Finite Group Databasebeta

← #11803589

Subgroups — #11803589

Order 1152.

1501 conjugacy classes of subgroups.

The subgroup lattice has 733 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C2×#63898C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic, complemented
5#10591721C212yesmaximal, complemented
6#10591707C212yesmaximal, complemented
7#10591379C212yesmaximal, complemented
8#10591357C211yesmaximal, characteristic, complemented
9#10591323C211yesmaximal, characteristic, complemented
10#10591316C212yesmaximal, complemented
11#10591274C211yesmaximal, characteristic, complemented
12#82633—31nomaximal
13#73872—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×D12C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×#3757C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20#64135—24no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#217C2212yes—
26C3×#930C418yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×Dic32C2212yes—
36#63898—24no—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#121—31no—
41C2×D4×Dic3—31no—
42C2×#930D311yescharacteristic
43C2×#926—31no—
44C2×#926—31no—
45C2×#926—61no—
46C2×#893—31no—
47C3×#380—31no—
48#5221—32no—
49#5221—31no—
50#5220—32no—
51#5212D311yescharacteristic, complemented
52#4988—31no—
53#4984—31no—
54Dic3×C4⋊C4—31no—
55Dic3×C4⋊C4—31no—
56#4972—31no—
57#4957—32no—
58#4956—32no—
59#4951—32no—
60#4950—32no—
61#4670—32no—
62#4668—32no—
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yescomplemented
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C2×C3×#67—42no—
75C2×C3×#67—42no—
76C2×C3×#67C2×C418yescomplemented
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C2×C3×D12—22no—
81C2×C3×D12—22no—
82C2×C3×D12C2×C414yes—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—42no—
85C2×D3×Dic3—42no—
86#3757—22no—
87#3757—22no—
88C4⋊(C3⋊Dic3)—22no—
89C4⋊(C3⋊Dic3)—22no—
90C4×C3⋊Dic3—22no—
91C4×C3⋊Dic3D414yescomplemented
92C3×#217—42no—
93C3×(C2×D3)⋊C4C2×C418yescomplemented
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3C2×C414yescomplemented
97Dic3⋊Dic3—42no—
98(C2×D3)⋊Dic3—24no—
99(C2×D3)⋊Dic3—42no—
100(C2×D3)⋊Dic3—42no—
101Dic32—42no—
102#2324—91noSylow
103C22×C3×D4—32no—
104C22×C3×D4—31no—
105C23×C3×C4—21no—
106C23×C3×C4C2×D311yescharacteristic
107C23×C3×C4C2×D311yescharacteristic
108C22×#67C2×D312yes—
109C23×Dic3—32no—
110C22×D12C2×D311yescharacteristic
111C22×C4×D3—32no—
112C3×#121—38no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C22⋊C4—32no—
117C2×C3×C22⋊C4—32no—
118C2×#217—31no—
119C2×#217—31no—
120C2×#217—31no—
121C2×#217—31no—
122C2×#217—32no—
123C2×#217—32no—
124C2×#217—32no—
125C2×#217—61no—
126C2×#217—61no—
127C2×#217C2×D312yes—
128D4×Dic3—64no—
129#930Dic318yescomplemented
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4C2×D312yes—
134#926—64no—
135#926—64no—
136#926—68no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—32no—
142C2×C4⋊Dic3—61no—
143C2×C4⋊Dic3—61no—
144C2×C4⋊Dic3C2×D311yescharacteristic
145C2×C4⋊Dic3C2×D311yescharacteristic
146C2×C4⋊Dic3C2×D311yescharacteristic
147C2×Dic3⋊C4—32no—
148C2×C4×Dic3—31no—
149C2×C4×Dic3—31no—
150C2×C4×Dic3—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—32no—
153C2×C4×Dic3—32no—
154C2×C4×Dic3—61no—
155C2×C4×Dic3—61no—
156#893—64no—
157C3×#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95C2×D312yes—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32C22×C412yes—
170C23×C32C2411yescharacteristic
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3C22×C414yes—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—28no—
181C2×C32×C4C22×C412yes—
182C2×C32×C4C22×C412yes—
183C2×C32×C4C2×D412yes—
184C2×C32×C4#4112yes—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3C2×D412yes—
196C2×C3⋊Dic3C2×D412yes—
197C3×#67—48no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3C22×C414yes—
207C3×D12—28no—
208D3×Dic3—48no—
209C2×#121—31no—
210C2×C4×D4—91no—
211C2×#117—91no—
212#390—92no—
213#390—91no—
214#389—91no—
215#388—92no—
216#386—92no—
217#385—92no—
218#380—31no—
219C4×C4⋊C4—91no—
220C24×C3—21no—
221C24×C3—32no—
222C24×C3C22×D311yescharacteristic
223C24×C3C22×D311yescharacteristic
224C23×D3C22×D312yes—
225C2×C3×D4—38no—
226C2×C3×D4—34no—
227C2×C3×D4—62no—
228C2×C3×D4—62no—
229C2×C3×D4—122no—
230C2×C3×D4—122no—
231C22×C3×C4—24no—
232C22×C3×C4—24no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—24no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4—32no—
243C22×C3×C4C4×D314yescomplemented
244C22×C3×C4C2×Dic314yescomplemented
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C2×#67—42no—
250C2×#67—42no—
251C2×#67C2×Dic318yescomplemented
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—61no—
261C22×Dic3—61no—
262C22×Dic3—61no—
263C22×Dic3—61no—
264C22×Dic3—64no—
265C22×Dic3—122no—
266C22×Dic3—122no—
267C22×Dic3C22×D312yes—
268C22×Dic3C22×D312yes—
269C22×Dic3C22×D312yes—
270C2×D12—22no—
271C2×D12—22no—
272C2×D12C2×Dic314yes—
273C2×C4×D3—64no—
274C2×C4×D3—122no—
275C2×C4×D3—122no—
276C3×C4⋊C4—34no—
277C3×C4⋊C4—62no—
278C3×C4⋊C4—62no—
279C3×C22⋊C4—38no—
280C3×C22⋊C4—122no—
281#217—42no—
282#217—64no—
283#217—62no—
284#217—62no—
285#217—62no—
286#217—62no—
287#217—64no—
288#217—64no—
289#217—122no—
290#217—122no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—122no—
293(C2×D3)⋊C4—122no—
294(C2×D3)⋊C4C2×Dic318yescomplemented
295C4⋊Dic3—22no—
296C4⋊Dic3—22no—
297C4⋊Dic3—62no—
298C4⋊Dic3—62no—
299C4⋊Dic3—62no—
300C4⋊Dic3—62no—
301C4⋊Dic3—64no—
302C4⋊Dic3—64no—
303C4⋊Dic3—122no—
304C4⋊Dic3C2×Dic314yescomplemented
305Dic3⋊C4—122no—
306C4×Dic3—34no—
307C4×Dic3—34no—
308C4×Dic3—64no—
309C4×Dic3—64no—
310C4×Dic3—62no—
311C4×Dic3—62no—
312C4×Dic3—122no—
313C4×Dic3—122no—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32—22no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32C23×C411yescharacteristic
322C22×C32C22×D411yescharacteristic
323C22×C32C2×#4111yescharacteristic
324C22×C32H(5,𝔽2)11yescharacteristic
325C22×C32H(5,𝔽2)11yescharacteristic
326C22×C32H(5,𝔽2)11yescharacteristic
327C22×C322−1+411yescharacteristic
328C2×C3×D3—24no—
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—42no—
332C2×C3×D3—42no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C32×C4—22no—
336C32×C4C4×D414yes—
337C3⋊Dic3—22no—
338C3⋊Dic3—22no—
339C3⋊Dic3—41no—
340C3⋊Dic3—41no—
341C3×Dic3—24no—
342C3×Dic3—42no—
343C3×Dic3—42no—
344C22×D4—32no—
345C22×D4—31no—
346C23×C4—92no—
347C23×C4D3211yescharacteristic
348#121—38no—
349C4×D4—184no—
350#117—184no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—92no—
357C2×C22⋊C4—32no—
358C2×C22⋊C4—32no—
359C2×C22⋊C4—92no—
360C2×C22⋊C4—91no—
361C2×C22⋊C4—91no—
362C2×C22⋊C4—92no—
363C2×C22⋊C4—92no—
364C2×C42—91no—
365C2×C42—91no—
366C2×C42—92no—
367#95—32no—
368#95—92no—
369#95—92no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—22no—
386C23×C3—34no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—62no—
392C23×C3—62no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3—62no—
397C23×C3C2×C4×D312yes—
398C23×C3C22×Dic312yes—
399C23×C3C23×D311yescharacteristic
400C23×C3C23×D311yescharacteristic
401C22×D3—22no—
402C22×D3—22no—
403C22×D3—22no—
404C22×D3—22no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3C22×Dic314yes—
408C3×D4—68no—
409C3×D4—128no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—216no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—28no—
418C2×C3×C4—28no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—34no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—62no—
431C2×C3×C4—62no—
432C2×C3×C4C2×C4×D312yes—
433C2×C3×C4C2×C4×D312yes—
434C2×C3×C4D3×D412yes—
435C2×C3×C4D3×D412yes—
436C2×C3×C4#23712yes—
437C2×C3×C4#23712yes—
438C2×C3×C4C22×Dic312yes—
439C2×C3×C4C22×Dic312yes—
440#67—48no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—32no—
450C2×Dic3—32no—
451C2×Dic3—32no—
452C2×Dic3—32no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—61no—
456C2×Dic3—61no—
457C2×Dic3—61no—
458C2×Dic3—61no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—62no—
464C2×Dic3—62no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—121no—
478C2×Dic3—121no—
479C2×Dic3—121no—
480C2×Dic3—121no—
481C2×Dic3—121no—
482C2×Dic3—121no—
483C2×Dic3—121no—
484C2×Dic3—121no—
485C2×Dic3—128no—
486C2×Dic3C22×Dic314yes—
487D12—28no—
488C4×D3—128no—
489C2×C32—42no—
490C2×C32C2×C4×D411yescharacteristic
491C2×C32#51811yescharacteristic
492C2×C32#52011yescharacteristic
493C2×C32#53511yescharacteristic
494C2×C32#53711yescharacteristic
495C2×C32#54011yescharacteristic
496C2×C32#54211yescharacteristic
497C3×D3—44no—
498C24—32no—
499C24C2×D3211yescharacteristic
500C2×D4—38no—
501C2×D4—34no—
502C2×D4—62no—
503C2×D4—62no—
504C2×D4—122no—
505C2×D4—122no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—32no—
511C22×C4—91no—
512C22×C4—91no—
513C22×C4—91no—
514C22×C4—91no—
515C22×C4—184no—
516C22×C4—362no—
517C22×C4—362no—
518C22×C4D3×Dic314yescomplemented
519C22×C4C2×D3211yescharacteristic
520C22×C4C2×D3211yescharacteristic
521C4⋊C4—34no—
522C4⋊C4—62no—
523C4⋊C4—62no—
524C4⋊C4—182no—
525C4⋊C4—182no—
526C4⋊C4—362no—
527C22⋊C4—38no—
528C22⋊C4—122no—
529C22⋊C4—184no—
530C22⋊C4—182no—
531C22⋊C4—182no—
532C22⋊C4—362no—
533C22⋊C4—362no—
534C42—94no—
535C42—182no—
536C42—362no—
537C22×C3—24no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—64no—
566C22×C3—64no—
567C22×C3—64no—
568C22×C3—122no—
569C22×C3—122no—
570C22×C3—122no—
571C22×C3—122no—
572C22×C3C22×C4×D311yescharacteristic
573C22×C3C2×D3×D411yescharacteristic
574C22×C3C2×D3×D411yescharacteristic
575C22×C3C2×#23711yescharacteristic
576C22×C3C2×#23711yescharacteristic
577C22×C3#100411yescharacteristic
578C22×C3#100411yescharacteristic
579C22×C3#100411yescharacteristic
580C22×C3#100711yescharacteristic
581C22×C3#100911yescharacteristic
582C22×C3#100911yescharacteristic
583C22×C3#100911yescharacteristic
584C22×C3#101011yescharacteristic
585C22×C3C23×Dic311yescharacteristic
586C2×D3—24no—
587C2×D3—24no—
588C2×D3—24no—
589C2×D3—42no—
590C2×D3—42no—
591C2×D3—42no—
592C2×D3—42no—
593C3×C4—24no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—24no—
597C3×C4—64no—
598C3×C4—122no—
599C3×C4—122no—
600C3×C4#67⋊C414yes—
601C3×C4D4×Dic314yes—
602Dic3—24no—
603Dic3—42no—
604Dic3—42no—
605Dic3—62no—
606Dic3—62no—
607Dic3—62no—
608Dic3—62no—
609Dic3—122no—
610Dic3—122no—
611Dic3—122no—
612Dic3—122no—
613Dic3—121no—
614Dic3—121no—
615Dic3—121no—
616Dic3—121no—
617C32#232411yescharacteristic, complemented, Sylow
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—34no—
625C23—62no—
626C23—62no—
627C23—62no—
628C23—62no—
629C23—62no—
630C23—62no—
631C23C2×D3×Dic312yes—
632C23C22×D3211yescharacteristic
633D4—68no—
634D4—128no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—28no—
638C2×C4—34no—
639C2×C4—62no—
640C2×C4—62no—
641C2×C4—62no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—62no—
647C2×C4—92no—
648C2×C4—92no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4—181no—
659C2×C4—368no—
660C2×C4C2×D3×Dic312yes—
661C2×C4C2×D3×Dic312yes—
662C2×C4#380512yes—
663C2×C4#381112yes—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—44no—
672C2×C3—42no—
673C2×C3—42no—
674C2×C3—124no—
675C2×C3C2×#67⋊C411yescharacteristic
676C2×C3#550411yescharacteristic
677C2×C3#552111yescharacteristic
678C2×C3#560311yescharacteristic
679C2×C3#560711yescharacteristic
680C2×C3#560711yescharacteristic
681C2×C3#560811yescharacteristic
682C2×C3#561911yescharacteristic
683C2×C3#561911yescharacteristic
684C2×C3#562911yescharacteristic
685C2×C3#564311yescharacteristic
686C2×C3C2×D4×Dic311yescharacteristic
687C2×C3#579811yescharacteristic
688C2×C3#582711yescharacteristic
689D3—44no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—64no—
698C22—64no—
699C22—64no—
700C22—122no—
701C22—122no—
702C22—122no—
703C22—122no—
704C22#6429711yescharacteristic
705C22#6430711yescharacteristic
706C22#6430711yescharacteristic
707C22#6430711yescharacteristic
708C22C22×D3×Dic311yescharacteristic
709C22C2×#380511yescharacteristic
710C22C2×#381111yescharacteristic
711C4—22no—
712C4—64no—
713C4—122no—
714C4—122no—
715C4—182no—
716C4—182no—
717C4—361no—
718C4—361no—
719C4#67⋊Dic314yes—
720C3—21no—
721C3#7387211yescharacteristic, complemented
722C3#8263311yescharacteristic, complemented
723C2—42no—
724C2—124no—
725C2#1059492311yescharacteristic
726C2#1059498211yescharacteristic
727C2#1059498411yescharacteristic
728C2#1059498611yescharacteristic
729C2#1059504111yescharacteristic
730C2#1059508211yescharacteristic
731C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64135C2semidirect
3. C2×#63898C2semidirect
4. C3×#5212C2semidirect
5. #10591721C2semidirect
6. #10591707C2semidirect
7. #10591379C2semidirect
8. #10591357C2semidirect
9. #10591323C2semidirect
10. #10591316C2semidirect
11. #10591274C2semidirect
26. C3×#930C4semidirect
51. #5212D3semidirect
67. C22×C32×C4C2×C4semidirect
76. C2×C3×#67C2×C4semidirect
91. C4×C3⋊Dic3D4semidirect
93. C3×(C2×D3)⋊C4C2×C4semidirect
96. C3×C4⋊Dic3C2×C4semidirect
129. #930Dic3semidirect
243. C22×C3×C4C4×D3semidirect
244. C22×C3×C4C2×Dic3semidirect
251. C2×#67C2×Dic3semidirect
294. (C2×D3)⋊C4C2×Dic3semidirect
304. C4⋊Dic3C2×Dic3semidirect
518. C22×C4D3×Dic3semidirect
617. C32#2324semidirect
721. C3#73872semidirect
722. C3#82633semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×#9302
C2×#638982
C3×#52122
#105917212
#105917072
#105913792
#105913572
#105913232
#105913162
#105912742
#826333
#738723