Finite Group Databasebeta

← C2×#11795925 #72227373

Subgroups — C2×#11795925 #72227373

Order 2304.

1904 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10590625C212yesmaximal
2C2×C3⋊D3×#97C211yesmaximal, characteristic
3C2×#10589106C212yesmaximal, complemented
4#11795925C218yesmaximal, direct product factor
5C2×C3×#4466C212yesmaximal, complemented
6C2×D3×#347—32nomaximal
7C22×C8×C3⋊D3C411yescharacteristic
8C22×C8×C3⋊D3C2211yescharacteristic
9C2×C42×C3⋊D3C411yescharacteristic
10C2×C32×#97C2211yescharacteristic
11C2×#63642C411yescharacteristic
12C2×#63642C2211yescharacteristic
13C2×#63630C411yescharacteristic
14C3⋊D3×#97C414yes—
15C3⋊D3×#97C2214yes—
16C2×C3×#812C2214yes—
17C2×#63544C414yescomplemented
18#10590625C418yescomplemented
19#10590625C2218yes—
20C2×#63542C414yescomplemented
21C3×#4466C2218yescomplemented
22#10589106C2218yescomplemented
23C2×D3×M32—34no—
24C2×D3×#97—32no—
25C2×D3×#97—61no—
26C2×C3×#347—32no—
27C2×#4512—34no—
28C2×#4466D312yescomplemented
29D3×#347—316no—
30C22×C4×C3⋊D3—21no—
31C22×C4×C3⋊D3C2×C411yescharacteristic
32C22×C32×C8C2×C411yescharacteristic
33C22×C32×C8C2311yescharacteristic
34C2×C32×C42C2×C411yescharacteristic
35C2×C4×C3⋊Dic3—21no—
36C2×C4×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊(C3⋊C8)C2×C411yescharacteristic
38C22×C3⋊(C3⋊C8)C2×C411yescharacteristic
39C2×C8×C3⋊D3—21no—
40C2×C8×C3⋊D3—22no—
41C2×C8×C3⋊D3—21no—
42C2×C8×C3⋊D3C2×C414yes—
43C2×C8×C3⋊D3C2×C412yes—
44C2×C8×C3⋊D3C2×C412yes—
45C2×C8×C3⋊D3C2×C414yes—
46C2×C8×C3⋊D3C2×C412yes—
47C2×C8×C3⋊D3C2312yes—
48C42×C3⋊D3—22no—
49C42×C3⋊D3C2×C414yes—
50C32×#97C2×C412yes—
51C32×#97C2312yes—
52#63642C2×C414yes—
53#63642C2×C412yes—
54#63642C2312yes—
55#63630C2×C414yes—
56C3×#812C2×C418yescomplemented
57C3×#812C2318yes—
58C2×C3×C3⋊C16C2×C418yescomplemented
59#63544C2×C4116yescomplemented
60#63542C2×C4116yescomplemented
61C22×#347—91noSylow
62C22×D3×C8—32no—
63C22×D3×C8—32no—
64C22×D3×C8—61no—
65C22×D3×C8—61no—
66C2×C42×D3—32no—
67C2×C42×D3—61no—
68C2×C3×M32—34no—
69C2×C3×#97—21no—
70C2×C3×#97C2×D312yes—
71C2×#815—32no—
72C2×#815—32no—
73C2×#815—61no—
74C2×#815—61no—
75C2×#812C2×D314yes—
76C2×#803—32no—
77C2×#803—61no—
78D3×M32—316no—
79D3×M32—316no—
80C2×#798—38no—
81C2×D3×C16—38no—
82D3×#97—38no—
83D3×#97—38no—
84D3×#97—64no—
85D3×#97—64no—
86C3×#347—38no—
87#4512—316no—
88#4466C2×D318yescomplemented
89C23×C3⋊D3M1611yescharacteristic
90C22×C32×C4—21no—
91C22×C32×C4C22×C411yescharacteristic
92C22×C3⋊Dic3—21no—
93C22×C3⋊Dic3M1611yescharacteristic
94C2×C4×C3⋊D3—24no—
95C2×C4×C3⋊D3—44no—
96C2×C4×C3⋊D3C4212yes—
97C2×C4×C3⋊D3C4211yescharacteristic
98C2×C4×C3⋊D3C4211yescharacteristic
99C2×C4×C3⋊D3M1612yes—
100C2×C4×C3⋊D3M1611yescharacteristic
101C2×C4×C3⋊D3M1612yes—
102C2×C4×C3⋊D3M1611yescharacteristic
103C2×C4×C3⋊D3C22×C412yes—
104C2×C32×C8—21no—
105C2×C32×C8—21no—
106C2×C32×C8C22×C412yes—
107C2×C32×C8C22×C411yescharacteristic
108C2×C32×C8C22×C412yes—
109C2×C32×C8C22×C412yes—
110C2×C32×C8C2411yescharacteristic
111C32×C42—21no—
112C32×C42C22×C412yes—
113C4×C3⋊Dic3—21no—
114C4×C3⋊Dic3—24no—
115C4×C3⋊Dic3C22×C412yes—
116C2×C3⋊(C3⋊C8)—21no—
117C2×C3⋊(C3⋊C8)—21no—
118C2×C3⋊(C3⋊C8)C4212yes—
119C2×C3⋊(C3⋊C8)C4212yes—
120C2×C3⋊(C3⋊C8)C22×C412yes—
121C2×C3⋊(C3⋊C8)C22×C412yes—
122C8×C3⋊D3—24no—
123C8×C3⋊D3—24no—
124C8×C3⋊D3C4214yes—
125C8×C3⋊D3C4214yes—
126C8×C3⋊D3C22×C414yes—
127C8×C3⋊D3C22×C414yes—
128C3×C3⋊C16C22×C4116yescomplemented
129C22×M32—92no—
130C22×#97—91no—
131C2×#347—32no—
132C2×#347—98no—
133C2×#347—92no—
134C22×C4×D3—32no—
135C22×C4×D3—61no—
136C22×C4×D3—62no—
137C22×C4×D3—62no—
138C22×C3×C8—21no—
139C22×C3×C8—21no—
140C22×C3×C8C4×D312yes—
141C22×C3×C8C22×D312yes—
142C2×C3×C42—21no—
143C2×C3×C42C4×D312yes—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—61no—
146C2×C4×Dic3—62no—
147C2×C4×Dic3—62no—
148C22×C3⋊C8—32no—
149C22×C3⋊C8—32no—
150C22×C3⋊C8—61no—
151C22×C3⋊C8—61no—
152C2×D3×C8—34no—
153C2×D3×C8—34no—
154C2×D3×C8—38no—
155C2×D3×C8—34no—
156C2×D3×C8—34no—
157C2×D3×C8—38no—
158C2×D3×C8—62no—
159C2×D3×C8—64no—
160C2×D3×C8—62no—
161C2×D3×C8—62no—
162C2×D3×C8—64no—
163C2×D3×C8—62no—
164C2×D3×C8—62no—
165C2×D3×C8—64no—
166C2×D3×C8—62no—
167C2×D3×C8—62no—
168C2×D3×C8—62no—
169C2×D3×C8—64no—
170C42×D3—38no—
171C42×D3—64no—
172C42×D3—64no—
173C42×D3—64no—
174C3×M32—38no—
175C3×M32—38no—
176C2×C3×C16—38no—
177C3×#97—22no—
178C3×#97—22no—
179C3×#97C4×D314yes—
180C3×#97C22×D314yes—
181#815—38no—
182#815—34no—
183#815—34no—
184#815—62no—
185#815—64no—
186#815—62no—
187#812C4×D318yescomplemented
188#812C22×D318yes—
189C2×C3⋊C16C4×D318yescomplemented
190#803—38no—
191#803—64no—
192#798—332no—
193D3×C16—332no—
194C23×C32C2×M1611yescharacteristic
195C22×C3⋊D3—24no—
196C22×C3⋊D3#9711yescharacteristic
197C22×C3⋊D3#9712yes—
198C22×C3⋊D3#9711yescharacteristic
199C22×C3⋊D3C2×M1612yes—
200C2×C32×C4—22no—
201C2×C32×C4—42no—
202C2×C32×C4C2×C4211yescharacteristic
203C2×C32×C4C2×C4211yescharacteristic
204C2×C32×C4C2×M1611yescharacteristic
205C2×C32×C4C2×M1611yescharacteristic
206C2×C32×C4C2×M1611yescharacteristic
207C2×C32×C4C23×C411yescharacteristic
208C2×C3⋊Dic3—22no—
209C2×C3⋊Dic3—42no—
210C2×C3⋊Dic3#9712yes—
211C2×C3⋊Dic3#9711yescharacteristic
212C2×C3⋊Dic3#9711yescharacteristic
213C2×C3⋊Dic3C2×M1612yes—
214C4×C3⋊D3—48no—
215C4×C3⋊D3#9712yes—
216C4×C3⋊D3#9712yes—
217C4×C3⋊D3#9712yes—
218C4×C3⋊D3#9712yes—
219C4×C3⋊D3C2×C4212yes—
220C4×C3⋊D3C2×C4212yes—
221C4×C3⋊D3C2×M1612yes—
222C4×C3⋊D3C2×M1612yes—
223C32×C8—22no—
224C32×C8C2×C4212yes—
225C32×C8C23×C412yes—
226C3⋊(C3⋊C8)—22no—
227C3⋊(C3⋊C8)C2×C4214yes—
228C23×C8—91no—
229C23×C8—91no—
230C22×C42—91no—
231C2×M32—34no—
232C2×M32—94no—
233C2×M32—98no—
234C2×M32—98no—
235C22×C16—94no—
236C2×#97—91no—
237C2×#97—91no—
238C2×#97—91no—
239C2×#97—94no—
240C2×#97—94no—
241C2×#97D3211yescharacteristic
242#347—38no—
243#347—98no—
244C23×D3—32no—
245C23×D3—61no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—21no—
249C22×C3×C4C2×C4×D312yes—
250C22×Dic3—32no—
251C22×Dic3—61no—
252C22×Dic3—62no—
253C22×Dic3—62no—
254C2×C4×D3—34no—
255C2×C4×D3—32no—
256C2×C4×D3—32no—
257C2×C4×D3—34no—
258C2×C4×D3—32no—
259C2×C4×D3—34no—
260C2×C4×D3—32no—
261C2×C4×D3—34no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—62no—
269C2×C4×D3—61no—
270C2×C4×D3—68no—
271C2×C4×D3—68no—
272C2×C4×D3—128no—
273C2×C4×D3—128no—
274C2×C3×C8—22no—
275C2×C3×C8—22no—
276C2×C3×C8—22no—
277C2×C3×C8—22no—
278C2×C3×C8—21no—
279C2×C3×C8—22no—
280C2×C3×C8—22no—
281C2×C3×C8—22no—
282C2×C3×C8—21no—
283C2×C3×C8C2×C4×D314yes—
284C2×C3×C8C2×C4×D314yes—
285C2×C3×C8C2×C4×D314yes—
286C2×C3×C8C2×C4×D312yes—
287C2×C3×C8C23×D312yes—
288C3×C42—22no—
289C3×C42—22no—
290C3×C42—22no—
291C3×C42C2×C4×D314yes—
292C4×Dic3—34no—
293C4×Dic3—62no—
294C4×Dic3—68no—
295C4×Dic3—68no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C2×C3⋊C8—34no—
299C2×C3⋊C8—34no—
300C2×C3⋊C8—34no—
301C2×C3⋊C8—34no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8—62no—
304C2×C3⋊C8—62no—
305C2×C3⋊C8—62no—
306C2×C3⋊C8—62no—
307C2×C3⋊C8—62no—
308C2×C3⋊C8—62no—
309C2×C3⋊C8—62no—
310D3×C8—38no—
311D3×C8—38no—
312D3×C8—38no—
313D3×C8—38no—
314D3×C8—64no—
315D3×C8—64no—
316D3×C8—64no—
317D3×C8—64no—
318D3×C8—68no—
319D3×C8—68no—
320D3×C8—68no—
321D3×C8—68no—
322C3×C16—316no—
323C3⋊C16C2×C4×D3116yescomplemented
324C22×C32—22no—
325C22×C32C2×#9711yescharacteristic
326C22×C32C2×#9711yescharacteristic
327C22×C32C22×M1611yescharacteristic
328C2×C3⋊D3—22no—
329C2×C3⋊D3—24no—
330C2×C3⋊D3—24no—
331C2×C3⋊D3#34714yescomplemented
332C2×C3⋊D3C2×#9712yes—
333C2×C3⋊D3C2×#9712yes—
334C32×C4—42no—
335C32×C4C2×#9711yescharacteristic
336C32×C4C2×#9711yescharacteristic
337C32×C4C22×C4211yescharacteristic
338C32×C4C22×M1611yescharacteristic
339C3⋊Dic3—42no—
340C3⋊Dic3C2×#9712yes—
341C3⋊Dic3C2×#9712yes—
342C23×C4—91no—
343C23×C4—181no—
344C22×C8—91no—
345C22×C8—92no—
346C22×C8—92no—
347C22×C8—94no—
348C22×C8—92no—
349C22×C8—92no—
350C22×C8—91no—
351C22×C8—94no—
352C22×C8—181no—
353C22×C8—181no—
354C22×C8—182no—
355C22×C8#62411yescharacteristic
356C22×C8C2×D3211yescharacteristic
357C2×C42—91no—
358C2×C42—94no—
359C2×C42—182no—
360C2×C42—181no—
361C2×C42#62411yescharacteristic
362M32—38no—
363M32—38no—
364M32—916no—
365C2×C16—38no—
366C2×C16—916no—
367#97—92no—
368#97—94no—
369#97—92no—
370#97—94no—
371#97#62412yes—
372#97C2×D3212yes—
373C23×C3—21no—
374C23×C3D3×M1612yes—
375C22×D3—32no—
376C22×D3—34no—
377C22×D3—32no—
378C22×D3—34no—
379C22×D3—61no—
380C22×D3—62no—
381C22×D3—61no—
382C22×D3—62no—
383C22×D3—68no—
384C22×D3—68no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—44no—
394C2×C3×C4—44no—
395C2×C3×C4C42×D312yes—
396C2×C3×C4C42×D312yes—
397C2×C3×C4D3×M1612yes—
398C2×C3×C4D3×M1612yes—
399C2×C3×C4D3×M1612yes—
400C2×C3×C4C22×C4×D312yes—
401C2×Dic3—34no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—34no—
405C2×Dic3—62no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—62no—
409C2×Dic3—64no—
410C2×Dic3—64no—
411C2×Dic3—124no—
412C2×Dic3—124no—
413C4×D3—34no—
414C4×D3—34no—
415C4×D3—34no—
416C4×D3—34no—
417C4×D3—34no—
418C4×D3—34no—
419C4×D3—34no—
420C4×D3—34no—
421C4×D3—62no—
422C4×D3—62no—
423C4×D3—62no—
424C4×D3—62no—
425C4×D3—62no—
426C4×D3—62no—
427C4×D3—62no—
428C4×D3—62no—
429C4×D3—1216no—
430C4×D3—1216no—
431C3×C8—24no—
432C3×C8—24no—
433C3×C8—22no—
434C3×C8—22no—
435C3×C8C42×D314yes—
436C3×C8C22×C4×D314yes—
437C3⋊C8—38no—
438C3⋊C8—64no—
439C3⋊C8—64no—
440C3⋊C8—64no—
441C2×C32—21no—
442C2×C32—21no—
443C2×C32C2×#34712yescomplemented
444C2×C32C22×#9711yescharacteristic
445C3⋊D3—22no—
446C3⋊D3C2×#34714yescomplemented
447C24—91no—
448C22×C4—21no—
449C22×C4—91no—
450C22×C4—92no—
451C22×C4—92no—
452C22×C4—91no—
453C22×C4—92no—
454C22×C4—91no—
455C22×C4—92no—
456C22×C4—91no—
457C22×C4—91no—
458C22×C4—184no—
459C22×C4—181no—
460C22×C4—364no—
461C22×C4C2×#62411yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—92no—
465C2×C8—92no—
466C2×C8—92no—
467C2×C8—94no—
468C2×C8—94no—
469C2×C8—94no—
470C2×C8—94no—
471C2×C8—92no—
472C2×C8—184no—
473C2×C8—184no—
474C2×C8—181no—
475C2×C8—181no—
476C2×C8C4×D3212yes—
477C2×C8C4×D3212yes—
478C2×C8C2×#62412yes—
479C2×C8C2×#62411yescharacteristic
480C2×C8C22×D3211yescharacteristic
481C42—21no—
482C42—92no—
483C42—184no—
484C42—181no—
485C42C2×#62412yes—
486C16—316no—
487C22×C3—24no—
488C22×C3—24no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3D3×#9712yes—
493C22×C3D3×#9712yes—
494C22×C3C2×D3×M1612yes—
495C2×D3—34no—
496C2×D3—38no—
497C2×D3—34no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—64no—
501C2×D3—68no—
502C2×D3—68no—
503C2×D3—68no—
504C2×D3—68no—
505C2×D3—64no—
506C2×D3—64no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—44no—
512C3×C4—44no—
513C3×C4D3×#9712yes—
514C3×C4D3×#9712yes—
515C3×C4C2×C42×D312yes—
516C3×C4C2×D3×M1612yes—
517Dic3—34no—
518Dic3—34no—
519Dic3—62no—
520Dic3—62no—
521Dic3—124no—
522Dic3—124no—
523C32C22×#34711yescharacteristic, complemented, Sylow
524C23—91no—
525C23—92no—
526C23—91no—
527C23—92no—
528C23—184no—
529C23#6381811yescharacteristic
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—92no—
533C2×C4—91no—
534C2×C4—91no—
535C2×C4—92no—
536C2×C4—92no—
537C2×C4—92no—
538C2×C4—92no—
539C2×C4—92no—
540C2×C4—92no—
541C2×C4—92no—
542C2×C4—92no—
543C2×C4—92no—
544C2×C4—182no—
545C2×C4—368no—
546C2×C4—362no—
547C2×C4#6381811yescharacteristic
548C2×C4#6381811yescharacteristic
549C2×C4#6381811yescharacteristic
550C2×C4C4×#62411yescharacteristic
551C2×C4C4×#62411yescharacteristic
552C2×C4C22×#62411yescharacteristic
553C8—22no—
554C8—94no—
555C8—182no—
556C8C4×#62412yes—
557C8C2×C4×D3212yes—
558C2×C3—22no—
559C2×C3—22no—
560C2×C3—22no—
561C2×C3—22no—
562C2×C3—22no—
563C2×C3—21no—
564C2×C3D3×#34714yescomplemented
565C2×C3C2×D3×#9712yes—
566D3—38no—
567D3—64no—
568D3—64no—
569D3—64no—
570C22—22no—
571C22—94no—
572C22—92no—
573C22—92no—
574C22—184no—
575C22—184no—
576C22—182no—
577C22#1059032211yescharacteristic
578C22#1059032211yescharacteristic
579C22C2×#6381811yescharacteristic
580C4—42no—
581C4—92no—
582C4—92no—
583C4—362no—
584C4#1059032211yescharacteristic
585C4#1059032211yescharacteristic
586C4C2×#6381811yescharacteristic
587C4C2×C4×#62411yescharacteristic
588C3—21no—
589C3C2×D3×#34712yescomplemented
590C2—21no—
591C2—21no—
592C2—94no—
593C2—182no—
594C2#1179592512yesdirect product factor
595C2C2×#1059032211yescharacteristic
subgroupG/H
centerC2×C4C4×#624
commutatorC32×C4C22×C42
FrattiniC2×C8C22×D32
FittingC2×C32×#97C22
socleC22×C32C2×#97
prime radicalC23×C3⋊D3M16
cosocleC2×C32×C8C24
hypercenterC2×#97D32
hypocenterC32C22×#347
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
3. C2×#10589106C2semidirect
4. #11795925C2direct (N × H)
5. C2×C3×#4466C2semidirect
17. C2×#63544C4semidirect
18. #10590625C4semidirect
20. C2×#63542C4semidirect
21. C3×#4466C22semidirect
22. #10589106C22semidirect
28. C2×#4466D3semidirect
56. C3×#812C2×C4semidirect
58. C2×C3×C3⋊C16C2×C4semidirect
59. #63544C2×C4semidirect
60. #63542C2×C4semidirect
88. #4466C2×D3semidirect
128. C3×C3⋊C16C22×C4semidirect
187. #812C4×D3semidirect
189. C2×C3⋊C16C4×D3semidirect
323. C3⋊C16C2×C4×D3semidirect
331. C2×C3⋊D3#347semidirect
443. C2×C32C2×#347semidirect
446. C3⋊D3C2×#347semidirect
523. C32C22×#347semidirect
564. C2×C3D3×#347semidirect
589. C3C2×D3×#347semidirect
594. C2#11795925direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#105906252
C2×C3⋊D3×#972
C2×#105891062
#117959252
C2×C3×#44662
C2×D3×#3473