Finite Group Databasebeta

← #11812864

Subgroups — #11812864

Order 1152.

1519 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64103C211yesmaximal, characteristic, complemented
2C2×#63909C211yesmaximal, characteristic
3C2×#63881C211yesmaximal, characteristic, complemented
4C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C3×#4989C211yesmaximal, characteristic, complemented
6C3×#4982C211yesmaximal, characteristic, complemented
7#10591364C211yesmaximal, characteristic, complemented
8#10591364C211yesmaximal, characteristic, complemented
9#10591364C211yesmaximal, characteristic, complemented
10#10591321C211yesmaximal, characteristic, complemented
11#10591290C211yesmaximal, characteristic, complemented
12#10591263C211yesmaximal, characteristic, complemented
13#10591259C211yesmaximal, characteristic, complemented
14#10591216C211yesmaximal, characteristic, complemented
15#10591203C211yesmaximal, characteristic, complemented
16#77951—31nomaximal
17#74418—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30#64103—24no—
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46#63909—24no—
47#63881—24no—
48D3×Dic3⋊C4—24no—
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#930—31no—
58C22×Dic3⋊C4—31no—
59C2×#895—31no—
60C2×#894—31no—
61C2×#894—31no—
62C2×#894—61no—
63C2×#893—31no—
64C2×D3×C4⋊C4—31no—
65C2×#67⋊C4—31no—
66C3×#398—31no—
67C3×#385—31no—
68#4993—31no—
69#4993—31no—
70#4991—31no—
71#4989—31no—
72#4989D311yescharacteristic, complemented
73#4982D311yescharacteristic, complemented
74#4978—31no—
75#4958—31no—
76#4958—31no—
77#4958—31no—
78#4675—31no—
79#4675—31no—
80#4672—31no—
81#4670—31no—
82#4669—31no—
83#4668—31no—
84#4665—31no—
85#4665—31no—
86#4665—31no—
87#4655—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—41no—
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—41no—
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—41no—
112C2×#626—22no—
113C2×#626—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#626—22no—
117C2×#626D414yes—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—41no—
124C32×C4⋊C4—22no—
125#3752—22no—
126#3752—22no—
127#3752—22no—
128#3750D414yescomplemented
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×C4⋊Dic3—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—41no—
135#3724—22no—
136Dic3⋊Dic3—22no—
137#3722—22no—
138#3722—22no—
139#3722—22no—
140#3722—22no—
141#3722—22no—
142#3722—41no—
143Dic32—22no—
144#2443—91noSylow
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C23×Dic3—31no—
149C23×Dic3—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—31no—
153C22×D12—31no—
154C22×D12—61no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—61no—
160C22×C4×D3C2×D311yescharacteristic
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4C2×D311yescharacteristic
167C2×C3×C4⋊C4C2×D311yescharacteristic
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170#930—64no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4—61no—
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3C2×D311yescharacteristic
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—61no—
202C2×Dic3⋊C4—64no—
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×Dic3⋊C4C2×D311yescharacteristic
205C2×Dic3⋊C4C2×D311yescharacteristic
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208#895—64no—
209#894—64no—
210#894—64no—
211#894—68no—
212#893—64no—
213D3×C4⋊C4—64no—
214#67⋊C4—64no—
215C3×#95—31no—
216C3×#95—31no—
217C3×#95—31no—
218C3×#95—31no—
219C3×#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C23×C32C2411yescharacteristic
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3C2×D412yes—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3C2×D412yes—
251C22×C3×D3#4112yes—
252C22×C3×D3#4112yes—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2×D412yes—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C2×D412yes—
267C2×C3⋊Dic3C2×D412yes—
268C4⋊(C3⋊D3)—44no—
269C4×C3⋊D3—44no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3#4112yes—
291C3×C4×D3—44no—
292#626—28no—
293#626—44no—
294D3×Dic3—28no—
295D3×Dic3—44no—
296C2×#123—91no—
297C2×#121—91no—
298C2×C4×D4—91no—
299C22×C4⋊C4—91no—
300#399—91no—
301#398—31no—
302#397—91no—
303#394—91no—
304#388—91no—
305#387—91no—
306#386—91no—
307#386—91no—
308#386—91no—
309#385—31no—
310#385—91no—
311C24×C3—31no—
312C23×D3—31no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—61no—
317C23×D3—61no—
318C23×D3C22×D311yescharacteristic
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4—121no—
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C2×#67—34no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—62no—
351C22×Dic3—62no—
352C22×Dic3—62no—
353C22×Dic3—62no—
354C22×Dic3—62no—
355C22×Dic3—121no—
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C2×D12—34no—
364C2×D12—62no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—64no—
369C2×D12—62no—
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—62no—
373C2×D12—62no—
374C2×D12—122no—
375C2×D12—121no—
376C2×D12—121no—
377C2×D12—122no—
378C2×C4×D3—22no—
379C2×C4×D3—22no—
380C2×C4×D3—41no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—62no—
389C2×C4×D3—64no—
390C2×C4×D3—62no—
391C2×C4×D3—122no—
392C2×C4×D3—121no—
393C2×C4×D3—121no—
394C2×C4×D3—121no—
395C2×C4×D3—122no—
396C3×C4⋊C4—24no—
397C3×C4⋊C4—22no—
398C3×C4⋊C4—22no—
399C3×C4⋊C4—62no—
400C3×C4⋊C4—62no—
401C3×C4⋊C4—62no—
402C3×C4⋊C4—121no—
403C3×C22⋊C4—62no—
404C3×C22⋊C4—62no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—64no—
421(C2×D3)⋊C4—64no—
422(C2×D3)⋊C4—64no—
423(C2×D3)⋊C4—62no—
424(C2×D3)⋊C4—62no—
425(C2×D3)⋊C4—62no—
426(C2×D3)⋊C4—121no—
427(C2×D3)⋊C4—121no—
428C4⋊Dic3—22no—
429C4⋊Dic3—62no—
430Dic3⋊C4—22no—
431Dic3⋊C4—22no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—41no—
435Dic3⋊C4—64no—
436Dic3⋊C4—62no—
437Dic3⋊C4—62no—
438Dic3⋊C4—62no—
439C4×Dic3—62no—
440C4×Dic3—62no—
441C22×C32C22×D411yescharacteristic
442C22×C32C22×D411yescharacteristic
443C22×C32C2×#4111yescharacteristic
444C22×C32C2×#4111yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C32H(5,𝔽2)11yescharacteristic
447C22×C322−1+411yescharacteristic
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3#12314yescomplemented
469C32×C4—22no—
470C32×C4—41no—
471C32×C4—41no—
472C3⋊Dic3—22no—
473C3⋊Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C22×D4—91no—
482C22×D4—91no—
483C22×D4—91no—
484C23×C4—31no—
485C23×C4—91no—
486C23×C4—91no—
487C23×C4—91no—
488#123—184no—
489#121—184no—
490C4×D4—184no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—184no—
499C2×C4⋊C4D3211yescharacteristic
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C42—91no—
512#95—31no—
513#95—31no—
514#95—31no—
515#95—31no—
516#95—31no—
517#95—91no—
518#95—91no—
519#95—91no—
520C23×C3—21no—
521C23×C3—32no—
522C23×C3—32no—
523C23×C3—32no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3C23×D311yescharacteristic
529C23×C3C23×D311yescharacteristic
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—32no—
535C22×D3—32no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—62no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—61no—
561C22×D3—61no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—121no—
567C22×D3—121no—
568C22×D3—121no—
569C22×D3—121no—
570C22×D3—121no—
571C22×D3—121no—
572C22×D3—121no—
573C22×D3—121no—
574C22×D3—121no—
575C22×D3—121no—
576C22×D3#23512yes—
577C22×D3D3×D412yes—
578C22×D3#23912yes—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—22no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—124no—
626C2×C3×C4D3×D412yes—
627C2×C3×C4D3×D412yes—
628#67—68no—
629#67—124no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—68no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—121no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—124no—
669C2×Dic3D3×D412yes—
670C2×Dic3#23912yes—
671D12—68no—
672D12—124no—
673D12—124no—
674D12—128no—
675D12—124no—
676C4×D3—44no—
677C4×D3—68no—
678C4×D3—124no—
679C4×D3—124no—
680C4×D3—124no—
681C4×D3—128no—
682C2×C32C2×#12311yescharacteristic
683C2×C32#52511yescharacteristic
684C2×C32#53911yescharacteristic
685C2×C32D4211yescharacteristic
686C2×C32#54711yescharacteristic
687C2×C32#54811yescharacteristic
688C2×C32#55311yescharacteristic
689C3⋊D3—42no—
690C3⋊D3—81no—
691C3×D3—24no—
692C24—31no—
693C24—91no—
694C24—91no—
695C2×D4—94no—
696C2×D4—182no—
697C2×D4—182no—
698C2×D4—182no—
699C2×D4—182no—
700C2×D4—182no—
701C2×D4—182no—
702C2×D4—182no—
703C2×D4—361no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—62no—
712C22×C4—62no—
713C22×C4—91no—
714C22×C4—91no—
715C22×C4—121no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—182no—
719C22×C4—182no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—182no—
723C22×C4—361no—
724C22×C4—361no—
725C22×C4C2×D3211yescharacteristic
726C22×C4C2×D3211yescharacteristic
727C22×C4C2×D3211yescharacteristic
728C4⋊C4—22no—
729C4⋊C4—62no—
730C4⋊C4—62no—
731C4⋊C4—62no—
732C4⋊C4—94no—
733C4⋊C4—121no—
734C4⋊C4—182no—
735C4⋊C4—182no—
736C22⋊C4—62no—
737C22⋊C4—62no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C22⋊C4—182no—
742C22⋊C4—182no—
743C22⋊C4—182no—
744C22⋊C4—182no—
745C22⋊C4—182no—
746C22⋊C4—361no—
747C42—182no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—34no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3C2×#23511yescharacteristic
763C22×C3C2×D3×D411yescharacteristic
764C22×C3C2×D3×D411yescharacteristic
765C22×C3C2×D3×D411yescharacteristic
766C22×C3C2×D3×D411yescharacteristic
767C22×C3#100411yescharacteristic
768C22×C3C2×#23911yescharacteristic
769C22×C3C2×#23911yescharacteristic
770C22×C3#100711yescharacteristic
771C22×C3D3×#4111yescharacteristic
772C22×C3D3×#4111yescharacteristic
773C22×C3D3×#4111yescharacteristic
774C22×C3#100911yescharacteristic
775C22×C3#101011yescharacteristic
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—64no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—62no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—122no—
792C2×D3—122no—
793C2×D3—122no—
794C2×D3—122no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—122no—
804C2×D3—122no—
805C2×D3—122no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—121no—
813C2×D3—121no—
814C2×D3—121no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—121no—
818C2×D3—121no—
819C2×D3—121no—
820C2×D3—241no—
821C2×D3—241no—
822C2×D3—241no—
823C2×D3—241no—
824C2×D3#89414yescomplemented
825C3×C4—22no—
826C3×C4—22no—
827C3×C4—42no—
828C3×C4—42no—
829C3×C4—42no—
830C3×C4—41no—
831C3×C4—41no—
832C3×C4—41no—
833C3×C4—41no—
834C3×C4—62no—
835C3×C4—62no—
836C3×C4—121no—
837C3×C4—121no—
838C3×C4—121no—
839C3×C4—121no—
840C3×C4—121no—
841Dic3—22no—
842Dic3—22no—
843Dic3—41no—
844Dic3—41no—
845Dic3—41no—
846Dic3—41no—
847Dic3—41no—
848Dic3—62no—
849Dic3—62no—
850Dic3—62no—
851Dic3—62no—
852Dic3—122no—
853Dic3—122no—
854C32#244311yescharacteristic, complemented, Sylow
855C23—32no—
856C23—32no—
857C23—32no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—92no—
863C23—181no—
864C23—181no—
865C23—181no—
866C23—181no—
867C23—181no—
868C23—181no—
869C23—181no—
870C23—181no—
871C23—181no—
872C23—181no—
873C23—181no—
874C23—181no—
875C23—181no—
876C23C22×D3211yescharacteristic
877D4—188no—
878D4—364no—
879D4—364no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—32no—
889C2×C4—32no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—92no—
910C2×C4—92no—
911C2×C4—124no—
912C2×C4—188no—
913C2×C4—181no—
914C2×C4—181no—
915C2×C4—181no—
916C2×C4—181no—
917C2×C4—364no—
918C2×C4—364no—
919C2×C4#381112yes—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—64no—
928C2×C3C2×#89411yescharacteristic
929C2×C3#554011yescharacteristic
930C2×C3#555211yescharacteristic
931C2×C3#559011yescharacteristic
932C2×C3#560911yescharacteristic
933C2×C3#562711yescharacteristic
934C2×C3#562711yescharacteristic
935C2×C3#563311yescharacteristic
936C2×C3#564511yescharacteristic
937C2×C3D3×#12311yescharacteristic
938C2×C3#565511yescharacteristic
939C2×C3#569211yescharacteristic
940C2×C3#569511yescharacteristic
941C2×C3#572611yescharacteristic
942D3—24no—
943D3—124no—
944D3—122no—
945D3—122no—
946D3—242no—
947D3—241no—
948D3—241no—
949C22—34no—
950C22—62no—
951C22—62no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—62no—
956C22—182no—
957C22—182no—
958C22—182no—
959C22—361no—
960C22—361no—
961C22—361no—
962C22—361no—
963C22—361no—
964C22—361no—
965C22—361no—
966C22—361no—
967C22—361no—
968C22—361no—
969C22—361no—
970C22#6429711yescharacteristic
971C22D3×#23511yescharacteristic
972C22D32×D411yescharacteristic
973C22#6431411yescharacteristic
974C22D3×#23911yescharacteristic
975C22D3×#23911yescharacteristic
976C22C2×#381111yescharacteristic
977C4—22no—
978C4—41no—
979C4—41no—
980C4—62no—
981C4—62no—
982C4—121no—
983C4—121no—
984C4—121no—
985C4—121no—
986C4—121no—
987C4—182no—
988C4—182no—
989C3—21no—
990C3#7441811yescharacteristic, complemented
991C3#7795111yescharacteristic, complemented
992C2—64no—
993C2—362no—
994C2—721no—
995C2#1059437211yescharacteristic
996C2#1059441511yescharacteristic
997C2#1059445411yescharacteristic
998C2D3×#89411yescharacteristic
999C2#1059491611yescharacteristic
1000C2#1059529211yescharacteristic
1001C2#1059543011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63909C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64103C2semidirect
3. C2×#63881C2semidirect
4. C2×D3×Dic3⋊C4C2semidirect
5. C3×#4989C2semidirect
6. C3×#4982C2semidirect
7. #10591364C2semidirect
8. #10591364C2semidirect
9. #10591364C2semidirect
10. #10591321C2semidirect
11. #10591290C2semidirect
12. #10591263C2semidirect
13. #10591259C2semidirect
14. #10591216C2semidirect
15. #10591203C2semidirect
72. #4989D3semidirect
73. #4982D3semidirect
128. #3750D4semidirect
468. C2×C3×D3#123semidirect
824. C2×D3#894semidirect
854. C32#2443semidirect
990. C3#74418semidirect
991. C3#77951semidirect

Maximal subgroups

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

subgroupindex
C2×#641032
C2×#639092
C2×#638812
C2×D3×Dic3⋊C42
C3×#49892
C3×#49822
#105913642
#105913212
#105912902
#105912632
#105912592
#105912162
#105912032
#779513
#744183