Finite Group Databasebeta

← #11808416

Subgroups — #11808416

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×#67C211yesmaximal, characteristic, complemented
2C2×Dic3×#67C211yesmaximal, characteristic, complemented
3C2×Dic3×D12C211yesmaximal, characteristic, complemented
4C2×#63877C211yesmaximal, characteristic, complemented
5#10592647C211yesmaximal, characteristic, complemented
6C3×#4960C211yesmaximal, characteristic
7C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
8#10591708C211yesmaximal, characteristic, complemented
9#10591708C211yesmaximal, characteristic, complemented
10Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#10591351C211yesmaximal, characteristic, complemented
12#10591309C211yesmaximal, characteristic, complemented
13#10591302C211yesmaximal, characteristic, complemented
14#10591297C211yesmaximal, characteristic, complemented
15#10591243C211yesmaximal, characteristic, complemented
16#76666—31nomaximal
17#73581—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35Dic3×#67—24no—
36Dic3×#67—24no—
37C2×#3724C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49Dic3×D12—24no—
50#63877—24no—
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×D4×Dic3—31no—
58C2×D4×Dic3—31no—
59C2×D4×Dic3—31no—
60C2×C4×#67—31no—
61C2×C4×#67—31no—
62C2×#877—31no—
63C2×C4×D12—31no—
64C2×#872—31no—
65C3×#392—31no—
66C3×C4×C22⋊C4—31no—
67#5222—31no—
68#5222—31no—
69#5222—31no—
70#4960D311yescharacteristic
71#4959—31no—
72#4959—31no—
73#4953—31no—
74#4948—31no—
75#4948—31no—
76#4948—31no—
77#4948—61no—
78Dic3×C22⋊C4—31no—
79Dic3×C22⋊C4D311yescharacteristic, complemented
80C4×(C2×D3)⋊C4—31no—
81C4×Dic3⋊C4—31no—
82#4676—31no—
83#4675—31no—
84#4672—31no—
85#4661—31no—
86#4657—31no—
87#4649—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—22no—
102C2×C3×#67—22no—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×D12—22no—
113C2×C3×D12—22no—
114C2×C3×D12—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3D414yescomplemented
121C32×C22⋊C4—22no—
122#3757—22no—
123#3757—22no—
124C4⋊(C3⋊Dic3)—22no—
125#3750—22no—
126#3750—22no—
127C3×#217—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×C4×Dic3—22no—
131C3×C4×Dic3—22no—
132#3724—22no—
133#3724—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—22no—
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142Dic32—22no—
143Dic32D414yescomplemented
144#2392—91noSylow
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C23×C3×C4—31no—
149C22×#67C2×D311yescharacteristic
150C22×#67C2×D311yescharacteristic
151C23×Dic3—31no—
152C23×Dic3—31no—
153C23×Dic3C2×D311yescharacteristic
154C22×D12C2×D311yescharacteristic
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4C2×D311yescharacteristic
162C2×C3×C22⋊C4C2×D311yescharacteristic
163C2×C3×C42—31no—
164C2×C3×C42—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—61no—
176C2×#217—61no—
177C2×#217C2×D311yescharacteristic
178D4×Dic3—64no—
179D4×Dic3—64no—
180D4×Dic3—64no—
181C4×#67—64no—
182C4×#67—64no—
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)⋊C4C2×D311yescharacteristic
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—61no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—61no—
207C2×Dic3⋊C4—61no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3C2×D311yescharacteristic
213C2×C4×Dic3C2×D311yescharacteristic
214#877—64no—
215C4×D12—64no—
216#872—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—61no—
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
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—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3C2×D412yes—
251C22×C3×D3#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4#4112yes—
258C2×C3⋊Dic3—21no—
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⋊Dic3—21no—
268C2×C3⋊Dic3C2×D412yes—
269C2×C3⋊Dic3C2×D412yes—
270C3×#67—28no—
271C3×#67—28no—
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—44no—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3#4112yes—
290C2×C3×Dic3#4112yes—
291C3×D12—28no—
292D3×Dic3—28no—
293D3×Dic3—44no—
294C2×C4×D4—91no—
295C2×C4×D4—91no—
296C2×C4×D4—91no—
297C2×#117—91no—
298#398—91no—
299#397—91no—
300#396—91no—
301#396—91no—
302#394—91no—
303#394—91no—
304#394—91no—
305#392—31no—
306C4×C4⋊C4—91no—
307C4×C22⋊C4—31no—
308C4×C22⋊C4—91no—
309C24×C3—21no—
310C24×C3—31no—
311C24×C3—31no—
312C24×C3C22×D311yescharacteristic
313C24×C3C22×D311yescharacteristic
314C23×D3C22×D311yescharacteristic
315C23×D3C22×D311yescharacteristic
316C2×C3×D4—62no—
317C2×C3×D4—62no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—62no—
322C2×C3×D4—62no—
323C2×C3×D4—62no—
324C2×C3×D4—62no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4—62no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C2×#67—22no—
341C2×#67—22no—
342C2×#67—22no—
343C2×#67—22no—
344C2×#67—22no—
345C2×#67—22no—
346C22×Dic3—22no—
347C22×Dic3—22no—
348C22×Dic3—22no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—34no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—62no—
363C22×Dic3—62no—
364C22×Dic3—62no—
365C22×Dic3—62no—
366C22×Dic3—62no—
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C2×D12—22no—
374C2×D12—22no—
375C2×D12—22no—
376C2×C4×D3—34no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C3×C22⋊C4—22no—
383C3×C22⋊C4—22no—
384C3×C22⋊C4—42no—
385C3×C22⋊C4—62no—
386C3×C22⋊C4—62no—
387C3×C22⋊C4—62no—
388C3×C42—62no—
389C3×C42—62no—
390#217—22no—
391#217—62no—
392#217—62no—
393#217—62no—
394#217—62no—
395#217—62no—
396#217—62no—
397#217—62no—
398#217—62no—
399#217—62no—
400#217—62no—
401#217—122no—
402#217—122no—
403(C2×D3)⋊C4—22no—
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—
411C4⋊Dic3—62no—
412C4⋊Dic3—62no—
413C4⋊Dic3—62no—
414C4⋊Dic3—62no—
415C4⋊Dic3—122no—
416Dic3⋊C4—62no—
417Dic3⋊C4—62no—
418Dic3⋊C4—62no—
419Dic3⋊C4—62no—
420Dic3⋊C4—62no—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—122no—
427Dic3⋊C4—122no—
428C4×Dic3—22no—
429C4×Dic3—22no—
430C4×Dic3—34no—
431C4×Dic3—34no—
432C4×Dic3—62no—
433C4×Dic3—62no—
434C22×C32—22no—
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32C22×D411yescharacteristic
442C22×C32C22×D411yescharacteristic
443C22×C32C2×#4111yescharacteristic
444C22×C32C2×#4111yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—22no—
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—
462C32×C4—22no—
463C32×C4—41no—
464C3⋊Dic3—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—41no—
467C3⋊Dic3—41no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3#12114yes—
474C22×D4—31no—
475C22×D4—31no—
476C22×D4—31no—
477C23×C4—31no—
478C23×C4—91no—
479C23×C4—91no—
480C4×D4—184no—
481C4×D4—184no—
482C4×D4—184no—
483#117—184no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
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⋊C4D3211yescharacteristic
503C2×C42—31no—
504C2×C42—31no—
505C2×C42—91no—
506C2×C42—91no—
507#95—31no—
508#95—31no—
509#95—31no—
510#95—91no—
511#95—91no—
512#95—91no—
513C23×C3—21no—
514C23×C3—21no—
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—22no—
527C23×C3—32no—
528C23×C3—32no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3#23512yes—
548C23×C3#23712yes—
549C23×C3C23×D311yescharacteristic
550C23×C3C23×D311yescharacteristic
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3D3×D412yes—
564C22×D3#23712yes—
565C3×D4—68no—
566C3×D4—68no—
567C3×D4—68no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—22no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—124no—
603C2×C3×C4#23512yes—
604C2×C3×C4#23712yes—
605#67—28no—
606#67—28no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—44no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—68no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
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—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3—121no—
656C2×Dic3—121no—
657C2×Dic3—121no—
658C2×Dic3—124no—
659C2×Dic3#23512yes—
660C2×Dic3D3×D412yes—
661C2×Dic3D3×D412yes—
662C2×Dic3D3×D412yes—
663C2×Dic3#23712yes—
664D12—28no—
665C4×D3—68no—
666C4×D3—124no—
667C2×C32—42no—
668C2×C32C2×#12111yescharacteristic
669C2×C32#52511yescharacteristic
670C2×C32#52511yescharacteristic
671C2×C32#52511yescharacteristic
672C2×C32#52911yescharacteristic
673C2×C32#52911yescharacteristic
674C2×C32#53211yescharacteristic
675C3×D3—42no—
676C3×D3—42no—
677C24—31no—
678C24—31no—
679C24C2×D3211yescharacteristic
680C2×D4—62no—
681C2×D4—62no—
682C2×D4—62no—
683C2×D4—62no—
684C2×D4—62no—
685C2×D4—62no—
686C2×D4—62no—
687C2×D4—62no—
688C2×D4—62no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—62no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—94no—
699C22×C4—91no—
700C22×C4—91no—
701C22×C4—91no—
702C22×C4—91no—
703C22×C4—182no—
704C22×C4—182no—
705C22×C4—182no—
706C22×C4—182no—
707C22×C4—182no—
708C22×C4C2×D3211yescharacteristic
709C22×C4C2×D3211yescharacteristic
710C4⋊C4—182no—
711C4⋊C4—182no—
712C4⋊C4—182no—
713C4⋊C4—182no—
714C4⋊C4—182no—
715C4⋊C4—182no—
716C4⋊C4—182no—
717C22⋊C4—22no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C22⋊C4—62no—
721C22⋊C4—182no—
722C22⋊C4—182no—
723C22⋊C4—182no—
724C22⋊C4—182no—
725C22⋊C4—182no—
726C22⋊C4—182no—
727C22⋊C4—182no—
728C22⋊C4—182no—
729C42—62no—
730C42—62no—
731C42—94no—
732C42—182no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—81no—
764C22×C3—81no—
765C22×C3—81no—
766C22×C3—81no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3C2×#23511yescharacteristic
776C22×C3C2×#23511yescharacteristic
777C22×C3C2×#23511yescharacteristic
778C22×C3C2×D3×D411yescharacteristic
779C22×C3C2×D3×D411yescharacteristic
780C22×C3C2×D3×D411yescharacteristic
781C22×C3C2×D3×D411yescharacteristic
782C22×C3C2×#23711yescharacteristic
783C22×C3C2×#23711yescharacteristic
784C22×C3C2×#23711yescharacteristic
785C22×C3C2×#23711yescharacteristic
786C22×C3D3×#4111yescharacteristic
787C22×C3D3×#4111yescharacteristic
788C22×C3D3×#4111yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—41no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C2×D3—41no—
802C2×D3—41no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—34no—
806C3×C4—42no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—81no—
812C3×C4—121no—
813C3×C4—121no—
814C3×C4—121no—
815Dic3—22no—
816Dic3—22no—
817Dic3—41no—
818Dic3—41no—
819Dic3—41no—
820Dic3—62no—
821Dic3—62no—
822Dic3—62no—
823Dic3—62no—
824Dic3—122no—
825Dic3—122no—
826Dic3—121no—
827Dic3—121no—
828Dic3—121no—
829Dic3—121no—
830Dic3—241no—
831Dic3—241no—
832Dic3#88414yes—
833C32#239211yescharacteristic, complemented, Sylow
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—32no—
841C23—32no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23#379512yes—
855C23C22×D3211yescharacteristic
856D4—68no—
857D4—68no—
858D4—68no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—32no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—92no—
883C2×C4—92no—
884C2×C4—124no—
885C2×C4—188no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4—181no—
896C2×C4—364no—
897C2×C4#380412yes—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—42no—
906C2×C3—42no—
907C2×C3—82no—
908C2×C3—122no—
909C2×C3—122no—
910C2×C3#547911yescharacteristic
911C2×C3C2×#88411yescharacteristic
912C2×C3#552811yescharacteristic
913C2×C3#554711yescharacteristic
914C2×C3#554711yescharacteristic
915C2×C3#554711yescharacteristic
916C2×C3#554811yescharacteristic
917C2×C3#558611yescharacteristic
918C2×C3#558611yescharacteristic
919C2×C3#558611yescharacteristic
920C2×C3#560011yescharacteristic
921C2×C3#560011yescharacteristic
922C2×C3D3×#12111yescharacteristic
923C2×C3#571611yescharacteristic
924D3—42no—
925D3—42no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—62no—
934C22—62no—
935C22—62no—
936C22—62no—
937C22—62no—
938C22—62no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22—121no—
946C22—121no—
947C22C2×#379511yescharacteristic
948C22D3×#23511yescharacteristic
949C22D32×D411yescharacteristic
950C22D32×D411yescharacteristic
951C22D3×#23711yescharacteristic
952C22D3×#23711yescharacteristic
953C22C2×#380411yescharacteristic
954C4—22no—
955C4—34no—
956C4—41no—
957C4—62no—
958C4—62no—
959C4—121no—
960C4—121no—
961C4—121no—
962C4—182no—
963C4—182no—
964C4—361no—
965C4—361no—
966C3—21no—
967C3#7358111yescharacteristic, complemented
968C3#7666611yescharacteristic, complemented
969C2—42no—
970C2—122no—
971C2—122no—
972C2#1059405411yescharacteristic
973C2#1059405411yescharacteristic
974C2#1059408611yescharacteristic
975C2D3×#88411yescharacteristic
976C2#1059494911yescharacteristic
977C2#1059512911yescharacteristic
978C2#1059513911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC3×#4960C2
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×Dic3×#67C2semidirect
2. C2×Dic3×#67C2semidirect
3. C2×Dic3×D12C2semidirect
4. C2×#63877C2semidirect
5. #10592647C2semidirect
7. C3×Dic3×C22⋊C4C2semidirect
8. #10591708C2semidirect
9. #10591708C2semidirect
10. Dic3×(C2×D3)⋊C4C2semidirect
11. #10591351C2semidirect
12. #10591309C2semidirect
13. #10591302C2semidirect
14. #10591297C2semidirect
15. #10591243C2semidirect
79. Dic3×C22⋊C4D3semidirect
120. C2×D3×Dic3D4semidirect
143. Dic32D4semidirect
833. C32#2392semidirect
967. C3#73581semidirect
968. C3#76666semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×#672
C2×Dic3×D122
C2×#638772
#105926472
C3×#49602
C3×Dic3×C22⋊C42
#105917082
Dic3×(C2×D3)⋊C42
#105913512
#105913092
#105913022
#105912972
#105912432
#766663
#735813