Finite Group Databasebeta

← #11812995

Subgroups — #11812995

Order 1152.

1305 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2C2×#63886C211yesmaximal, characteristic
3#10592691C211yesmaximal, characteristic, complemented
4C3×#4985C211yesmaximal, characteristic, complemented
5#10591382C211yesmaximal, characteristic, complemented
6#10591382C211yesmaximal, characteristic, complemented
7#10591376C211yesmaximal, characteristic, complemented
8#10591373C211yesmaximal, characteristic, complemented
9#10591364C211yesmaximal, characteristic, complemented
10D3×C3⋊#95C211yesmaximal, characteristic, complemented
11#10591296C211yesmaximal, characteristic, complemented
12#10591294C211yesmaximal, characteristic, complemented
13#10591292C211yesmaximal, characteristic, complemented
14#10591194C211yesmaximal, characteristic, complemented
15#10591193C211yesmaximal, characteristic, complemented
16#82357—31nomaximal
17#78343—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×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×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×#893—24no—
34C2×#3724C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42#63886—24no—
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×C3×C4×D4—31no—
56C2×#939—31no—
57C2×#895—31no—
58C2×#893D311yescharacteristic, complemented
59C3×#400—31no—
60#5220—31no—
61#5213—31no—
62#5213—31no—
63#5211—31no—
64C2×C3⋊#95—31no—
65#4992—31no—
66#4992—31no—
67#4992—61no—
68#4985D311yescharacteristic, complemented
69#4978—31no—
70#4959—31no—
71#4958—31no—
72#4952—31no—
73#4946—31no—
74#4940—31no—
75#4933—31no—
76#4674—31no—
77#4672—31no—
78#4670—31no—
79#4668—31no—
80#4665—31no—
81#4665—31no—
82#4665—31no—
83#4665—31no—
84#4664—31no—
85D3×#95—31no—
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C2×C3×D12—22no—
102C2×C3×D12—22no—
103C2×C3×D12D414yes—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—41no—
109C2×C3×C4×D3—41no—
110C2×#626—22no—
111C2×#626—22no—
112C2×#626—22no—
113C2×#626—22no—
114C2×#626—22no—
115C2×#626—41no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3—41no—
121C2×D3×Dic3—41no—
122C32×C4⋊C4—22no—
123#3752—22no—
124#3752—41no—
125#3752—41no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×Dic3⋊C4—22no—
129C3×C4×Dic3—22no—
130#3724—22no—
131Dic3⋊Dic3—41no—
132#3722—22no—
133#3722—41no—
134(C2×D3)⋊Dic3—22no—
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3—41no—
137(C2×D3)⋊Dic3—41no—
138#2444—91noSylow
139C22×C3×D4—31no—
140C23×C3×C4—31no—
141C23×C3×C4—31no—
142C22×#67—31no—
143C22×#67—31no—
144C23×Dic3—31no—
145C23×Dic3—31no—
146C22×D12—31no—
147C22×D12—31no—
148C22×D12C2×D311yescharacteristic
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3C2×D311yescharacteristic
152C22×C4×D3C2×D311yescharacteristic
153C3×C4×D4—64no—
154C2×C3×C4⋊C4—21no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4C2×D311yescharacteristic
157C2×C3×C4⋊C4C2×D311yescharacteristic
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C42—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—31no—
165#939—64no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
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—61no—
181C2×(C2×D3)⋊C4—61no—
182C2×(C2×D3)⋊C4—61no—
183C2×(C2×D3)⋊C4C2×D311yescharacteristic
184C2×(C2×D3)⋊C4C2×D311yescharacteristic
185C2×C4⋊Dic3—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4C2×D311yescharacteristic
190C2×C4×Dic3C2×D311yescharacteristic
191#895—64no—
192#893—24no—
193C3×#95—31no—
194C3×#95—31no—
195C3×#95—31no—
196C3×#95—31no—
197C3×#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—61no—
213C3⋊#95—61no—
214C3⋊#95—61no—
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C23×C32C2411yescharacteristic
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—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D412yes—
239C22×C3×D3C2×D412yes—
240C22×C3×D3#4112yes—
241C22×C3×D3#4112yes—
242C2×C32×C4—21no—
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×C4C2×D412yes—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
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×Dic3—21no—
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#4112yes—
277C2×C3×Dic3#4112yes—
278C3×D12—28no—
279C3×C4×D3—44no—
280C3×C4×D3—44no—
281#626—44no—
282#626—44no—
283D3×Dic3—44no—
284D3×Dic3—44no—
285C2×#121—91no—
286C2×C4×D4—31no—
287#400—31no—
288#397—91no—
289#397—91no—
290#394—91no—
291#388—91no—
292#387—91no—
293#386—91no—
294#386—91no—
295#386—91no—
296#386—91no—
297#385—91no—
298#381—91no—
299C2×#95—91no—
300C24×C3—31no—
301C24×C3—31no—
302C23×D3—31no—
303C23×D3—31no—
304C23×D3—61no—
305C23×D3C22×D311yescharacteristic
306C23×D3C22×D311yescharacteristic
307C2×C3×D4—34no—
308C2×C3×D4—62no—
309C2×C3×D4—62no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—62no—
320C22×C3×C4—62no—
321C22×C3×C4—62no—
322C22×C3×C4—62no—
323C22×C3×C4—121no—
324C22×C3×C4—121no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C2×#67—62no—
332C2×#67—62no—
333C2×#67—62no—
334C2×#67—62no—
335C2×#67—62no—
336C2×#67—121no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—62no—
347C22×Dic3—62no—
348C22×Dic3—62no—
349C22×Dic3—121no—
350C22×Dic3—121no—
351C22×Dic3—121no—
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C2×D12—22no—
359C2×D12—22no—
360C2×D12—62no—
361C2×D12—62no—
362C2×D12—62no—
363C2×D12—62no—
364C2×D12—62no—
365C2×D12—121no—
366C2×D12#6714yes—
367C2×C4×D3—22no—
368C2×C4×D3—22no—
369C2×C4×D3—22no—
370C2×C4×D3—22no—
371C2×C4×D3—41no—
372C2×C4×D3—41no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—42no—
382C3×C4⋊C4—62no—
383C3×C22⋊C4—62no—
384C3×C22⋊C4—62no—
385C3×C42—62no—
386#217—62no—
387#217—62no—
388#217—121no—
389#217—121no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—22no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—122no—
399(C2×D3)⋊C4—121no—
400(C2×D3)⋊C4—121no—
401(C2×D3)⋊C4—121no—
402(C2×D3)⋊C4—121no—
403(C2×D3)⋊C4—121no—
404(C2×D3)⋊C4—121no—
405(C2×D3)⋊C4—121no—
406(C2×D3)⋊C4—121no—
407(C2×D3)⋊C4—122no—
408(C2×D3)⋊C4—122no—
409C4⋊Dic3—121no—
410Dic3⋊C4—22no—
411Dic3⋊C4—62no—
412Dic3⋊C4—62no—
413Dic3⋊C4—121no—
414C4×Dic3—22no—
415C22×C32C22×D411yescharacteristic
416C22×C32C2×#4111yescharacteristic
417C22×C32C2×#4111yescharacteristic
418C22×C32C2×#4111yescharacteristic
419C22×C32C2×#4111yescharacteristic
420C22×C32H(5,𝔽2)11yescharacteristic
421C22×C32H(5,𝔽2)11yescharacteristic
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3#12314yes—
443C32×C4—22no—
444C32×C4—41no—
445C32×C4—41no—
446C3⋊Dic3—41no—
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C22×D4—31no—
456C22×D4—91no—
457C22×D4—91no—
458C23×C4—31no—
459C23×C4—31no—
460C23×C4—91no—
461C23×C4—91no—
462#121—184no—
463C4×D4—64no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—91no—
466C2×C4⋊C4—91no—
467C2×C4⋊C4D3211yescharacteristic
468C2×C22⋊C4—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—91no—
471C2×C22⋊C4—91no—
472C2×C22⋊C4—91no—
473C2×C22⋊C4—91no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4—91no—
477C2×C22⋊C4—91no—
478C2×C22⋊C4—91no—
479C2×C42—31no—
480#95—31no—
481#95—31no—
482#95—31no—
483#95—31no—
484#95—31no—
485#95—91no—
486#95—91no—
487#95—91no—
488#95—91no—
489#95—91no—
490#95—91no—
491#95—91no—
492C23×C3—21no—
493C23×C3—32no—
494C23×C3—32no—
495C23×C3—32no—
496C23×C3—32no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3C23×D311yescharacteristic
508C23×C3C23×D311yescharacteristic
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—62no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—121no—
535C22×D3—121no—
536C22×D3—121no—
537C22×D3—121no—
538C22×D3—121no—
539C22×D3—121no—
540C22×D3#23512yes—
541C22×D3#23512yes—
542C22×D3C2×#6712yes—
543C22×D3C2×#6712yes—
544C3×D4—68no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—22no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—124no—
589C2×C3×C4—124no—
590C2×C3×C4D3×D412yes—
591C2×C3×C4C2×#6712yes—
592#67—124no—
593#67—124no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—121no—
629C2×Dic3—121no—
630C2×Dic3—121no—
631C2×Dic3—121no—
632C2×Dic3—121no—
633C2×Dic3—121no—
634C2×Dic3—121no—
635C2×Dic3—121no—
636C2×Dic3—121no—
637C2×Dic3—124no—
638C2×Dic3—124no—
639C2×Dic3#23712yes—
640C2×Dic3#23912yes—
641D12—28no—
642D12—124no—
643D12—124no—
644C4×D3—44no—
645C4×D3—44no—
646C4×D3—124no—
647C4×D3—124no—
648C2×C32C2×#12311yescharacteristic
649C2×C32#52911yescharacteristic
650C2×C32#53811yescharacteristic
651C2×C32#54611yescharacteristic
652C2×C32#54611yescharacteristic
653C2×C32#55311yescharacteristic
654C2×C32#55311yescharacteristic
655C3⋊D3—81no—
656C3×D3—24no—
657C3×D3—42no—
658C24—31no—
659C24—31no—
660C24—91no—
661C2×D4—34no—
662C2×D4—62no—
663C2×D4—62no—
664C2×D4—182no—
665C2×D4—182no—
666C2×D4—182no—
667C2×D4—182no—
668C2×D4—182no—
669C2×D4—361no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—121no—
684C22×C4—121no—
685C22×C4—182no—
686C22×C4—182no—
687C22×C4—182no—
688C22×C4—361no—
689C22×C4—361no—
690C22×C4—361no—
691C22×C4C2×D3211yescharacteristic
692C22×C4C2×D3211yescharacteristic
693C22×C4C2×D3211yescharacteristic
694C4⋊C4—22no—
695C4⋊C4—62no—
696C4⋊C4—182no—
697C4⋊C4—361no—
698C22⋊C4—62no—
699C22⋊C4—62no—
700C22⋊C4—182no—
701C22⋊C4—182no—
702C22⋊C4—182no—
703C22⋊C4—182no—
704C22⋊C4—361no—
705C22⋊C4—361no—
706C22⋊C4—361no—
707C22⋊C4—361no—
708C22⋊C4—361no—
709C42—62no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—34no—
718C22×C3—62no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3C2×#23511yescharacteristic
732C22×C3C2×#23511yescharacteristic
733C22×C3C2×D3×D411yescharacteristic
734C22×C3C2×#23711yescharacteristic
735C22×C3#100411yescharacteristic
736C22×C3C2×#23911yescharacteristic
737C22×C3D3×#4111yescharacteristic
738C22×C3D3×#4111yescharacteristic
739C22×C3D3×#4111yescharacteristic
740C22×C3D3×#4111yescharacteristic
741C22×C3#100911yescharacteristic
742C22×C3#100911yescharacteristic
743C22×C3#100911yescharacteristic
744C22×C3C22×#6711yescharacteristic
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—122no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3#92914yes—
780C3×C4—22no—
781C3×C4—22no—
782C3×C4—42no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—62no—
788C3×C4—62no—
789C3×C4—81no—
790C3×C4—81no—
791C3×C4—121no—
792C3×C4—121no—
793C3×C4—121no—
794C3×C4—121no—
795Dic3—22no—
796Dic3—22no—
797Dic3—41no—
798Dic3—41no—
799Dic3—41no—
800Dic3—41no—
801Dic3—121no—
802Dic3—121no—
803Dic3—121no—
804Dic3—121no—
805Dic3—121no—
806Dic3—121no—
807Dic3—241no—
808Dic3—241no—
809Dic3—241no—
810C32#244411yescharacteristic, complemented, Sylow
811C23—32no—
812C23—32no—
813C23—32no—
814C23—32no—
815C23—61no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—61no—
823C23—61no—
824C23—61no—
825C23—181no—
826C23—181no—
827C23—181no—
828C23—181no—
829C23—181no—
830C23—181no—
831C23—181no—
832C23C22×D3211yescharacteristic
833D4—68no—
834D4—364no—
835D4—364no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—32no—
845C2×C4—32no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—124no—
863C2×C4—124no—
864C2×C4—181no—
865C2×C4—181no—
866C2×C4—181no—
867C2×C4—181no—
868C2×C4—181no—
869C2×C4—181no—
870C2×C4—181no—
871C2×C4—181no—
872C2×C4—181no—
873C2×C4—364no—
874C2×C4—364no—
875C2×C4D3×#6712yes—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—64no—
884C2×C3—122no—
885C2×C3#553811yescharacteristic
886C2×C3#554011yescharacteristic
887C2×C3#556011yescharacteristic
888C2×C3#556511yescharacteristic
889C2×C3#563011yescharacteristic
890C2×C3D3×#12311yescharacteristic
891C2×C3#567611yescharacteristic
892C2×C3#569111yescharacteristic
893C2×C3#569511yescharacteristic
894C2×C3#570411yescharacteristic
895C2×C3#570911yescharacteristic
896C2×C3C2×#92911yescharacteristic
897C2×C3#580611yescharacteristic
898C2×C3#582911yescharacteristic
899D3—24no—
900D3—42no—
901D3—242no—
902D3—241no—
903D3—241no—
904C22—34no—
905C22—62no—
906C22—62no—
907C22—62no—
908C22—62no—
909C22—62no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22—121no—
918C22—361no—
919C22—361no—
920C22—361no—
921C22—361no—
922C22—361no—
923C22—361no—
924C22—361no—
925C22D3×#23511yescharacteristic
926C22D3×#23511yescharacteristic
927C22D3×#23711yescharacteristic
928C22#6431411yescharacteristic
929C22D3×#23911yescharacteristic
930C22#6432011yescharacteristic
931C22C2×D3×#6711yescharacteristic
932C4—22no—
933C4—41no—
934C4—41no—
935C4—62no—
936C4—62no—
937C4—121no—
938C4—121no—
939C4—121no—
940C4—121no—
941C4—361no—
942C4—361no—
943C4—361no—
944C3—21no—
945C3#7834311yescharacteristic, complemented
946C3#8235711yescharacteristic, complemented
947C2—64no—
948C2—122no—
949C2—721no—
950C2#1059440311yescharacteristic
951C2#1059441411yescharacteristic
952C2#1059441511yescharacteristic
953C2#1059463811yescharacteristic
954C2D3×#92911yescharacteristic
955C2#1059522911yescharacteristic
956C2#1059542711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63886C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2444
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×C3×#893C2semidirect
3. #10592691C2semidirect
4. C3×#4985C2semidirect
5. #10591382C2semidirect
6. #10591382C2semidirect
7. #10591376C2semidirect
8. #10591373C2semidirect
9. #10591364C2semidirect
10. D3×C3⋊#95C2semidirect
11. #10591296C2semidirect
12. #10591294C2semidirect
13. #10591292C2semidirect
14. #10591194C2semidirect
15. #10591193C2semidirect
58. C2×#893D3semidirect
68. #4985D3semidirect
810. C32#2444semidirect
945. C3#78343semidirect
946. C3#82357semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#638862
#105926912
C3×#49852
#105913822
#105913762
#105913732
#105913642
D3×C3⋊#952
#105912962
#105912942
#105912922
#105911942
#105911932
#823573
#783433