Finite Group Databasebeta

← #11675104

Subgroups — #11675104

Order 768.

1814 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#41C211yesmaximal, characteristic, complemented
2C2×#5584C211yesmaximal, characteristic, complemented
3#83704C212yesmaximal, complemented
4#83700C214yesmaximal, complemented
5#83689C212yesmaximal, complemented
6#83645C214yesmaximal, complemented
7#83637C212yesmaximal, complemented
8#83563C212yesmaximal, complemented
9#83367C212yesmaximal, complemented
10#83350C211yesmaximal, characteristic, complemented
11#83338C212yesmaximal, complemented
12#83337C211yesmaximal, characteristic, complemented
13#82533C211yesmaximal, characteristic, complemented
14C4×#951C212yesmaximal, complemented
15#82527C212yesmaximal
16C4×#949C211yesmaximal, characteristic
17Q8×#208C211yesmaximal, characteristic, complemented
18#61323—31nomaximal, Sylow
19C3×Q82C2211yescharacteristic, complemented
20C3×#557C2211yescharacteristic, complemented
21C3×#557C2212yescomplemented
22C3×#554—21no—
23C3×#554—22no—
24C3×#554C2211yescharacteristic, complemented
25C3×#554C2212yescomplemented
26C3×D4×Q8—21no—
27C3×D4×Q8C2211yescharacteristic, complemented
28C3×#533—22no—
29C3×#533—21no—
30C3×#533C2211yescharacteristic
31C3×#533C2212yes—
32C3×C4×#41C2211yescharacteristic
33C3×C4×#41C2212yes—
34C2×C3×C4×Q8—21no—
35C2×C3×C4×Q8C2211yescharacteristic
36C2×#951C2212yes—
37C2×#949C2211yescharacteristic
38C2×#946—21no—
39#5584—21no—
40#5584—22no—
41#5584—21no—
42#5584C2212yes—
43#5584C2212yes—
44#5584C2214yes—
45C2×#898—22no—
46C2×#892—21no—
47C2×#875C2212yes—
48C2×C4×D12C2211yescharacteristic
49C2×#869C2211yescharacteristic
50C2×C4×Dic6C2212yes—
51#5232C2211yescharacteristic
52#5094C2214yescomplemented
53#5093C2212yescomplemented
54#5093C2212yescomplemented
55#5091C2214yescomplemented
56#5089C2214yes—
57#5089C2214yes—
58#5087C2212yes—
59#5084C2212yes—
60#5069C2214yescomplemented
61#5068C2214yes—
62#5068C2214yes—
63#5066C2214yes—
64#5063C2214yescomplemented
65#5063C2214yescomplemented
66#5031C2212yescomplemented
67#5031C2212yescomplemented
68#5030C2214yescomplemented
69C4×#216C2214yescomplemented
70#5028C2214yes—
71#5028C2214yes—
72#5026C2212yes—
73C4×#215C2212yes—
74#5024C2212yescomplemented
75#5024C2214yescomplemented
76Q8×C3⋊C8C2212yescomplemented
77#5019C2212yescomplemented
78#5019C2212yescomplemented
79#5018C2214yescomplemented
80C4×#214C2214yescomplemented
81#5016C2214yes—
82#5016C2214yes—
83#5014C2212yes—
84C4×#213C2212yes—
85#5004C2212yes—
86#5004C2212yes—
87#5004C2212yes—
88#5001C2211yescharacteristic
89#5001C2212yes—
90#4995C2211yescharacteristic
91#4995C2212yes—
92#4924C2212yes—
93#4924C2211yescharacteristic
94C4×#208C2211yescharacteristic
95C4×#208C2212yes—
96Q8×#41D311yescharacteristic, complemented
97C2×#556—31no—
98#3377—34no—
99#3376—34no—
100#3369—32no—
101#3367—32no—
102#3364—32no—
103#3360—32no—
104#3140—32no—
105#3139—31no—
106#3078—32no—
107#3077—31no—
108#3040—32no—
109#3039—31no—
110Q8×M16—31no—
111C4×#137—32no—
112C4×AGL(1,ℤ/8)—31no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8—21no—
115C22×C3×Q8D411yescharacteristic
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C22×Dic6C2312yes—
119C3×C4⋊Q8—21no—
120C3×C4⋊Q8—22no—
121C3×C4⋊Q8—21no—
122C3×C4⋊Q8—22no—
123C3×C4⋊Q8C2311yescharacteristic
124C3×C4⋊Q8C2312yes—
125C3×C4⋊Q8C2311yescharacteristic
126C3×C4⋊Q8C2312yes—
127C3×#125—22no—
128C3×#125—22no—
129C3×#125—22no—
130C3×#125C2312yes—
131C3×#125C2312yes—
132C3×#125C2312yes—
133C3×C22⋊Q8—21no—
134C3×C22⋊Q8—22no—
135C3×C22⋊Q8—21no—
136C3×C22⋊Q8—22no—
137C3×C22⋊Q8—22no—
138C3×C22⋊Q8—21no—
139C3×C22⋊Q8—21no—
140C3×C22⋊Q8—22no—
141C3×C22⋊Q8—22no—
142C3×C22⋊Q8—22no—
143C3×C22⋊Q8—22no—
144C3×C4×Q8—21no—
145C3×C4×Q8—21no—
146C3×C4×Q8—22no—
147C3×C4×Q8—22no—
148C3×C4×Q8—21no—
149C3×C4×Q8—22no—
150C3×C4×Q8—21no—
151C3×C4×Q8D411yescharacteristic
152C3×C4×Q8D412yes—
153C3×C4×Q8D411yescharacteristic
154C3×C4×Q8C2311yescharacteristic
155C3×C4×Q8C2312yes—
156C3×C4×Q8C2311yescharacteristic
157C3×C4×Q8C2312yes—
158C3×C4×Q8C2311yescharacteristic
159C3×C4×Q8C2311yescharacteristic
160C3×C4×Q8C2312yes—
161C3×C4×D4—21no—
162C3×C4×D4—22no—
163C3×C4×D4—22no—
164C3×C4×D4—21no—
165C3×C4×D4C2311yescharacteristic
166C3×C4×D4C2311yescharacteristic
167C3×C4×D4C2312yes—
168C3×C4×D4C2312yes—
169C3×#117—22no—
170C3×#117—21no—
171C3×#117C2311yescharacteristic
172C3×#117C2312yes—
173C2×C3×C4⋊C4—21no—
174C2×C3×C4⋊C4—22no—
175C2×C3×C4⋊C4D411yescharacteristic
176C2×C3×C4⋊C4D412yes—
177C2×C3×C42—22no—
178C2×C3×C42—21no—
179C2×C3×C42C2312yes—
180C2×C3×C42C2311yescharacteristic
181#951—28no—
182#949—24no—
183#946—22no—
184#946—22no—
185#946—24no—
186C2×#216C2314yes—
187C2×#215C2312yes—
188C2×#214C2314yes—
189C2×#213C2312yes—
190C2×(C2×D3)⋊C4—21no—
191C2×(C2×D3)⋊C4—22no—
192C2×(C2×D3)⋊C4—22no—
193C2×C4⋊Dic3—21no—
194C2×C4⋊Dic3—21no—
195C2×C4⋊Dic3C2311yescharacteristic
196C2×Dic3⋊C4—22no—
197C2×C4×Dic3—22no—
198C2×#208C2311yescharacteristic
199C2×#208C2312yes—
200C2×#208C2311yescharacteristic
201#898—24no—
202#898—24no—
203#898—24no—
204#898—24no—
205#892—22no—
206#892—24no—
207#892—22no—
208#875—22no—
209#875—22no—
210#875C2314yes—
211#875C2314yes—
212C4×D12—21no—
213C4×D12—21no—
214C4×D12C2312yes—
215C4×D12C2312yes—
216#869—21no—
217#869—21no—
218#869C2312yes—
219#869C2312yes—
220C4×Dic6—22no—
221C4×Dic6—22no—
222C4×Dic6C2314yes—
223C4×Dic6C2314yes—
224#835C2312yes—
225#832C2312yes—
226#810C2314yes—
227#810C2314yes—
228#810C2314yes—
229#810C2314yes—
230#810C2314yes—
231#810C2314yes—
232#809C2312yes—
233#809C2312yes—
234#809C2314yes—
235#809C2314yes—
236#808C2312yes—
237#808C2314yes—
238#807C2312yes—
239#807C2314yes—
240C4⋊(C3⋊C8)C2314yes—
241C4⋊(C3⋊C8)C2314yes—
242C4⋊(C3⋊C8)C2312yes—
243C4⋊(C3⋊C8)C2312yes—
244#803C2312yes—
245#803C2314yes—
246C4×C3⋊C8C2312yes—
247C4×C3⋊C8C2314yes—
248C2×#137—32no—
249C2×AGL(1,ℤ/8)—31no—
250Q82C2×D311yescharacteristic, complemented
251#557C2×D311yescharacteristic, complemented
252#557C2×D312yescomplemented
253#556—32no—
254#556—32no—
255#556—34no—
256#556—61no—
257#556—62no—
258#556—61no—
259#554—21no—
260#554—22no—
261#554C2×D311yescharacteristic, complemented
262#554C2×D312yescomplemented
263D4×Q8—21no—
264D4×Q8C2×D311yescharacteristic, complemented
265#533—21no—
266#533—22no—
267#533C2×D311yescharacteristic
268#533C2×D312yes—
269C2×C4⋊Q8—31no—
270C2×#126—62no—
271C2×#124—32no—
272C2×C22⋊Q8—61no—
273C4×#41C2×D311yescharacteristic
274C4×#41C2×D312yes—
275C2×C4×Q8—21no—
276C2×C4×Q8—32no—
277C2×C4×Q8C2×D311yescharacteristic
278C2×C4×D4—31no—
279C2×#117—61no—
280#491—34no—
281#489—34no—
282#489—34no—
283#488—34no—
284#488—34no—
285#487—32no—
286#487—32no—
287#479—34no—
288#479—34no—
289#478—34no—
290#477—34no—
291#476—32no—
292#475—34no—
293#474—32no—
294#464—34no—
295#464—34no—
296#463—34no—
297#463—34no—
298#462—32no—
299#462—32no—
300#461—32no—
301#461—32no—
302#446—32no—
303#446—34no—
304C8×Q8—32no—
305#442—32no—
306#441—34no—
307#440—32no—
308#440—34no—
309C4×Q16—34no—
310C4×SD16—32no—
311C4×SD16—34no—
312C4×D8—32no—
313#428—32no—
314#428—31no—
315#423—31no—
316#423—32no—
317#419—32no—
318#419—32no—
319#419—32no—
320#418—32no—
321#418—31no—
322#417—31no—
323C4×M16—31no—
324C4×M16—32no—
325C23×D3—21no—
326C3×#41—22no—
327C3×#41#4114yes—
328C2×C3×Q8—22no—
329C2×C3×Q8—21no—
330C2×C3×Q8—22no—
331C2×C3×Q8—21no—
332C2×C3×Q8—42no—
333C2×C3×Q8—44no—
334C2×C3×Q8C2×D411yescharacteristic
335C2×C3×Q8C2×D411yescharacteristic
336C2×C3×Q8C2×D412yes—
337C2×C3×Q8C2411yescharacteristic
338C2×C3×D4—21no—
339C2×C3×D4C2411yescharacteristic
340C22×C3×C4—21no—
341C22×C3×C4—22no—
342C22×C3×C4—21no—
343C22×C3×C4—22no—
344C22×C3×C4—21no—
345C22×C3×C4C2×D411yescharacteristic
346C22×C3×C4C2×D412yes—
347C22×C3×C4C2×D412yes—
348C22×C3×C4C2×D411yescharacteristic
349C22×C3×C4C2411yescharacteristic
350C22×Dic3—21no—
351C22×Dic3—22no—
352C2×D12—22no—
353C2×D12—22no—
354C2×D12—21no—
355C2×D12C2412yes—
356C2×C4×D3—22no—
357C2×C4×D3—22no—
358C2×C4×D3—44no—
359C2×Dic6—24no—
360C2×Dic6—24no—
361C2×Dic6—22no—
362C2×Dic6C2414yes—
363C3×C4⋊C4—22no—
364C3×C4⋊C4—22no—
365C3×C4⋊C4—22no—
366C3×C4⋊C4—22no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—22no—
369C3×C4⋊C4—22no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—22no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—22no—
375C3×C4⋊C4—22no—
376C3×C4⋊C4—22no—
377C3×C4⋊C4C2×D411yescharacteristic
378C3×C4⋊C4C2×D412yes—
379C3×C4⋊C4C2×D411yescharacteristic
380C3×C4⋊C4C2×D412yes—
381C3×C4⋊C4C2×D412yes—
382C3×C4⋊C4C2×D412yes—
383C3×C4⋊C4C2×D412yes—
384C3×C4⋊C4C2411yescharacteristic
385C3×C4⋊C4C2412yes—
386C3×C4⋊C4C2411yescharacteristic
387C3×C4⋊C4C2412yes—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—22no—
390C3×C22⋊C4—22no—
391C3×C22⋊C4—22no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C42—22no—
395C3×C42—21no—
396C3×C42—22no—
397C3×C42—21no—
398C3×C42—22no—
399C3×C42—21no—
400C3×C42C2×D412yes—
401C3×C42C2×D412yes—
402C3×C42C2×D411yescharacteristic
403C3×C42C2×D411yescharacteristic
404C3×C42C2412yes—
405C3×C42C2411yescharacteristic
406C3×C42C2412yes—
407C3×C42C2411yescharacteristic
408#216—28no—
409#215—24no—
410#214—28no—
411#213—24no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—24no—
415(C2×D3)⋊C4—24no—
416(C2×D3)⋊C4—24no—
417(C2×D3)⋊C4—24no—
418C4⋊Dic3—21no—
419C4⋊Dic3—22no—
420C4⋊Dic3—22no—
421C4⋊Dic3—22no—
422C4⋊Dic3—22no—
423C4⋊Dic3C2412yes—
424Dic3⋊C4—24no—
425Dic3⋊C4—24no—
426C4×Dic3—24no—
427C4×Dic3—24no—
428#208—22no—
429#208—24no—
430#208—22no—
431C2×C3⋊C8C2412yes—
432C2×C3⋊C8C2414yes—
433C2×C3⋊C8C2412yes—
434C2×#41C22×D311yescharacteristic
435C22×Q8—21no—
436C22×Q8—32no—
437C22×Q8#6711yescharacteristic
438C22×D4—31no—
439C23×C4—61no—
440#137—68no—
441AGL(1,ℤ/8)—64no—
442C2×Q16—34no—
443C2×SD16—32no—
444C2×SD16—34no—
445C2×D8—32no—
446C2×M16—31no—
447C2×M16—32no—
448C2×M16—31no—
449C4⋊Q8—21no—
450C4⋊Q8—22no—
451C4⋊Q8—21no—
452C4⋊Q8—22no—
453C4⋊Q8—32no—
454C4⋊Q8—32no—
455C4⋊Q8—61no—
456C4⋊Q8—61no—
457C4⋊Q8C22×D311yescharacteristic
458C4⋊Q8C22×D312yes—
459C4⋊Q8C22×D312yes—
460C4⋊Q8C22×D311yescharacteristic
461#126—64no—
462#126—64no—
463#126—64no—
464#126—64no—
465#125—22no—
466#125—22no—
467#125—22no—
468#125C22×D312yes—
469#125C22×D312yes—
470#125C22×D312yes—
471#124—34no—
472#124—34no—
473#124—62no—
474#124—62no—
475C22⋊Q8—21no—
476C22⋊Q8—22no—
477C22⋊Q8—21no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—22no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C22⋊Q8—64no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—22no—
492C4×Q8—21no—
493C4×Q8—22no—
494C4×Q8—21no—
495C4×Q8—22no—
496C4×Q8—34no—
497C4×Q8—34no—
498C4×Q8—62no—
499C4×Q8—62no—
500C4×Q8#6711yescharacteristic
501C4×Q8#6711yescharacteristic
502C4×Q8#6712yes—
503C4×Q8C22×D312yes—
504C4×Q8C22×D311yescharacteristic
505C4×Q8C22×D311yescharacteristic
506C4×Q8C22×D312yes—
507C4×Q8C22×D311yescharacteristic
508C4×Q8C22×D311yescharacteristic
509C4×Q8C22×D312yes—
510C4×D4—21no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—32no—
515C4×D4—32no—
516C4×D4—61no—
517C4×D4—61no—
518C4×D4C22×D311yescharacteristic
519C4×D4C22×D312yes—
520C4×D4C22×D312yes—
521C4×D4C22×D311yescharacteristic
522#117—21no—
523#117—22no—
524#117—62no—
525#117—64no—
526#117—62no—
527#117C22×D311yescharacteristic
528#117C22×D312yes—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—61no—
533C2×C4⋊C4—62no—
534C2×C4⋊C4—61no—
535C2×C4⋊C4#6711yescharacteristic
536C2×C4⋊C4#6712yes—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—61no—
539C2×C22⋊C4—62no—
540C2×C42—21no—
541C2×C42—22no—
542C2×C42—62no—
543C2×C42C22×D311yescharacteristic
544C2×C42C22×D312yes—
545#107—32no—
546#107—34no—
547#106—34no—
548#106—32no—
549C4⋊C8—32no—
550C4⋊C8—34no—
551C4⋊C8—32no—
552C4⋊C8—34no—
553#103—32no—
554#103—34no—
555#103—34no—
556#103—34no—
557#103—34no—
558#103—34no—
559#103—34no—
560#102—32no—
561#102—32no—
562#102—32no—
563#102—34no—
564#102—34no—
565#97—34no—
566#97—32no—
567C4×C8—32no—
568C4×C8—34no—
569C23×C3—21no—
570C23×C3C22×D411yescharacteristic
571C22×D3—22no—
572C22×D3—42no—
573C22×D3—42no—
574C22×D3—42no—
575C3×Q8—22no—
576C3×Q8—22no—
577C3×Q8—21no—
578C3×Q8—42no—
579C3×Q8—44no—
580C3×Q8—42no—
581C3×Q8—82no—
582C3×Q8—81no—
583C3×Q8C2×#4112yes—
584C3×D4—24no—
585C3×D4—21no—
586C3×D4C2×#4112yes—
587C2×C3×C4—21no—
588C2×C3×C4—24no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—21no—
592C2×C3×C4—22no—
593C2×C3×C4—21no—
594C2×C3×C4—42no—
595C2×C3×C4—41no—
596C2×C3×C4—42no—
597C2×C3×C4—44no—
598C2×C3×C4—42no—
599C2×C3×C4—82no—
600C2×C3×C4—81no—
601C2×C3×C4C22×D412yes—
602C2×C3×C4C22×D412yes—
603C2×C3×C4C22×D412yes—
604C2×C3×C4C22×D412yes—
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4C22×D411yescharacteristic
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C22×D411yescharacteristic
610C2×C3×C4C2×#4112yes—
611C2×C3×C42−1+412yes—
612C2×C3×C4C2511yescharacteristic
613C2×Dic3—22no—
614C2×Dic3—24no—
615C2×Dic3—42no—
616C2×Dic3—44no—
617D12—22no—
618D12—22no—
619D12—42no—
620C4×D3—44no—
621C4×D3—44no—
622Dic6—24no—
623Dic6—24no—
624Dic6—44no—
625C3⋊C8—22no—
626C3⋊C8—24no—
627C3⋊C8—22no—
628C24—61no—
629#41—22no—
630#41#23914yes—
631C2×Q8—22no—
632C2×Q8—21no—
633C2×Q8—22no—
634C2×Q8—21no—
635C2×Q8—34no—
636C2×Q8—42no—
637C2×Q8—44no—
638C2×Q8—62no—
639C2×Q8—64no—
640C2×Q8—64no—
641C2×Q8C2×#6711yescharacteristic
642C2×Q8C2×#6711yescharacteristic
643C2×Q8C2×#6712yes—
644C2×Q8C23×D311yescharacteristic
645C2×D4—21no—
646C2×D4—32no—
647C2×D4—62no—
648C2×D4—62no—
649C2×D4—61no—
650C2×D4C23×D311yescharacteristic
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—22no—
655C22×C4—21no—
656C22×C4—61no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—124no—
661C22×C4C2×#6711yescharacteristic
662C22×C4C2×#6712yes—
663C22×C4C2×#6711yescharacteristic
664C22×C4C2×#6712yes—
665C22×C4C23×D311yescharacteristic
666Q16—68no—
667SD16—64no—
668SD16—68no—
669D8—64no—
670M16—62no—
671M16—64no—
672M16—62no—
673C2×C8—32no—
674C2×C8—34no—
675C2×C8—32no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—22no—
686C4⋊C4—21no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—32no—
691C4⋊C4—61no—
692C4⋊C4—62no—
693C4⋊C4—62no—
694C4⋊C4—64no—
695C4⋊C4—64no—
696C4⋊C4—62no—
697C4⋊C4—62no—
698C4⋊C4C2×#6711yescharacteristic
699C4⋊C4C2×#6712yes—
700C4⋊C4C2×#6712yes—
701C4⋊C4C2×#6711yescharacteristic
702C4⋊C4C2×#6712yes—
703C4⋊C4C2×#6712yes—
704C4⋊C4C2×#6712yes—
705C4⋊C4C23×D311yescharacteristic
706C4⋊C4C23×D312yes—
707C4⋊C4C23×D311yescharacteristic
708C4⋊C4C23×D312yes—
709C22⋊C4—21no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—64no—
716C22⋊C4—64no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—64no—
720C22⋊C4—64no—
721C42—21no—
722C42—22no—
723C42—22no—
724C42—21no—
725C42—22no—
726C42—21no—
727C42—64no—
728C42—64no—
729C42C2×#6711yescharacteristic
730C42C2×#6712yes—
731C42C2×#6711yescharacteristic
732C42C2×#6712yes—
733C42C23×D311yescharacteristic
734C42C23×D312yes—
735C42C23×D311yescharacteristic
736C42C23×D312yes—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—22no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3#54812yes—
743C22×C3C23×D411yescharacteristic
744C2×D3—42no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—84no—
748C3×C4—22no—
749C3×C4—21no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—22no—
753C3×C4—21no—
754C3×C4—22no—
755C3×C4—22no—
756C3×C4—42no—
757C3×C4—41no—
758C3×C4—42no—
759C3×C4—41no—
760C3×C4#54812yes—
761C3×C4#57512yes—
762C3×C4C22×#4111yescharacteristic
763C3×C4C2×2−1+411yescharacteristic
764Dic3—44no—
765Dic3—42no—
766C23—21no—
767C23—62no—
768C23—122no—
769C23—122no—
770C23—122no—
771C23C22×#6711yescharacteristic
772Q8—21no—
773Q8—22no—
774Q8—22no—
775Q8—42no—
776Q8—44no—
777Q8—42no—
778Q8—64no—
779Q8—64no—
780Q8—82no—
781Q8—81no—
782Q8—124no—
783Q8C2×#23912yes—
784D4—24no—
785D4—21no—
786D4—62no—
787D4—62no—
788D4—122no—
789D4C2×#23912yes—
790C2×C4—21no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—62no—
803C2×C4—64no—
804C2×C4—82no—
805C2×C4—81no—
806C2×C4—124no—
807C2×C4—122no—
808C2×C4—124no—
809C2×C4—124no—
810C2×C4C2×#23912yes—
811C2×C4#100712yes—
812C2×C4C22×#6712yes—
813C2×C4C22×#6711yescharacteristic
814C2×C4C22×#6712yes—
815C2×C4C22×#6712yes—
816C2×C4C22×#6712yes—
817C2×C4C22×#6711yescharacteristic
818C2×C4C22×#6711yescharacteristic
819C2×C4C22×#6711yescharacteristic
820C2×C4C22×#6711yescharacteristic
821C2×C4C24×D311yescharacteristic
822C8—62no—
823C8—64no—
824C8—62no—
825C2×C3—22no—
826C2×C3—42no—
827C2×C3C2×#54811yescharacteristic
828C2×C3C2×#57511yescharacteristic
829C2×C3#358611yescharacteristic
830D3—82no—
831C22—21no—
832C22—21no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—122no—
837C22—122no—
838C22—122no—
839C22—244no—
840C22#581712yes—
841C22C23×#6711yescharacteristic
842C4—22no—
843C4—21no—
844C4—22no—
845C4—21no—
846C4—22no—
847C4—21no—
848C4—22no—
849C4—22no—
850C4—42no—
851C4—41no—
852C4—42no—
853C4—41no—
854C4—124no—
855C4—122no—
856C4#581712yes—
857C4#582212yes—
858C4C22×#23911yescharacteristic
859C4C2×#100711yescharacteristic
860C3#6132311yescharacteristic, complemented, Sylow
861C2—22no—
862C2—42no—
863C2—242no—
864C2C2×#581711yescharacteristic
865C2C2×#582211yescharacteristic
866C2#8729911yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×Q8×#41C2
socleC22×C3C23×D4
prime radicalC2×#949C22
hypercenterQ8×#41D3
hypocenterC3#61323
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. C3×Q8×#41C2semidirect
2. C2×#5584C2semidirect
3. #83704C2semidirect
4. #83700C2semidirect
5. #83689C2semidirect
6. #83645C2semidirect
7. #83637C2semidirect
8. #83563C2semidirect
9. #83367C2semidirect
10. #83350C2semidirect
11. #83338C2semidirect
12. #83337C2semidirect
13. #82533C2semidirect
14. C4×#951C2semidirect
17. Q8×#208C2semidirect
19. C3×Q82C22semidirect
20. C3×#557C22semidirect
21. C3×#557C22semidirect
24. C3×#554C22semidirect
25. C3×#554C22semidirect
27. C3×D4×Q8C22semidirect
52. #5094C22semidirect
53. #5093C22semidirect
54. #5093C22semidirect
55. #5091C22semidirect
60. #5069C22semidirect
64. #5063C22semidirect
65. #5063C22semidirect
66. #5031C22semidirect
67. #5031C22semidirect
68. #5030C22semidirect
69. C4×#216C22semidirect
74. #5024C22semidirect
75. #5024C22semidirect
76. Q8×C3⋊C8C22semidirect
77. #5019C22semidirect
78. #5019C22semidirect
79. #5018C22semidirect
80. C4×#214C22semidirect
96. Q8×#41D3semidirect
250. Q82C2×D3semidirect
251. #557C2×D3semidirect
252. #557C2×D3semidirect
261. #554C2×D3semidirect
262. #554C2×D3semidirect
264. D4×Q8C2×D3semidirect
860. C3#61323semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#412
C2×#55842
#837042
#837002
#836892
#836452
#836372
#835632
#833672
#833502
#833382
#833372
#825332
C4×#9512
#825272
C4×#9492
Q8×#2082
#613233