Finite Group Databasebeta

← #11804924

Subgroups — #11804924

Order 1152.

1873 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4#10592638C211yesmaximal, characteristic, complemented
5C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#10591384C212yesmaximal, complemented
7#10591383C212yesmaximal, complemented
8#10591367C212yesmaximal, complemented
9#10591320C211yesmaximal, characteristic, complemented
10#10591313C211yesmaximal, characteristic, complemented
11#10591233C212yesmaximal, complemented
12#82457—31nomaximal
13#73454—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C22×#626C2212yes—
18C22×#624C2212yes—
19C2×#3799—24no—
20C2×#3799—24no—
21C2×#3799C418yescomplemented
22C2×C32×C42C2211yescharacteristic
23C2×#3752C2212yes—
24C2×#3752C2212yes—
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2212yes—
32C3×C4×Dic6—24no—
33C2×Dic3⋊Dic3C2212yes—
34C2×#3722C2212yes—
35C2×#3722C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×Dic32C2212yes—
38Dic3×Dic6—24no—
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41#63579C2212yes—
42C22×#239—31no—
43C22×#235—31no—
44C2×C3×C4×Q8—31no—
45C2×Q8×Dic3—31no—
46C2×C4×Dic6—31no—
47C2×C4×Dic6D311yescharacteristic, complemented
48C3×C4×C22⋊C4—31no—
49#5212—31no—
50#4988—32no—
51#4988—31no—
52#4987—31no—
53#4987—32no—
54#4957—32no—
55#4957—32no—
56#4939—31no—
57#4939—31no—
58#4939—32no—
59#4939—31no—
60#4939—61no—
61C4×(C2×D3)⋊C4—32no—
62C4×(C2×D3)⋊C4D311yescharacteristic, complemented
63#4667—32no—
64#4666—32no—
65C23×C3⋊D3C2312yes—
66C23×C3×D3C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C2×C4⋊(C3⋊D3)—22no—
72C2×C4⋊(C3⋊D3)—22no—
73C2×C4⋊(C3⋊D3)C2×C414yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2312yes—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3C2×C414yes—
82C2×C3×Dic6C2×C414yes—
83C2×C3×Dic6D414yes—
84C2×C3×Dic6D414yes—
85C2×#626—24no—
86C2×#626—24no—
87C2×#626C2×C418yes—
88C2×#624—24no—
89C2×#624—24no—
90C2×#624C2×C418yes—
91#3799—232no—
92C32×C42—22no—
93#3752—24no—
94#3752—42no—
95C4⋊(C3⋊Dic3)—22no—
96C3×(C2×D3)⋊C4—22no—
97C3×(C2×D3)⋊C4—22no—
98C3×C4⋊Dic3—22no—
99C3×Dic3⋊C4—24no—
100C3×C4×Dic3—22no—
101C3×C4×Dic3—24no—
102Dic3⋊Dic3—24no—
103#3722—24no—
104#3722—42no—
105(C2×D3)⋊Dic3—42no—
106Dic32—24no—
107#2341—91noSylow
108C22×C3×Q8—31no—
109C23×C3×C4—31no—
110C22×#67—32no—
111C2×#239—38no—
112C2×#239—64no—
113C2×#239—64no—
114C2×#235—38no—
115C2×#235—64no—
116C2×#235—64no—
117C22×D12—32no—
118C22×D12—31no—
119C22×D12—31no—
120C22×D12—61no—
121C22×C4×D3—32no—
122C22×C4×D3—32no—
123C22×C4×D3C2×D311yescharacteristic
124C22×Dic6C2×D311yescharacteristic
125C3×C4×Q8—64no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C22⋊C4—31no—
129C2×C3×C22⋊C4—31no—
130C2×C3×C42—21no—
131C2×C3×C42—32no—
132C2×C3×C42—31no—
133C2×C3×C42C2×D311yescharacteristic
134C2×C3×C42C2×D311yescharacteristic
135C2×#217—32no—
136Q8×Dic3—64no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—62no—
147C2×(C2×D3)⋊C4—62no—
148C2×(C2×D3)⋊C4C2×D311yescharacteristic
149C2×(C2×D3)⋊C4C2×D311yescharacteristic
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—32no—
153C2×C4⋊Dic3—61no—
154C2×C4⋊Dic3C2×D311yescharacteristic
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4C2×D312yes—
157C2×C4×Dic3—32no—
158C2×C4×Dic3—32no—
159C2×C4×Dic3C2×D312yes—
160C2×C4×Dic3C2×D311yescharacteristic
161C4×Dic6—24no—
162C4×Dic6—64no—
163C3×#95—31no—
164C3×#95—31no—
165C3⋊#95—32no—
166C3⋊#95—32no—
167C3⋊#95C2×D311yescharacteristic
168C3⋊#95C2×D311yescharacteristic
169C23×C32C2411yescharacteristic
170C22×C3⋊D3—22no—
171C22×C3⋊D3—22no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—22no—
174C22×C3⋊D3—22no—
175C22×C3⋊D3—22no—
176C22×C3⋊D3C22×C414yes—
177C22×C3×D3—21no—
178C22×C3×D3—21no—
179C22×C3×D3—21no—
180C22×C3×D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—21no—
183C22×C3×D3C22×C412yes—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4C22×C412yes—
190C2×C32×C4C2×D412yes—
191C2×C32×C4C2×D412yes—
192C2×C32×C4#4112yescomplemented
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—22no—
196C4⋊(C3⋊D3)—28no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3C22×C412yes—
208C2×C3×Dic3C22×C414yes—
209C2×C3×Dic3C2×D414yes—
210C2×C3×Dic3C2×D414yes—
211C2×C3×Dic3#4112yescomplemented
212C3×C4×D3—28no—
213C3×Dic6C22⋊C4116yescomplemented
214#626—216no—
215#624—216no—
216C22×#41—91no—
217C2×C4×Q8—31no—
218C2×C4×Q8—91no—
219#390—92no—
220#390—91no—
221#390—92no—
222#390—91no—
223#380—92no—
224#380—91no—
225C4×C22⋊C4—31no—
226C4×C22⋊C4—92no—
227C24×C3—31no—
228C23×D3—32no—
229C23×D3—32no—
230C23×D3—62no—
231C23×D3C22×D311yescharacteristic
232C2×C3×Q8—34no—
233C2×C3×Q8—34no—
234C2×C3×Q8—34no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—32no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—34no—
242C22×C3×C4—32no—
243C22×C3×C4—31no—
244C22×C3×C4—62no—
245C22×C3×C4—62no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—38no—
253C2×#67—64no—
254C2×#67—64no—
255C22×Dic3—32no—
256C22×Dic3—32no—
257C22×Dic3—62no—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D311yescharacteristic
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D312yes—
263#239—632no—
264#235—632no—
265C2×D12—38no—
266C2×D12—34no—
267C2×D12—34no—
268C2×D12—64no—
269C2×D12—64no—
270C2×D12—64no—
271C2×D12—62no—
272C2×D12—62no—
273C2×D12—62no—
274C2×D12—62no—
275C2×D12—122no—
276C2×D12—122no—
277C2×C4×D3—22no—
278C2×C4×D3—22no—
279C2×C4×D3—38no—
280C2×C4×D3—38no—
281C2×C4×D3—64no—
282C2×C4×D3—64no—
283C2×C4×D3—64no—
284C2×C4×D3—64no—
285C2×C4×D3C4×D314yes—
286C2×Dic6C4×D314yes—
287C2×Dic6D1214yes—
288C2×Dic6#6714yes—
289C3×C4⋊C4—64no—
290C3×C4⋊C4—62no—
291C3×C22⋊C4—62no—
292C3×C22⋊C4—62no—
293C3×C42—22no—
294C3×C42—22no—
295C3×C42—42no—
296C3×C42—64no—
297C3×C42—62no—
298#217—122no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—22no—
301(C2×D3)⋊C4—64no—
302(C2×D3)⋊C4—64no—
303(C2×D3)⋊C4—64no—
304(C2×D3)⋊C4—64no—
305(C2×D3)⋊C4—124no—
306(C2×D3)⋊C4—122no—
307(C2×D3)⋊C4—122no—
308(C2×D3)⋊C4—122no—
309(C2×D3)⋊C4—122no—
310(C2×D3)⋊C4—122no—
311(C2×D3)⋊C4—124no—
312C4⋊Dic3—22no—
313C4⋊Dic3—64no—
314C4⋊Dic3—62no—
315C4⋊Dic3—62no—
316C4⋊Dic3—122no—
317Dic3⋊C4—24no—
318Dic3⋊C4—64no—
319C4×Dic3—22no—
320C4×Dic3—24no—
321C4×Dic3—64no—
322C4×Dic3—64no—
323C22×C32C23×C411yescharacteristic
324C22×C32C22×D411yescharacteristic
325C22×C32C22×D411yescharacteristic
326C22×C32C2×#4111yescharacteristic
327C22×C32C2×#4111yescharacteristic
328C22×C32H(5,𝔽2)11yescharacteristic
329C22×C322−1+411yescharacteristic
330C2×C3⋊D3—24no—
331C2×C3⋊D3—24no—
332C2×C3⋊D3—24no—
333C2×C3⋊D3—42no—
334C2×C3⋊D3—42no—
335C2×C3⋊D3—42no—
336C2×C3⋊D3—42no—
337C2×C3×D3—22no—
338C2×C3×D3—22no—
339C2×C3×D3—22no—
340C2×C3×D3—41no—
341C2×C3×D3—41no—
342C2×C3×D3—41no—
343C2×C3×D3—41no—
344C32×C4—22no—
345C32×C4—41no—
346C32×C4C2×C22⋊C414yes—
347C3⋊Dic3—42no—
348C3×Dic3—22no—
349C3×Dic3—22no—
350C3×Dic3—41no—
351C3×Dic3—42no—
352C3×Dic3C2×C22⋊C418yes—
353C2×#41—98no—
354C2×#41—184no—
355C2×#41—184no—
356C22×Q8—31no—
357C22×D4—92no—
358C22×D4—91no—
359C23×C4—31no—
360C23×C4—92no—
361C4×Q8—64no—
362C4×Q8—184no—
363C2×C4⋊C4—32no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4—91no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—92no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C42—32no—
375C2×C42—31no—
376C2×C42—92no—
377C2×C42D3211yescharacteristic
378#95—31no—
379#95—31no—
380#95—92no—
381C23×C3—21no—
382C23×C3—32no—
383C23×C3—61no—
384C23×C3—61no—
385C23×C3—61no—
386C23×C3—61no—
387C23×C3—61no—
388C23×C3—61no—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—34no—
398C22×D3—34no—
399C22×D3—64no—
400C22×D3—62no—
401C22×D3—62no—
402C22×D3—62no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—62no—
406C22×D3—62no—
407C22×D3—62no—
408C22×D3—62no—
409C22×D3—62no—
410C22×D3—62no—
411C22×D3—62no—
412C22×D3—122no—
413C22×D3—122no—
414C22×D3—122no—
415C22×D3—122no—
416C22×D3—122no—
417C22×D3—122no—
418C22×D3C2×C4×D312yes—
419C3×Q8—316no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—34no—
436C2×C3×C4—34no—
437C2×C3×C4—34no—
438C2×C3×C4—32no—
439C2×C3×C4—32no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—61no—
445C2×C3×C4—61no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—68no—
449C2×C3×C4—61no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—61no—
453C2×C3×C4—62no—
454C2×C3×C4—61no—
455C2×C3×C4C2×C4×D312yes—
456C2×C3×C4C2×C4×D312yes—
457C2×C3×C4C2×D1212yes—
458C2×C3×C4#23512yescomplemented
459C2×C3×C4D3×D412yes—
460C2×C3×C4D3×D412yes—
461C2×C3×C4#23912yescomplemented
462C2×C3×C4C2×#6712yes—
463#67—616no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—22no—
471C2×Dic3—21no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—62no—
475C2×Dic3—62no—
476C2×Dic3—62no—
477C2×Dic3—62no—
478C2×Dic3—62no—
479C2×Dic3—62no—
480C2×Dic3—122no—
481C2×Dic3—122no—
482C2×Dic3—122no—
483C2×Dic3C2×C4×D312yes—
484C2×Dic3C2×C4×D314yes—
485C2×Dic3C2×D1214yes—
486C2×Dic3#23512yescomplemented
487C2×Dic3C2×#6714yes—
488D12—616no—
489D12—68no—
490D12—68no—
491D12—128no—
492C4×D3—28no—
493C4×D3—616no—
494C4×D3—616no—
495Dic6(C2×D3)⋊C4116yescomplemented
496C2×C32C22×C22⋊C411yescharacteristic
497C2×C32C4×#4111yescharacteristic
498C2×C32#52011yescharacteristic
499C2×C32#54811yescharacteristic
500C2×C32#54811yescharacteristic
501C2×C32#55011yescharacteristic
502C2×C32#55011yescharacteristic
503C3⋊D3—44no—
504C3×D3—42no—
505C24—31no—
506C24—92no—
507#41—1832no—
508C2×Q8—34no—
509C2×Q8—34no—
510C2×Q8—34no—
511C2×D4—98no—
512C2×D4—94no—
513C2×D4—184no—
514C2×D4—184no—
515C2×D4—182no—
516C2×D4—182no—
517C22×C4—32no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—34no—
521C22×C4—31no—
522C22×C4—32no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—98no—
526C22×C4—92no—
527C22×C4—184no—
528C22×C4—184no—
529C22×C4C2×D3211yescharacteristic
530C22×C4C2×D3211yescharacteristic
531C22×C4C2×D3211yescharacteristic
532C4⋊C4—64no—
533C4⋊C4—62no—
534C4⋊C4—184no—
535C4⋊C4—182no—
536C22⋊C4—62no—
537C22⋊C4—62no—
538C22⋊C4—184no—
539C22⋊C4—184no—
540C22⋊C4—362no—
541C22⋊C4—362no—
542C22⋊C4—362no—
543C42—22no—
544C42—64no—
545C42—62no—
546C42—184no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—62no—
555C22×C3—62no—
556C22×C3—62no—
557C22×C3—121no—
558C22×C3—121no—
559C22×C3—121no—
560C22×C3—121no—
561C22×C3C22×C4×D311yescharacteristic
562C22×C3C22×C4×D311yescharacteristic
563C22×C3C22×D1211yescharacteristic
564C22×C3C2×#23511yescharacteristic
565C22×C3C2×#23511yescharacteristic
566C22×C3C2×D3×D411yescharacteristic
567C22×C3C2×D3×D411yescharacteristic
568C22×C3C2×#23911yescharacteristic
569C22×C3#100711yescharacteristic
570C22×C3D3×#4111yescharacteristic
571C22×C3#100911yescharacteristic
572C22×C3#100911yescharacteristic
573C22×C3#101011yescharacteristic
574C22×C3C22×#6711yescharacteristic
575C2×D3—22no—
576C2×D3—22no—
577C2×D3—22no—
578C2×D3—41no—
579C2×D3—41no—
580C2×D3—41no—
581C2×D3—41no—
582C2×D3—64no—
583C2×D3—64no—
584C2×D3—64no—
585C2×D3—64no—
586C2×D3—64no—
587C2×D3—64no—
588C2×D3—124no—
589C2×D3—124no—
590C2×D3—124no—
591C2×D3—122no—
592C2×D3—122no—
593C2×D3—122no—
594C2×D3—122no—
595C2×D3—122no—
596C2×D3—122no—
597C2×D3—122no—
598C2×D3—122no—
599C2×D3—242no—
600C2×D3—242no—
601C2×D3—242no—
602C2×D3—242no—
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—24no—
606C3×C4—38no—
607C3×C4—42no—
608C3×C4—42no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—62no—
612C3×C4—62no—
613C3×C4—122no—
614C3×C4—121no—
615C3×C4D3×C22⋊C414yes—
616C3×C4C2×(C2×D3)⋊C414yes—
617Dic3—22no—
618Dic3—22no—
619Dic3—41no—
620Dic3—42no—
621Dic3—122no—
622Dic3—122no—
623Dic3—242no—
624Dic3C2×(C2×D3)⋊C418yes—
625C32#234111yescharacteristic, complemented, Sylow
626C23—32no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23—61no—
633C23—94no—
634C23—182no—
635C23—182no—
636C23—182no—
637C23—182no—
638C23—182no—
639C23—182no—
640C23C22×D3211yescharacteristic
641Q8—316no—
642D4—1816no—
643D4—188no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—34no—
650C2×C4—34no—
651C2×C4—34no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—68no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—62no—
662C2×C4—61no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—1816no—
666C2×C4—182no—
667C2×C4—182no—
668C2×C4—182no—
669C2×C4#379912yescomplemented
670C2×C4C4×D3212yes—
671C2×C4D3×D1212yes—
672C2×C4D3×#6712yes—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—122no—
681C2×C3C4×#23511yescharacteristic
682C2×C3C2×D3×C22⋊C411yescharacteristic
683C2×C3#552311yescharacteristic
684C2×C3#555211yescharacteristic
685C2×C3#555211yescharacteristic
686C2×C3#555311yescharacteristic
687C2×C3#555311yescharacteristic
688C2×C3C4×#23911yescharacteristic
689C2×C3#557411yescharacteristic
690C2×C3#557611yescharacteristic
691C2×C3#557711yescharacteristic
692C2×C3C22×(C2×D3)⋊C411yescharacteristic
693C2×C3#581711yescharacteristic
694C2×C3#583411yescharacteristic
695D3—42no—
696D3—124no—
697D3—124no—
698D3—244no—
699C22—62no—
700C22—62no—
701C22—62no—
702C22—121no—
703C22—121no—
704C22—121no—
705C22—121no—
706C22—184no—
707C22—184no—
708C22—184no—
709C22—362no—
710C22—362no—
711C22—362no—
712C22—362no—
713C22#6429711yescharacteristic
714C22C2×#379911yescharacteristic
715C22C2×C4×D3211yescharacteristic
716C22C2×D3×D1211yescharacteristic
717C22D3×#23511yescharacteristic
718C22#6430811yescharacteristic
719C22C2×D3×#6711yescharacteristic
720C4—22no—
721C4—38no—
722C4—41no—
723C4—62no—
724C4—62no—
725C4—121no—
726C4—122no—
727C4—362no—
728C4D3×(C2×D3)⋊C414yes—
729C3—21no—
730C3#7345411yescharacteristic, complemented
731C3#8245711yescharacteristic, complemented
732C2—122no—
733C2—364no—
734C2#1059389011yescharacteristic
735C2#1059389911yescharacteristic
736C2#1059390211yescharacteristic
737C2C4×#379911yescharacteristic
738C2#1059490211yescharacteristic
739C2#1059500711yescharacteristic
740C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#3799C2
hypercenterC2×C42D32
hypocenterC32#2341
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C2×Dic3×Dic6C2semidirect
4. #10592638C2semidirect
5. C3×C4×(C2×D3)⋊C4C2semidirect
6. #10591384C2semidirect
7. #10591383C2semidirect
8. #10591367C2semidirect
9. #10591320C2semidirect
10. #10591313C2semidirect
11. #10591233C2semidirect
21. C2×#3799C4semidirect
47. C2×C4×Dic6D3semidirect
62. C4×(C2×D3)⋊C4D3semidirect
192. C2×C32×C4#41semidirect
211. C2×C3×Dic3#41semidirect
213. C3×Dic6C22⋊C4semidirect
458. C2×C3×C4#235semidirect
461. C2×C3×C4#239semidirect
486. C2×Dic3#235semidirect
495. Dic6(C2×D3)⋊C4semidirect
625. C32#2341semidirect
669. C2×C4#3799semidirect
730. C3#73454semidirect
731. C3#82457semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
C2×C3×C4×Dic62
C2×Dic3×Dic62
#105926382
C3×C4×(C2×D3)⋊C42
#105913842
#105913832
#105913672
#105913202
#105913132
#105912332
#824573
#734543