Finite Group Databasebeta

← #11803598

Subgroups — #11803598

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×#64081C211yesmaximal, characteristic, complemented
2C2×#63916C211yesmaximal, characteristic
3C2×#63898C211yesmaximal, characteristic, complemented
4C3×#4939C211yesmaximal, characteristic, complemented
5C3×#4928C211yesmaximal, characteristic, complemented
6#10591384C212yesmaximal, complemented
7#10591372C212yesmaximal, complemented
8#10591364C212yesmaximal, complemented
9#10591325C211yesmaximal, characteristic, complemented
10#10591281C212yesmaximal, complemented
11#10591274C211yesmaximal, characteristic, complemented
12#76430—31nomaximal
13#76198—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×#626C2212yes—
17C22×D3×Dic3C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24#64081—24no—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2212yes—
31C2×#3722C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×Dic32C2212yes—
35#63916C418yescomplemented
36#63898—24no—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×#938—31no—
41C2×D4×Dic3—31no—
42C2×#895—31no—
43C2×#893—31no—
44C2×#872—31no—
45C2×#872—31no—
46C2×#872—61no—
47C3×#390—31no—
48C3×#389—31no—
49#4989—32no—
50#4988—32no—
51#4987—31no—
52#4987—31no—
53Dic3×C4⋊C4—31no—
54Dic3×C4⋊C4—31no—
55#4958—32no—
56#4957—32no—
57#4946—32no—
58#4944—32no—
59#4939D311yescharacteristic, complemented
60#4928D311yescharacteristic, complemented
61#4669—32no—
62#4665—32no—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C2×C4×C3⋊D3—22no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3C2×C414yescomplemented
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×D12—22no—
78C2×C3×D12—22no—
79C2×C3×D12C2×C414yes—
80C2×#626—42no—
81C2×#626—42no—
82C2×#626C2×C418yescomplemented
83C2×D3×Dic3—24no—
84C2×D3×Dic3—42no—
85C2×D3×Dic3—42no—
86C32×C42—22no—
87#3752—22no—
88#3752—22no—
89#3750—22no—
90#3750—22no—
91C4×C3⋊Dic3D414yescomplemented
92C3×(C2×D3)⋊C4—42no—
93C3×(C2×D3)⋊C4—42no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3C2×C414yescomplemented
97C3×Dic3⋊C4—42no—
98#3722—42no—
99(C2×D3)⋊Dic3—24no—
100(C2×D3)⋊Dic3C2×C418yescomplemented
101Dic32—42no—
102#2324—91noSylow
103C22×C3×D4—31no—
104C22×#67—32no—
105C23×Dic3—32no—
106C22×D12—32no—
107C22×D12C2×D311yescharacteristic
108C22×C4×D3—31no—
109C22×C4×D3—31no—
110C22×C4×D3—32no—
111C22×C4×D3—61no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—32no—
116C2×C3×C22⋊C4—32no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C42—21no—
119C2×C3×C42C2×D311yescharacteristic
120C2×C3×C42C2×D311yescharacteristic
121C2×#217—32no—
122C2×#217—32no—
123#938—38no—
124D4×Dic3—64no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—61no—
134C2×(C2×D3)⋊C4—61no—
135C2×(C2×D3)⋊C4C2×D312yes—
136C2×(C2×D3)⋊C4C2×D312yes—
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×C4⋊Dic3C2×D311yescharacteristic
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×Dic3⋊C4—31no—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—61no—
145C2×Dic3⋊C4—61no—
146C2×Dic3⋊C4C2×D312yes—
147C2×C4×Dic3—31no—
148C2×C4×Dic3—31no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151C2×C4×Dic3—61no—
152#895—38no—
153#893—64no—
154#872—64no—
155#872—64no—
156#872—68no—
157C3×#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95C2×D312yes—
163C23×C32C2411yescharacteristic
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3C22×C412yes—
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—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C2×D412yes—
186C2×C32×C4#4112yes—
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⋊Dic3C22×C412yes—
194C2×C3⋊Dic3C2×D412yes—
195C2×C3⋊Dic3C2×D412yes—
196C4×C3⋊D3—28no—
197C2×C3×Dic3—22no—
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×Dic3C22×C414yes—
206C3×D12—28no—
207#626—48no—
208D3×Dic3—48no—
209C2×#121—91no—
210C2×C4×D4—91no—
211C2×#117—91no—
212#390—31no—
213#390—92no—
214#389—31no—
215#388—92no—
216#386—92no—
217#385—92no—
218#380—91no—
219C4×C4⋊C4—91no—
220C24×C3—32no—
221C23×D3—31no—
222C23×D3—31no—
223C23×D3—61no—
224C23×D3C22×D312yes—
225C2×C3×D4—34no—
226C2×C3×D4—62no—
227C2×C3×D4—62no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4—32no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—38no—
241C2×#67—122no—
242C2×#67—122no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—31no—
249C22×Dic3—61no—
250C22×Dic3—61no—
251C22×Dic3—61no—
252C22×Dic3—64no—
253C22×Dic3—122no—
254C22×Dic3—122no—
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D312yes—
258C2×D12—22no—
259C2×D12—22no—
260C2×D12—38no—
261C2×D12—122no—
262C2×D12—122no—
263C2×D12C4×D314yes—
264C2×C4×D3—34no—
265C2×C4×D3—34no—
266C2×C4×D3—64no—
267C2×C4×D3—64no—
268C2×C4×D3—64no—
269C2×C4×D3—62no—
270C2×C4×D3—62no—
271C2×C4×D3—62no—
272C2×C4×D3—62no—
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×C4⋊C4—122no—
280C3×C22⋊C4—122no—
281C3×C22⋊C4—122no—
282C3×C42—24no—
283C3×C42—22no—
284C3×C42—22no—
285#217—38no—
286#217—64no—
287(C2×D3)⋊C4—38no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—62no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—64no—
297(C2×D3)⋊C4—122no—
298(C2×D3)⋊C4—122no—
299C4⋊Dic3—22no—
300C4⋊Dic3—22no—
301C4⋊Dic3C4×D314yescomplemented
302Dic3⋊C4—42no—
303Dic3⋊C4—62no—
304Dic3⋊C4—62no—
305Dic3⋊C4—62no—
306Dic3⋊C4—62no—
307Dic3⋊C4—64no—
308Dic3⋊C4—64no—
309C4×Dic3—34no—
310C4×Dic3—34no—
311C4×Dic3—64no—
312C4×Dic3—122no—
313C4×Dic3—122no—
314C22×C32C23×C411yescharacteristic
315C22×C32C22×D411yescharacteristic
316C22×C32C2×#4111yescharacteristic
317C22×C32H(5,𝔽2)11yescharacteristic
318C22×C32H(5,𝔽2)11yescharacteristic
319C22×C32H(5,𝔽2)11yescharacteristic
320C22×C322−1+411yescharacteristic
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—22no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—41no—
326C2×C3⋊D3—41no—
327C2×C3⋊D3—41no—
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—41no—
336C32×C4—41no—
337C32×C4C4×D414yes—
338C3⋊Dic3—22no—
339C3⋊Dic3—22no—
340C3⋊Dic3—22no—
341C3×Dic3—24no—
342C3×Dic3—42no—
343C3×Dic3—42no—
344C22×D4—31no—
345C22×D4—92no—
346C23×C4—92no—
347C23×C4—91no—
348#121—98no—
349C4×D4—184no—
350#117—184no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—32no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—91no—
357C2×C22⋊C4—32no—
358C2×C22⋊C4—32no—
359C2×C22⋊C4—92no—
360C2×C22⋊C4—92no—
361C2×C22⋊C4—91no—
362C2×C22⋊C4—91no—
363C2×C22⋊C4—92no—
364C2×C42—91no—
365C2×C42—92no—
366C2×C42D3211yescharacteristic
367#95—32no—
368#95—92no—
369#95—92no—
370C23×C3—21no—
371C23×C3—34no—
372C23×C3—62no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3—62no—
376C23×C3—62no—
377C23×C3—62no—
378C23×C3C23×D311yescharacteristic
379C23×C3C23×D311yescharacteristic
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—32no—
387C22×D3—32no—
388C22×D3—62no—
389C22×D3—62no—
390C22×D3—62no—
391C22×D3—61no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—61no—
400C22×D3—61no—
401C22×D3—61no—
402C22×D3—61no—
403C22×D3—121no—
404C22×D3—121no—
405C22×D3—121no—
406C22×D3—121no—
407C22×D3C2×C4×D314yes—
408C3×D4—68no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—34no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4—62no—
435C2×C3×C4—62no—
436C2×C3×C4—62no—
437C2×C3×C4—62no—
438C2×C3×C4—62no—
439C2×C3×C4C2×C4×D312yes—
440C2×C3×C4C2×C4×D312yes—
441C2×C3×C4D3×D412yes—
442C2×C3×C4D3×D412yes—
443C2×C3×C4#23712yes—
444C2×C3×C4#23912yes—
445#67—128no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—32no—
455C2×Dic3—32no—
456C2×Dic3—32no—
457C2×Dic3—32no—
458C2×Dic3—32no—
459C2×Dic3—32no—
460C2×Dic3—62no—
461C2×Dic3—62no—
462C2×Dic3—62no—
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—128no—
482C2×Dic3C2×C4×D314yes—
483D12—28no—
484D12—128no—
485C4×D3—616no—
486C4×D3—68no—
487C4×D3—68no—
488C4×D3—128no—
489C2×C32C2×C4×D411yescharacteristic
490C2×C32#51811yescharacteristic
491C2×C32#52011yescharacteristic
492C2×C32#53511yescharacteristic
493C2×C32#53711yescharacteristic
494C2×C32#54011yescharacteristic
495C2×C32#54211yescharacteristic
496C3⋊D3—42no—
497C3×D3—44no—
498C24—32no—
499C24—91no—
500C2×D4—34no—
501C2×D4—62no—
502C2×D4—62no—
503C2×D4—98no—
504C2×D4—362no—
505C2×D4—362no—
506C22×C4—32no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—91no—
510C22×C4—91no—
511C22×C4—91no—
512C22×C4—94no—
513C22×C4—184no—
514C22×C4—182no—
515C22×C4—182no—
516C22×C4—362no—
517C22×C4—362no—
518C22×C4C2×D3211yescharacteristic
519C22×C4C2×D3211yescharacteristic
520C22×C4C2×D3211yescharacteristic
521C4⋊C4—34no—
522C4⋊C4—62no—
523C4⋊C4—62no—
524C4⋊C4—122no—
525C4⋊C4—182no—
526C4⋊C4—182no—
527C22⋊C4—98no—
528C22⋊C4—122no—
529C22⋊C4—122no—
530C22⋊C4—182no—
531C22⋊C4—182no—
532C22⋊C4—184no—
533C22⋊C4—362no—
534C42—22no—
535C42—94no—
536C42—362no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—64no—
545C22×C3—64no—
546C22×C3—64no—
547C22×C3—122no—
548C22×C3—122no—
549C22×C3—122no—
550C22×C3—122no—
551C22×C3C22×C4×D311yescharacteristic
552C22×C3C22×C4×D311yescharacteristic
553C22×C3C2×D3×D411yescharacteristic
554C22×C3C2×D3×D411yescharacteristic
555C22×C3C2×#23711yescharacteristic
556C22×C3#100411yescharacteristic
557C22×C3#100411yescharacteristic
558C22×C3#100411yescharacteristic
559C22×C3C2×#23911yescharacteristic
560C22×C3#100711yescharacteristic
561C22×C3#100911yescharacteristic
562C22×C3#100911yescharacteristic
563C22×C3#100911yescharacteristic
564C22×C3#101011yescharacteristic
565C2×D3—24no—
566C2×D3—24no—
567C2×D3—24no—
568C2×D3—42no—
569C2×D3—42no—
570C2×D3—42no—
571C2×D3—42no—
572C2×D3—64no—
573C2×D3—62no—
574C2×D3—62no—
575C2×D3—62no—
576C2×D3—62no—
577C2×D3—62no—
578C2×D3—62no—
579C2×D3—122no—
580C2×D3—122no—
581C2×D3—122no—
582C2×D3—122no—
583C2×D3—122no—
584C2×D3—122no—
585C2×D3—121no—
586C2×D3—121no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—121no—
593C3×C4—24no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—64no—
601C3×C4—122no—
602C3×C4—122no—
603C3×C4#67⋊C414yes—
604C3×C4#89314yes—
605Dic3—24no—
606Dic3—42no—
607Dic3—42no—
608Dic3—64no—
609Dic3—62no—
610Dic3—62no—
611Dic3—62no—
612Dic3—62no—
613Dic3—62no—
614Dic3—62no—
615Dic3—122no—
616Dic3—122no—
617C32#232411yescharacteristic, complemented, Sylow
618C23—34no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23—62no—
623C23—62no—
624C23—62no—
625C23—92no—
626C23—181no—
627C23—181no—
628C23—181no—
629C23—181no—
630C23—181no—
631C23—181no—
632C23C22×D3211yescharacteristic
633D4—68no—
634D4—368no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—34no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—92no—
651C2×C4—92no—
652C2×C4—92no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4—181no—
659C2×C4—188no—
660C2×C4—368no—
661C2×C4#379612yes—
662C2×C4C4×D3212yes—
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—124no—
672C2×C3C2×#67⋊C411yescharacteristic
673C2×C3C2×#89311yescharacteristic
674C2×C3#554511yescharacteristic
675C2×C3#554511yescharacteristic
676C2×C3#554611yescharacteristic
677C2×C3#557411yescharacteristic
678C2×C3#560711yescharacteristic
679C2×C3#560711yescharacteristic
680C2×C3#560811yescharacteristic
681C2×C3#562911yescharacteristic
682C2×C3#568211yescharacteristic
683C2×C3#569711yescharacteristic
684C2×C3#571911yescharacteristic
685C2×C3#573311yescharacteristic
686D3—44no—
687D3—124no—
688D3—122no—
689D3—122no—
690C22—64no—
691C22—64no—
692C22—64no—
693C22—122no—
694C22—122no—
695C22—122no—
696C22—122no—
697C22—182no—
698C22—182no—
699C22—182no—
700C22—361no—
701C22—361no—
702C22—361no—
703C22—361no—
704C22C2×#379611yescharacteristic
705C22#6429711yescharacteristic
706C22C2×C4×D3211yescharacteristic
707C22#6430711yescharacteristic
708C22#6430711yescharacteristic
709C22#6430711yescharacteristic
710C22C2×#381111yescharacteristic
711C4—41no—
712C4—41no—
713C4—64no—
714C4—122no—
715C4—122no—
716C4—182no—
717C4—182no—
718C4—182no—
719C4#6388114yes—
720C3—21no—
721C3#7619811yescharacteristic, complemented
722C3#7643011yescharacteristic, complemented
723C2—124no—
724C2—362no—
725C2#1059388911yescharacteristic
726C2#1059395011yescharacteristic
727C2#1059395511yescharacteristic
728C2#1059399611yescharacteristic
729C2C2×#6388111yescharacteristic
730C2#1059492311yescharacteristic
731C2#1059508211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#63916C2
hypercenterC2×C42D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64081C2semidirect
3. C2×#63898C2semidirect
4. C3×#4939C2semidirect
5. C3×#4928C2semidirect
6. #10591384C2semidirect
7. #10591372C2semidirect
8. #10591364C2semidirect
9. #10591325C2semidirect
10. #10591281C2semidirect
11. #10591274C2semidirect
35. #63916C4semidirect
59. #4939D3semidirect
60. #4928D3semidirect
73. C2×C4×C3⋊D3C2×C4semidirect
82. C2×#626C2×C4semidirect
91. C4×C3⋊Dic3D4semidirect
96. C3×C4⋊Dic3C2×C4semidirect
100. (C2×D3)⋊Dic3C2×C4semidirect
301. C4⋊Dic3C4×D3semidirect
617. C32#2324semidirect
721. C3#76198semidirect
722. C3#76430semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×#639162
C2×#638982
C3×#49392
C3×#49282
#105913842
#105913722
#105913642
#105913252
#105912812
#105912742
#764303
#761983