Finite Group Databasebeta

← #11812988

Subgroups — #11812988

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic, complemented
2C2×#63958C211yesmaximal, characteristic
3C3×#4959C211yesmaximal, characteristic, complemented
4C3×#4952C211yesmaximal, characteristic, complemented
5#10591722C211yesmaximal, characteristic, complemented
6#10591713C211yesmaximal, characteristic, complemented
7#10591697C211yesmaximal, characteristic, complemented
8#10591387C211yesmaximal, characteristic, complemented
9#10591374C211yesmaximal, characteristic, complemented
10#10591370C211yesmaximal, characteristic, complemented
11#10591298C211yesmaximal, characteristic, complemented
12#10591283C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591210C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#77674—31nomaximal
17#77118—31nomaximal
18C22×#638C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29#64090—24no—
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42#63958—24no—
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#938—31no—
56C2×#884—31no—
57C2×#67⋊C4—31no—
58C2×#67⋊C4—31no—
59C2×#67⋊C4—61no—
60C3×#397—31no—
61C3×#394—31no—
62#5220—31no—
63#4990—31no—
64#4989—31no—
65#4989—31no—
66#4980—31no—
67#4959D311yescharacteristic, complemented
68#4958—31no—
69#4956—31no—
70#4956—31no—
71#4956—31no—
72#4956—31no—
73#4952—31no—
74#4952D311yescharacteristic, complemented
75#4945—31no—
76#4943—31no—
77#4943—31no—
78#4675—31no—
79#4665—31no—
80#4665—31no—
81D3×#95—31no—
82D3×#95—31no—
83#4660—31no—
84#4658—31no—
85#4652—31no—
86C24×C32C2311yescharacteristic
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C2×#638—22no—
92C2×#638—22no—
93C2×#638D414yes—
94C22×C3⋊Dic3—22no—
95C22×C3⋊Dic3—22no—
96C22×C3⋊Dic3—41no—
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3—41no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—41no—
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×#626—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#624—22no—
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—41no—
120C2×#624—41no—
121C2×#624—41no—
122C32×C22⋊C4—22no—
123#3752—22no—
124#3750—22no—
125C4×C3⋊Dic3—22no—
126C3×#217—22no—
127C3×#217—41no—
128C3×#217—41no—
129C3×(C2×D3)⋊C4—41no—
130C3×(C2×D3)⋊C4—41no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—41no—
133Dic3⋊Dic3—22no—
134#3722—22no—
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—41no—
138#2444—91noSylow
139C22×C3×D4—31no—
140C22×#67—31no—
141C22×#67—31no—
142C22×#67—31no—
143C22×#67—61no—
144C22×#67C2×D311yescharacteristic
145C23×Dic3—31no—
146C23×Dic3—31no—
147C23×Dic3—61no—
148C22×D12—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—61no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4C2×D311yescharacteristic
165C2×C3×C22⋊C4C2×D311yescharacteristic
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217C2×D311yescharacteristic
170C2×#217C2×D311yescharacteristic
171C2×#217C2×D311yescharacteristic
172#938—64no—
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)⋊C4C2×D311yescharacteristic
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×C4⋊Dic3—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—61no—
188C2×Dic3⋊C4C2×D311yescharacteristic
189C2×Dic3⋊C4C2×D311yescharacteristic
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—61no—
193#884—64no—
194#67⋊C4—64no—
195#67⋊C4—64no—
196#67⋊C4—68no—
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—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32C2×D412yes—
228C23×C32C2411yescharacteristic
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3C2×D412yes—
234C22×C3⋊D3#4112yes—
235C22×C3⋊D3#4112yes—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—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—
249#638—28no—
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—44no—
258C2×C3⋊Dic3C2×D412yes—
259C2×C3⋊Dic3#4112yes—
260C4×C3⋊D3—44no—
261C3×#67—44no—
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×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3#4112yes—
283#626—44no—
284#624—44no—
285#624—44no—
286C2×#121—91no—
287C2×C4×D4—91no—
288#400—91no—
289#397—31no—
290#397—91no—
291#394—31no—
292#388—91no—
293#387—91no—
294#386—91no—
295#386—91no—
296#386—91no—
297#386—91no—
298#385—91no—
299#381—91no—
300C2×#95—91no—
301C24×C3—21no—
302C24×C3—31no—
303C24×C3C22×D311yescharacteristic
304C24×C3C22×D311yescharacteristic
305C23×D3—31no—
306C23×D3—31no—
307C23×D3—61no—
308C23×D3C22×D311yescharacteristic
309C2×C3×D4—62no—
310C2×C3×D4—62no—
311C2×C3×D4—121no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
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—31no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—22no—
326C2×#67—22no—
327C2×#67—34no—
328C2×#67—34no—
329C2×#67—41no—
330C2×#67—64no—
331C2×#67—62no—
332C2×#67—62no—
333C2×#67—62no—
334C2×#67—62no—
335C2×#67—62no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—64no—
339C2×#67—64no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—62no—
350C22×Dic3—62no—
351C22×Dic3—64no—
352C22×Dic3—62no—
353C22×Dic3—62no—
354C22×Dic3—122no—
355C22×Dic3—121no—
356C22×Dic3—121no—
357C22×Dic3—122no—
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—62no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
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—64no—
378C2×C4×D3—62no—
379C2×C4×D3—122no—
380C2×C4×D3—121no—
381C2×C4×D3—121no—
382C2×C4×D3—121no—
383C2×C4×D3—121no—
384C2×C4×D3—121no—
385C2×C4×D3—121no—
386C2×C4×D3—121no—
387C2×C4×D3—121no—
388C2×C4×D3—122no—
389C3×C4⋊C4—62no—
390C3×C4⋊C4—121no—
391C3×C22⋊C4—24no—
392C3×C22⋊C4—22no—
393C3×C22⋊C4—22no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—121no—
396C3×C22⋊C4—121no—
397C3×C22⋊C4—121no—
398C3×C22⋊C4—121no—
399#217—22no—
400#217—41no—
401#217—41no—
402#217—62no—
403#217—62no—
404#217—121no—
405(C2×D3)⋊C4—41no—
406(C2×D3)⋊C4—41no—
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—64no—
414(C2×D3)⋊C4—121no—
415C4⋊Dic3—62no—
416Dic3⋊C4—22no—
417Dic3⋊C4—41no—
418Dic3⋊C4—62no—
419Dic3⋊C4—62no—
420Dic3⋊C4—62no—
421Dic3⋊C4—64no—
422C4×Dic3—62no—
423C4×Dic3—62no—
424C4×Dic3—64no—
425C22×C32—22no—
426C22×C32—22no—
427C22×C32—22no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32C22×D411yescharacteristic
433C22×C32C2×#4111yescharacteristic
434C22×C32C2×#4111yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32H(5,𝔽2)11yescharacteristic
438C22×C32H(5,𝔽2)11yescharacteristic
439C2×C3⋊D3—22no—
440C2×C3⋊D3—22no—
441C2×C3⋊D3—22no—
442C2×C3⋊D3—22no—
443C2×C3⋊D3—22no—
444C2×C3⋊D3—22no—
445C2×C3⋊D3#12314yes—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C32×C4—41no—
454C32×C4—41no—
455C3⋊Dic3—22no—
456C3⋊Dic3—22no—
457C3⋊Dic3—41no—
458C3×Dic3—22no—
459C3×Dic3—41no—
460C3×Dic3—41no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C22×D4—31no—
466C22×D4—91no—
467C22×D4—91no—
468C23×C4—91no—
469C23×C4—91no—
470C23×C4—91no—
471C23×C4—91no—
472#121—184no—
473C4×D4—184no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—31no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C22⋊C4—31no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—31no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—91no—
484C2×C22⋊C4—91no—
485C2×C22⋊C4—91no—
486C2×C22⋊C4—91no—
487C2×C22⋊C4—91no—
488C2×C22⋊C4D3211yescharacteristic
489C2×C42—91no—
490#95—31no—
491#95—31no—
492#95—31no—
493#95—31no—
494#95—91no—
495#95—91no—
496#95—91no—
497#95—91no—
498#95—91no—
499#95—91no—
500#95—91no—
501#95—91no—
502C23×C3—22no—
503C23×C3—22no—
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—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—22no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3D3×D412yes—
530C23×C3D3×D412yes—
531C23×C3C23×D311yescharacteristic
532C23×C3C23×D311yescharacteristic
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—32no—
541C22×D3—32no—
542C22×D3—32no—
543C22×D3—32no—
544C22×D3—32no—
545C22×D3—32no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—121no—
561C3×D4—124no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
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—32no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
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—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601#67—44no—
602#67—68no—
603#67—68no—
604#67—616no—
605#67—124no—
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—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—32no—
627C2×Dic3—32no—
628C2×Dic3—32no—
629C2×Dic3—32no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—62no—
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—62no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—121no—
652C2×Dic3—121no—
653C2×Dic3—124no—
654C2×Dic3—124no—
655C2×Dic3—128no—
656C2×Dic3#23712yes—
657D12—124no—
658C4×D3—124no—
659C4×D3—124no—
660C4×D3—124no—
661C4×D3—124no—
662C4×D3—124no—
663C4×D3—124no—
664C4×D3—128no—
665C2×C32—42no—
666C2×C32C2×#12311yescharacteristic
667C2×C32#52911yescharacteristic
668C2×C32#53811yescharacteristic
669C2×C32#54611yescharacteristic
670C2×C32#54611yescharacteristic
671C2×C32#55311yescharacteristic
672C2×C32#55311yescharacteristic
673C3⋊D3—24no—
674C3×D3—81no—
675C24—31no—
676C24—91no—
677C24C2×D3211yescharacteristic
678C2×D4—62no—
679C2×D4—62no—
680C2×D4—94no—
681C2×D4—121no—
682C2×D4—182no—
683C2×D4—182no—
684C2×D4—182no—
685C2×D4—182no—
686C2×D4—182no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—182no—
698C22×C4—182no—
699C22×C4—182no—
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—
709C22×C4C2×D3211yescharacteristic
710C22×C4C2×D3211yescharacteristic
711C4⋊C4—62no—
712C4⋊C4—121no—
713C4⋊C4—182no—
714C4⋊C4—182no—
715C22⋊C4—22no—
716C22⋊C4—62no—
717C22⋊C4—121no—
718C22⋊C4—121no—
719C22⋊C4—121no—
720C22⋊C4—121no—
721C22⋊C4—182no—
722C22⋊C4—182no—
723C22⋊C4—182no—
724C22⋊C4—182no—
725C22⋊C4—361no—
726C42—182no—
727C22×C3—24no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—42no—
746C22×C3—42no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3C2×D3×D411yescharacteristic
763C22×C3C2×D3×D411yescharacteristic
764C22×C3C2×#23711yescharacteristic
765C22×C3#100411yescharacteristic
766C22×C3#100411yescharacteristic
767C22×C3#100411yescharacteristic
768C22×C3D3×#4111yescharacteristic
769C22×C3D3×#4111yescharacteristic
770C22×C3D3×#4111yescharacteristic
771C22×C3D3×#4111yescharacteristic
772C22×C3D3×#4111yescharacteristic
773C22×C3D3×#4111yescharacteristic
774C22×C3D3×#4111yescharacteristic
775C22×C3#100911yescharacteristic
776C2×D3—34no—
777C2×D3—34no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—64no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—62no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—122no—
799C2×D3—122no—
800C2×D3—122no—
801C2×D3—122no—
802C2×D3—122no—
803C2×D3—122no—
804C3×C4—42no—
805C3×C4—42no—
806C3×C4—41no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—41no—
810C3×C4—62no—
811C3×C4—121no—
812C3×C4—121no—
813C3×C4—121no—
814C3×C4—121no—
815C3×C4—121no—
816C3×C4—121no—
817Dic3—22no—
818Dic3—41no—
819Dic3—41no—
820Dic3—41no—
821Dic3—41no—
822Dic3—41no—
823Dic3—41no—
824Dic3—64no—
825Dic3—64no—
826Dic3—62no—
827Dic3—62no—
828Dic3—62no—
829Dic3—62no—
830Dic3—122no—
831Dic3—121no—
832Dic3—121no—
833C32#244411yescharacteristic, complemented, Sylow
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—92no—
848C23—92no—
849C23—92no—
850C23—181no—
851C23—181no—
852C23—181no—
853C23—181no—
854C23#381112yes—
855C23C22×D3211yescharacteristic
856D4—124no—
857D4—188no—
858D4—364no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—32no—
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—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—92no—
887C2×C4—92no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4—364no—
896C2×C4—364no—
897C2×C4—364no—
898C2×C4—364no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—44no—
907C2×C3—42no—
908C2×C3—42no—
909C2×C3—241no—
910C2×C3#559111yescharacteristic
911C2×C3#561011yescharacteristic
912C2×C3#561011yescharacteristic
913C2×C3#561311yescharacteristic
914C2×C3#561411yescharacteristic
915C2×C3D3×#12311yescharacteristic
916C2×C3D3×#12311yescharacteristic
917C2×C3#565411yescharacteristic
918C2×C3#566111yescharacteristic
919C2×C3#566111yescharacteristic
920C2×C3#567811yescharacteristic
921C2×C3#568011yescharacteristic
922C2×C3#570611yescharacteristic
923C2×C3#570911yescharacteristic
924D3—64no—
925D3—64no—
926D3—81no—
927D3—124no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—94no—
936C22—121no—
937C22—121no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—182no—
944C22—182no—
945C22—182no—
946C22—182no—
947C22—182no—
948C22—182no—
949C22#6430611yescharacteristic
950C22#6430611yescharacteristic
951C22D3×#23711yescharacteristic
952C22#6431211yescharacteristic
953C22#6431311yescharacteristic
954C22#6431411yescharacteristic
955C22C2×#381111yescharacteristic
956C4—41no—
957C4—41no—
958C4—62no—
959C4—121no—
960C4—121no—
961C4—121no—
962C4—121no—
963C4—121no—
964C4—121no—
965C4—182no—
966C4—182no—
967C4—361no—
968C3—21no—
969C3#7711811yescharacteristic, complemented
970C3#7767411yescharacteristic, complemented
971C2—42no—
972C2—184no—
973C2—241no—
974C2#1059413711yescharacteristic
975C2#1059421711yescharacteristic
976C2#1059422911yescharacteristic
977C2#1059430611yescharacteristic
978C2#1059507911yescharacteristic
979C2#1059516311yescharacteristic
980C2#1059530711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63958C2
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
1. C2×#64090C2semidirect
3. C3×#4959C2semidirect
4. C3×#4952C2semidirect
5. #10591722C2semidirect
6. #10591713C2semidirect
7. #10591697C2semidirect
8. #10591387C2semidirect
9. #10591374C2semidirect
10. #10591370C2semidirect
11. #10591298C2semidirect
12. #10591283C2semidirect
13. #10591275C2semidirect
14. #10591210C2semidirect
15. #10591192C2semidirect
67. #4959D3semidirect
74. #4952D3semidirect
833. C32#2444semidirect
969. C3#77118semidirect
970. C3#77674semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×#639582
C3×#49592
C3×#49522
#105917222
#105917132
#105916972
#105913872
#105913742
#105913702
#105912982
#105912832
#105912752
#105912102
#105911922
#776743
#771183