Finite Group Databasebeta

← #11808420

Subgroups — #11808420

Order 1152.

1511 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
2C2×#63952C211yesmaximal, characteristic, complemented
3C2×#63904C211yesmaximal, characteristic, complemented
4C2×#63841C211yesmaximal, characteristic, complemented
5#10592660C211yesmaximal, characteristic, complemented
6C3×#4948C211yesmaximal, characteristic, complemented
7#10591724C211yesmaximal, characteristic
8#10591709C211yesmaximal, characteristic, complemented
9Dic3×#217C211yesmaximal, characteristic, complemented
10#10591311C211yesmaximal, characteristic, complemented
11#10591299C211yesmaximal, characteristic, complemented
12#10591291C211yesmaximal, characteristic, complemented
13Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591215C211yesmaximal, characteristic, complemented
16#82345—31nomaximal
17#77281—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C3×#67⋊C4—24no—
38C2×#3724C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48#63952—24no—
49#63904—24no—
50#63841—24no—
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×C4×D4—31no—
58C2×C4×#67—31no—
59C2×C4×#67—31no—
60C2×#926—31no—
61C2×#893—31no—
62C2×#892—31no—
63C2×#67⋊C4—31no—
64C2×#67⋊C4D311yescharacteristic, complemented
65C3×#396—31no—
66#5223—31no—
67#5222—31no—
68C4×#217—31no—
69#4994—31no—
70#4994—31no—
71#4991—31no—
72#4982—31no—
73#4982—31no—
74Dic3×C4⋊C4—31no—
75#4961—31no—
76#4961—31no—
77#4961—31no—
78#4961—61no—
79#4960—31no—
80#4959—31no—
81#4952—31no—
82#4948D311yescharacteristic, complemented
83Dic3×C22⋊C4—31no—
84C4×(C2×D3)⋊C4—31no—
85C4×Dic3⋊C4—31no—
86#4675—31no—
87#4666—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—22no—
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—22no—
102C22×C3×Dic3—22no—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3D414yescomplemented
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#624—22no—
119C2×#624—22no—
120C2×#624—22no—
121C32×C22⋊C4—22no—
122#3757—22no—
123#3752—22no—
124#3752—22no—
125C4⋊(C3⋊Dic3)—22no—
126C3×#217—22no—
127C3×#217—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×C4⋊Dic3—22no—
130C3×Dic3⋊C4—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×C4×Dic3—22no—
134#3724—22no—
135Dic3⋊Dic3—22no—
136#3722—22no—
137#3722—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141Dic32—22no—
142Dic32—22no—
143Dic32D414yescomplemented
144#2392—91noSylow
145C22×C3×D4—31no—
146C23×C3×C4—31no—
147C23×C3×C4—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—61no—
152C22×#67C2×D311yescharacteristic
153C23×Dic3C2×D311yescharacteristic
154C22×D12—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3C2×D311yescharacteristic
158C3×C4×D4—64no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C22⋊C4—21no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4C2×D311yescharacteristic
168C2×C3×C22⋊C4C2×D311yescharacteristic
169C2×C3×C42—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—61no—
176C2×#217C2×D311yescharacteristic
177C2×#217C2×D311yescharacteristic
178C4×#67—64no—
179C4×#67—64no—
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—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—61no—
192C2×(C2×D3)⋊C4—61no—
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194#926—64no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—61no—
199C2×C4⋊Dic3C2×D311yescharacteristic
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×Dic3⋊C4C2×D311yescharacteristic
205C2×Dic3⋊C4C2×D311yescharacteristic
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3C2×D311yescharacteristic
213#893—64no—
214#892—64no—
215#67⋊C4—24no—
216#67⋊C4—64no—
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⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—61no—
229C3⋊#95C2×D311yescharacteristic
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32#4112yes—
237C23×C32C2411yescharacteristic
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#4112yes—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3C2×D412yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D412yes—
258#638—28no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3C2×D412yes—
268C3×#67—28no—
269C2×C3×Dic3—21no—
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—44no—
285C2×C3×Dic3C2×D412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3#4112yes—
289C2×C3×Dic3#4112yes—
290C2×C3×Dic3#4112yes—
291C3×C4×D3—28no—
292#626—28no—
293#624—44no—
294C2×C4×D4—31no—
295C2×C4×D4—91no—
296C2×C4×D4—91no—
297C2×#117—91no—
298#398—91no—
299#397—91no—
300#396—31no—
301#396—91no—
302#394—91no—
303#394—91no—
304#394—91no—
305#392—91no—
306C4×C4⋊C4—91no—
307C4×C22⋊C4—91no—
308C4×C22⋊C4—91no—
309C24×C3—21no—
310C24×C3—31no—
311C24×C3C22×D311yescharacteristic
312C24×C3C22×D311yescharacteristic
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—61no—
316C23×D3C22×D311yescharacteristic
317C2×C3×D4—62no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
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—34no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—22no—
340C2×#67—22no—
341C2×#67—22no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—122no—
352C2×#67—122no—
353C2×#67—122no—
354C22×Dic3—22no—
355C22×Dic3—22no—
356C22×Dic3—22no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C2×D12—62no—
374C2×D12—62no—
375C2×D12—62no—
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3#6714yescomplemented
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C4⋊C4—62no—
388C3×C4⋊C4—62no—
389C3×C22⋊C4—22no—
390C3×C22⋊C4—22no—
391C3×C22⋊C4—42no—
392C3×C22⋊C4—62no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—62no—
395C3×C42—62no—
396#217—22no—
397#217—22no—
398#217—62no—
399#217—62no—
400#217—62no—
401#217—62no—
402#217—62no—
403#217—122no—
404(C2×D3)⋊C4—22no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
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—122no—
417(C2×D3)⋊C4—122no—
418C4⋊Dic3—22no—
419C4⋊Dic3—62no—
420C4⋊Dic3—62no—
421C4⋊Dic3—62no—
422C4⋊Dic3—122no—
423Dic3⋊C4—22no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429C4×Dic3—22no—
430C4×Dic3—34no—
431C4×Dic3—34no—
432C4×Dic3—62no—
433C4×Dic3—62no—
434C4×Dic3—62no—
435C4×Dic3—62no—
436C22×C32—22no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32C22×D411yescharacteristic
444C22×C32C22×D411yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C22×C32C2×#4111yescharacteristic
449C22×C32C2×#4111yescharacteristic
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C32×C4—22no—
465C32×C4—41no—
466C3⋊Dic3—22no—
467C3⋊Dic3—41no—
468C3⋊Dic3—41no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—41no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3#12114yes—
476C22×D4—31no—
477C22×D4—91no—
478C22×D4—91no—
479C23×C4—31no—
480C23×C4—31no—
481C23×C4—91no—
482C4×D4—64no—
483C4×D4—184no—
484C4×D4—184no—
485#117—184no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4D3211yescharacteristic
505C2×C42—31no—
506C2×C42—91no—
507C2×C42—91no—
508C2×C42—91no—
509#95—31no—
510#95—91no—
511#95—91no—
512#95—91no—
513#95—91no—
514#95—91no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—22no—
529C23×C3—32no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3#23512yes—
543C23×C3#23912yes—
544C23×C3C23×D311yescharacteristic
545C23×C3C23×D311yescharacteristic
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—32no—
553C22×D3—32no—
554C22×D3—62no—
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—61no—
567C22×D3—121no—
568C22×D3—121no—
569C22×D3—121no—
570C22×D3—121no—
571C22×D3—121no—
572C22×D3—121no—
573C22×D3C2×#6712yes—
574C3×D4—68no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—22no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—32no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—68no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
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—124no—
614C2×C3×C4D3×D412yes—
615C2×C3×C4C2×#6712yes—
616#67—28no—
617#67—68no—
618#67—68no—
619#67—68no—
620#67—128no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—32no—
637C2×Dic3—32no—
638C2×Dic3—44no—
639C2×Dic3—62no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—121no—
657C2×Dic3—121no—
658C2×Dic3—121no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—121no—
662C2×Dic3—121no—
663C2×Dic3—121no—
664C2×Dic3#23512yes—
665C2×Dic3D3×D412yes—
666C2×Dic3D3×D412yes—
667C2×Dic3#23712yes—
668C2×Dic3#23712yes—
669C2×Dic3C2×#6712yes—
670D12—68no—
671C4×D3—28no—
672C4×D3—124no—
673C4×D3—124no—
674C2×C32—42no—
675C2×C32C2×#12111yescharacteristic
676C2×C32#52511yescharacteristic
677C2×C32#52511yescharacteristic
678C2×C32#52511yescharacteristic
679C2×C32#52911yescharacteristic
680C2×C32#52911yescharacteristic
681C2×C32#53211yescharacteristic
682C3⋊D3—42no—
683C3×D3—42no—
684C24—31no—
685C24—91no—
686C24C2×D3211yescharacteristic
687C2×D4—62no—
688C2×D4—62no—
689C2×D4—62no—
690C2×D4—182no—
691C2×D4—182no—
692C2×D4—182no—
693C2×D4—182no—
694C2×D4—182no—
695C2×D4—182no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—34no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—62no—
705C22×C4—62no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—62no—
709C22×C4—91no—
710C22×C4—91no—
711C22×C4—91no—
712C22×C4—182no—
713C22×C4—182no—
714C22×C4—182no—
715C22×C4C2×D3211yescharacteristic
716C22×C4C2×D3211yescharacteristic
717C4⋊C4—62no—
718C4⋊C4—62no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—182no—
722C4⋊C4—182no—
723C4⋊C4—182no—
724C22⋊C4—22no—
725C22⋊C4—62no—
726C22⋊C4—62no—
727C22⋊C4—62no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—182no—
731C22⋊C4—182no—
732C22⋊C4—182no—
733C22⋊C4—182no—
734C22⋊C4—182no—
735C22⋊C4—182no—
736C42—62no—
737C42—94no—
738C42—182no—
739C42—182no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—62no—
767C22×C3—81no—
768C22×C3—81no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3C2×#23511yescharacteristic
776C22×C3C2×#23511yescharacteristic
777C22×C3C2×D3×D411yescharacteristic
778C22×C3C2×D3×D411yescharacteristic
779C22×C3C2×D3×D411yescharacteristic
780C22×C3C2×#23711yescharacteristic
781C22×C3C2×#23711yescharacteristic
782C22×C3C2×#23911yescharacteristic
783C22×C3D3×#4111yescharacteristic
784C22×C3D3×#4111yescharacteristic
785C22×C3D3×#4111yescharacteristic
786C22×C3D3×#4111yescharacteristic
787C22×C3D3×#4111yescharacteristic
788C22×C3C22×#6711yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—41no—
793C2×D3—41no—
794C2×D3—41no—
795C2×D3—41no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—122no—
803C2×D3—122no—
804C2×D3—122no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—121no—
813C2×D3—241no—
814C2×D3—241no—
815C2×D3—241no—
816C2×D3—241no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—34no—
820C3×C4—42no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—62no—
826C3×C4—81no—
827C3×C4—121no—
828C3×C4—121no—
829C3×C4—121no—
830Dic3—22no—
831Dic3—22no—
832Dic3—22no—
833Dic3—41no—
834Dic3—41no—
835Dic3—41no—
836Dic3—62no—
837Dic3—62no—
838Dic3—122no—
839Dic3—121no—
840Dic3—121no—
841Dic3—121no—
842Dic3—121no—
843Dic3—241no—
844Dic3—241no—
845Dic3#93914yes—
846C32#239211yescharacteristic, complemented, Sylow
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—32no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—92no—
861C23—181no—
862C23—181no—
863C23—181no—
864C23—181no—
865C23—181no—
866C23—181no—
867C23#379912yes—
868C23C22×D3211yescharacteristic
869D4—68no—
870D4—188no—
871D4—188no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—32no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—68no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
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—92no—
900C2×C4—124no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—364no—
910C2×C4D3×#6712yes—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—42no—
919C2×C3—42no—
920C2×C3—82no—
921C2×C3—122no—
922C2×C3#553811yescharacteristic
923C2×C3#554711yescharacteristic
924C2×C3#554811yescharacteristic
925C2×C3#555711yescharacteristic
926C2×C3#559611yescharacteristic
927C2×C3D3×#12111yescharacteristic
928C2×C3#560611yescharacteristic
929C2×C3#562411yescharacteristic
930C2×C3#562711yescharacteristic
931C2×C3#562711yescharacteristic
932C2×C3#570611yescharacteristic
933C2×C3#579111yescharacteristic
934C2×C3C2×#93911yescharacteristic
935C2×C3#582811yescharacteristic
936D3—42no—
937D3—122no—
938D3—122no—
939D3—242no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—121no—
951C22—121no—
952C22—121no—
953C22—121no—
954C22—182no—
955C22—182no—
956C22—182no—
957C22—361no—
958C22—361no—
959C22—361no—
960C22—361no—
961C22C2×#379911yescharacteristic
962C22D3×#23511yescharacteristic
963C22D32×D411yescharacteristic
964C22D3×#23711yescharacteristic
965C22D3×#23711yescharacteristic
966C22#6431211yescharacteristic
967C22C2×D3×#6711yescharacteristic
968C4—22no—
969C4—34no—
970C4—41no—
971C4—62no—
972C4—62no—
973C4—62no—
974C4—121no—
975C4—121no—
976C4—121no—
977C4—182no—
978C4—361no—
979C4—361no—
980C3—21no—
981C3#7728111yescharacteristic, complemented
982C3#8234511yescharacteristic, complemented
983C2—42no—
984C2—122no—
985C2—362no—
986C2#1059405811yescharacteristic
987C2#1059406611yescharacteristic
988C2#1059410711yescharacteristic
989C2#1059421611yescharacteristic
990C2#1059500511yescharacteristic
991C2D3×#93911yescharacteristic
992C2#1059530111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radical#10591724C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#67⋊C4C2semidirect
2. C2×#63952C2semidirect
3. C2×#63904C2semidirect
4. C2×#63841C2semidirect
5. #10592660C2semidirect
6. C3×#4948C2semidirect
8. #10591709C2semidirect
9. Dic3×#217C2semidirect
10. #10591311C2semidirect
11. #10591299C2semidirect
12. #10591291C2semidirect
13. Dic3×Dic3⋊C4C2semidirect
14. #10591233C2semidirect
15. #10591215C2semidirect
64. C2×#67⋊C4D3semidirect
82. #4948D3semidirect
114. C2×C3×C4×D3D4semidirect
143. Dic32D4semidirect
384. C2×C4×D3#67semidirect
846. C32#2392semidirect
981. C3#77281semidirect
982. C3#82345semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C2×#639522
C2×#639042
C2×#638412
#105926602
C3×#49482
#105917242
#105917092
Dic3×#2172
#105913112
#105912992
#105912912
Dic3×Dic3⋊C42
#105912332
#105912152
#823453
#772813