Finite Group Databasebeta

← #11873001

Subgroups — #11873001

Order 1152.

816 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5574C211yesmaximal, characteristic, complemented
2#10593961C211yesmaximal, characteristic, complemented
3#10592720C211yesmaximal, characteristic, complemented
4C3×#5028C211yesmaximal, characteristic, complemented
5#10591597C211yesmaximal, characteristic, complemented
6#10591586C211yesmaximal, characteristic
7Dic3×#216C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10590517C211yesmaximal, characteristic, complemented
10#10590498C211yesmaximal, characteristic, complemented
11#10590478C211yesmaximal, characteristic, complemented
12#10590452C211yesmaximal, characteristic, complemented
13#10590348C211yesmaximal, characteristic, complemented
14#10590272C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82569—31nomaximal
17#80574—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20#64078C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C3×#893—21no—
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4—21no—
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#875C2211yescharacteristic
29C3×C4×D12—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872—21no—
32C3×#872C2211yescharacteristic
33#63913—21no—
34#63908C2211yescharacteristic
35#63896—21no—
36Dic3×D12C2211yescharacteristic
37#63891—21no—
38#63861—21no—
39#63856C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63662C2211yescharacteristic
44#63662C2211yescharacteristic
45#63634C2211yescharacteristic
46#63634C2211yescharacteristic
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63565C2211yescharacteristic
54#63563C2211yescharacteristic
55#63563C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#520—31no—
62#5682—31no—
63#5574D311yescharacteristic, complemented
64#5534—31no—
65C3×#464—31no—
66#5239—31no—
67#5238—31no—
68#5187—31no—
69Dic3×Q16—31no—
70#5172—31no—
71#5164—31no—
72#5057—31no—
73C4×#216—31no—
74#5028D311yescharacteristic, complemented
75#5026—31no—
76#5021—31no—
77#5021—31no—
78#5021—61no—
79#5018—31no—
80#5016—31no—
81C4×#213—31no—
82#5007—31no—
83#5000—31no—
84#4970—31no—
85#4967—31no—
86#4846—31no—
87#4840—31no—
88#4817—31no—
89#4811—31no—
90#4774—31no—
91#4756—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C3×#239—22no—
95C3×#239—22no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C42—21no—
110C32×C42C2311yescharacteristic
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#216—22no—
117C3×#215—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3715—22no—
140#3713—22no—
141#3124—91noSylow
142C2×C3×#41—31no—
143C2×#239C2×D311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×SD16—31no—
146C3×#124—31no—
147C3×C4×Q8—21no—
148C3×C4×Q8—31no—
149C3×C4×Q8C2×D311yescharacteristic
150C3×C4×Q8C2×D311yescharacteristic
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153C3×C4×D4—61no—
154C3×C4×D4—61no—
155C3×#117—31no—
156C3×#117—61no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—61no—
159#946—31no—
160Q8×Dic3—31no—
161Q8×Dic3C2×D311yescharacteristic
162C2×#216C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215C2×D311yescharacteristic
165#938—31no—
166D4×Dic3—31no—
167C2×#214—31no—
168C2×#213—31no—
169C2×#213—31no—
170#930—31no—
171#924—31no—
172#898—61no—
173#896—61no—
174#893—21no—
175#893C2×D311yescharacteristic
176D3×C4⋊C4—21no—
177D3×C4⋊C4C2×D311yescharacteristic
178#886—61no—
179#885—61no—
180#885—61no—
181#883—61no—
182#879—61no—
183#878—61no—
184#875C2×D311yescharacteristic
185C4×D12—21no—
186C4×D12—31no—
187C4×D12C2×D311yescharacteristic
188#872—21no—
189#872C2×D311yescharacteristic
190#869—31no—
191#869—31no—
192#869—61no—
193C4×Dic6—31no—
194C3×C4⋊C8—31no—
195C3×#103—31no—
196C3×#102—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—61no—
203#835—61no—
204#832—31no—
205#832—31no—
206#832—31no—
207#830—31no—
208#830—31no—
209#821—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213#818—31no—
214#818—31no—
215#815—31no—
216C8×Dic3—31no—
217#810—31no—
218#810C2×D311yescharacteristic
219#809—31no—
220#809C2×D311yescharacteristic
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807—31no—
227#807—61no—
228#807—61no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803—31no—
234C4×C3⋊C8—31no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8#4112yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247#634—81no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×D12—24no—
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12#4112yes—
258C3×C4×D3—24no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—81no—
262C3×C4×D3—81no—
263C3×C4×D3—81no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266#625—81no—
267D3×Dic3—81no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#542—91no—
273#520—31no—
274#484—91no—
275#480—91no—
276#477—91no—
277#474—91no—
278#464—31no—
279#463—91no—
280#452—91no—
281#449—91no—
282#440—91no—
283#440—91no—
284C4×Q16—91no—
285C4×D8—91no—
286#433—91no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C2×#67—61no—
302C2×#67—61no—
303C22×Dic3—61no—
304#239—22no—
305#239—22no—
306C2×D12—21no—
307C2×D12C22×D311yescharacteristic
308C2×D12C22×D311yescharacteristic
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—61no—
314C2×C4×D3C22×D311yescharacteristic
315C2×Dic6—61no—
316C2×Dic6—61no—
317C2×Dic6—121no—
318C2×Dic6C22×D311yescharacteristic
319C3×Q16—62no—
320C3×SD16—62no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—41no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C22⋊C4—31no—
335C3×C22⋊C4—31no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C42—21no—
341C3×C42—21no—
342C3×C42—21no—
343C3×C42—31no—
344C3×C42—41no—
345C3×C42—61no—
346C3×C42C22×D311yescharacteristic
347C3×C42C22×D311yescharacteristic
348#217—61no—
349#217—61no—
350#217—61no—
351#216—22no—
352#215—22no—
353#215—62no—
354#214—62no—
355#213—62no—
356#213—62no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4#6711yescharacteristic
365(C2×D3)⋊C4#6711yescharacteristic
366C4⋊Dic3—21no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—121no—
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4#6711yescharacteristic
383Dic3⋊C4#6711yescharacteristic
384C4×Dic3—21no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396C22×C32C22×D411yescharacteristic
397C2×C3×D3—21no—
398C2×C3×D3—22no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—21no—
407C32×C4—22no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3⋊Dic3—41no—
413C3⋊Dic3—41no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C2×#41—31no—
420C2×Q16—31no—
421C2×SD16—31no—
422C2×SD16—91no—
423C2×D8—91no—
424C4⋊Q8—91no—
425#126—181no—
426#124—31no—
427#124—181no—
428#123—181no—
429C22⋊Q8—91no—
430C22⋊Q8—181no—
431#121—91no—
432C4×Q8—31no—
433C4×Q8—91no—
434C4×Q8D3211yescharacteristic
435C4×D4—31no—
436C4×D4—31no—
437C4×D4—61no—
438C4×D4—61no—
439C4×D4—91no—
440#117—31no—
441#117—61no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—61no—
444#107—91no—
445#107—91no—
446#107—91no—
447#107—91no—
448C4⋊C8—31no—
449C4⋊C8—91no—
450#103—31no—
451#103—91no—
452#103—91no—
453#103—91no—
454#102—31no—
455#102—91no—
456#102—91no—
457#102—91no—
458C22⋊C8—91no—
459C22⋊C8—91no—
460#97—91no—
461C4×C8—91no—
462C23×C3—31no—
463C23×C3—61no—
464C23×C3—61no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3C2×#6711yescharacteristic
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—22no—
471C3×Q8—41no—
472C3×Q8—61no—
473C3×Q8—61no—
474C3×Q8#23512yes—
475C3×Q8#23712yes—
476C3×D4—32no—
477C3×D4—64no—
478C3×D4—61no—
479C3×D4—61no—
480C3×D4—61no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—64no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—241no—
499C2×C3×C4—241no—
500C2×C3×C4—241no—
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4D3×D411yescharacteristic
503C2×C3×C4C2×#6711yescharacteristic
504C2×C3×C4C2×#6711yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—241no—
508#67—241no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—121no—
516C2×Dic3—121no—
517C2×Dic3—241no—
518C2×Dic3C2×#6711yescharacteristic
519C2×Dic3C2×#6711yescharacteristic
520C2×Dic3C2×#6711yescharacteristic
521D12—24no—
522D12—21no—
523D12—21no—
524D12—21no—
525D12#23512yes—
526C4×D3—24no—
527C4×D3—21no—
528C4×D3—21no—
529C4×D3—81no—
530C4×D3—81no—
531C4×D3—81no—
532C4×D3—241no—
533Dic6—21no—
534Dic6—21no—
535Dic6—241no—
536Dic6—241no—
537Dic6—242no—
538C3×C8—61no—
539C3×C8—61no—
540C3⋊C8—21no—
541C3⋊C8—21no—
542C3⋊C8—61no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C3⋊C8—61no—
546C3⋊C8—121no—
547C3⋊C8—121no—
548C2×C32#52511yescharacteristic
549C2×C32#57611yescharacteristic
550C2×C32#57811yescharacteristic
551C3×D3—41no—
552C3×D3—42no—
553C3×D3—81no—
554#41—62no—
555#41—62no—
556C2×Q8—31no—
557C2×Q8—181no—
558C2×Q8C2×D3211yescharacteristic
559C2×D4—31no—
560C2×D4—31no—
561C2×D4—61no—
562C2×D4—181no—
563C22×C4—31no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—181no—
569Q16—62no—
570SD16—62no—
571SD16—182no—
572D8—182no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8—91no—
576C2×C8—91no—
577C4⋊C4—21no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—91no—
584C4⋊C4—91no—
585C4⋊C4—181no—
586C4⋊C4—181no—
587C4⋊C4—181no—
588C4⋊C4C2×D3211yescharacteristic
589C22⋊C4—31no—
590C22⋊C4—31no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C42—21no—
599C42—31no—
600C42—61no—
601C42—181no—
602C42C2×D3211yescharacteristic
603C22×C3—21no—
604C22×C3—61no—
605C22×C3—61no—
606C22×C3—62no—
607C22×C3—61no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3C2×D3×D411yescharacteristic
614C22×C3C22×#6711yescharacteristic
615C2×D3—21no—
616C2×D3—22no—
617C2×D3—21no—
618C2×D3—21no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—41no—
624C3×C4—22no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—22no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—22no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—41no—
634C3×C4—42no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—61no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—81no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4C2×#23511yescharacteristic
644C3×C4C2×#23511yescharacteristic
645C3×C4C2×#23711yescharacteristic
646C3×C4D3×#4111yescharacteristic
647Dic3—21no—
648Dic3—21no—
649Dic3—21no—
650Dic3—41no—
651Dic3—41no—
652Dic3—121no—
653Dic3—121no—
654Dic3—121no—
655Dic3—121no—
656Dic3—241no—
657Dic3—241no—
658C32#312411yescharacteristic, complemented, Sylow
659C23—31no—
660C23—61no—
661C23—61no—
662Q8—21no—
663Q8—61no—
664Q8—61no—
665Q8—721no—
666Q8#379512yes—
667D4—32no—
668D4—64no—
669D4—61no—
670D4—61no—
671D4—61no—
672D4—721no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—31no—
678C2×C4—64no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—181no—
684C2×C4—181no—
685C2×C4—241no—
686C2×C4—241no—
687C2×C4—241no—
688C2×C4—721no—
689C2×C4D3×#6711yescharacteristic
690C2×C4D3×#6711yescharacteristic
691C2×C4C22×D3211yescharacteristic
692C8—61no—
693C8—61no—
694C8—181no—
695C8—181no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—121no—
700C2×C3—122no—
701C2×C3—241no—
702C2×C3#560611yescharacteristic
703C2×C3#576911yescharacteristic
704C2×C3#577911yescharacteristic
705C2×C3#579111yescharacteristic
706C2×C3#583511yescharacteristic
707C2×C3#583811yescharacteristic
708D3—41no—
709D3—42no—
710D3—81no—
711C22—61no—
712C22—62no—
713C22—61no—
714C22—61no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22—121no—
720C22C2×D3×#6711yescharacteristic
721C4—21no—
722C4—22no—
723C4—21no—
724C4—41no—
725C4—61no—
726C4—61no—
727C4—61no—
728C4—121no—
729C4—121no—
730C4—361no—
731C4—361no—
732C4C2×#379511yescharacteristic
733C4D3×#23511yescharacteristic
734C3—21no—
735C3#8057411yescharacteristic, complemented
736C3#8256911yescharacteristic, complemented
737C2—121no—
738C2—122no—
739C2—241no—
740C2#1059489211yescharacteristic
741C2#1059532811yescharacteristic
742C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10591586C2
hypercenterC4×Q8D32
hypocenterC32#3124
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5574C2semidirect
2. #10593961C2semidirect
3. #10592720C2semidirect
4. C3×#5028C2semidirect
5. #10591597C2semidirect
7. Dic3×#216C2semidirect
8. #10591566C2semidirect
9. #10590517C2semidirect
10. #10590498C2semidirect
11. #10590478C2semidirect
12. #10590452C2semidirect
13. #10590348C2semidirect
14. #10590272C2semidirect
15. #10590253C2semidirect
63. #5574D3semidirect
74. #5028D3semidirect
658. C32#3124semidirect
735. C3#80574semidirect
736. C3#82569semidirect

Maximal subgroups

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

subgroupindex
C3×#55742
#105939612
#105927202
C3×#50282
#105915972
#105915862
Dic3×#2162
#105915662
#105905172
#105904982
#105904782
#105904522
#105903482
#105902722
#105902532
#825693
#805743