Finite Group Databasebeta

← #11812990

Subgroups — #11812990

Order 1152.

1339 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63971C211yesmaximal, characteristic
2C2×#63904C211yesmaximal, characteristic, complemented
3#10592660C211yesmaximal, characteristic, complemented
4C3×#4956C211yesmaximal, characteristic, complemented
5C3×#4952C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic, complemented
7#10591721C211yesmaximal, characteristic, complemented
8#10591701C211yesmaximal, characteristic, complemented
9#10591379C211yesmaximal, characteristic, complemented
10#10591371C211yesmaximal, characteristic, complemented
11#10591364C211yesmaximal, characteristic, complemented
12D3×C3⋊#95C211yesmaximal, characteristic, complemented
13#10591271C211yesmaximal, characteristic, complemented
14#10591208C211yesmaximal, characteristic, complemented
15#10591199C211yesmaximal, characteristic, complemented
16#77675—31nomaximal
17#74705—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35#63971—24no—
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42#63904—24no—
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#939—31no—
56C2×C4×#67—31no—
57C2×#893—31no—
58C2×#884—31no—
59C3×#397—31no—
60C3×#386—31no—
61#5220—31no—
62C2×C3⋊#95—31no—
63#4985—31no—
64#4961—31no—
65#4961—31no—
66#4961—61no—
67#4958—31no—
68#4956—31no—
69#4956—31no—
70#4956—31no—
71#4956D311yescharacteristic, complemented
72#4952D311yescharacteristic, complemented
73#4951—31no—
74#4950—31no—
75#4944—31no—
76#4675—31no—
77#4674—31no—
78#4668—31no—
79#4665—31no—
80#4664—31no—
81#4664—31no—
82D3×#95—31no—
83#4658—31no—
84#4654—31no—
85#4653—31no—
86C24×C32C2311yescharacteristic
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C2×#638—22no—
92C2×#638—22no—
93C2×#638—41no—
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—41no—
110C2×#626—22no—
111C2×#626—22no—
112C2×#626D414yes—
113C2×#624—22no—
114C2×#624—22no—
115C2×#624—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×C22⋊C4—41no—
123#3757—41no—
124#3752—22no—
125#3752—41no—
126C4⋊(C3⋊Dic3)—22no—
127C3×#217—22no—
128C3×#217—22no—
129C3×#217—41no—
130C3×(C2×D3)⋊C4—22no—
131C3×Dic3⋊C4—22no—
132#3724—22no—
133Dic3⋊Dic3—41no—
134#3722—22no—
135#3722—41no—
136(C2×D3)⋊Dic3—22no—
137Dic32—22no—
138#2444—91noSylow
139C22×C3×D4—31no—
140C23×C3×C4—31no—
141C22×#67—31no—
142C22×#67—31no—
143C22×#67—31no—
144C22×#67—61no—
145C22×#67C2×D311yescharacteristic
146C23×Dic3—31no—
147C23×Dic3—31no—
148C22×D12—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3C2×D311yescharacteristic
154C2×C3×C4⋊C4—31no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4C2×D311yescharacteristic
161C2×C3×C22⋊C4C2×D311yescharacteristic
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—61no—
166C2×#217C2×D311yescharacteristic
167C2×#217C2×D311yescharacteristic
168C2×#217C2×D311yescharacteristic
169#939—64no—
170C4×#67—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—61no—
181C2×(C2×D3)⋊C4—61no—
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—61no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4C2×D311yescharacteristic
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193#893—64no—
194#884—64no—
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—31no—
214C3⋊#95—61no—
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32C2411yescharacteristic
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⋊D3C2×D412yes—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
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—
248#638—44no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
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#4112yes—
258C3×#67—44no—
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—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D412yes—
279C2×C3×Dic3#4112yes—
280C3×C4×D3—44no—
281#626—28no—
282#624—44no—
283D3×Dic3—44no—
284D3×Dic3—44no—
285C2×#121—91no—
286C2×C4×D4—91no—
287#400—91no—
288#397—31no—
289#397—91no—
290#394—91no—
291#388—91no—
292#387—91no—
293#386—31no—
294#386—91no—
295#386—91no—
296#386—91no—
297#385—91no—
298#381—91no—
299C2×#95—91no—
300C24×C3—21no—
301C24×C3—31no—
302C24×C3C22×D311yescharacteristic
303C24×C3C22×D311yescharacteristic
304C23×D3—31no—
305C23×D3—31no—
306C23×D3—61no—
307C23×D3C22×D311yescharacteristic
308C2×C3×D4—62no—
309C2×C3×D4—62no—
310C2×C3×D4—62no—
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—31no—
320C22×C3×C4—62no—
321C22×C3×C4—62no—
322C22×C3×C4—121no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—22no—
328C2×#67—22no—
329C2×#67—22no—
330C2×#67—34no—
331C2×#67—62no—
332C2×#67—62no—
333C2×#67—62no—
334C2×#67—62no—
335C2×#67—62no—
336C2×#67—62no—
337C2×#67—122no—
338C2×#67—122no—
339C2×#67—121no—
340C2×#67—121no—
341C2×#67—122no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—62no—
352C22×Dic3—62no—
353C22×Dic3—62no—
354C22×Dic3—121no—
355C22×Dic3—121no—
356C22×Dic3—121no—
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C2×D12—34no—
365C2×D12—62no—
366C2×D12—62no—
367C2×C4×D3—22no—
368C2×C4×D3—22no—
369C2×C4×D3—41no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C2×C4×D3—121no—
380C2×C4×D3—121no—
381C2×C4×D3—121no—
382C3×C4⋊C4—62no—
383C3×C22⋊C4—41no—
384C3×C22⋊C4—41no—
385C3×C22⋊C4—42no—
386C3×C22⋊C4—62no—
387C3×C22⋊C4—62no—
388C3×C22⋊C4—62no—
389C3×C22⋊C4—121no—
390#217—22no—
391#217—22no—
392#217—41no—
393#217—62no—
394#217—121no—
395#217—121no—
396#217—122no—
397(C2×D3)⋊C4—22no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—122no—
404(C2×D3)⋊C4—121no—
405(C2×D3)⋊C4—121no—
406(C2×D3)⋊C4—121no—
407(C2×D3)⋊C4—121no—
408(C2×D3)⋊C4—122no—
409C4⋊Dic3—62no—
410C4⋊Dic3—62no—
411C4⋊Dic3—122no—
412C4⋊Dic3—121no—
413Dic3⋊C4—22no—
414Dic3⋊C4—62no—
415Dic3⋊C4—62no—
416Dic3⋊C4—121no—
417C4×Dic3—62no—
418C4×Dic3—62no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32C22×D411yescharacteristic
427C22×C32C2×#4111yescharacteristic
428C22×C32C2×#4111yescharacteristic
429C22×C32C2×#4111yescharacteristic
430C22×C32C2×#4111yescharacteristic
431C22×C32H(5,𝔽2)11yescharacteristic
432C22×C32H(5,𝔽2)11yescharacteristic
433C2×C3⋊D3—22no—
434C2×C3⋊D3—22no—
435C2×C3⋊D3—22no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3—41no—
438C2×C3⋊D3—41no—
439C2×C3⋊D3—41no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3#12314yes—
447C32×C4—41no—
448C32×C4—41no—
449C3⋊Dic3—22no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C22×D4—31no—
460C22×D4—91no—
461C22×D4—91no—
462C23×C4—31no—
463C23×C4—91no—
464C23×C4—91no—
465C23×C4—91no—
466#121—184no—
467C4×D4—184no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—91no—
470C2×C4⋊C4—91no—
471C2×C4⋊C4—91no—
472C2×C22⋊C4—31no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—31no—
475C2×C22⋊C4—31no—
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×C22⋊C4D3211yescharacteristic
483C2×C42—91no—
484#95—31no—
485#95—31no—
486#95—31no—
487#95—31no—
488#95—31no—
489#95—91no—
490#95—91no—
491#95—91no—
492#95—91no—
493#95—91no—
494#95—91no—
495#95—91no—
496C23×C3—22no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—32no—
513C23×C3—32no—
514C23×C3—32no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3C23×D311yescharacteristic
526C23×C3C23×D311yescharacteristic
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—32no—
532C22×D3—32no—
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—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—121no—
550C22×D3—121no—
551C22×D3—121no—
552C22×D3#23512yes—
553C22×D3D3×D412yes—
554C22×D3#23712yes—
555C3×D4—124no—
556C2×C3×C4—22no—
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—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
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—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—124no—
596#67—44no—
597#67—68no—
598#67—124no—
599#67—124no—
600#67—128no—
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—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—62no—
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—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—121no—
640C2×Dic3—121no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—124no—
648C2×Dic3—124no—
649C2×Dic3D3×D412yes—
650C2×Dic3#23712yes—
651D12—68no—
652C4×D3—44no—
653C4×D3—124no—
654C4×D3—124no—
655C4×D3—124no—
656C4×D3—124no—
657C2×C32—81no—
658C2×C32C2×#12311yescharacteristic
659C2×C32#52911yescharacteristic
660C2×C32#53811yescharacteristic
661C2×C32#54611yescharacteristic
662C2×C32#54611yescharacteristic
663C2×C32#55311yescharacteristic
664C2×C32#55311yescharacteristic
665C3⋊D3—42no—
666C3×D3—24no—
667C24—31no—
668C24—91no—
669C24C2×D3211yescharacteristic
670C2×D4—62no—
671C2×D4—62no—
672C2×D4—62no—
673C2×D4—94no—
674C2×D4—182no—
675C2×D4—182no—
676C2×D4—182no—
677C2×D4—182no—
678C2×D4—361no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—91no—
689C22×C4—91no—
690C22×C4—91no—
691C22×C4—121no—
692C22×C4—182no—
693C22×C4—182no—
694C22×C4—182no—
695C22×C4—182no—
696C22×C4—182no—
697C22×C4—361no—
698C22×C4—361no—
699C22×C4—361no—
700C22×C4—361no—
701C22×C4C2×D3211yescharacteristic
702C22×C4C2×D3211yescharacteristic
703C4⋊C4—62no—
704C4⋊C4—182no—
705C4⋊C4—182no—
706C4⋊C4—361no—
707C22⋊C4—41no—
708C22⋊C4—62no—
709C22⋊C4—62no—
710C22⋊C4—62no—
711C22⋊C4—121no—
712C22⋊C4—182no—
713C22⋊C4—182no—
714C22⋊C4—182no—
715C22⋊C4—361no—
716C22⋊C4—361no—
717C22⋊C4—361no—
718C42—182no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—34no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—62no—
745C22×C3—62no—
746C22×C3—62no—
747C22×C3—62no—
748C22×C3—62no—
749C22×C3—62no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3—81no—
753C22×C3—81no—
754C22×C3C2×#23511yescharacteristic
755C22×C3C2×D3×D411yescharacteristic
756C22×C3C2×D3×D411yescharacteristic
757C22×C3C2×#23711yescharacteristic
758C22×C3C2×#23711yescharacteristic
759C22×C3#100411yescharacteristic
760C22×C3#100411yescharacteristic
761C22×C3D3×#4111yescharacteristic
762C22×C3D3×#4111yescharacteristic
763C22×C3D3×#4111yescharacteristic
764C22×C3D3×#4111yescharacteristic
765C22×C3D3×#4111yescharacteristic
766C22×C3#100911yescharacteristic
767C22×C3#100911yescharacteristic
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—62no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—122no—
781C2×D3—122no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—241no—
792C2×D3—241no—
793C2×D3—241no—
794C2×D3—241no—
795C2×D3#88314yes—
796C3×C4—42no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—62no—
802C3×C4—62no—
803C3×C4—81no—
804C3×C4—121no—
805C3×C4—121no—
806C3×C4—121no—
807C3×C4—121no—
808C3×C4—121no—
809Dic3—22no—
810Dic3—22no—
811Dic3—41no—
812Dic3—41no—
813Dic3—41no—
814Dic3—41no—
815Dic3—41no—
816Dic3—62no—
817Dic3—62no—
818Dic3—122no—
819Dic3—121no—
820Dic3—121no—
821Dic3—121no—
822Dic3—121no—
823Dic3—241no—
824Dic3—241no—
825C32#244411yescharacteristic, complemented, Sylow
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—32no—
834C23—32no—
835C23—32no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—92no—
841C23—181no—
842C23—181no—
843C23—181no—
844C23—181no—
845C23—181no—
846C23—181no—
847C23C22×D3211yescharacteristic
848D4—124no—
849D4—188no—
850D4—364no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
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—92no—
879C2×C4—124no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—364no—
889C2×C4—364no—
890C2×C4—364no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—64no—
899C2×C3—82no—
900C2×C3—81no—
901C2×C3—81no—
902C2×C3C2×#88311yescharacteristic
903C2×C3#553811yescharacteristic
904C2×C3#556011yescharacteristic
905C2×C3#559111yescharacteristic
906C2×C3#560111yescharacteristic
907C2×C3#561211yescharacteristic
908C2×C3#561811yescharacteristic
909C2×C3D3×#12311yescharacteristic
910C2×C3#565411yescharacteristic
911C2×C3#565711yescharacteristic
912C2×C3#566111yescharacteristic
913C2×C3#567611yescharacteristic
914C2×C3#570611yescharacteristic
915C2×C3#570911yescharacteristic
916D3—24no—
917D3—122no—
918D3—122no—
919D3—242no—
920C22—34no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—62no—
932C22—62no—
933C22—62no—
934C22—182no—
935C22—182no—
936C22—182no—
937C22—361no—
938C22—361no—
939C22—361no—
940C22—361no—
941C22D3×#23511yescharacteristic
942C22#6430811yescharacteristic
943C22D32×D411yescharacteristic
944C22D3×#23711yescharacteristic
945C22D3×#23711yescharacteristic
946C22#6431211yescharacteristic
947C22#6433011yescharacteristic
948C4—41no—
949C4—41no—
950C4—62no—
951C4—62no—
952C4—121no—
953C4—121no—
954C4—121no—
955C4—121no—
956C4—121no—
957C4—182no—
958C4—361no—
959C4—361no—
960C3—21no—
961C3#7470511yescharacteristic, complemented
962C3#7767511yescharacteristic, complemented
963C2—64no—
964C2—81no—
965C2—362no—
966C2#1059408911yescharacteristic
967C2#1059412511yescharacteristic
968C2D3×#88311yescharacteristic
969C2#1059428211yescharacteristic
970C2#1059508511yescharacteristic
971C2#1059518311yescharacteristic
972C2#1059529411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63971C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2444
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63904C2semidirect
3. #10592660C2semidirect
4. C3×#4956C2semidirect
5. C3×#4952C2semidirect
6. #10591722C2semidirect
7. #10591721C2semidirect
8. #10591701C2semidirect
9. #10591379C2semidirect
10. #10591371C2semidirect
11. #10591364C2semidirect
12. D3×C3⋊#95C2semidirect
13. #10591271C2semidirect
14. #10591208C2semidirect
15. #10591199C2semidirect
71. #4956D3semidirect
72. #4952D3semidirect
825. C32#2444semidirect
961. C3#74705semidirect
962. C3#77675semidirect

Maximal subgroups

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

subgroupindex
C2×#639712
C2×#639042
#105926602
C3×#49562
C3×#49522
#105917222
#105917212
#105917012
#105913792
#105913712
#105913642
D3×C3⋊#952
#105912712
#105912082
#105911992
#776753
#747053