Finite Group Databasebeta

← #11813006

Subgroups — #11813006

Order 1152.

1337 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63916C211yesmaximal, characteristic
2C2×#63880C211yesmaximal, characteristic, complemented
3#10592688C211yesmaximal, characteristic, complemented
4C3×#4991C211yesmaximal, characteristic, complemented
5C3×#4980C211yesmaximal, characteristic, complemented
6#10591376C211yesmaximal, characteristic, complemented
7#10591370C211yesmaximal, characteristic, complemented
8#10591362C211yesmaximal, characteristic, complemented
9#10591343C211yesmaximal, characteristic, complemented
10#10591298C211yesmaximal, characteristic, complemented
11#10591296C211yesmaximal, characteristic, complemented
12#10591280C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#77118—31nomaximal
17#75320—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41#63916—24no—
42#63880—24no—
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#938—31no—
56C2×#895—31no—
57C2×#67⋊C4—31no—
58C2×C4×D12—31no—
59C3×#394—31no—
60C3×#387—31no—
61#5220—31no—
62#4991D311yescharacteristic, complemented
63#4989—31no—
64#4989—31no—
65#4989—61no—
66#4986—31no—
67#4980D311yescharacteristic, complemented
68#4956—31no—
69#4956—31no—
70#4956—31no—
71#4952—31no—
72#4952—31no—
73#4945—31no—
74#4943—31no—
75#4940—31no—
76#4675—31no—
77#4674—31no—
78#4665—31no—
79#4665—31no—
80#4665—31no—
81#4665—31no—
82#4664—31no—
83D3×#95—31no—
84D3×#95—31no—
85#4660—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
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3—41no—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×D12—22no—
105C2×C3×D12—22no—
106C2×C3×D12—41no—
107C2×#626—22no—
108C2×#626—22no—
109C2×#626—22no—
110C2×#626—22no—
111C2×#626—22no—
112C2×#626D414yes—
113C2×#624—22no—
114C2×#624—22no—
115C2×#624—22no—
116C2×#624—41no—
117C2×#624—41no—
118C2×#624—41no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—41no—
122C32×C4⋊C4—22no—
123#3752—22no—
124#3752—22no—
125#3750—41no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—41no—
128C3×(C2×D3)⋊C4—41no—
129C3×(C2×D3)⋊C4—41no—
130C3×C4⋊Dic3—22no—
131C3×C4×Dic3—22no—
132Dic3⋊Dic3—22no—
133(C2×D3)⋊Dic3—22no—
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—
140C22×#67—31no—
141C22×#67—31no—
142C23×Dic3—31no—
143C22×D12—31no—
144C22×D12—31no—
145C22×D12C2×D311yescharacteristic
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—61no—
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×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C42—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168#938—64no—
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—61no—
179C2×(C2×D3)⋊C4—61no—
180C2×(C2×D3)⋊C4C2×D311yescharacteristic
181C2×(C2×D3)⋊C4C2×D311yescharacteristic
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×(C2×D3)⋊C4C2×D311yescharacteristic
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3C2×D311yescharacteristic
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—61no—
190C2×C4×Dic3C2×D311yescharacteristic
191#895—64no—
192#67⋊C4—64no—
193C4×D12—64no—
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—31no—
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⋊D3C2×D412yes—
226C22×C3⋊D3#4112yes—
227C22×C3⋊D3#4112yes—
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×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D412yes—
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×C4#4112yes—
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—
260C4×C3⋊D3—44no—
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—21no—
277C2×C3×Dic3C2×D412yes—
278C2×C3×Dic3#4112yes—
279C3×D12—44no—
280#626—28no—
281#626—44no—
282#624—44no—
283#624—44no—
284D3×Dic3—44no—
285C2×#121—91no—
286C2×C4×D4—91no—
287#400—91no—
288#397—91no—
289#397—91no—
290#394—31no—
291#388—91no—
292#387—31no—
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—62no—
308C2×C3×D4—62no—
309C2×C3×D4—121no—
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×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—34no—
326C2×#67—62no—
327C2×#67—62no—
328C2×#67—62no—
329C2×#67—62no—
330C2×#67—62no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—62no—
341C22×Dic3—62no—
342C22×Dic3—121no—
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C2×D12—22no—
350C2×D12—22no—
351C2×D12—34no—
352C2×D12—41no—
353C2×D12—62no—
354C2×D12—62no—
355C2×D12—62no—
356C2×D12—62no—
357C2×D12—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—62no—
366C2×C4×D3—62no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×C4×D3—122no—
371C2×C4×D3—122no—
372C2×C4×D3—121no—
373C2×C4×D3—121no—
374C2×C4×D3—121no—
375C2×C4×D3—121no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C2×C4×D3—121no—
380C2×C4×D3—122no—
381C2×C4×D3—121no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—42no—
385C3×C4⋊C4—62no—
386C3×C22⋊C4—62no—
387C3×C22⋊C4—121no—
388C3×C22⋊C4—121no—
389C3×C22⋊C4—121no—
390C3×C42—62no—
391#217—62no—
392#217—62no—
393#217—62no—
394#217—121no—
395#217—121no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4—41no—
398(C2×D3)⋊C4—41no—
399(C2×D3)⋊C4—41no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—64no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—122no—
409(C2×D3)⋊C4—121no—
410(C2×D3)⋊C4—121no—
411C4⋊Dic3—22no—
412C4⋊Dic3—62no—
413Dic3⋊C4—62no—
414Dic3⋊C4—121no—
415Dic3⋊C4—121no—
416Dic3⋊C4—122no—
417C4×Dic3—22no—
418C22×C32C22×D411yescharacteristic
419C22×C32C2×#4111yescharacteristic
420C22×C32C2×#4111yescharacteristic
421C22×C32C2×#4111yescharacteristic
422C22×C32C2×#4111yescharacteristic
423C22×C32H(5,𝔽2)11yescharacteristic
424C22×C32H(5,𝔽2)11yescharacteristic
425C2×C3⋊D3—22no—
426C2×C3⋊D3—22no—
427C2×C3⋊D3—22no—
428C2×C3⋊D3—22no—
429C2×C3⋊D3—22no—
430C2×C3⋊D3—22no—
431C2×C3⋊D3#12314yes—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C32×C4—22no—
447C32×C4—41no—
448C32×C4—41no—
449C3⋊Dic3—41no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C22×D4—31no—
459C22×D4—91no—
460C22×D4—91no—
461C23×C4—91no—
462C23×C4—91no—
463C23×C4—91no—
464C23×C4—91no—
465#121—184no—
466C4×D4—184no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—91no—
469C2×C4⋊C4—91no—
470C2×C4⋊C4D3211yescharacteristic
471C2×C22⋊C4—31no—
472C2×C22⋊C4—31no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4—91no—
477C2×C22⋊C4—91no—
478C2×C22⋊C4—91no—
479C2×C22⋊C4—91no—
480C2×C22⋊C4—91no—
481C2×C22⋊C4—91no—
482C2×C42—31no—
483#95—31no—
484#95—31no—
485#95—31no—
486#95—31no—
487#95—31no—
488#95—91no—
489#95—91no—
490#95—91no—
491#95—91no—
492#95—91no—
493#95—91no—
494#95—91no—
495C23×C3—21no—
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×C3—61no—
508C23×C3—61no—
509C23×C3—61no—
510C23×C3C23×D311yescharacteristic
511C23×C3C23×D311yescharacteristic
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—32no—
526C22×D3—32no—
527C22×D3—32no—
528C22×D3—32no—
529C22×D3—32no—
530C22×D3—32no—
531C22×D3—62no—
532C22×D3—62no—
533C22×D3—62no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—121no—
543C22×D3—121no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3D3×D412yes—
547C3×D4—124no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—22no—
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—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—22no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
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—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4#23512yes—
592C2×C3×C4#23712yes—
593#67—68no—
594#67—124no—
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—21no—
611C2×Dic3—62no—
612C2×Dic3—62no—
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—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—121no—
632C2×Dic3—121no—
633C2×Dic3—121no—
634C2×Dic3—121no—
635C2×Dic3—121no—
636C2×Dic3—121no—
637C2×Dic3—121no—
638C2×Dic3—124no—
639C2×Dic3D3×D412yes—
640C2×Dic3#23912yes—
641D12—44no—
642D12—68no—
643D12—124no—
644C4×D3—124no—
645C4×D3—124no—
646C4×D3—124no—
647C4×D3—124no—
648C4×D3—124no—
649C4×D3—124no—
650C4×D3—128no—
651C4×D3—124no—
652C2×C32C2×#12311yescharacteristic
653C2×C32#52911yescharacteristic
654C2×C32#53811yescharacteristic
655C2×C32#54611yescharacteristic
656C2×C32#54611yescharacteristic
657C2×C32#55311yescharacteristic
658C2×C32#55311yescharacteristic
659C3⋊D3—24no—
660C3×D3—42no—
661C3×D3—81no—
662C24—31no—
663C24—31no—
664C24—91no—
665C2×D4—62no—
666C2×D4—62no—
667C2×D4—94no—
668C2×D4—121no—
669C2×D4—182no—
670C2×D4—182no—
671C2×D4—182no—
672C2×D4—182no—
673C2×D4—182no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—91no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—182no—
684C22×C4—182no—
685C22×C4—182no—
686C22×C4—182no—
687C22×C4—182no—
688C22×C4—182no—
689C22×C4—182no—
690C22×C4—361no—
691C22×C4—361no—
692C22×C4—361no—
693C22×C4—361no—
694C22×C4—361no—
695C22×C4C2×D3211yescharacteristic
696C22×C4C2×D3211yescharacteristic
697C22×C4C2×D3211yescharacteristic
698C4⋊C4—22no—
699C4⋊C4—62no—
700C4⋊C4—182no—
701C4⋊C4—361no—
702C22⋊C4—62no—
703C22⋊C4—121no—
704C22⋊C4—121no—
705C22⋊C4—121no—
706C22⋊C4—182no—
707C22⋊C4—182no—
708C22⋊C4—182no—
709C22⋊C4—182no—
710C22⋊C4—182no—
711C22⋊C4—361no—
712C22⋊C4—361no—
713C42—62no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3C2×#23511yescharacteristic
736C22×C3C2×D3×D411yescharacteristic
737C22×C3C2×D3×D411yescharacteristic
738C22×C3C2×#23711yescharacteristic
739C22×C3#100411yescharacteristic
740C22×C3#100411yescharacteristic
741C22×C3C2×#23911yescharacteristic
742C22×C3D3×#4111yescharacteristic
743C22×C3D3×#4111yescharacteristic
744C22×C3D3×#4111yescharacteristic
745C22×C3D3×#4111yescharacteristic
746C22×C3D3×#4111yescharacteristic
747C22×C3#100911yescharacteristic
748C22×C3#100911yescharacteristic
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—34no—
753C2×D3—34no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—64no—
766C2×D3—62no—
767C2×D3—62no—
768C2×D3—62no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—62no—
778C2×D3—122no—
779C2×D3—122no—
780C2×D3—122no—
781C2×D3—122no—
782C2×D3—122no—
783C2×D3—122no—
784C3×C4—22no—
785C3×C4—22no—
786C3×C4—42no—
787C3×C4—42no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—62no—
793C3×C4—62no—
794C3×C4—81no—
795C3×C4—121no—
796C3×C4—121no—
797C3×C4—121no—
798C3×C4—121no—
799Dic3—22no—
800Dic3—22no—
801Dic3—41no—
802Dic3—41no—
803Dic3—41no—
804Dic3—41no—
805Dic3—122no—
806Dic3—122no—
807Dic3—121no—
808Dic3—121no—
809Dic3—121no—
810Dic3—121no—
811Dic3—121no—
812Dic3—121no—
813Dic3—241no—
814C32#244411yescharacteristic, complemented, Sylow
815C23—32no—
816C23—61no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—61no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—92no—
830C23—92no—
831C23—92no—
832C23—181no—
833C23—181no—
834C23—181no—
835C23—181no—
836C23C22×D3211yescharacteristic
837D4—124no—
838D4—188no—
839D4—364no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—32no—
849C2×C4—32no—
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—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—181no—
867C2×C4—181no—
868C2×C4—181no—
869C2×C4—181no—
870C2×C4—181no—
871C2×C4—181no—
872C2×C4—181no—
873C2×C4—181no—
874C2×C4—181no—
875C2×C4—364no—
876C2×C4—364no—
877C2×C4—364no—
878C2×C4—364no—
879C2×C4#380412yes—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—122no—
888C2×C3—241no—
889C2×C3#553011yescharacteristic
890C2×C3#555011yescharacteristic
891C2×C3#558011yescharacteristic
892C2×C3#559111yescharacteristic
893C2×C3#561011yescharacteristic
894C2×C3#561311yescharacteristic
895C2×C3#561411yescharacteristic
896C2×C3#563011yescharacteristic
897C2×C3D3×#12311yescharacteristic
898C2×C3D3×#12311yescharacteristic
899C2×C3#566111yescharacteristic
900C2×C3#568011yescharacteristic
901C2×C3#569511yescharacteristic
902C2×C3#570411yescharacteristic
903D3—42no—
904D3—64no—
905D3—64no—
906D3—81no—
907D3—124no—
908C22—62no—
909C22—62no—
910C22—62no—
911C22—94no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—121no—
923C22—182no—
924C22—182no—
925C22—182no—
926C22—182no—
927C22—182no—
928C22—182no—
929C22#6430611yescharacteristic
930C22#6430711yescharacteristic
931C22D32×D411yescharacteristic
932C22#6431411yescharacteristic
933C22D3×#23911yescharacteristic
934C22#6431911yescharacteristic
935C22C2×#380411yescharacteristic
936C4—22no—
937C4—41no—
938C4—41no—
939C4—62no—
940C4—62no—
941C4—121no—
942C4—121no—
943C4—121no—
944C4—121no—
945C4—361no—
946C4—361no—
947C4—361no—
948C3—21no—
949C3#7532011yescharacteristic, complemented
950C3#7711811yescharacteristic, complemented
951C2—122no—
952C2—184no—
953C2—241no—
954C2#1059446111yescharacteristic
955C2#1059460811yescharacteristic
956C2#1059462211yescharacteristic
957C2#1059466011yescharacteristic
958C2#1059496711yescharacteristic
959C2#1059513511yescharacteristic
960C2#1059538211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63916C2
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
2. C2×#63880C2semidirect
3. #10592688C2semidirect
4. C3×#4991C2semidirect
5. C3×#4980C2semidirect
6. #10591376C2semidirect
7. #10591370C2semidirect
8. #10591362C2semidirect
9. #10591343C2semidirect
10. #10591298C2semidirect
11. #10591296C2semidirect
12. #10591280C2semidirect
13. #10591275C2semidirect
14. #10591275C2semidirect
15. #10591275C2semidirect
62. #4991D3semidirect
67. #4980D3semidirect
814. C32#2444semidirect
949. C3#75320semidirect
950. C3#77118semidirect

Maximal subgroups

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

subgroupindex
C2×#639162
C2×#638802
#105926882
C3×#49912
C3×#49802
#105913762
#105913702
#105913622
#105913432
#105912982
#105912962
#105912802
#105912752
#771183
#753203