Finite Group Databasebeta

← #10764092

Subgroups — #10764092

Order 768.

988 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86245C211yesmaximal, characteristic
2#79340C211yesmaximal, characteristic, complemented
3#79294C211yesmaximal, characteristic, complemented
4C3×#1553C211yesmaximal, characteristic, complemented
5#71806C211yesmaximal, characteristic, complemented
6#70819C211yesmaximal, characteristic, complemented
7#70772C211yesmaximal, characteristic, complemented
8#68431C211yesmaximal, characteristic, complemented
9#68426C211yesmaximal, characteristic, complemented
10#68421C211yesmaximal, characteristic, complemented
11#68419C211yesmaximal, characteristic, complemented
12#68388C211yesmaximal, characteristic, complemented
13#68383C211yesmaximal, characteristic, complemented
14#68383C211yesmaximal, characteristic, complemented
15#68381C211yesmaximal, characteristic, complemented
16#17776—31nomaximal, Sylow
17C3×#532C2211yescharacteristic
18#5834—21no—
19#5829—21no—
20#5728C2211yescharacteristic
21#5725C2211yescharacteristic
22#5716C2211yescharacteristic
23D3×#127C2211yescharacteristic
24#5681—21no—
25#5676—21no—
26#5619C412yes—
27#5612—21no—
28#5607C412yes—
29#5599—21no—
30#5562C412yes—
31#5559—21no—
32#5554—21no—
33#5545C412yes—
34#5477C2211yescharacteristic
35C4×#235C2211yescharacteristic
36C3×#432C2211yescharacteristic, complemented
37C3×#431C2211yescharacteristic, complemented
38#4924C2211yescharacteristic, complemented
39C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#4837C2211yescharacteristic
41#4837C2211yescharacteristic
42#4837C2211yescharacteristic, complemented
43#4835C2211yescharacteristic, complemented
44#4833C2211yescharacteristic
45#4833C2211yescharacteristic
46#4833C2211yescharacteristic, complemented
47D3×C4⋊C8C2211yescharacteristic, complemented
48#4730—21no—
49#4729—21no—
50#4729—21no—
51#67⋊C8—21no—
52#4706—21no—
53#4701—21no—
54#4688—21no—
55C8×Dic6—21no—
56C3×#332C2211yescharacteristic, complemented
57C3×#332C2211yescharacteristic, complemented
58C3×#331C2211yescharacteristic
59C3×#331C2211yescharacteristic
60#4547C2211yescharacteristic, complemented
61#4547C2211yescharacteristic, complemented
62#4544C2211yescharacteristic
63#4544C2211yescharacteristic
64#4486C2211yescharacteristic, complemented
65#4486C2211yescharacteristic, complemented
66#4485C2211yescharacteristic
67#4485C2211yescharacteristic
68#4485C2211yescharacteristic
69#4485C2211yescharacteristic
70#4482C2211yescharacteristic, complemented
71#4482C2211yescharacteristic, complemented
72#3508—31no—
73#2991—31no—
74#2990—31no—
75#1561—31no—
76#1557—31no—
77#1557—31no—
78#1553—31no—
79#1553D311yescharacteristic, complemented
80#1547—31no—
81#1547—31no—
82#1545—31no—
83#1545—31no—
84#1544—31no—
85#1540—31no—
86#1540—31no—
87C2×C3×#41—21no—
88C2×#239—21no—
89C2×#237—21no—
90C2×D3×D4—21no—
91C2×D3×D4—21no—
92C2×D3×D4C2×C412yes—
93C2×#235—21no—
94C2×#235C2×C411yescharacteristic
95C3×C4⋊Q8C2311yescharacteristic
96C3×#127C2311yescharacteristic
97C3×#124—21no—
98C3×#121—21no—
99C3×#121C2×C412yes—
100C3×C4×D4—21no—
101C3×C4×D4C2×C412yes—
102C2×C3×C42C2311yescharacteristic
103#947—21no—
104#946—21no—
105Q8×Dic3—21no—
106#940—22no—
107#940—21no—
108#940—21no—
109#940C2×C412yes—
110#939—22no—
111#938—21no—
112#938—22no—
113#938C2×C412yes—
114#937—22no—
115#936—21no—
116D4×Dic3—21no—
117D4×Dic3C2×C412yes—
118#930—21no—
119#930—22no—
120#930C2×C412yes—
121#929—22no—
122C4×#67—22no—
123C4×#67D411yescharacteristic
124C4×#67D411yescharacteristic
125C4×#67D411yescharacteristic
126C4×#67D411yescharacteristic
127C2×(C2×D3)⋊C4—22no—
128#926C2×C411yescharacteristic
129C2×#208—21no—
130C22×C3⋊C8—21no—
131C2×ΓL(1,𝔽25)—21no—
132C2×ΓL(1,𝔽25)—21no—
133C2×ΓL(1,𝔽25)—21no—
134C2×D3×C8—21no—
135#897—21no—
136#895—21no—
137#895C2×C412yes—
138#893—21no—
139#893C2×C412yes—
140#892C2×C412yes—
141#890C2×C412yes—
142#887—21no—
143#886—22no—
144#885—22no—
145#884—22no—
146#883—22no—
147#883—22no—
148#882—22no—
149#67⋊C4—22no—
150D3×C22⋊C4—22no—
151#875—21no—
152#874C2311yescharacteristic
153C4×D12—21no—
154C4×D12C2×C412yes—
155C4×D12D411yescharacteristic
156C4×D12D411yescharacteristic
157#872C2×C411yescharacteristic
158#872C2×C411yescharacteristic
159C42×D3C2311yescharacteristic
160C42×D3C2311yescharacteristic
161#869C2311yescharacteristic
162C4×Dic6D411yescharacteristic
163C4×Dic6D411yescharacteristic
164C3×C4⋊C8C2311yescharacteristic
165C3×C4⋊C8C2311yescharacteristic
166C3×C4⋊C8C2311yescharacteristic
167C3×C4⋊C8C2311yescharacteristic
168C3×C22⋊C8—21no—
169C3×C22⋊C8—21no—
170C3×#97—21no—
171C3×C4×C8—21no—
172(C2×D3)⋊C8—21no—
173(C2×D3)⋊C8—21no—
174(C2×D3)⋊C8—21no—
175(C2×D3)⋊C8—21no—
176#815—21no—
177Dic3⋊C8—21no—
178Dic3⋊C8—21no—
179Dic3⋊C8—21no—
180Dic3⋊C8—21no—
181C8×Dic3—21no—
182C8×Dic3—21no—
183C8×Dic3—21no—
184C4⋊(C3⋊C8)—21no—
185C4⋊(C3⋊C8)—21no—
186C4⋊(C3⋊C8)C2311yescharacteristic
187C4⋊(C3⋊C8)C2311yescharacteristic
188C4⋊(C3⋊C8)C2311yescharacteristic
189C4⋊(C3⋊C8)C2311yescharacteristic
190#559—61no—
191#559—61no—
192#550—61no—
193#550—61no—
194#546—61no—
195#546—61no—
196#546—61no—
197#546—61no—
198#540—32no—
199#540—32no—
200#535—32no—
201#533—31no—
202#532—31no—
203#532—31no—
204#532—31no—
205#532C2×D311yescharacteristic
206C2×#127—31no—
207#518—32no—
208C4×#41—31no—
209#446—61no—
210C8×Q8—61no—
211#436—61no—
212#436—61no—
213#436—61no—
214#435—61no—
215#435—61no—
216C8×D4—61no—
217#432—31no—
218#432C2×D311yescharacteristic, complemented
219#431—31no—
220#431—31no—
221#431—31no—
222#431C2×D311yescharacteristic, complemented
223#423—31no—
224#423—31no—
225#423—31no—
226#423—31no—
227C2×C4⋊C8—31no—
228C2×C4⋊C8—31no—
229#332—31no—
230#332—31no—
231#332—31no—
232#332—31no—
233#332—31no—
234#332—31no—
235#332C2×D311yescharacteristic, complemented
236#332C2×D311yescharacteristic, complemented
237#331—31no—
238#331—31no—
239#331—31no—
240#331—31no—
241#331—31no—
242#331—31no—
243#331C2×D311yescharacteristic
244#331C2×D311yescharacteristic
245C23×D3—22no—
246C3×#41—81no—
247C3×#41—81no—
248C2×C3×Q8—21no—
249C2×C3×D4—22no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4C22×C412yes—
253C22×C3×C4—22no—
254C22×C3×C4C22×C411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C2×#67—22no—
258C2×#67—22no—
259C2×#67—22no—
260C2×#67—22no—
261C2×#67—22no—
262C2×#67C22⋊C411yescharacteristic
263C2×#67C22⋊C411yescharacteristic
264C22×Dic3—22no—
265#239—81no—
266#239—81no—
267#237—81no—
268#237—81no—
269D3×D4—44no—
270D3×D4—81no—
271D3×D4—81no—
272D3×D4—81no—
273D3×D4—81no—
274#235—42no—
275#235—81no—
276#235—81no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—22no—
280C2×D12C22⋊C411yescharacteristic
281C2×D12C22×C412yes—
282C2×C4×D3—22no—
283C2×C4×D3—22no—
284C2×C4×D3C22×C411yescharacteristic
285C2×C4×D3C22×C411yescharacteristic
286C2×C4×D3C2×D411yescharacteristic
287C2×C4×D3C2×D411yescharacteristic
288C2×C4×D3C2×D411yescharacteristic
289C2×C4×D3C2×D411yescharacteristic
290C2×Dic6—21no—
291C2×Dic6C22⋊C411yescharacteristic
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4C22×C412yes—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C42C22×C411yescharacteristic
301C3×C42C2×D411yescharacteristic
302C3×C42C2×D411yescharacteristic
303C3×C42C2411yescharacteristic
304#217—22no—
305#217—22no—
306#217C22⋊C411yescharacteristic
307#217C22⋊C411yescharacteristic
308(C2×D3)⋊C4—22no—
309(C2×D3)⋊C4—22no—
310(C2×D3)⋊C4—22no—
311(C2×D3)⋊C4—22no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4C22⋊C411yescharacteristic
314(C2×D3)⋊C4C22⋊C411yescharacteristic
315(C2×D3)⋊C4C22⋊C411yescharacteristic
316(C2×D3)⋊C4C22⋊C411yescharacteristic
317C4⋊Dic3—21no—
318C4⋊Dic3—22no—
319C4⋊Dic3C22⋊C411yescharacteristic
320C4⋊Dic3C22⋊C411yescharacteristic
321C4⋊Dic3C22×C412yes—
322Dic3⋊C4—22no—
323Dic3⋊C4C22⋊C411yescharacteristic
324Dic3⋊C4C22⋊C411yescharacteristic
325Dic3⋊C4C22⋊C411yescharacteristic
326Dic3⋊C4C22⋊C411yescharacteristic
327C4×Dic3—22no—
328C4×Dic3C22×C411yescharacteristic
329C4×Dic3C22×C411yescharacteristic
330C4×Dic3C2×D411yescharacteristic
331C4×Dic3C2×D411yescharacteristic
332C4×Dic3C2×D411yescharacteristic
333C4×Dic3C2×D411yescharacteristic
334#208—81no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—81no—
340ΓL(1,𝔽25)—81no—
341ΓL(1,𝔽25)—81no—
342ΓL(1,𝔽25)—81no—
343D3×C8—81no—
344C2×#41—21no—
345C2×#41—31no—
346C2×#41—61no—
347C2×#41—61no—
348C2×#41—61no—
349C22×D4—32no—
350C22×D4—61no—
351C22×D4—61no—
352C2×M16—61no—
353C2×M16—61no—
354C2×M16—61no—
355C2×M16—61no—
356C22×C8—61no—
357C22×C8—61no—
358C4⋊Q8—31no—
359C4⋊Q8C22×D311yescharacteristic
360#127—32no—
361#127—31no—
362#127—61no—
363#127—61no—
364#127—62no—
365#127C22×D311yescharacteristic
366#125—32no—
367#124—21no—
368#124—61no—
369#124—61no—
370#124—62no—
371#124—61no—
372#123—62no—
373#123—62no—
374#123—62no—
375#123—62no—
376C22⋊Q8—61no—
377C22⋊Q8—61no—
378#121—21no—
379#121—32no—
380#121—32no—
381#121—32no—
382#121—62no—
383#121—62no—
384#121—62no—
385#121—62no—
386#121—61no—
387#121—61no—
388#121—61no—
389#121C4×D312yes—
390#120—62no—
391#120—62no—
392C4×Q8—31no—
393C4×Q8—31no—
394C4×Q8—61no—
395C4×Q8—61no—
396C4×D4—21no—
397C4×D4—31no—
398C4×D4—31no—
399C4×D4—31no—
400C4×D4—31no—
401C4×D4—32no—
402C4×D4—32no—
403C4×D4—32no—
404C4×D4—31no—
405C4×D4—31no—
406C4×D4—61no—
407C4×D4—61no—
408C4×D4—62no—
409C4×D4—62no—
410C4×D4—61no—
411C4×D4C4×D312yes—
412#117—31no—
413#117—31no—
414#117—31no—
415#117—32no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C42—31no—
419C2×C42—31no—
420C2×C42C22×D311yescharacteristic
421C4⋊C8—31no—
422C4⋊C8—31no—
423C4⋊C8—31no—
424C4⋊C8—31no—
425C4⋊C8—61no—
426C4⋊C8—61no—
427C4⋊C8—61no—
428C4⋊C8—61no—
429C4⋊C8—61no—
430C4⋊C8—61no—
431C4⋊C8C22×D311yescharacteristic
432C4⋊C8C22×D311yescharacteristic
433C4⋊C8C22×D311yescharacteristic
434C4⋊C8C22×D311yescharacteristic
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—61no—
438C22⋊C8—61no—
439C22⋊C8—61no—
440C22⋊C8—61no—
441#97—21no—
442#97—61no—
443C4×C8—21no—
444C4×C8—61no—
445C4×C8—61no—
446C4×C8—61no—
447C23×C3—22no—
448C23×C3C2×C22⋊C411yescharacteristic
449C22×D3—22no—
450C22×D3—44no—
451C22×D3—82no—
452C22×D3—82no—
453C22×D3C2×C22⋊C411yescharacteristic
454C22×D3C2×C22⋊C411yescharacteristic
455C3×Q8—41no—
456C3×Q8—41no—
457C3×D4—42no—
458C3×D4—41no—
459C3×D4—41no—
460C3×D4—41no—
461C3×D4—41no—
462C3×D4—82no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—41no—
469C2×C3×C4—82no—
470C2×C3×C4C2×C22⋊C411yescharacteristic
471C2×C3×C4C2×C22⋊C411yescharacteristic
472C2×C3×C4C2×C22⋊C411yescharacteristic
473C2×C3×C4C23×C411yescharacteristic
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476#67—22no—
477#67—41no—
478#67—44no—
479#67—82no—
480#67—82no—
481#67—82no—
482#67—82no—
483C2×Dic3—22no—
484C2×Dic3—82no—
485C2×Dic3C2×C22⋊C411yescharacteristic
486C2×Dic3C2×C22⋊C411yescharacteristic
487C2×Dic3C2×C22⋊C411yescharacteristic
488C2×Dic3C2×C22⋊C411yescharacteristic
489C2×Dic3C2×C22⋊C411yescharacteristic
490C2×Dic3C2×C22⋊C411yescharacteristic
491D12—41no—
492D12—42no—
493D12—41no—
494D12—41no—
495D12—41no—
496D12—41no—
497D12—82no—
498C4×D3—21no—
499C4×D3—21no—
500C4×D3—21no—
501C4×D3—21no—
502C4×D3—21no—
503C4×D3—21no—
504C4×D3—21no—
505C4×D3—21no—
506C4×D3—22no—
507C4×D3—41no—
508C4×D3—82no—
509C4×D3—82no—
510Dic6—22no—
511Dic6—41no—
512Dic6—41no—
513C3×C8—41no—
514C3×C8—41no—
515C3×C8—41no—
516C3×C8—41no—
517C3⋊C8—41no—
518C3⋊C8—41no—
519C3⋊C8—41no—
520C3⋊C8—41no—
521C24—62no—
522#41—81no—
523#41—81no—
524#41—122no—
525#41—241no—
526#41—241no—
527#41—241no—
528#41—241no—
529#41—241no—
530#41—241no—
531C2×Q8—21no—
532C2×Q8—31no—
533C2×Q8—61no—
534C2×D4—22no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—31no—
538C2×D4—31no—
539C2×D4—31no—
540C2×D4—32no—
541C2×D4—62no—
542C2×D4—62no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—62no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—124no—
550C2×D4—241no—
551C2×D4—241no—
552C2×D4—241no—
553C2×D4—241no—
554C2×D4C2×C4×D312yes—
555C22×C4—22no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4C2×C4×D311yescharacteristic
566C22×C4D3×D411yescharacteristic
567C22×C4D3×D411yescharacteristic
568M16—241no—
569M16—241no—
570M16—241no—
571M16—241no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—241no—
581C2×C8—241no—
582C4⋊C4—21no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—31no—
588C4⋊C4—31no—
589C4⋊C4—32no—
590C4⋊C4—62no—
591C4⋊C4—62no—
592C4⋊C4—61no—
593C4⋊C4C2×C4×D312yes—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—31no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—62no—
603C22⋊C4—62no—
604C22⋊C4—62no—
605C22⋊C4—62no—
606C22⋊C4—62no—
607C22⋊C4—62no—
608C22⋊C4—62no—
609C42—31no—
610C42—31no—
611C42—31no—
612C42—31no—
613C42—31no—
614C42—31no—
615C42—62no—
616C42C2×C4×D311yescharacteristic
617C42D3×D411yescharacteristic
618C42D3×D411yescharacteristic
619C42C23×D311yescharacteristic
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3C22×C22⋊C411yescharacteristic
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—164no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—42no—
642C3×C4#57611yescharacteristic
643C3×C4#57611yescharacteristic
644C3×C4#57711yescharacteristic
645C3×C4#57711yescharacteristic
646Dic3—21no—
647Dic3—21no—
648Dic3—21no—
649Dic3—21no—
650Dic3—21no—
651Dic3—42no—
652Dic3#41312yes—
653C23—22no—
654C23—31no—
655C23—31no—
656C23—62no—
657C23—124no—
658C23—242no—
659C23—242no—
660C23D3×C22⋊C411yescharacteristic
661Q8—41no—
662Q8—41no—
663Q8—62no—
664Q8—121no—
665Q8—121no—
666D4—42no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—62no—
672D4—82no—
673D4—121no—
674D4—122no—
675D4—124no—
676D4—121no—
677D4—121no—
678D4—121no—
679D4—121no—
680D4—121no—
681D4—242no—
682D4—242no—
683D4—242no—
684D4—242no—
685D4—242no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—41no—
698C2×C4—62no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—62no—
708C2×C4—82no—
709C2×C4—121no—
710C2×C4—242no—
711C2×C4—242no—
712C2×C4—242no—
713C2×C4D3×C22⋊C411yescharacteristic
714C2×C4D3×C22⋊C411yescharacteristic
715C2×C4D3×C22⋊C411yescharacteristic
716C2×C4C22×C4×D311yescharacteristic
717C2×C4C2×D3×D411yescharacteristic
718C2×C4C2×D3×D411yescharacteristic
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—121no—
724C8—121no—
725C8—121no—
726C8—121no—
727C2×C3—41no—
728C2×C3—82no—
729C2×C3C2×#41311yescharacteristic
730C2×C3#289711yescharacteristic
731C2×C3#289711yescharacteristic
732D3—41no—
733D3—41no—
734D3—82no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—61no—
745C22—61no—
746C22—61no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—484no—
751C22C2×D3×C22⋊C411yescharacteristic
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—32no—
757C4—42no—
758C4—61no—
759C4—61no—
760C4—61no—
761C4—61no—
762C4—61no—
763C4—122no—
764C4#576911yescharacteristic
765C4#577011yescharacteristic
766C4#577411yescharacteristic
767C4#577511yescharacteristic
768C3#1777611yescharacteristic, complemented, Sylow
769C2—41no—
770C2—82no—
771C2—121no—
772C2—121no—
773C2—242no—
774C2D3×#41311yescharacteristic
775C2#7883111yescharacteristic
776C2#7892511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
FittingC3×#1553C2
socleC22×C3C22×C22⋊C4
prime radical#86245C2
cosocleC3×C42C24
hypercenter#1553D3
hypocenterC3#17776
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1553

Complements

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

NH ≅ G/Ntype
2. #79340C2semidirect
3. #79294C2semidirect
4. C3×#1553C2semidirect
5. #71806C2semidirect
6. #70819C2semidirect
7. #70772C2semidirect
8. #68431C2semidirect
9. #68426C2semidirect
10. #68421C2semidirect
11. #68419C2semidirect
12. #68388C2semidirect
13. #68383C2semidirect
14. #68383C2semidirect
15. #68381C2semidirect
36. C3×#432C22semidirect
37. C3×#431C22semidirect
38. #4924C22semidirect
39. C2×C4⋊(C3⋊C8)C22semidirect
42. #4837C22semidirect
43. #4835C22semidirect
46. #4833C22semidirect
47. D3×C4⋊C8C22semidirect
56. C3×#332C22semidirect
57. C3×#332C22semidirect
60. #4547C22semidirect
61. #4547C22semidirect
64. #4486C22semidirect
65. #4486C22semidirect
70. #4482C22semidirect
71. #4482C22semidirect
79. #1553D3semidirect
218. #432C2×D3semidirect
222. #431C2×D3semidirect
235. #332C2×D3semidirect
236. #332C2×D3semidirect
768. C3#17776semidirect

Maximal subgroups

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

subgroupindex
#862452
#793402
#792942
C3×#15532
#718062
#708192
#707722
#684312
#684262
#684212
#684192
#683882
#683832
#683812
#177763