Finite Group Databasebeta

← C2×#10596126 #11902487

Subgroups — C2×#10596126 #11902487

Order 1152.

4896 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C22×#3828C211yesmaximal, characteristic, complemented
3C2×C32×#123C211yesmaximal, characteristic, complemented
4C2×#64148C211yesmaximal, characteristic, complemented
5C22×#3750C211yesmaximal, characteristic, complemented
6#10596126C2116yesmaximal, direct product factor
7C2×#64105C211yesmaximal, characteristic, complemented
8C2×#64103C211yesmaximal, characteristic, complemented
9C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
10C2×#64097C211yesmaximal, characteristic, complemented
11C2×#64095C211yesmaximal, characteristic, complemented
12C2×#64093C211yesmaximal, characteristic, complemented
13C2×#64092C211yesmaximal, characteristic, complemented
14C2×#64090C211yesmaximal, characteristic, complemented
15C2×#64090C211yesmaximal, characteristic, complemented
16C2×#64087C211yesmaximal, characteristic, complemented
17C2×#5655—34nomaximal
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic
24C23×C3⋊Dic3C2211yescharacteristic
25C23×C3⋊Dic3C2211yescharacteristic
26C23×C3⋊Dic3C2211yescharacteristic
27C2×#3830—28no—
28C2×#3830C2218yescomplemented
29C2×#3828—28no—
30C2×#3828C2218yescomplemented
31C22×C4⋊(C3⋊D3)C2211yescharacteristic
32C22×C4×C3⋊D3C2211yescharacteristic
33C22×C4×C3⋊D3C2211yescharacteristic
34C22×C4×C3⋊D3C2211yescharacteristic
35C22×C4×C3⋊D3C2211yescharacteristic
36C22×#634C2211yescharacteristic
37C22×#634C2211yescharacteristic
38C32×#123C2218yescomplemented
39C2×C32×C4⋊C4C2211yescharacteristic
40C2×C32×C4⋊C4C2211yescharacteristic
41C2×C32×C22⋊C4C2211yescharacteristic
42C2×C32×C22⋊C4C2211yescharacteristic
43C2×C32×C22⋊C4C2211yescharacteristic
44C2×#3757C2211yescharacteristic
45#64148C2218yescomplemented
46C2×#3752C2211yescharacteristic
47C2×#3752C2211yescharacteristic
48C2×#3752C2211yescharacteristic
49C2×#3752C2211yescharacteristic
50C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
51C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
52C2×#3750C2211yescharacteristic
53C2×#3750C2211yescharacteristic
54C2×#3750C2211yescharacteristic
55C2×#3750C2211yescharacteristic
56C2×#3750C2211yescharacteristic
57C2×#3750C2211yescharacteristic
58C2×#3750C2218yescomplemented
59C2×C4×C3⋊Dic3C2211yescharacteristic
60#64105C2218yescomplemented
61#64103C2218yescomplemented
62C4⋊C4×C3⋊D3C2218yescomplemented
63#64097C2218yescomplemented
64#64095C2218yescomplemented
65#64093C2218yescomplemented
66#64092C2218yescomplemented
67#64090C2218yescomplemented
68#64090C2218yescomplemented
69#64087C2218yescomplemented
70C22×#237—34no—
71C22×#235—34no—
72C2×C3×#123D314yescomplemented
73C2×#939—34no—
74C22×Dic3⋊C4—34no—
75#5655—364no—
76C2×#896—34no—
77C2×#894—34no—
78C2×D3×C4⋊C4—34no—
79C2×#888—34no—
80C2×#886—34no—
81C2×#884—34no—
82C2×#883—34no—
83C2×#67⋊C4—34no—
84C2×#67⋊C4—34no—
85C2×#878—34no—
86C24×C32C2311yescharacteristic
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C2×C32×D4—24no—
91C2×C32×D4C2314yes—
92C22×C32×C4—24no—
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2314yes—
98C22×C32×C4C2311yescharacteristic
99C2×#638—24no—
100C2×#638—24no—
101C2×#638—24no—
102C2×#638D418yescomplemented
103C2×#638C2314yes—
104C2×#638C2314yes—
105C2×#638C2314yes—
106C2×#638C2314yes—
107C22×C3⋊Dic3—24no—
108C22×C3⋊Dic3—24no—
109C22×C3⋊Dic3—24no—
110C22×C3⋊Dic3C2314yes—
111C22×C3⋊Dic3C2314yes—
112C22×C3⋊Dic3C2314yes—
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119#3830—232no—
120#3828—232no—
121C2×C4⋊(C3⋊D3)—24no—
122C2×C4⋊(C3⋊D3)C2314yes—
123C2×C4×C3⋊D3—24no—
124C2×C4×C3⋊D3—24no—
125C2×C4×C3⋊D3—24no—
126C2×C4×C3⋊D3—24no—
127C2×C4×C3⋊D3C2314yes—
128C2×C4×C3⋊D3C2314yes—
129C2×C4×C3⋊D3C2314yes—
130C2×C4×C3⋊D3C2314yes—
131C2×#634—24no—
132C2×#634—24no—
133C2×#634C2314yes—
134C2×#634C2314yes—
135C32×C4⋊C4C2314yes—
136C32×C4⋊C4C2314yes—
137C32×C22⋊C4C2314yes—
138C32×C22⋊C4C2314yes—
139C32×C22⋊C4C2314yes—
140#3757C2314yes—
141#3752C2314yes—
142#3752C2314yes—
143#3752C2314yes—
144#3752C2314yes—
145C4⋊(C3⋊Dic3)C2314yes—
146C4⋊(C3⋊Dic3)C2314yes—
147#3750C2314yes—
148#3750C2314yes—
149#3750C2314yes—
150#3750C2314yes—
151#3750C2314yes—
152#3750C2314yes—
153C4×C3⋊Dic3C2314yes—
154C2×#547—91noSylow
155C22×C3×D4C2×D314yes—
156C23×C3×C4C2×D314yes—
157C22×#67—34no—
158C22×#67—34no—
159C22×#67—34no—
160C22×#67—34no—
161C23×Dic3—34no—
162C23×Dic3—34no—
163C23×Dic3—34no—
164C2×#237—332no—
165C2×#237—632no—
166C2×#235—332no—
167C2×#235—632no—
168C22×D12—34no—
169C22×C4×D3—34no—
170C22×C4×D3—34no—
171C22×C4×D3—34no—
172C22×C4×D3—34no—
173C22×Dic6—34no—
174C22×Dic6—34no—
175C3×#123C2×D3132yescomplemented
176C2×C3×C4⋊C4C2×D314yes—
177C2×C3×C4⋊C4C2×D314yes—
178C2×C3×C22⋊C4C2×D314yes—
179C2×C3×C22⋊C4C2×D314yes—
180C2×C3×C22⋊C4C2×D314yes—
181C2×#217—34no—
182#939—332no—
183C2×(C2×D3)⋊C4—34no—
184C2×(C2×D3)⋊C4—34no—
185C2×(C2×D3)⋊C4—34no—
186C2×(C2×D3)⋊C4—34no—
187C2×C4⋊Dic3—34no—
188C2×C4⋊Dic3—34no—
189C2×Dic3⋊C4—332no—
190C2×Dic3⋊C4—34no—
191C2×Dic3⋊C4—34no—
192C2×Dic3⋊C4—34no—
193C2×Dic3⋊C4—34no—
194C2×Dic3⋊C4—34no—
195C2×Dic3⋊C4—34no—
196C2×C4×Dic3—34no—
197#896—332no—
198#894—332no—
199D3×C4⋊C4—332no—
200#888—332no—
201#886—332no—
202#884—332no—
203#883—332no—
204#67⋊C4—332no—
205#67⋊C4—332no—
206#878—332no—
207C23×C32—22no—
208C23×C32—22no—
209C23×C32—22no—
210C23×C32—22no—
211C23×C32—22no—
212C23×C32C2×D414yes—
213C23×C32C2412yes—
214C23×C32C2412yes—
215C23×C32C2411yescharacteristic
216C22×C3⋊D3—22no—
217C22×C3⋊D3—22no—
218C22×C3⋊D3—22no—
219C22×C3⋊D3—22no—
220C22×C3⋊D3—22no—
221C22×C3⋊D3C2×D414yes—
222C22×C3⋊D3C2412yes—
223C22×C3⋊D3C2412yes—
224C32×D4—28no—
225C2×C32×C4—22no—
226C2×C32×C4—22no—
227C2×C32×C4—22no—
228C2×C32×C4—28no—
229C2×C32×C4—22no—
230C2×C32×C4—22no—
231C2×C32×C4C2412yes—
232C2×C32×C4C2412yes—
233C2×C32×C4C2412yes—
234C2×C32×C4C2412yes—
235C2×C32×C4C2412yes—
236#638—28no—
237#638—28no—
238#638—28no—
239#638C2×D4116yescomplemented
240C2×C3⋊Dic3—22no—
241C2×C3⋊Dic3—22no—
242C2×C3⋊Dic3—22no—
243C2×C3⋊Dic3—28no—
244C2×C3⋊Dic3—22no—
245C2×C3⋊Dic3—28no—
246C2×C3⋊Dic3—28no—
247C2×C3⋊Dic3C2×D414yes—
248C2×C3⋊Dic3#4114yescomplemented
249C2×C3⋊Dic3C2412yes—
250C2×C3⋊Dic3C2412yes—
251C2×C3⋊Dic3C2412yes—
252C2×C3⋊Dic3C2412yes—
253C2×C3⋊Dic3C2412yes—
254C2×C3⋊Dic3C2412yes—
255C4⋊(C3⋊D3)—28no—
256C4×C3⋊D3—28no—
257C4×C3⋊D3—28no—
258C4×C3⋊D3—28no—
259C4×C3⋊D3—28no—
260#634—28no—
261#634—28no—
262C22×#41—91no—
263C22×#41—91no—
264#547—916no—
265C2×C4⋊Q8—91no—
266C2×#123—91no—
267C2×#123—91no—
268C2×#123—91no—
269C2×#123C3⋊D311yescharacteristic, complemented
270C2×C22⋊Q8—91no—
271C2×C22⋊Q8—91no—
272C2×#121—91no—
273C2×#121—91no—
274C2×C4×D4—91no—
275C2×C4×D4—91no—
276C22×C4⋊C4—91no—
277C22×C4⋊C4—91no—
278C24×C3C22×D314yes—
279C24×C3C22×D314yes—
280C23×D3—34no—
281C23×D3—34no—
282C2×C3×D4—216no—
283C2×C3×D4C22×D3116yes—
284C22×C3×C4—216no—
285C22×C3×C4C22×D314yes—
286C22×C3×C4C22×D314yes—
287C22×C3×C4C22×D314yes—
288C22×C3×C4C22×D3116yes—
289C22×C3×C4C22×D314yes—
290C22×C3×C4C22×D314yes—
291C2×#67—332no—
292C2×#67—316no—
293C2×#67—316no—
294C2×#67—316no—
295C2×#67—316no—
296C2×#67—616no—
297C2×#67—616no—
298C2×#67—616no—
299C22×Dic3—34no—
300C22×Dic3—34no—
301C22×Dic3—316no—
302C22×Dic3—316no—
303C22×Dic3—316no—
304C22×Dic3—34no—
305C22×Dic3—34no—
306C22×Dic3—34no—
307C22×Dic3—34no—
308C22×Dic3—616no—
309C22×Dic3—616no—
310C22×Dic3—616no—
311#237—6128no—
312#235—6128no—
313C2×D12—316no—
314C2×D12—616no—
315C2×C4×D3—316no—
316C2×C4×D3—316no—
317C2×C4×D3—316no—
318C2×C4×D3—316no—
319C2×C4×D3—616no—
320C2×C4×D3—616no—
321C2×C4×D3—616no—
322C2×C4×D3—616no—
323C2×Dic6—316no—
324C2×Dic6—316no—
325C2×Dic6—616no—
326C2×Dic6—616no—
327C3×C4⋊C4C22×D3116yes—
328C3×C4⋊C4C22×D3116yes—
329C3×C22⋊C4C22×D3116yes—
330C3×C22⋊C4C22×D3116yes—
331C3×C22⋊C4C22×D3116yes—
332#217—316no—
333(C2×D3)⋊C4—316no—
334(C2×D3)⋊C4—316no—
335(C2×D3)⋊C4—316no—
336(C2×D3)⋊C4—316no—
337C4⋊Dic3—316no—
338C4⋊Dic3—316no—
339Dic3⋊C4—316no—
340Dic3⋊C4—316no—
341Dic3⋊C4—316no—
342Dic3⋊C4—316no—
343Dic3⋊C4—316no—
344Dic3⋊C4—316no—
345C4×Dic3—316no—
346C22×C32—28no—
347C22×C32—22no—
348C22×C32—22no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—44no—
353C22×C32C22×D414yes—
354C22×C32C22×D412yes—
355C22×C32C2×#4112yes—
356C22×C322−1+412yes—
357C22×C32C2511yescharacteristic
358C2×C3⋊D3—28no—
359C2×C3⋊D3—22no—
360C2×C3⋊D3—22no—
361C2×C3⋊D3—22no—
362C2×C3⋊D3—22no—
363C2×C3⋊D3—22no—
364C2×C3⋊D3—44no—
365C2×C3⋊D3C22×D414yes—
366C32×C4—22no—
367C32×C4—22no—
368C32×C4—22no—
369C32×C4—22no—
370C32×C4—22no—
371C3⋊Dic3—22no—
372C3⋊Dic3—22no—
373C3⋊Dic3—22no—
374C3⋊Dic3—22no—
375C3⋊Dic3C22×D414yes—
376C3⋊Dic3C2×#4114yescomplemented
377C2×#41—98no—
378C2×#41—98no—
379C2×#41—188no—
380C2×#41—188no—
381C22×Q8—91no—
382C22×Q8—91no—
383C22×D4—91no—
384C22×D4—91no—
385C22×D4—91no—
386C22×D4—91no—
387C22×D4—91no—
388C22×D4C2×C3⋊D311yescharacteristic
389C23×C4—91no—
390C23×C4—91no—
391C23×C4—91no—
392C23×C4—91no—
393C23×C4—91no—
394C23×C4—91no—
395C23×C4—91no—
396C23×C4C2×C3⋊D311yescharacteristic
397C4⋊Q8—98no—
398#123—98no—
399#123—98no—
400#123—98no—
401#123C2×C3⋊D318yescomplemented
402C22⋊Q8—98no—
403C22⋊Q8—98no—
404#121—98no—
405#121—98no—
406C4×D4—98no—
407C4×D4—98no—
408C2×C4⋊C4—91no—
409C2×C4⋊C4—91no—
410C2×C4⋊C4—91no—
411C2×C4⋊C4—91no—
412C2×C4⋊C4—91no—
413C2×C4⋊C4—91no—
414C2×C4⋊C4—98no—
415C2×C4⋊C4—91no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—98no—
418C2×C4⋊C4C2×C3⋊D311yescharacteristic
419C2×C4⋊C4C2×C3⋊D311yescharacteristic
420C2×C22⋊C4—91no—
421C2×C22⋊C4—91no—
422C2×C22⋊C4—91no—
423C2×C22⋊C4—91no—
424C2×C22⋊C4—91no—
425C2×C22⋊C4C2×C3⋊D311yescharacteristic
426C2×C22⋊C4C2×C3⋊D311yescharacteristic
427C2×C22⋊C4C2×C3⋊D311yescharacteristic
428C2×C42—91no—
429C23×C3—28no—
430C23×C3—28no—
431C23×C3—28no—
432C23×C3—28no—
433C23×C3—28no—
434C23×C3D3×D4116yes—
435C23×C3C23×D318yes—
436C23×C3C23×D318yes—
437C23×C3C23×D314yes—
438C22×D3—316no—
439C22×D3—38no—
440C22×D3—38no—
441C22×D3—68no—
442C22×D3—68no—
443C22×D3—68no—
444C22×D3—68no—
445C22×D3—68no—
446C3×D4—232no—
447C2×C3×C4—28no—
448C2×C3×C4—28no—
449C2×C3×C4—28no—
450C2×C3×C4—232no—
451C2×C3×C4—28no—
452C2×C3×C4—28no—
453C2×C3×C4C23×D318yes—
454C2×C3×C4C23×D318yes—
455C2×C3×C4C23×D318yes—
456C2×C3×C4C23×D318yes—
457C2×C3×C4C23×D318yes—
458#67—364no—
459#67—632no—
460#67—632no—
461#67—632no—
462C2×Dic3—316no—
463C2×Dic3—316no—
464C2×Dic3—38no—
465C2×Dic3—38no—
466C2×Dic3—38no—
467C2×Dic3—38no—
468C2×Dic3—38no—
469C2×Dic3—38no—
470C2×Dic3—632no—
471C2×Dic3—632no—
472C2×Dic3—68no—
473C2×Dic3—68no—
474C2×Dic3—68no—
475C2×Dic3—632no—
476C2×Dic3—68no—
477D12—632no—
478C4×D3—632no—
479C4×D3—632no—
480C4×D3—632no—
481C4×D3—632no—
482Dic6—632no—
483Dic6—632no—
484C2×C32—24no—
485C2×C32—42no—
486C2×C32#54714yescomplemented
487C2×C32C23×D411yescharacteristic
488C2×C32C22×#4111yescharacteristic
489C2×C32C2×2−1+411yescharacteristic
490C3⋊D3—24no—
491C3⋊D3—42no—
492C24—91no—
493C24—91no—
494C24C22×C3⋊D311yescharacteristic
495C24C22×C3⋊D311yescharacteristic
496#41—1832no—
497#41—1832no—
498C2×Q8—94no—
499C2×Q8—94no—
500C2×Q8—184no—
501C2×Q8—184no—
502C2×D4—24no—
503C2×D4—94no—
504C2×D4—98no—
505C2×D4—94no—
506C2×D4—94no—
507C2×D4—94no—
508C2×D4—94no—
509C2×D4—184no—
510C2×D4—184no—
511C2×D4—184no—
512C2×D4—184no—
513C2×D4C22×C3⋊D314yes—
514C22×C4—24no—
515C22×C4—91no—
516C22×C4—91no—
517C22×C4—94no—
518C22×C4—94no—
519C22×C4—94no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4—94no—
525C22×C4—94no—
526C22×C4—94no—
527C22×C4—94no—
528C22×C4—184no—
529C22×C4—184no—
530C22×C4—184no—
531C22×C4—184no—
532C22×C4—184no—
533C22×C4—184no—
534C22×C4—184no—
535C22×C4C22×C3⋊D314yes—
536C22×C4C22×C3⋊D311yescharacteristic
537C22×C4C22×C3⋊D311yescharacteristic
538C22×C4C22×C3⋊D311yescharacteristic
539C22×C4C22×C3⋊D311yescharacteristic
540C22×C4C22×C3⋊D311yescharacteristic
541C4⋊C4—94no—
542C4⋊C4—94no—
543C4⋊C4—94no—
544C4⋊C4—94no—
545C4⋊C4—94no—
546C4⋊C4—94no—
547C4⋊C4—94no—
548C4⋊C4—94no—
549C4⋊C4C22×C3⋊D314yes—
550C4⋊C4C22×C3⋊D314yes—
551C22⋊C4—94no—
552C22⋊C4—94no—
553C22⋊C4—94no—
554C22⋊C4—94no—
555C22⋊C4—94no—
556C22⋊C4C22×C3⋊D314yes—
557C22⋊C4C22×C3⋊D314yes—
558C22⋊C4C22×C3⋊D314yes—
559C42—94no—
560C22×C3—232no—
561C22×C3—28no—
562C22×C3—28no—
563C22×C3—28no—
564C22×C3—28no—
565C22×C3—28no—
566C22×C3—416no—
567C22×C3C2×D3×D4116yes—
568C22×C3C2×D3×D418yes—
569C22×C3D3×#4118yes—
570C22×C3#101018yes—
571C22×C3C24×D314yes—
572C2×D3—316no—
573C2×D3—632no—
574C2×D3—68no—
575C2×D3—68no—
576C2×D3—68no—
577C2×D3—68no—
578C2×D3—68no—
579C2×D3—1216no—
580C3×C4—28no—
581C3×C4—28no—
582C3×C4—28no—
583C3×C4—28no—
584C3×C4—28no—
585Dic3—316no—
586Dic3—316no—
587Dic3—68no—
588Dic3—68no—
589Dic3—68no—
590Dic3—68no—
591C32C2×#54711yescharacteristic, complemented, Sylow
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—94no—
598C23—92no—
599C23—92no—
600C23—182no—
601C23—182no—
602C23—182no—
603C23—182no—
604C23—182no—
605C23D4×C3⋊D314yes—
606C23C23×C3⋊D312yes—
607C23C23×C3⋊D312yes—
608C23C23×C3⋊D311yescharacteristic
609Q8—188no—
610Q8—188no—
611D4—28no—
612D4—916no—
613D4—188no—
614D4—188no—
615D4—188no—
616D4—188no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—94no—
624C2×C4—94no—
625C2×C4—92no—
626C2×C4—92no—
627C2×C4—92no—
628C2×C4—92no—
629C2×C4—92no—
630C2×C4—92no—
631C2×C4—188no—
632C2×C4—188no—
633C2×C4—188no—
634C2×C4—188no—
635C2×C4—188no—
636C2×C4—188no—
637C2×C4—182no—
638C2×C4—182no—
639C2×C4—182no—
640C2×C4—188no—
641C2×C4—182no—
642C2×C4C23×C3⋊D312yes—
643C2×C4C23×C3⋊D312yes—
644C2×C4C23×C3⋊D312yes—
645C2×C4C23×C3⋊D312yes—
646C2×C4C23×C3⋊D312yes—
647C2×C3—216no—
648C2×C3—48no—
649C2×C3#5655116yescomplemented
650C2×C3C22×D3×D414yes—
651C2×C3C2×D3×#4114yes—
652C2×C3C2×#101014yes—
653D3—616no—
654D3—128no—
655C22—28no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—44no—
662C22—94no—
663C22—188no—
664C22—182no—
665C22—182no—
666C22—182no—
667C22—182no—
668C22—182no—
669C22—364no—
670C22C2×D4×C3⋊D314yes—
671C22C2×D4×C3⋊D312yes—
672C22#41×C3⋊D312yes—
673C22#6436712yes—
674C22C24×C3⋊D311yescharacteristic
675C4—22no—
676C4—22no—
677C4—22no—
678C4—22no—
679C4—22no—
680C4—94no—
681C4—94no—
682C4—182no—
683C4—182no—
684C4—182no—
685C4—182no—
686C3C2×#565514yescomplemented
687C2—24no—
688C2—42no—
689C2—184no—
690C2—362no—
691C2#1059612614yesdirect product factor
692C2C22×D4×C3⋊D311yescharacteristic
693C2C2×#41×C3⋊D311yescharacteristic
694C2C2×#6436711yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#123C2
socleC23×C32C24
hypercenterC2×#123C3⋊D3
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C22×#3828C2semidirect
3. C2×C32×#123C2semidirect
4. C2×#64148C2semidirect
5. C22×#3750C2semidirect
6. #10596126C2direct (N × H)
7. C2×#64105C2semidirect
8. C2×#64103C2semidirect
9. C2×C4⋊C4×C3⋊D3C2semidirect
10. C2×#64097C2semidirect
11. C2×#64095C2semidirect
12. C2×#64093C2semidirect
13. C2×#64092C2semidirect
14. C2×#64090C2semidirect
15. C2×#64090C2semidirect
16. C2×#64087C2semidirect
28. C2×#3830C22semidirect
30. C2×#3828C22semidirect
38. C32×#123C22semidirect
45. #64148C22semidirect
58. C2×#3750C22semidirect
60. #64105C22semidirect
61. #64103C22semidirect
62. C4⋊C4×C3⋊D3C22semidirect
63. #64097C22semidirect
64. #64095C22semidirect
65. #64093C22semidirect
66. #64092C22semidirect
67. #64090C22semidirect
68. #64090C22semidirect
69. #64087C22semidirect
72. C2×C3×#123D3semidirect
102. C2×#638D4semidirect
175. C3×#123C2×D3semidirect
239. #638C2×D4semidirect
248. C2×C3⋊Dic3#41semidirect
269. C2×#123C3⋊D3semidirect
376. C3⋊Dic3C2×#41semidirect
401. #123C2×C3⋊D3semidirect
486. C2×C32#547semidirect
591. C32C2×#547semidirect
649. C2×C3#5655semidirect
686. C3C2×#5655semidirect
691. C2#10596126direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×#38282
C2×C32×#1232
C2×#641482
C22×#37502
#105961262
C2×#641052
C2×#641032
C2×C4⋊C4×C3⋊D32
C2×#640972
C2×#640952
C2×#640932
C2×#640922
C2×#640902
C2×#640872
C2×#56553