Finite Group Databasebeta

← #11805660

Subgroups — #11805660

Order 1152.

1529 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C4×#626C211yesmaximal, characteristic
3C2×#63841C211yesmaximal, characteristic, complemented
4C3×#4987C211yesmaximal, characteristic, complemented
5C3×#4977C211yesmaximal, characteristic, complemented
6#10591387C212yesmaximal
7#10591325C211yesmaximal, characteristic, complemented
8#10591281C212yesmaximal, complemented
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#10591260C212yesmaximal, complemented
11#10591251C212yesmaximal, complemented
12#74229—31nomaximal
13#74012—31nomaximal
14C22×C4×C3⋊D3C2212yes—
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#626C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750C2212yes—
21C4⋊C4×C3⋊D3—24no—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×#3722C2212yes—
28C2×#3722C2211yescharacteristic
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2211yescharacteristic
31C2×Dic32C2212yes—
32C2×Dic32C2212yes—
33C4×#626C418yescomplemented
34#63841—24no—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C4×#67—31no—
41C2×#926—31no—
42C2×#892—31no—
43C2×D3×C4⋊C4—31no—
44C2×D3×C4⋊C4—31no—
45C2×D3×C4⋊C4—61no—
46C2×C4×D12—31no—
47C3×#382—31no—
48C3×#380—31no—
49#4987—31no—
50#4987—31no—
51#4987D311yescharacteristic, complemented
52#4977D311yescharacteristic, complemented
53Dic3×C4⋊C4—31no—
54#4956—32no—
55#4944—32no—
56C4×C4⋊Dic3—31no—
57#4669—32no—
58#4666—32no—
59#4666—32no—
60#4665—32no—
61#4654—32no—
62#4652—32no—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3—24no—
72C2×C4×C3⋊D3—24no—
73C2×C4×C3⋊D3—42no—
74C2×C4×C3⋊D3C2×C414yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3C2×C414yescomplemented
83C2×#626—22no—
84C2×#626—22no—
85C2×#626C2×C414yes—
86C32×C4⋊C4—22no—
87C4⋊(C3⋊Dic3)D414yescomplemented
88#3750—24no—
89C3×(C2×D3)⋊C4—42no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—22no—
92C3×C4×Dic3C2×C414yescomplemented
93Dic3⋊Dic3C2×C414yescomplemented
94#3722—24no—
95#3722C2×C414yes—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3C2×C414yescomplemented
98Dic32—24no—
99Dic32—42no—
100#2352—91noSylow
101C23×C3×C4—31no—
102C22×#67—31no—
103C22×D12—31no—
104C22×C4×D3—31no—
105C22×C4×D3—31no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3—61no—
109C22×C4×D3—62no—
110C22×C4×D3C2×D311yescharacteristic
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C4⋊C4C2×D311yescharacteristic
116C2×C3×C22⋊C4—32no—
117C2×C3×C42—31no—
118C2×#217—31no—
119C2×#217—32no—
120C4×#67—38no—
121C2×(C2×D3)⋊C4—31no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—31no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4C2×D312yes—
128#926—64no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—61no—
133C2×C4⋊Dic3C2×D311yescharacteristic
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×Dic3⋊C4—31no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—62no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3C2×D311yescharacteristic
144#892—64no—
145D3×C4⋊C4—64no—
146D3×C4⋊C4—64no—
147D3×C4⋊C4—68no—
148C4×D12—38no—
149C3×#95—32no—
150C3×#95—32no—
151C3×#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95C2×D312yes—
157C3⋊#95C2×D312yes—
158C3⋊#95C2×D312yes—
159C23×C32C2411yescharacteristic
160C22×C3⋊D3—21no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3C22×C412yes—
165C22×C3⋊D3#4112yes—
166C22×C3⋊D3#4112yes—
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—21no—
172C22×C3×D3—21no—
173C22×C3×D3C22×C412yes—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4#4112yes—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3C22×C412yes—
185C2×C3⋊Dic3C2×D414yes—
186C4×C3⋊D3—28no—
187C4×C3⋊D3—48no—
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—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3C22×C412yes—
201C2×C3×Dic3C22×C412yes—
202C2×C3×Dic3C22×C412yes—
203C3×C4×D3—28no—
204#626—28no—
205C2×C4×D4—91no—
206C2×#117—91no—
207C22×C4⋊C4—91no—
208#388—92no—
209#387—92no—
210#386—92no—
211#382—31no—
212#380—31no—
213#380—91no—
214C4×C4⋊C4—91no—
215C4×C22⋊C4—92no—
216C24×C3—31no—
217C23×D3—31no—
218C23×D3—31no—
219C23×D3—61no—
220C23×D3C22×D311yescharacteristic
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—34no—
227C22×C3×C4—32no—
228C22×C3×C4—32no—
229C22×C3×C4—62no—
230C22×C3×C4—62no—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—34no—
236C2×#67—62no—
237C2×#67—62no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—32no—
241C22×Dic3—32no—
242C22×Dic3—61no—
243C22×Dic3—62no—
244C22×Dic3C22×D312yes—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D311yescharacteristic
247C22×Dic3C22×D311yescharacteristic
248C22×Dic3C22×D311yescharacteristic
249C2×D12—34no—
250C2×D12—62no—
251C2×D12—62no—
252C2×C4×D3—22no—
253C2×C4×D3—22no—
254C2×C4×D3—34no—
255C2×C4×D3—34no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—62no—
260C2×C4×D3—62no—
261C2×C4×D3—62no—
262C2×C4×D3—62no—
263C2×C4×D3—64no—
264C2×C4×D3—64no—
265C2×C4×D3—64no—
266C2×C4×D3—64no—
267C2×C4×D3—68no—
268C2×C4×D3—124no—
269C2×C4×D3—122no—
270C2×C4×D3—122no—
271C2×C4×D3—124no—
272C2×C4×D3C4×D314yescomplemented
273C3×C4⋊C4—24no—
274C3×C4⋊C4—22no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—62no—
277C3×C4⋊C4—62no—
278C3×C22⋊C4—122no—
279C3×C42—34no—
280#217—34no—
281#217—64no—
282(C2×D3)⋊C4—34no—
283(C2×D3)⋊C4—34no—
284(C2×D3)⋊C4—34no—
285(C2×D3)⋊C4—42no—
286(C2×D3)⋊C4—64no—
287(C2×D3)⋊C4—64no—
288(C2×D3)⋊C4—64no—
289C4⋊Dic3—22no—
290C4⋊Dic3—22no—
291C4⋊Dic3—34no—
292C4⋊Dic3—34no—
293C4⋊Dic3—34no—
294C4⋊Dic3—64no—
295Dic3⋊C4—34no—
296Dic3⋊C4—64no—
297Dic3⋊C4—64no—
298Dic3⋊C4—68no—
299C4×Dic3—64no—
300C4×Dic3—64no—
301C4×Dic3—122no—
302C4×Dic3—122no—
303C4×Dic3C4×D314yescomplemented
304C22×C32C23×C411yescharacteristic
305C22×C32C22×D411yescharacteristic
306C22×C32C2×#4111yescharacteristic
307C22×C32C2×#4111yescharacteristic
308C22×C32C2×#4111yescharacteristic
309C22×C32H(5,𝔽2)11yescharacteristic
310C22×C322−1+411yescharacteristic
311C2×C3⋊D3—22no—
312C2×C3⋊D3—22no—
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—22no—
316C2×C3⋊D3—22no—
317C2×C3⋊D3#11714yescomplemented
318C2×C3×D3—22no—
319C2×C3×D3—22no—
320C2×C3×D3—22no—
321C2×C3×D3—41no—
322C2×C3×D3—41no—
323C2×C3×D3—41no—
324C2×C3×D3—41no—
325C32×C4—42no—
326C32×C4C4×D414yes—
327C3⋊Dic3—22no—
328C3⋊Dic3—24no—
329C3×Dic3—22no—
330C3×Dic3—22no—
331C3×Dic3—22no—
332C3×Dic3—42no—
333C3×Dic3—42no—
334C22×D4—91no—
335C23×C4—31no—
336C23×C4—91no—
337C23×C4—92no—
338C4×D4—98no—
339#117—184no—
340C2×C4⋊C4—31no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4—91no—
344C2×C4⋊C4—92no—
345C2×C4⋊C4—184no—
346C2×C4⋊C4D3211yescharacteristic
347C2×C22⋊C4—32no—
348C2×C22⋊C4—91no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4—92no—
351C2×C22⋊C4—92no—
352C2×C42—31no—
353C2×C42—92no—
354C2×C42—92no—
355#95—32no—
356#95—32no—
357#95—32no—
358#95—92no—
359#95—92no—
360C23×C3—21no—
361C23×C3—32no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3—61no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3C23×D311yescharacteristic
369C23×C3C23×D311yescharacteristic
370C22×D3—21no—
371C22×D3—21no—
372C22×D3—21no—
373C22×D3—21no—
374C22×D3—21no—
375C22×D3—21no—
376C22×D3—32no—
377C22×D3—32no—
378C22×D3—32no—
379C22×D3—32no—
380C22×D3—32no—
381C22×D3—32no—
382C22×D3—62no—
383C22×D3—62no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—62no—
387C22×D3—62no—
388C22×D3—62no—
389C22×D3—61no—
390C22×D3—61no—
391C22×D3—61no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3C2×C4×D312yes—
398C2×C3×C4—24no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—32no—
409C2×C3×C4—32no—
410C2×C3×C4—32no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—68no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4C2×C4×D312yes—
427C2×C3×C4C2×C4×D312yes—
428C2×C3×C4D3×D412yes—
429C2×C3×C4D3×D412yes—
430C2×C3×C4#23712yes—
431C2×C3×C4#23912yes—
432#67—68no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—32no—
446C2×Dic3—32no—
447C2×Dic3—34no—
448C2×Dic3—34no—
449C2×Dic3—62no—
450C2×Dic3—64no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—61no—
456C2×Dic3—62no—
457C2×Dic3—61no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461C2×Dic3—122no—
462C2×Dic3—122no—
463C2×Dic3C2×C4×D312yes—
464C2×Dic3C2×C4×D312yes—
465C2×Dic3C2×C4×D312yes—
466D12—68no—
467C4×D3—28no—
468C4×D3—616no—
469C4×D3—68no—
470C4×D3—68no—
471C4×D3—128no—
472C4×D3—128no—
473C4×D3—1216no—
474C2×C32C2×#11711yescharacteristic
475C2×C32C2×C4×D411yescharacteristic
476C2×C32#52011yescharacteristic
477C2×C32#54611yescharacteristic
478C2×C32#54811yescharacteristic
479C2×C32#55211yescharacteristic
480C2×C32#55311yescharacteristic
481C3⋊D3—24no—
482C3×D3—42no—
483C24—31no—
484C24—91no—
485C2×D4—94no—
486C2×D4—182no—
487C2×D4—182no—
488C22×C4—31no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4—34no—
492C22×C4—32no—
493C22×C4—32no—
494C22×C4—62no—
495C22×C4—62no—
496C22×C4—91no—
497C22×C4—92no—
498C22×C4—94no—
499C22×C4—184no—
500C22×C4—184no—
501C22×C4—182no—
502C22×C4—182no—
503C22×C4—362no—
504C22×C4C2×D3212yes—
505C22×C4C2×D3211yescharacteristic
506C4⋊C4—22no—
507C4⋊C4—62no—
508C4⋊C4—62no—
509C4⋊C4—94no—
510C4⋊C4—94no—
511C4⋊C4—184no—
512C22⋊C4—94no—
513C22⋊C4—94no—
514C22⋊C4—122no—
515C22⋊C4—184no—
516C22⋊C4—184no—
517C42—34no—
518C42—184no—
519C42—362no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—62no—
528C22×C3—62no—
529C22×C3—62no—
530C22×C3—121no—
531C22×C3—121no—
532C22×C3—121no—
533C22×C3—121no—
534C22×C3C22×C4×D311yescharacteristic
535C22×C3C22×C4×D311yescharacteristic
536C22×C3C2×D3×D411yescharacteristic
537C22×C3C2×D3×D411yescharacteristic
538C22×C3C2×#23711yescharacteristic
539C22×C3#100411yescharacteristic
540C22×C3C2×#23911yescharacteristic
541C22×C3#100711yescharacteristic
542C22×C3D3×#4111yescharacteristic
543C22×C3D3×#4111yescharacteristic
544C22×C3D3×#4111yescharacteristic
545C22×C3D3×#4111yescharacteristic
546C22×C3#100911yescharacteristic
547C22×C3#101011yescharacteristic
548C2×D3—22no—
549C2×D3—22no—
550C2×D3—22no—
551C2×D3—34no—
552C2×D3—34no—
553C2×D3—41no—
554C2×D3—41no—
555C2×D3—41no—
556C2×D3—41no—
557C2×D3—64no—
558C2×D3—64no—
559C2×D3—64no—
560C2×D3—64no—
561C2×D3—64no—
562C2×D3—64no—
563C2×D3—64no—
564C2×D3—62no—
565C2×D3—62no—
566C2×D3—62no—
567C2×D3—62no—
568C2×D3—62no—
569C2×D3—62no—
570C2×D3—62no—
571C2×D3—62no—
572C2×D3—62no—
573C2×D3—62no—
574C2×D3—62no—
575C2×D3—62no—
576C3×C4—24no—
577C3×C4—44no—
578C3×C4—42no—
579C3×C4—42no—
580C3×C4—62no—
581C3×C4—62no—
582C3×C4—62no—
583C3×C4—122no—
584C3×C4—122no—
585C3×C4#67⋊C414yes—
586C3×C4#89314yes—
587Dic3—22no—
588Dic3—22no—
589Dic3—22no—
590Dic3—42no—
591Dic3—42no—
592Dic3—64no—
593Dic3—64no—
594Dic3—62no—
595Dic3—62no—
596Dic3—64no—
597Dic3—124no—
598C32#235211yescharacteristic, complemented, Sylow
599C23—32no—
600C23—61no—
601C23—61no—
602C23—61no—
603C23—61no—
604C23—61no—
605C23—61no—
606C23—92no—
607C23—92no—
608C23—92no—
609C23—181no—
610C23—181no—
611C23—181no—
612C23—181no—
613C23C22×D3211yescharacteristic
614D4—188no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—32no—
619C2×C4—32no—
620C2×C4—32no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—68no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4—62no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—92no—
635C2×C4—94no—
636C2×C4—181no—
637C2×C4—182no—
638C2×C4—182no—
639C2×C4—181no—
640C2×C4—188no—
641C2×C4—368no—
642C2×C4#379612yes—
643C2×C4C4×D3212yes—
644C2×C4#381112yes—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—122no—
653C2×C3C2×#67⋊C411yescharacteristic
654C2×C3C2×#89311yescharacteristic
655C2×C3#550411yescharacteristic
656C2×C3D3×#11711yescharacteristic
657C2×C3D3×#11711yescharacteristic
658C2×C3#552311yescharacteristic
659C2×C3#561211yescharacteristic
660C2×C3#561411yescharacteristic
661C2×C3#563311yescharacteristic
662C2×C3#563911yescharacteristic
663C2×C3#567611yescharacteristic
664C2×C3#567711yescharacteristic
665C2×C3#569411yescharacteristic
666C2×C3#569511yescharacteristic
667D3—42no—
668D3—68no—
669D3—64no—
670D3—64no—
671C22—62no—
672C22—62no—
673C22—62no—
674C22—94no—
675C22—121no—
676C22—121no—
677C22—121no—
678C22—121no—
679C22—182no—
680C22—182no—
681C22—182no—
682C22—182no—
683C22—182no—
684C22—182no—
685C22C2×#379611yescharacteristic
686C22C2×C4×D3211yescharacteristic
687C22#6431211yescharacteristic
688C22#6431411yescharacteristic
689C22#6431511yescharacteristic
690C22#6431911yescharacteristic
691C22C2×#381111yescharacteristic
692C4—42no—
693C4—62no—
694C4—62no—
695C4—62no—
696C4—122no—
697C4—122no—
698C4—182no—
699C4—184no—
700C4#6388114yes—
701C3—21no—
702C3#7401211yescharacteristic, complemented
703C3#7422911yescharacteristic, complemented
704C2—122no—
705C2—184no—
706C2#1059448911yescharacteristic
707C2#1059451011yescharacteristic
708C2#1059457911yescharacteristic
709C2#1059460211yescharacteristic
710C2C2×#6388111yescharacteristic
711C2#1059524311yescharacteristic
712C2#1059536211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
3. C2×#63841C2semidirect
4. C3×#4987C2semidirect
5. C3×#4977C2semidirect
7. #10591325C2semidirect
8. #10591281C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591260C2semidirect
11. #10591251C2semidirect
33. C4×#626C4semidirect
51. #4987D3semidirect
52. #4977D3semidirect
82. C2×C3×C4×D3C2×C4semidirect
87. C4⋊(C3⋊Dic3)D4semidirect
92. C3×C4×Dic3C2×C4semidirect
93. Dic3⋊Dic3C2×C4semidirect
97. (C2×D3)⋊Dic3C2×C4semidirect
272. C2×C4×D3C4×D3semidirect
303. C4×Dic3C4×D3semidirect
317. C2×C3⋊D3#117semidirect
598. C32#2352semidirect
702. C3#74012semidirect
703. C3#74229semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×C4×#6262
C2×#638412
C3×#49872
C3×#49772
#105913872
#105913252
#105912812
Dic3×C4⋊Dic32
#105912602
#105912512
#742293
#740123