Finite Group Databasebeta

← #11872927

Subgroups — #11872927

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5827C211yesmaximal, characteristic, complemented
2#10594814C211yesmaximal, characteristic, complemented
3#10592937C211yesmaximal, characteristic
4C3×#5239C211yesmaximal, characteristic, complemented
5#10591607C211yesmaximal, characteristic, complemented
6Dic3×#216C211yesmaximal, characteristic, complemented
7#10591546C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591471C211yesmaximal, characteristic, complemented
10#10591440C211yesmaximal, characteristic, complemented
11#10591410C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10591133C211yesmaximal, characteristic, complemented
14#10591132C211yesmaximal, characteristic, complemented
15#10591056C211yesmaximal, characteristic, complemented
16#82569—31nomaximal
17#80218—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3755C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21#64139C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×D4×Dic3—21no—
26C3×D4×Dic3—21no—
27C3×D4×Dic3C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×#926—21no—
31C3×#926C2211yescharacteristic
32C2×C3×C4⋊Dic3—21no—
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C3×#924C2211yescharacteristic
35#63975—21no—
36#63953—21no—
37#63918C2211yescharacteristic
38#63895—21no—
39#63894C2211yescharacteristic
40#63864C2211yescharacteristic
41#63848—21no—
42Dic3×Dic6C2211yescharacteristic
43#63662C2211yescharacteristic
44#63659C2211yescharacteristic
45#63657C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#830C2211yescharacteristic
49#63576C2211yescharacteristic
50#63576C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#520—31no—
62#5827D311yescharacteristic, complemented
63#5643—31no—
64#5534—31no—
65C3×#452—31no—
66#5239D311yescharacteristic, complemented
67#5238—31no—
68#5238—31no—
69#5238—61no—
70#5185—31no—
71Dic3×Q16—31no—
72#5165—31no—
73#5164—31no—
74#5044—31no—
75C4×#216—31no—
76#5028—31no—
77#5026—31no—
78#5021—31no—
79#5018—31no—
80#5016—31no—
81C4×#213—31no—
82#5007—31no—
83#5000—31no—
84#4970—31no—
85#4967—31no—
86#4817—31no—
87#4793—31no—
88#4759—31no—
89#4756—31no—
90#4736—31no—
91#4720—31no—
92C32×#41—22no—
93C32×#41—22no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#624—21no—
107#3755—22no—
108#3753—22no—
109#3752—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C3×#217—21no—
114C3×#217—21no—
115C3×#217—21no—
116C3×#217D411yescharacteristic
117C3×#217D411yescharacteristic
118C3×#216—22no—
119C3×#214—22no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140Dic32—21no—
141#3124—91noSylow
142C2×C3×#41—21no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C2×D311yescharacteristic
145C2×C3×Q16—31no—
146C2×C3×SD16—31no—
147C3×C22⋊Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×D4—31no—
151C3×C4×D4—31no—
152C3×C4×D4—61no—
153C3×C4×D4—61no—
154C3×#117—31no—
155C3×#117—61no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—61no—
158#947—31no—
159Q8×Dic3—31no—
160Q8×Dic3C2×D311yescharacteristic
161Q8×Dic3C2×D311yescharacteristic
162C2×#216C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—61no—
166D4×Dic3—21no—
167D4×Dic3—21no—
168D4×Dic3C2×D311yescharacteristic
169D4×Dic3C2×D311yescharacteristic
170C2×#214C2×D311yescharacteristic
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—61no—
174#930—31no—
175#930—31no—
176#930—61no—
177#926—21no—
178#926C2×D311yescharacteristic
179C2×C4⋊Dic3—21no—
180C2×C4⋊Dic3C2×D311yescharacteristic
181#924C2×D311yescharacteristic
182#898—61no—
183#898—61no—
184#897—61no—
185#896—61no—
186#893—31no—
187#888—31no—
188#885—61no—
189#885—61no—
190#883—61no—
191#883—61no—
192#875—31no—
193C4×D12—31no—
194#869—31no—
195C4×Dic6—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×C22⋊C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835C2×D311yescharacteristic
205#832—31no—
206#832—31no—
207#832—61no—
208#832C2×D311yescharacteristic
209#830—31no—
210#830—31no—
211#830—61no—
212#830C2×D311yescharacteristic
213#821—31no—
214#821—31no—
215#818—31no—
216#818—31no—
217#815—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220C8×Dic3—31no—
221#810—31no—
222#810—31no—
223#809—31no—
224#809—31no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C23×C32C2×D411yescharacteristic
237C22×C3⋊D3—21no—
238C32×Q8—21no—
239C32×Q8#4112yes—
240C32×D4—24no—
241C32×D4—21no—
242C32×D4#4112yes—
243C2×C32×C4—24no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—81no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—81no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×Dic6—21no—
265C3×Dic6—21no—
266#627—81no—
267#624—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—91no—
279#463—91no—
280#452—31no—
281#449—91no—
282#440—91no—
283#440—91no—
284C4×Q16—91no—
285C4×D8—91no—
286#433—91no—
287C3×#41—22no—
288C3×#41—22no—
289C3×#41—22no—
290C3×#41—22no—
291C3×#41—42no—
292C3×#41—42no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—41no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—41no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—121no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6C22×D311yescharacteristic
326C3×Q16—62no—
327C3×SD16—62no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C22⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—31no—
345C3×C42—31no—
346C3×C42—61no—
347C3×C42—61no—
348#217—21no—
349#217—21no—
350#217—21no—
351#217#6711yescharacteristic
352#217#6711yescharacteristic
353#216—22no—
354#215—62no—
355#215—62no—
356#215—122no—
357#214—22no—
358#213—62no—
359#213—62no—
360#213—122no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—121no—
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3#6711yescharacteristic
379C4⋊Dic3#6711yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3C22×D311yescharacteristic
391C4×Dic3C22×D311yescharacteristic
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400C22×C32—21no—
401C22×C32—22no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C32×C4—21no—
411C32×C4—22no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3⋊Dic3—41no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C2×#41D3211yescharacteristic
424C2×Q16—31no—
425C2×SD16—31no—
426C2×SD16—91no—
427C2×D8—91no—
428C4⋊Q8—91no—
429#126—181no—
430#124—91no—
431#124—181no—
432#123—181no—
433C22⋊Q8—31no—
434C22⋊Q8—181no—
435#121—91no—
436C4×Q8—31no—
437C4×Q8—31no—
438C4×Q8—91no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—61no—
442C4×D4—61no—
443C4×D4—91no—
444#117—31no—
445#117—61no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—61no—
448#107—91no—
449#107—91no—
450#107—91no—
451#107—91no—
452C4⋊C8—91no—
453C4⋊C8—91no—
454#103—31no—
455#103—91no—
456#103—91no—
457#103—91no—
458#102—31no—
459#102—91no—
460#102—91no—
461#102—91no—
462C22⋊C8—31no—
463C22⋊C8—91no—
464#97—91no—
465C4×C8—91no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—41no—
470C23×C3D3×D411yescharacteristic
471C23×C3C2×#6711yescharacteristic
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—121no—
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—22no—
478C3×Q8—41no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8#23512yes—
482C3×Q8#23712yes—
483C3×D4—24no—
484C3×D4—24no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—22no—
488C3×D4—41no—
489C3×D4—44no—
490C3×D4#23512yes—
491C3×D4#23712yes—
492C2×C3×C4—24no—
493C2×C3×C4—24no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—44no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4—241no—
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—241no—
522#67—241no—
523#67—242no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—81no—
531C2×Dic3—81no—
532C2×Dic3—81no—
533C2×Dic3—121no—
534C2×Dic3C2×#6711yescharacteristic
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538D12—61no—
539D12—61no—
540D12—61no—
541D12—61no—
542D12—121no—
543D12—121no—
544C4×D3—241no—
545C4×D3—241no—
546Dic6—21no—
547Dic6—21no—
548Dic6—241no—
549Dic6—241no—
550C3×C8—61no—
551C3×C8—61no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—121no—
559C3⋊C8—121no—
560C2×C32—41no—
561C2×C32—42no—
562C2×C32#52511yescharacteristic
563C2×C32#57611yescharacteristic
564C2×C32#57811yescharacteristic
565C3⋊D3—81no—
566#41—22no—
567#41—22no—
568C2×Q8—31no—
569C2×Q8—181no—
570C2×Q8C2×D3211yescharacteristic
571C2×D4—21no—
572C2×D4—91no—
573C2×D4—181no—
574C2×D4C2×D3211yescharacteristic
575C22×C4—21no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—181no—
580C22×C4C2×D3211yescharacteristic
581Q16—62no—
582SD16—62no—
583SD16—182no—
584D8—182no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—91no—
588C2×C8—91no—
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C22⋊C4—31no—
602C22⋊C4—31no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—31no—
611C42—31no—
612C42—61no—
613C42—61no—
614C42—181no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—22no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—41no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C22×#6711yescharacteristic
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—241no—
643C2×D3—241no—
644C2×D3—241no—
645C3×C4—21no—
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—22no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—41no—
652C3×C4—42no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4C2×#23511yescharacteristic
662C3×C4C2×#23511yescharacteristic
663C3×C4C2×#23711yescharacteristic
664C3×C4C2×#23711yescharacteristic
665Dic3—21no—
666Dic3—21no—
667Dic3—21no—
668Dic3—21no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—121no—
674Dic3—121no—
675Dic3—241no—
676C32#312411yescharacteristic, complemented, Sylow
677C23—21no—
678C23—181no—
679C23D3×#6711yescharacteristic
680Q8—21no—
681Q8—61no—
682Q8—61no—
683Q8—721no—
684Q8#380412yes—
685D4—24no—
686D4—21no—
687D4—181no—
688D4—181no—
689D4—721no—
690D4#380412yes—
691C2×C4—24no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—181no—
704C2×C4—241no—
705C2×C4—241no—
706C2×C4—241no—
707C2×C4—721no—
708C2×C4D3×#6711yescharacteristic
709C2×C4C22×D3211yescharacteristic
710C8—61no—
711C8—61no—
712C8—181no—
713C8—181no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—41no—
718C2×C3—42no—
719C2×C3—41no—
720C2×C3—42no—
721C2×C3—81no—
722C2×C3—82no—
723C2×C3#558611yescharacteristic
724C2×C3#576911yescharacteristic
725C2×C3#577911yescharacteristic
726C2×C3#579111yescharacteristic
727C2×C3#583511yescharacteristic
728C2×C3#583811yescharacteristic
729D3—241no—
730D3—241no—
731D3—481no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—361no—
739C22—361no—
740C22—361no—
741C22C2×D3×#6711yescharacteristic
742C4—21no—
743C4—22no—
744C4—61no—
745C4—61no—
746C4—61no—
747C4—61no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4—121no—
752C4—361no—
753C4C2×#380411yescharacteristic
754C4C2×#380411yescharacteristic
755C3—21no—
756C3#8021811yescharacteristic, complemented
757C3#8256911yescharacteristic, complemented
758C2—41no—
759C2—42no—
760C2—721no—
761C2#1059545611yescharacteristic
762C2#1059546511yescharacteristic
763C2#1059549811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radical#10592937C2
hypercenterC2×#41D32
hypocenterC32#3124
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5827C2semidirect
2. #10594814C2semidirect
4. C3×#5239C2semidirect
5. #10591607C2semidirect
6. Dic3×#216C2semidirect
7. #10591546C2semidirect
8. #10591540C2semidirect
9. #10591471C2semidirect
10. #10591440C2semidirect
11. #10591410C2semidirect
12. #10591400C2semidirect
13. #10591133C2semidirect
14. #10591132C2semidirect
15. #10591056C2semidirect
62. #5827D3semidirect
66. #5239D3semidirect
676. C32#3124semidirect
756. C3#80218semidirect
757. C3#82569semidirect

Maximal subgroups

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

subgroupindex
C3×#58272
#105948142
#105929372
C3×#52392
#105916072
Dic3×#2162
#105915462
#105915402
#105914712
#105914402
#105914102
#105914002
#105911332
#105911322
#105910562
#825693
#802183