88#4971C2214yescomplemented
89#4970C2214yescomplemented
90C2×#810C2212yescomplemented
91#4964C2212yescomplemented
92#4926C2212yescomplemented
93#4925C2212yescomplemented
94#4924C2211yescharacteristic, complemented
95C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
96#3509—31no—
97C4×H(5,𝔽2)D311yescharacteristic
98#3123—34no—
99#3120—34no—
100#3116—32no—
101#3110—32no—
102#3107—32no—
103#3101—32no—
104#3097—32no—
105#3077—31no—
106#3076—31no—
107#3039—31no—
108C2×#461—31no—
109#3009—32no—
110#2949—32no—
111#2947—32no—
112#2925—31no—
113C3×H(5,𝔽2)—24no—
114C3×H(5,𝔽2)—24no—
115C2×C3×#41—21no—
116C2×C3×#41C2312yes—
117C2×C3×#41C2311yescharacteristic
118C2×C3×#41C2311yescharacteristic
119C22×C3×D4—22no—
120C22×C3×D4—21no—
121C22×C3×D4C2312yes—
122C22×C3×D4C2311yescharacteristic
123C23×C3×C4—21no—
124C23×C3×C4—22no—
125C22×Dic6C2312yes—
126C3×C4×Q8—21no—
127C3×C4×Q8D411yescharacteristic
128C3×C4×Q8D411yescharacteristic
129C3×C4×Q8C2311yescharacteristic
130C3×C4×Q8C2311yescharacteristic
131C3×C4×Q8C2312yes—
132C3×C4×D4—22no—
133C3×C4×D4—21no—
134C3×C4×D4—21no—
135C3×C4×D4—22no—
136C3×C4×D4—21no—
137C3×C4×D4—22no—
138C3×C4×D4—21no—
139C3×C4×D4—22no—
140C3×C4×D4—21no—
141C3×C4×D4—22no—
142C3×C4×D4—22no—
143C3×C4×D4—22no—
144C3×C4×D4—22no—
145C3×C4×D4—21no—
146C3×C4×D4—22no—
147C3×C4×D4—21no—
148C3×C4×D4—22no—
149C3×C4×D4D412yes—
150C3×C4×D4D412yes—
151C3×C4×D4D411yescharacteristic
152C3×C4×D4D411yescharacteristic
153C3×C4×D4C2311yescharacteristic
154C3×C4×D4C2312yes—
155C3×C4×D4C2312yes—
156C3×C4×D4C2311yescharacteristic
157C3×C4×D4C2312yes—
158C3×C4×D4C2312yes—
159C3×C4×D4C2312yes—
160C3×#117—21no—
161C3×#117—22no—
162C3×#117—21no—
163C3×#117—22no—
164C3×#117C2312yes—
165C3×#117C2311yescharacteristic
166C3×#117C2311yescharacteristic
167C3×#117C2312yes—
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4—22no—
170C2×C3×C4⋊C4C2311yescharacteristic
171C2×C3×C4⋊C4C2312yes—
172C2×C3×C22⋊C4—21no—
173C2×C3×C22⋊C4—22no—
174C2×C3×C22⋊C4—22no—
175C2×C3×C22⋊C4—22no—
176C2×C3×C22⋊C4—22no—
177C2×C3×C42—21no—
178C2×C3×C42—22no—
179C2×C3×C42C2311yescharacteristic
180C2×C3×C42C2312yes—
181#951—28no—
182#944—22no—
183C2×#216C2314yes—
184#936—22no—
185#935—24no—
186C2×#214—28no—
187C2×#214C2314yes—
188C2×#214C2314yes—
189C2×#214C2314yes—
190#926—22no—
191#926—22no—
192#926C2312yes—
193C2×C4⋊Dic3—21no—
194C2×C4⋊Dic3—21no—
195#924—21no—
196#924—21no—
197#924—22no—
198#924—22no—
199#924C2314yes—
200#924C2314yes—
201C2×#208C2312yes—
202C22×C3⋊C8C2312yes—
203#889—24no—
204#889—24no—
205#887—22no—
206#887—22no—
207#879—24no—
208#879—24no—
209#877—24no—
210#870—22no—
211#870—22no—
212#870C2312yes—
213#869—21no—
214#869—21no—
215#869C2312yes—
216#869C2312yes—
217#869C2311yescharacteristic
218#869C2311yescharacteristic
219C4×Dic6—22no—
220C4×Dic6—22no—
221C4×Dic6—21no—
222C4×Dic6—21no—
223C4×Dic6C2314yes—
224C4×Dic6C2314yes—
225#835C2312yes—
226#835C2312yes—
227#832C2314yes—
228#832C2314yes—
229#832C2312yes—
230#832C2312yes—
231#830C2314yes—
232#830C2314yes—
233#810C2314yes—
234#810C2314yes—
235#810C2314yes—
236#810C2314yes—
237#808C2314yes—
238#808C2312yes—
239#808C2312yes—
240#807C2314yes—
241#807C2312yes—
242#807C2312yes—
243C4⋊(C3⋊C8)C2311yescharacteristic
244C4⋊(C3⋊C8)C2311yescharacteristic
245C4⋊(C3⋊C8)C2312yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248#803C2314yes—
249C4×C3⋊C8C2314yes—
250C2×H(5,𝔽2)C2×D311yescharacteristic
251C2×#137—32no—
252C22×SD16—32no—
253#557—61no—
254#557—61no—
255#556—61no—
256#556—61no—
257#552—62no—
258#552—62no—
259#541—34no—
260#536—32no—
261#533—31no—
262#533—32no—
263#533—32no—
264C2×C4⋊Q8—31no—
265#520—21no—
266#520C2×D312yes—
267#520C2×D311yescharacteristic
268#520C2×D311yescharacteristic
269#519—32no—
270#518—22no—
271#518—21no—
272#518C2×D312yes—
273#518C2×D311yescharacteristic
274C4×#41—21no—
275C4×#41C2×D311yescharacteristic
276C4×#41C2×D312yes—
277C4×#41C2×D311yescharacteristic
278C2×C4×D4—22no—
279C2×C4×D4—21no—
280C2×C4×D4C2×D311yescharacteristic
281C2×C4×D4C2×D312yes—
282#485—34no—
283#485—34no—
284#484—34no—
285#483—34no—
286#479—32no—
287#478—32no—
288#478—34no—
289#477—31no—
290#476—31no—
291#476—32no—
292#475—31no—
293#474—31no—
294#474—32no—
295#462—32no—
296#462—32no—
297#461—32no—
298#461—32no—
299#461—32no—
300#461—34no—
301#461—32no—
302#452—34no—
303#452—34no—
304#450—34no—
305#450—34no—
306#441—34no—
307#440—34no—
308#440—34no—
309#440—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×SD16—34no—
313C4×SD16—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318#427—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#419—32no—
322#418—32no—
323#416—32no—
324C2×#103—32no—
325#408—32no—
326#405—32no—
327C24×C3—22no—
328C24×C3—21no—
329C3×#41—28no—
330C3×#41—24no—
331C3×#41—24no—
332C3×#41—22no—
333C3×#41—22no—
334C3×#41—22no—
335C3×#41#4114yes—
336C2×C3×Q8C2×D411yescharacteristic
337C2×C3×Q8C2411yescharacteristic
338C2×C3×D4—216no—
339C2×C3×D4—28no—
340C2×C3×D4—22no—
341C2×C3×D4—21no—
342C2×C3×D4—24no—
343C2×C3×D4—24no—
344C2×C3×D4—22no—
345C2×C3×D4—21no—
346C2×C3×D4—22no—
347C2×C3×D4C2×D412yes—
348C2×C3×D4C2×D411yescharacteristic
349C2×C3×D4#4114yes—
350C2×C3×D4C2411yescharacteristic
351C2×C3×D4C2412yes—
352C22×C3×C4—22no—
353C22×C3×C4—21no—
354C22×C3×C4—22no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—22no—
358C22×C3×C4—22no—
359C22×C3×C4—21no—
360C22×C3×C4—22no—
361C22×C3×C4—22no—
362C22×C3×C4—22no—
363C22×C3×C4—82no—
364C22×C3×C4—84no—
365C22×C3×C4C2×D411yescharacteristic
366C22×C3×C4C2×D412yes—
367C22×C3×C4C2×D411yescharacteristic
368C22×C3×C4C2×D412yes—
369C22×C3×C4C2412yes—
370C22×C3×C4C2411yescharacteristic
371C22×Dic3—22no—
372C2×Dic6—24no—
373C2×Dic6—24no—
374C2×Dic6—21no—
375C2×Dic6—21no—
376C2×Dic6—22no—
377C2×Dic6C2414yes—
378C3×C4⋊C4—22no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4C2×D411yescharacteristic
384C3×C4⋊C4C2×D411yescharacteristic
385C3×C4⋊C4C2×D412yes—
386C3×C4⋊C4C2×D412yes—
387C3×C4⋊C4C2412yes—
388C3×C4⋊C4C2411yescharacteristic
389C3×C4⋊C4C2411yescharacteristic
390C3×C22⋊C4—22no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—22no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—22no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4C2×D412yes—
400C3×C22⋊C4C2×D412yes—
401C3×C22⋊C4C2×D412yes—
402C3×C42—21no—
403C3×C42—22no—
404C3×C42—21no—
405C3×C42—22no—
406C3×C42—21no—
407C3×C42C2×D411yescharacteristic
408C3×C42C2×D411yescharacteristic
409C3×C42C2×D412yes—
410C3×C42C2×D412yes—
411C3×C42C2412yes—
412C3×C42C2411yescharacteristic
413C3×C42C2411yescharacteristic
414#217—22no—
415#217—24no—
416#217—24no—
417#216—28no—
418#214—28no—
419#214—28no—
420#214—28no—
421C4⋊Dic3—22no—
422C4⋊Dic3—22no—
423C4⋊Dic3—21no—
424C4⋊Dic3—21no—
425C4⋊Dic3—22no—
426C4⋊Dic3—22no—
427C4⋊Dic3C2412yes—
428C4⋊Dic3C2412yes—
429Dic3⋊C4—24no—
430Dic3⋊C4—24no—
431Dic3⋊C4—22no—
432Dic3⋊C4—22no—
433Dic3⋊C4—24no—
434Dic3⋊C4—24no—
435C4×Dic3—22no—
436C4×Dic3—24no—
437C4×Dic3—24no—
438#208—24no—
439C2×C3⋊C8—24no—
440C2×C3⋊C8C2412yes—
441C2×C3⋊C8C2414yes—
442C2×C3⋊C8C2412yes—
443H(5,𝔽2)—24no—
444H(5,𝔽2)—24no—
445C2×#41—21no—
446C2×#41C22×D312yes—
447C2×#41C22×D311yescharacteristic
448C2×#41C22×D311yescharacteristic
449C22×Q8—32no—
450C22×D4—22no—
451C22×D4—21no—
452C22×D4C22×D312yes—
453C22×D4C22×D311yescharacteristic
454C23×C4—21no—
455C23×C4—22no—
456#137—68no—
457C2×Q16—34no—
458C2×SD16—34no—
459C2×SD16—34no—
460C2×SD16—34no—
461C2×SD16—68no—
462C2×M16—32no—
463C22×C8—32no—
464C4⋊Q8—31no—
465C4⋊Q8—31no—
466C4⋊Q8—32no—
467C4⋊Q8—32no—
468C4⋊Q8—62no—
469C4⋊Q8—61no—
470C4⋊Q8—61no—
471#126—64no—
472#126—64no—
473#125—32no—
474#125—64no—
475#125—64no—
476#125—62no—
477#125—62no—
478#124—62no—
479#123—64no—
480C22⋊Q8—34no—
481C22⋊Q8—34no—
482C22⋊Q8—61no—
483C22⋊Q8—61no—
484C22⋊Q8—62no—
485C22⋊Q8—62no—
486C4×Q8—21no—
487C4×Q8—34no—
488C4×Q8—34no—
489C4×Q8—62no—
490C4×Q8—62no—
491C4×Q8—62no—
492C4×Q8—62no—
493C4×Q8—61no—
494C4×Q8—61no—
495C4×Q8#6711yescharacteristic
496C4×Q8#6711yescharacteristic
497C4×Q8C22×D311yescharacteristic
498C4×Q8C22×D312yes—
499C4×Q8C22×D311yescharacteristic
500C4×D4—22no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—22no—
504C4×D4—21no—
505C4×D4—22no—
506C4×D4—21no—
507C4×D4—22no—
508C4×D4—21no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—21no—
515C4×D4—22no—
516C4×D4—21no—
517C4×D4#6712yes—
518C4×D4#6711yescharacteristic
519C4×D4#6712yes—
520C4×D4#6711yescharacteristic
521C4×D4C22×D312yes—
522C4×D4C22×D311yescharacteristic
523C4×D4C22×D312yes—
524C4×D4C22×D312yes—
525C4×D4C22×D312yes—
526C4×D4C22×D312yes—
527C4×D4C22×D311yescharacteristic
528#117—21no—
529#117—22no—
530#117—22no—
531#117—21no—
532#117—32no—
533#117—62no—
534#117—62no—
535#117—64no—
536#117C22×D311yescharacteristic
537#117C22×D312yes—
538#117C22×D311yescharacteristic
539#117C22×D312yes—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—61no—
543C2×C4⋊C4—61no—
544C2×C4⋊C4C22×D311yescharacteristic
545C2×C4⋊C4C22×D312yes—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C42—22no—
552C2×C42—21no—
553C2×C42C22×D311yescharacteristic
554C2×C42C22×D312yes—
555#107—32no—
556#107—32no—
557#107—34no—
558#106—32no—
559#106—32no—
560#106—34no—
561C4⋊C8—31no—
562C4⋊C8—31no—
563C4⋊C8—32no—
564C4⋊C8—32no—
565C4⋊C8—32no—
566#103—32no—
567#103—32no—
568#103—34no—
569#103—34no—
570#103—34no—
571#103—34no—
572#102—32no—
573#102—32no—
574#102—34no—
575#102—34no—
576C22⋊C8—34no—
577C22⋊C8—34no—
578#97—34no—
579C4×C8—34no—
580C23×C3—28no—
581C23×C3—22no—
582C23×C3—21no—
583C23×C3—24no—
584C23×C3—81no—
585C23×C3—82no—
586C23×C3—81no—
587C23×C3—82no—
588C23×C3C22×D412yes—
589C23×C3C22×D411yescharacteristic
590C3×Q8—22no—
591C3×Q8—21no—
592C3×Q8C2×#4112yes—
593C3×D4—28no—
594C3×D4—28no—
595C3×D4—24no—
596C3×D4—24no—
597C3×D4—22no—
598C3×D4—24no—
599C3×D4—22no—
600C3×D4—21no—
601C3×D4C2×#4112yes—
602C3×D4C2×#4114yes—
603C2×C3×C4—28no—
604C2×C3×C4—21no—
605C2×C3×C4—24no—
606C2×C3×C4—22no—
607C2×C3×C4—24no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—21no—
611C2×C3×C4—22no—
612C2×C3×C4—21no—
613C2×C3×C4—41no—
614C2×C3×C4—42no—
615C2×C3×C4—44no—
616C2×C3×C4—42no—
617C2×C3×C4—82no—
618C2×C3×C4—81no—
619C2×C3×C4—82no—
620C2×C3×C4—82no—
621C2×C3×C4—82no—
622C2×C3×C4—81no—
623C2×C3×C4—82no—
624C2×C3×C4C22×D412yes—
625C2×C3×C4C22×D412yes—
626C2×C3×C4C22×D412yes—
627C2×C3×C4C22×D411yescharacteristic
628C2×C3×C4C22×D411yescharacteristic
629C2×C3×C4C22×D411yescharacteristic
630C2×C3×C4C22×D411yescharacteristic
631C2×C3×C4C22×D411yescharacteristic
632C2×C3×C4C2×#4112yes—
633C2×C3×C4C2×#4112yes—
634C2×C3×C4C2511yescharacteristic
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—24no—
638C2×Dic3—44no—
639Dic6—24no—
640Dic6—24no—
641Dic6—42no—
642Dic6—44no—
643Dic6—42no—
644C3⋊C8—22no—
645C3⋊C8—22no—
646C3⋊C8—24no—
647C24—22no—
648C24—21no—
649#41—28no—
650#41—24no—
651#41—24no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41#23514yes—
656C2×Q8—34no—
657C2×Q8—61no—
658C2×Q8—61no—
659C2×Q8—62no—
660C2×Q8—64no—
661C2×Q8—64no—
662C2×Q8C2×#6711yescharacteristic
663C2×Q8C23×D311yescharacteristic
664C2×D4—216no—
665C2×D4—28no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—21no—
673C2×D4#23514yes—
674C2×D4C2×#6712yes—
675C2×D4C2×#6711yescharacteristic
676C2×D4C23×D311yescharacteristic
677C2×D4C23×D312yes—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—62no—
690C22×C4—82no—
691C22×C4—84no—
692C22×C4C2×#6711yescharacteristic
693C22×C4C2×#6712yes—
694C22×C4C2×#6711yescharacteristic
695C22×C4C2×#6712yes—
696C22×C4C23×D312yes—
697C22×C4C23×D311yescharacteristic
698Q16—68no—
699SD16—68no—
700SD16—68no—
701SD16—68no—
702M16—64no—
703C2×C8—32no—
704C2×C8—34no—
705C2×C8—32no—
706C2×C8—64no—
707C4⋊C4—22no—
708C4⋊C4—21no—
709C4⋊C4—22no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—32no—
713C4⋊C4—32no—
714C4⋊C4—62no—
715C4⋊C4—62no—
716C4⋊C4—62no—
717C4⋊C4—62no—
718C4⋊C4—61no—
719C4⋊C4—61no—
720C4⋊C4—64no—
721C4⋊C4—64no—
722C4⋊C4—64no—
723C4⋊C4—64no—
724C4⋊C4—62no—
725C4⋊C4—62no—
726C4⋊C4C2×#6711yescharacteristic
727C4⋊C4C2×#6712yes—
728C4⋊C4C2×#6711yescharacteristic
729C4⋊C4C2×#6712yes—
730C4⋊C4C23×D312yes—
731C4⋊C4C23×D311yescharacteristic
732C4⋊C4C23×D311yescharacteristic
733C22⋊C4—22no—
734C22⋊C4—21no—
735C22⋊C4—22no—
736C22⋊C4—21no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—21no—
742C22⋊C4—62no—
743C22⋊C4—64no—
744C22⋊C4—64no—
745C22⋊C4C2×#6712yes—
746C22⋊C4C2×#6712yes—
747C22⋊C4C2×#6712yes—
748C42—21no—
749C42—22no—
750C42—21no—
751C42—22no—
752C42—21no—
753C42—62no—
754C42—64no—
755C42—64no—
756C42C2×#6712yes—
757C42C2×#6711yescharacteristic
758C42C2×#6712yes—
759C42C2×#6711yescharacteristic
760C42C23×D312yes—
761C42C23×D311yescharacteristic
762C42C23×D311yescharacteristic
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—24no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—42no—
771C22×C3—41no—
772C22×C3—42no—
773C22×C3—41no—
774C22×C3—84no—
775C22×C3—88no—
776C22×C3#52512yes—
777C22×C3C23×D411yescharacteristic
778C3×C4—21no—
779C3×C4—22no—
780C3×C4—21no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—21no—
785C3×C4—41no—
786C3×C4—42no—
787C3×C4—41no—
788C3×C4#52512yes—
789C3×C4#57712yes—
790C3×C4C22×#4111yescharacteristic
791C3×C4C22×#4111yescharacteristic
792Dic3—42no—
793Dic3—44no—
794Dic3—42no—
795C23—28no—
796C23—22no—
797C23—21no—
798C23—24no—
799C23—81no—
800C23—82no—
801C23—81no—
802C23—82no—
803C23C22×#6712yes—
804C23C22×#6711yescharacteristic
805Q8—21no—
806Q8—22no—
807Q8—64no—
808Q8—64no—
809Q8—122no—
810Q8—124no—
811Q8—122no—
812Q8C2×#23512yes—
813D4—28no—
814D4—28no—
815D4—24no—
816D4—24no—
817D4—22no—
818D4—21no—
819D4—24no—
820D4—22no—
821D4C2×#23512yes—
822D4C2×#23514yes—
823C2×C4—28no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—21no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—64no—
840C2×C4—82no—
841C2×C4—82no—
842C2×C4—82no—
843C2×C4—82no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—82no—
847C2×C4—124no—
848C2×C4C2×#23512yes—
849C2×C4C2×#23512yes—
850C2×C4C22×#6712yes—
851C2×C4C22×#6712yes—
852C2×C4C22×#6711yescharacteristic
853C2×C4C22×#6712yes—
854C2×C4C22×#6711yescharacteristic
855C2×C4C22×#6711yescharacteristic
856C2×C4C22×#6711yescharacteristic
857C2×C4C22×#6711yescharacteristic
858C2×C4C24×D311yescharacteristic
859C8—62no—
860C8—62no—
861C8—64no—
862C2×C3—22no—
863C2×C3—42no—
864C2×C3—44no—
865C2×C3—42no—
866C2×C3C2×#52511yescharacteristic
867C2×C3C2×#57711yescharacteristic
868C2×C3#358611yescharacteristic
869C22—21no—
870C22—21no—
871C22—22no—
872C22—22no—
873C22—24no—
874C22—22no—
875C22—22no—
876C22—42no—
877C22—41no—
878C22—42no—
879C22—41no—
880C22—84no—
881C22—88no—
882C22#579112yes—
883C22C23×#6711yescharacteristic
884C4—21no—
885C4—22no—
886C4—21no—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—21no—
891C4—41no—
892C4—42no—
893C4—41no—
894C4—122no—
895C4—124no—
896C4—122no—
897C4#579112yes—
898C4#583612yes—
899C4C22×#23511yescharacteristic
900C4C22×#23511yescharacteristic
901C3#6059111yescharacteristic, complemented, Sylow
902C2—22no—
903C2—42no—
904C2—44no—
905C2—42no—
906C2C2×#579111yescharacteristic
907C2C2×#583611yescharacteristic
908C2#8729911yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×H(5,𝔽2)C2
socleC22×C3C23×D4
prime radicalC2×C3×H(5,𝔽2)C22
hypercenterC4×H(5,𝔽2)D3
hypocenterC3#60591
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. #85830C2semidirect
4. #82575C2semidirect
5. #82573C2semidirect
6. #82571C2semidirect
7. #82545C2semidirect
8. #82543C2semidirect
9. #82535C2semidirect
10. #82534C2semidirect
11. #82533C2semidirect
12. #82515C2semidirect
13. #82507C2semidirect
14. #82315C2semidirect
15. #82314C2semidirect
16. C2×#5019C2semidirect
17. #82296C2semidirect
45. #5518C22semidirect
46. #5516C22semidirect
47. #5470C22semidirect
48. #5470C22semidirect
49. #5470C22semidirect
50. C2×#869C22semidirect
58. #5031C22semidirect
59. #5031C22semidirect
60. #5030C22semidirect
61. C4×#216C22semidirect
62. #5022C22semidirect
63. #5021C22semidirect
64. #5020C22semidirect
65. #5019C22semidirect
66. #5019C22semidirect
67. #5019C22semidirect
68. #5019C22semidirect
69. #5019C22semidirect
70. #5018C22semidirect
71. #5018C22semidirect
72. #5018C22semidirect
73. C4×#214C22semidirect
74. C4×#214C22semidirect
75. C4×#214C22semidirect
76. #5009C22semidirect
77. #5009C22semidirect
78. #5008C22semidirect
79. #5008C22semidirect
80. #5007C22semidirect
81. #5007C22semidirect
82. #5004C22semidirect
83. #5000C22semidirect
84. #4998C22semidirect
85. #4997C22semidirect
86. #4996C22semidirect
87. #4996C22semidirect
88. #4971C22semidirect
89. #4970C22semidirect
90. C2×#810C22semidirect
91. #4964C22semidirect
92. #4926C22semidirect
93. #4925C22semidirect
94. #4924C22semidirect
95. C2×C4⋊(C3⋊C8)C22semidirect
901. C3#60591semidirect

Maximal subgroups

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

subgroupindex
C3×C4×H(5,𝔽2)2
#858302
#841052
#825752
#825732
#825712
#825452
#825432
#825352
#825342
#825332
#825152
#825072
#823152
#823142
C2×#50192
#822962
#605913