Finite Group Databasebeta

← #11836023

Subgroups — #11836023

Order 1152.

2796 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2C2×#64093C211yesmaximal, characteristic, complemented
3C2×#64091C211yesmaximal, characteristic, complemented
4C2×#64091C211yesmaximal, characteristic, complemented
5C2×#64091C211yesmaximal, characteristic, complemented
6C2×#64083C211yesmaximal, characteristic, complemented
7C32×#388C211yesmaximal, characteristic, complemented
8#10592690C211yesmaximal, characteristic, complemented
9#10592659C211yesmaximal, characteristic, complemented
10#10592659C211yesmaximal, characteristic, complemented
11#10592639C211yesmaximal, characteristic, complemented
12#10592371C211yesmaximal, characteristic, complemented
13#10592370C211yesmaximal, characteristic, complemented
14#10592370C211yesmaximal, characteristic, complemented
15#10592364C211yesmaximal, characteristic, complemented
16#75912—34nomaximal
17C24×C3⋊D3C2211yescharacteristic
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C22×C4⋊(C3⋊D3)C2211yescharacteristic
25C22×C4⋊(C3⋊D3)C2211yescharacteristic
26C22×C4⋊(C3⋊D3)C2211yescharacteristic
27C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
28C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
29C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
30C22×C4×C3⋊D3C2211yescharacteristic, complemented
31C2×C32×C4⋊C4C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×C32×C42C2211yescharacteristic, complemented
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C2×#3752C2211yescharacteristic, complemented
46C2×#3752C2211yescharacteristic, complemented
47C2×#3750C2211yescharacteristic, complemented
48#64104—24no—
49#64093—24no—
50#64091—24no—
51#64091—24no—
52#64091—24no—
53#64083—24no—
54C32×#95C2211yescharacteristic, complemented
55C32×#95C2211yescharacteristic, complemented
56#63658C2211yescharacteristic, complemented
57#63658C2211yescharacteristic, complemented
58C2×#895—34no—
59C2×#884—34no—
60C2×#882—34no—
61C2×#882—34no—
62C2×#882—34no—
63C2×#874—34no—
64C3×#388D314yescomplemented
65#4991—34no—
66#4960—34no—
67#4960—34no—
68#4940—34no—
69#4672—34no—
70#4671—34no—
71#4671—34no—
72#4665—34no—
73C24×C32C2311yescharacteristic
74C23×C3⋊D3—22no—
75C23×C3⋊D3—22no—
76C23×C3⋊D3—22no—
77C23×C3⋊D3—41no—
78C23×C3⋊D3—41no—
79C23×C3⋊D3—41no—
80C23×C3⋊D3—41no—
81C23×C3⋊D3C2311yescharacteristic
82C23×C3⋊D3C2311yescharacteristic
83C23×C3⋊D3C2311yescharacteristic
84C23×C3⋊D3C2311yescharacteristic
85C23×C3⋊D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638—22no—
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—41no—
98C2×#638—41no—
99C2×#638—41no—
100C2×#638—41no—
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C4⋊(C3⋊D3)—22no—
105C2×C4⋊(C3⋊D3)—22no—
106C2×C4⋊(C3⋊D3)—22no—
107C2×C4⋊(C3⋊D3)—22no—
108C2×C4⋊(C3⋊D3)—22no—
109C2×C4⋊(C3⋊D3)—22no—
110C2×C4⋊(C3⋊D3)—22no—
111C2×C4⋊(C3⋊D3)—22no—
112C2×C4⋊(C3⋊D3)—22no—
113C2×C4⋊(C3⋊D3)—22no—
114C2×C4⋊(C3⋊D3)—22no—
115C2×C4⋊(C3⋊D3)—22no—
116C2×C4⋊(C3⋊D3)—22no—
117C2×C4⋊(C3⋊D3)—22no—
118C2×C4⋊(C3⋊D3)—41no—
119C2×C4⋊(C3⋊D3)—41no—
120C2×C4⋊(C3⋊D3)—41no—
121C2×C4⋊(C3⋊D3)—41no—
122C2×C4⋊(C3⋊D3)—41no—
123C2×C4⋊(C3⋊D3)—41no—
124C2×C4⋊(C3⋊D3)—41no—
125C2×C4⋊(C3⋊D3)—41no—
126C2×C4⋊(C3⋊D3)—41no—
127C2×C4⋊(C3⋊D3)—41no—
128C2×C4⋊(C3⋊D3)—41no—
129C2×C4⋊(C3⋊D3)—41no—
130C2×C4⋊(C3⋊D3)D414yescomplemented
131C2×C4×C3⋊D3—22no—
132C2×C4×C3⋊D3—22no—
133C2×C4×C3⋊D3—41no—
134C32×C4⋊C4—22no—
135C32×C22⋊C4—22no—
136C32×C22⋊C4—22no—
137C32×C22⋊C4D414yescomplemented
138C32×C42—22no—
139#3752—22no—
140#3752—22no—
141#3752—22no—
142#3752—22no—
143#3752—22no—
144#3752—22no—
145#3752—22no—
146#3752—41no—
147#3752—41no—
148#3752—41no—
149#3752D414yescomplemented
150#3750—22no—
151#2669—91noSylow
152C24×D3—34no—
153C22×#67—34no—
154C22×#67—34no—
155C22×#67—34no—
156C22×D12—34no—
157C22×D12—34no—
158C22×D12—34no—
159C22×D12—34no—
160C22×D12—34no—
161C22×D12—34no—
162C22×D12—34no—
163C22×D12—34no—
164C22×D12—34no—
165C22×C4×D3—34no—
166C2×C3×C4⋊C4C2×D314yescomplemented
167C2×C3×C22⋊C4C2×D314yes—
168C2×C3×C22⋊C4C2×D314yes—
169C2×C3×C22⋊C4C2×D314yes—
170C2×C3×C42C2×D314yescomplemented
171C2×(C2×D3)⋊C4—34no—
172C2×(C2×D3)⋊C4—34no—
173C2×(C2×D3)⋊C4—34no—
174C2×(C2×D3)⋊C4—34no—
175C2×(C2×D3)⋊C4—34no—
176C2×(C2×D3)⋊C4—34no—
177C2×(C2×D3)⋊C4—34no—
178C2×(C2×D3)⋊C4—34no—
179C2×(C2×D3)⋊C4—34no—
180C2×(C2×D3)⋊C4—34no—
181C2×(C2×D3)⋊C4—34no—
182C2×Dic3⋊C4—34no—
183#895—616no—
184#884—616no—
185#882—616no—
186#882—616no—
187#882—616no—
188#874—616no—
189C3×#95C2×D314yescomplemented
190C3×#95C2×D314yescomplemented
191C3⋊#95—34no—
192C3⋊#95—34no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—21no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32C2×D412yes—
200C23×C32C2411yescharacteristic
201C22×C3⋊D3—21no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3—21no—
205C22×C3⋊D3—21no—
206C22×C3⋊D3—21no—
207C22×C3⋊D3—21no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3—21no—
214C22×C3⋊D3—21no—
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3—21no—
221C22×C3⋊D3—21no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—44no—
234C22×C3⋊D3—44no—
235C22×C3⋊D3—44no—
236C22×C3⋊D3—44no—
237C22×C3⋊D3—44no—
238C22×C3⋊D3—44no—
239C22×C3⋊D3—44no—
240C22×C3⋊D3C2×D412yes—
241C22×C3⋊D3C2×D412yes—
242C22×C3⋊D3C2×D412yes—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D412yes—
258C2×C32×C4C2×D412yes—
259C2×C32×C4C2×D412yes—
260C2×C32×C4C2×D412yes—
261#638—44no—
262#638—44no—
263#638—44no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3C2×D412yes—
273C4⋊(C3⋊D3)—44no—
274C4⋊(C3⋊D3)—44no—
275C4⋊(C3⋊D3)—44no—
276C4⋊(C3⋊D3)—44no—
277C4⋊(C3⋊D3)—44no—
278C4⋊(C3⋊D3)—44no—
279C4⋊(C3⋊D3)—44no—
280C4⋊(C3⋊D3)—44no—
281C4⋊(C3⋊D3)—44no—
282C4×C3⋊D3—44no—
283C2×#127—91no—
284C2×#121—91no—
285C2×#121—91no—
286C2×#120—91no—
287C2×#120—91no—
288C2×#120—91no—
289#394—91no—
290#394—91no—
291#392—91no—
292#392—91no—
293#392—91no—
294#392—91no—
295#388—91no—
296#388C3⋊D311yescharacteristic, complemented
297#386—91no—
298C24×C3C22×D314yes—
299C23×D3—34no—
300C23×D3—34no—
301C23×D3—34no—
302C23×D3—34no—
303C23×D3—34no—
304C23×D3—68no—
305C23×D3—68no—
306C23×D3—68no—
307C23×D3—124no—
308C23×D3—124no—
309C23×D3—124no—
310C23×D3—124no—
311C22×C3×C4C22×D314yes—
312C22×C3×C4C22×D314yes—
313C22×C3×C4C22×D314yes—
314C22×C3×C4C22×D314yes—
315C22×C3×C4C22×D314yes—
316C22×C3×C4C22×D314yes—
317C2×#67—68no—
318C2×#67—68no—
319C2×#67—68no—
320C2×#67—68no—
321C2×#67—68no—
322C2×#67—124no—
323C2×#67—124no—
324C2×#67—124no—
325C2×#67—124no—
326C22×Dic3—34no—
327C22×Dic3—34no—
328C22×Dic3—34no—
329C2×D12—316no—
330C2×D12—68no—
331C2×D12—68no—
332C2×D12—68no—
333C2×D12—68no—
334C2×D12—68no—
335C2×D12—68no—
336C2×D12—68no—
337C2×D12—68no—
338C2×D12—68no—
339C2×D12—68no—
340C2×D12—68no—
341C2×D12—68no—
342C2×D12—68no—
343C2×D12—68no—
344C2×D12—124no—
345C2×D12—124no—
346C2×D12—124no—
347C2×D12—124no—
348C2×D12—124no—
349C2×D12—124no—
350C2×D12—124no—
351C2×D12—124no—
352C2×D12—124no—
353C2×D12—124no—
354C2×D12—124no—
355C2×D12—124no—
356C2×C4×D3—68no—
357C2×C4×D3—68no—
358C2×C4×D3—124no—
359C3×C4⋊C4—28no—
360C3×C22⋊C4—28no—
361C3×C22⋊C4—28no—
362C3×C22⋊C4D12116yescomplemented
363C3×C42—28no—
364(C2×D3)⋊C4—316no—
365(C2×D3)⋊C4—68no—
366(C2×D3)⋊C4—68no—
367(C2×D3)⋊C4—68no—
368(C2×D3)⋊C4—68no—
369(C2×D3)⋊C4—68no—
370(C2×D3)⋊C4—68no—
371(C2×D3)⋊C4—68no—
372(C2×D3)⋊C4—124no—
373(C2×D3)⋊C4—124no—
374(C2×D3)⋊C4—124no—
375Dic3⋊C4—68no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—22no—
379C22×C32—41no—
380C22×C32—41no—
381C22×C32—41no—
382C22×C32—41no—
383C22×C32C22×D411yescharacteristic
384C22×C32C22×D411yescharacteristic
385C22×C32C22×D411yescharacteristic
386C22×C32H(5,𝔽2)11yescharacteristic
387C22×C32H(5,𝔽2)11yescharacteristic
388C22×C32H(5,𝔽2)11yescharacteristic
389C22×C32H(5,𝔽2)11yescharacteristic
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—22no—
394C2×C3⋊D3—22no—
395C2×C3⋊D3—22no—
396C2×C3⋊D3—22no—
397C2×C3⋊D3—22no—
398C2×C3⋊D3—22no—
399C2×C3⋊D3—416no—
400C2×C3⋊D3—41no—
401C2×C3⋊D3—41no—
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C32×C4—22no—
427C32×C4—22no—
428C32×C4—22no—
429C32×C4—22no—
430C32×C4—41no—
431C32×C4—41no—
432C3⋊Dic3—22no—
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C25—91no—
436C22×D4—91no—
437C22×D4—91no—
438C22×D4—91no—
439C22×D4—91no—
440C22×D4—91no—
441C22×D4—91no—
442C22×D4—91no—
443C22×D4—91no—
444C22×D4—91no—
445C22×D4—91no—
446C22×D4—91no—
447C22×D4—91no—
448C23×C4—91no—
449#127—184no—
450#121—184no—
451#121—184no—
452#120—184no—
453#120—184no—
454#120—184no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
457C2×C22⋊C4—91no—
458C2×C22⋊C4—91no—
459C2×C22⋊C4—91no—
460C2×C22⋊C4—91no—
461C2×C22⋊C4—91no—
462C2×C22⋊C4—91no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—91no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—91no—
467C2×C22⋊C4—91no—
468C2×C22⋊C4C2×C3⋊D311yescharacteristic
469C2×C22⋊C4C2×C3⋊D311yescharacteristic
470C2×C22⋊C4C2×C3⋊D311yescharacteristic
471C2×C42C2×C3⋊D311yescharacteristic, complemented
472#95—91no—
473#95—91no—
474#95C2×C3⋊D311yescharacteristic, complemented
475#95C2×C3⋊D311yescharacteristic, complemented
476C23×C3—24no—
477C23×C3—24no—
478C23×C3—24no—
479C23×C3—24no—
480C23×C3—24no—
481C23×C3—24no—
482C23×C3C2×D1218yes—
483C23×C3C23×D314yes—
484C22×D3—38no—
485C22×D3—38no—
486C22×D3—38no—
487C22×D3—64no—
488C22×D3—64no—
489C22×D3—64no—
490C22×D3—64no—
491C22×D3—64no—
492C22×D3—64no—
493C22×D3—64no—
494C22×D3—64no—
495C22×D3—64no—
496C22×D3—64no—
497C22×D3—64no—
498C22×D3—64no—
499C22×D3—64no—
500C22×D3—64no—
501C22×D3—64no—
502C22×D3—64no—
503C22×D3—64no—
504C22×D3—64no—
505C22×D3—64no—
506C22×D3—64no—
507C22×D3—64no—
508C22×D3—64no—
509C22×D3—64no—
510C22×D3—64no—
511C22×D3—64no—
512C22×D3—64no—
513C22×D3—64no—
514C22×D3—64no—
515C22×D3—64no—
516C22×D3—64no—
517C22×D3—64no—
518C22×D3—64no—
519C22×D3—1216no—
520C22×D3—1216no—
521C22×D3—1216no—
522C22×D3—1216no—
523C22×D3—1216no—
524C22×D3—1216no—
525C22×D3—1216no—
526C2×C3×C4—24no—
527C2×C3×C4—24no—
528C2×C3×C4—24no—
529C2×C3×C4—24no—
530C2×C3×C4—24no—
531C2×C3×C4—24no—
532C2×C3×C4—24no—
533C2×C3×C4—24no—
534C2×C3×C4—24no—
535C2×C3×C4—24no—
536C2×C3×C4—24no—
537C2×C3×C4—24no—
538C2×C3×C4—24no—
539C2×C3×C4—24no—
540C2×C3×C4C2×D1218yes—
541C2×C3×C4C2×D1218yes—
542C2×C3×C4D3×D418yes—
543C2×C3×C4D3×D418yes—
544#67—1216no—
545#67—1216no—
546#67—1216no—
547C2×Dic3—38no—
548C2×Dic3—64no—
549C2×Dic3—64no—
550C2×Dic3—64no—
551C2×Dic3—64no—
552C2×Dic3—64no—
553C2×Dic3—64no—
554C2×Dic3—64no—
555C2×Dic3—64no—
556D12—1216no—
557D12—1216no—
558D12—1216no—
559D12—1216no—
560D12—1216no—
561D12—1216no—
562D12—1216no—
563D12—1216no—
564D12—1216no—
565C4×D3—1216no—
566C2×C32—42no—
567C2×C32#53411yescharacteristic
568C2×C32#53511yescharacteristic
569C2×C32#53511yescharacteristic
570C2×C32D4211yescharacteristic
571C2×C32D4211yescharacteristic
572C2×C32D4211yescharacteristic
573C2×C32#56011yescharacteristic
574C3⋊D3—42no—
575C3⋊D3—42no—
576C3⋊D3—42no—
577C3⋊D3—81no—
578C3⋊D3—81no—
579C24—91no—
580C24—91no—
581C24—91no—
582C24—91no—
583C24—91no—
584C24—182no—
585C24—182no—
586C24—182no—
587C24—361no—
588C24—361no—
589C24—361no—
590C24—361no—
591C24C22×C3⋊D311yescharacteristic
592C2×D4—94no—
593C2×D4—182no—
594C2×D4—182no—
595C2×D4—182no—
596C2×D4—182no—
597C2×D4—182no—
598C2×D4—182no—
599C2×D4—182no—
600C2×D4—182no—
601C2×D4—182no—
602C2×D4—182no—
603C2×D4—182no—
604C2×D4—182no—
605C2×D4—182no—
606C2×D4—182no—
607C2×D4—182no—
608C2×D4—182no—
609C2×D4—182no—
610C2×D4—182no—
611C2×D4—182no—
612C2×D4—361no—
613C2×D4—361no—
614C2×D4—361no—
615C2×D4—361no—
616C2×D4—361no—
617C2×D4—361no—
618C2×D4—361no—
619C2×D4—361no—
620C2×D4—361no—
621C2×D4—361no—
622C2×D4—361no—
623C2×D4—361no—
624C2×D4—361no—
625C2×D4—361no—
626C2×D4—361no—
627C2×D4—361no—
628C22×C4—91no—
629C22×C4—91no—
630C22×C4—91no—
631C22×C4—182no—
632C22×C4—182no—
633C22×C4—361no—
634C22×C4C22×C3⋊D311yescharacteristic
635C22×C4C22×C3⋊D311yescharacteristic
636C22×C4C22×C3⋊D311yescharacteristic
637C22×C4C22×C3⋊D311yescharacteristic
638C22×C4C22×C3⋊D311yescharacteristic
639C22×C4C22×C3⋊D311yescharacteristic
640C4⋊C4—22no—
641C4⋊C4—182no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—94no—
645C22⋊C4—182no—
646C22⋊C4—182no—
647C22⋊C4—182no—
648C22⋊C4—182no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—361no—
653C22⋊C4—361no—
654C22⋊C4—361no—
655C22⋊C4C4⋊(C3⋊D3)14yescomplemented
656C42—22no—
657C22×C3—28no—
658C22×C3—28no—
659C22×C3—28no—
660C22×C3—44no—
661C22×C3—44no—
662C22×C3—44no—
663C22×C3—44no—
664C22×C3C22×D1214yes—
665C22×C3C2×D3×D414yes—
666C22×C3C2×D3×D414yes—
667C22×C3#100914yes—
668C22×C3#100914yes—
669C22×C3#100914yes—
670C22×C3#100914yes—
671C2×D3—68no—
672C2×D3—68no—
673C2×D3—68no—
674C2×D3—68no—
675C2×D3—68no—
676C2×D3—68no—
677C2×D3—68no—
678C2×D3—68no—
679C2×D3—68no—
680C2×D3—1264no—
681C2×D3—124no—
682C2×D3—124no—
683C2×D3—124no—
684C2×D3—124no—
685C2×D3—124no—
686C2×D3—124no—
687C2×D3—124no—
688C2×D3—124no—
689C2×D3—124no—
690C2×D3—124no—
691C2×D3—124no—
692C2×D3—124no—
693C2×D3—124no—
694C2×D3—124no—
695C2×D3—124no—
696C2×D3—124no—
697C2×D3—124no—
698C2×D3—124no—
699C2×D3—124no—
700C2×D3—124no—
701C2×D3—124no—
702C2×D3—124no—
703C2×D3—124no—
704C2×D3—124no—
705C2×D3—124no—
706C2×D3—124no—
707C3×C4—28no—
708C3×C4—28no—
709C3×C4—28no—
710C3×C4—28no—
711C3×C4—44no—
712C3×C4—44no—
713Dic3—68no—
714Dic3—124no—
715Dic3—124no—
716C32#266911yescharacteristic, complemented, Sylow
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—92no—
724C23—92no—
725C23—92no—
726C23—181no—
727C23—181no—
728C23—181no—
729C23—181no—
730C23—181no—
731C23—181no—
732C23—181no—
733C23—181no—
734C23—181no—
735C23—181no—
736C23—181no—
737C23—181no—
738C23—181no—
739C23—181no—
740C23—181no—
741C23—181no—
742C23—181no—
743C23—181no—
744C23—181no—
745C23—181no—
746C23—181no—
747C23—181no—
748C23—181no—
749C23—181no—
750C23—181no—
751C23—181no—
752C23—181no—
753C23—181no—
754C23—181no—
755C23—181no—
756C23—181no—
757C23—181no—
758C23—364no—
759C23—364no—
760C23—364no—
761C23—364no—
762C23—364no—
763C23—364no—
764C23—364no—
765C23C2×C4⋊(C3⋊D3)12yes—
766C23C23×C3⋊D311yescharacteristic
767D4—364no—
768D4—364no—
769D4—364no—
770D4—364no—
771D4—364no—
772D4—364no—
773D4—364no—
774D4—364no—
775D4—364no—
776D4—364no—
777D4—364no—
778D4—364no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—92no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—364no—
803C2×C4C2×C4⋊(C3⋊D3)12yes—
804C2×C4C2×C4⋊(C3⋊D3)12yes—
805C2×C4D4×C3⋊D312yes—
806C2×C4D4×C3⋊D312yes—
807C2×C3—48no—
808C2×C3#552514yes—
809C2×C3D4×D1214yes—
810C2×C3D4×D1214yes—
811C2×C3#560914yes—
812C2×C3#565314yes—
813C2×C3#567414yes—
814C2×C3#571114yes—
815D3—128no—
816D3—128no—
817D3—128no—
818D3—244no—
819D3—244no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—182no—
828C22—182no—
829C22—182no—
830C22—182no—
831C22—182no—
832C22—182no—
833C22—182no—
834C22—182no—
835C22—182no—
836C22—3616no—
837C22—361no—
838C22—361no—
839C22—361no—
840C22—361no—
841C22—361no—
842C22—361no—
843C22—361no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—361no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22—361no—
855C22—361no—
856C22—361no—
857C22—361no—
858C22—361no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22—361no—
863C22C22×C4⋊(C3⋊D3)11yescharacteristic
864C22C2×D4×C3⋊D311yescharacteristic
865C22C2×D4×C3⋊D311yescharacteristic
866C22#6436611yescharacteristic
867C22#6436611yescharacteristic
868C22#6436611yescharacteristic
869C22#6436611yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—22no—
874C4—41no—
875C4—41no—
876C4—182no—
877C4—361no—
878C4—361no—
879C3#7591214yescomplemented
880C2—42no—
881C2—362no—
882C2—362no—
883C2—362no—
884C2—721no—
885C2—721no—
886C2#1059599611yescharacteristic
887C2D4×C4⋊(C3⋊D3)11yescharacteristic
888C2D4×C4⋊(C3⋊D3)11yescharacteristic
889C2#1059608011yescharacteristic
890C2#1059612411yescharacteristic
891C2#1059614511yescharacteristic
892C2#1059618211yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#388C2
hypercenter#388C3⋊D3
hypocenterC32#2669
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#64104C2semidirect
2. C2×#64093C2semidirect
3. C2×#64091C2semidirect
4. C2×#64091C2semidirect
5. C2×#64091C2semidirect
6. C2×#64083C2semidirect
7. C32×#388C2semidirect
8. #10592690C2semidirect
9. #10592659C2semidirect
10. #10592659C2semidirect
11. #10592639C2semidirect
12. #10592371C2semidirect
13. #10592370C2semidirect
14. #10592370C2semidirect
15. #10592364C2semidirect
27. C22×C4⋊(C3⋊D3)C22semidirect
28. C22×C4⋊(C3⋊D3)C22semidirect
29. C22×C4⋊(C3⋊D3)C22semidirect
30. C22×C4×C3⋊D3C22semidirect
31. C2×C32×C4⋊C4C22semidirect
35. C2×C32×C42C22semidirect
42. C2×#3752C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. C2×#3752C22semidirect
46. C2×#3752C22semidirect
47. C2×#3750C22semidirect
54. C32×#95C22semidirect
55. C32×#95C22semidirect
56. #63658C22semidirect
57. #63658C22semidirect
64. C3×#388D3semidirect
130. C2×C4⋊(C3⋊D3)D4semidirect
137. C32×C22⋊C4D4semidirect
149. #3752D4semidirect
166. C2×C3×C4⋊C4C2×D3semidirect
170. C2×C3×C42C2×D3semidirect
189. C3×#95C2×D3semidirect
190. C3×#95C2×D3semidirect
296. #388C3⋊D3semidirect
362. C3×C22⋊C4D12semidirect
456. C2×C4⋊C4C2×C3⋊D3semidirect
471. C2×C42C2×C3⋊D3semidirect
474. #95C2×C3⋊D3semidirect
475. #95C2×C3⋊D3semidirect
655. C22⋊C4C4⋊(C3⋊D3)semidirect
716. C32#2669semidirect
879. C3#75912semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×#640932
C2×#640912
C2×#640832
C32×#3882
#105926902
#105926592
#105926392
#105923712
#105923702
#105923642
#759123