Finite Group Databasebeta

← #11805503

Subgroups — #11805503

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C2×#63952C211yesmaximal, characteristic
3C2×#63952C211yesmaximal, characteristic
4C3×#5210C211yesmaximal, characteristic, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6#10591718C211yesmaximal, characteristic, complemented
7#10591716C211yesmaximal, characteristic, complemented
8#10591375C211yesmaximal, characteristic, complemented
9#10591370C211yesmaximal, characteristic, complemented
10#10591367C211yesmaximal, characteristic, complemented
11#10591328C211yesmaximal, characteristic, complemented
12#10591290C211yesmaximal, characteristic, complemented
13#10591256C211yesmaximal, characteristic, complemented
14#10591247C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#74394—31nomaximal
17#73369—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C4×#638—24no—
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63952—24no—
45#63952C418yescomplemented
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C4×#67—31no—
57C2×C4×#67—31no—
58C2×C4×#67—31no—
59C2×C4×#67—31no—
60C2×C4×#67—61no—
61C2×#67⋊C4—31no—
62C2×#67⋊C4—31no—
63C3×#385—31no—
64C2×C3×#95—31no—
65#5212—31no—
66#5210—31no—
67#5210D311yescharacteristic, complemented
68C2×C3⋊#95D311yescharacteristic, complemented
69#4989—31no—
70#4987—31no—
71#4976—31no—
72Dic3×C4⋊C4—31no—
73#4950—31no—
74#4942—31no—
75#4668—31no—
76#4668—31no—
77#4668—31no—
78#4667—31no—
79D3×#95—31no—
80D3×#95—31no—
81#4650—31no—
82#4650—31no—
83#4649—31no—
84#4647—31no—
85#4647—31no—
86#4647—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C22×C32×C4—22no—
90C22×C32×C4—22no—
91C22×C32×C4—41no—
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638C2×C414yes—
95C2×#638D414yes—
96C2×#638Q814yes—
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3—41no—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—41no—
106C22×C3×Dic3—41no—
107C22×C3×Dic3—41no—
108C22×C3×Dic3C2×C414yescomplemented
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—41no—
120C2×#624—41no—
121C2×#624—41no—
122C2×#624C2×C414yescomplemented
123#3757—22no—
124#3752—22no—
125#3750—22no—
126C4×C3⋊Dic3—22no—
127C3×#217—22no—
128C3×#217C2×C414yescomplemented
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—41no—
131#3724—22no—
132#3724C2×C414yescomplemented
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—41no—
135Dic3⋊Dic3—41no—
136Dic3⋊Dic3—41no—
137#3722—22no—
138#3722C2×C414yescomplemented
139Dic32—22no—
140Dic32C2×C414yescomplemented
141#2349—91noSylow
142C23×C3×C4—21no—
143C23×C3×C4—31no—
144C23×C3×C4—31no—
145C23×C3×C4C2×D311yescharacteristic
146C23×C3×C4C2×D311yescharacteristic
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—61no—
150C23×Dic3C2×D311yescharacteristic
151C23×Dic3C2×D311yescharacteristic
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—61no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—61no—
166C2×#217C2×D311yescharacteristic
167C2×#217C2×D311yescharacteristic
168C4×#67—38no—
169C4×#67—64no—
170C4×#67—64no—
171C4×#67—64no—
172C4×#67—68no—
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—61no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—61no—
195C2×Dic3⋊C4C2×D311yescharacteristic
196C2×Dic3⋊C4C2×D311yescharacteristic
197C2×C4×Dic3—31no—
198C2×C4×Dic3—31no—
199C2×C4×Dic3—31no—
200C2×C4×Dic3—31no—
201C2×C4×Dic3—31no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—61no—
204#67⋊C4—38no—
205#67⋊C4—64no—
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⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95C2×D311yescharacteristic
221C3⋊#95C2×D311yescharacteristic
222C3⋊#95C2×D311yescharacteristic
223C3⋊#95C2×D311yescharacteristic
224C3⋊#95C2×D311yescharacteristic
225C3⋊#95C2×D311yescharacteristic
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32—21no—
230C23×C32C22×C412yes—
231C23×C32C2×D412yes—
232C23×C32C2×Q812yes—
233C23×C32C2411yescharacteristic
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3C22×C412yes—
239C22×C3⋊D3C2×D412yes—
240C22×C3⋊D3C2×Q812yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—44no—
247C2×C32×C4#4112yes—
248#638C4⋊C4116yescomplemented
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⋊Dic3C22×C412yes—
256C2×C3⋊Dic3C2×D412yes—
257C2×C3⋊Dic3C2×Q812yes—
258C4×C3⋊D3—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×Dic3—44no—
279C2×C3×Dic3—44no—
280C2×C3×Dic3C22×C412yes—
281C2×C3×Dic3C22×C412yes—
282C2×C3×Dic3C22×C412yes—
283C2×C3×Dic3C22×C412yes—
284C2×C3×Dic3#4112yes—
285#624—44no—
286#624—44no—
287C2×C4×D4—91no—
288C2×C4×D4—91no—
289C2×C4×D4—91no—
290#389—91no—
291#389—91no—
292#385—31no—
293#385—91no—
294#385—91no—
295#385—91no—
296#382—91no—
297#380—91no—
298#380—91no—
299C4×C4⋊C4—91no—
300C2×#95—31no—
301C2×#95—91no—
302C24×C3—21no—
303C24×C3C22×D311yescharacteristic
304C24×C3C22×D311yescharacteristic
305C23×D3—31no—
306C23×D3—31no—
307C23×D3—61no—
308C22×C3×C4—24no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—34no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—42no—
325C22×C3×C4—41no—
326C22×C3×C4—41no—
327C22×C3×C4—42no—
328C22×C3×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4—121no—
331C22×C3×C4—121no—
332C22×C3×C4—121no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—34no—
340C2×#67—34no—
341C2×#67—34no—
342C2×#67—34no—
343C2×#67—64no—
344C2×#67—64no—
345C2×#67—64no—
346C22×Dic3—22no—
347C22×Dic3—22no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—41no—
355C22×Dic3—41no—
356C22×Dic3—41no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3C4×D314yescomplemented
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C2×C4×D3—34no—
370C2×C4×D3—34no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—64no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—122no—
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—121no—
389C2×C4×D3—122no—
390C3×C4⋊C4—62no—
391C3×C4⋊C4—121no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—62no—
394#217—22no—
395#217—64no—
396#217—62no—
397#217—62no—
398#217C4×D314yescomplemented
399(C2×D3)⋊C4—34no—
400(C2×D3)⋊C4—34no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—64no—
406C4⋊Dic3—62no—
407C4⋊Dic3—121no—
408C4⋊Dic3—121no—
409C4⋊Dic3—121no—
410Dic3⋊C4—22no—
411Dic3⋊C4—34no—
412Dic3⋊C4—34no—
413Dic3⋊C4—41no—
414Dic3⋊C4—62no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417Dic3⋊C4—62no—
418Dic3⋊C4—62no—
419Dic3⋊C4—64no—
420Dic3⋊C4—121no—
421Dic3⋊C4—121no—
422Dic3⋊C4—121no—
423C4×Dic3—34no—
424C4×Dic3—34no—
425C4×Dic3—62no—
426C4×Dic3—62no—
427C4×Dic3—62no—
428C4×Dic3—62no—
429C4×Dic3—64no—
430C22×C32—22no—
431C22×C32—22no—
432C22×C32—22no—
433C22×C32—22no—
434C22×C32—22no—
435C22×C32—22no—
436C22×C32C2×C4⋊C414yes—
437C22×C32C23×C411yescharacteristic
438C22×C32C22×D411yescharacteristic
439C22×C32C22×Q811yescharacteristic
440C22×C32C2×#4111yescharacteristic
441C22×C32C2×#4111yescharacteristic
442C22×C32H(5,𝔽2)11yescharacteristic
443C22×C32H(5,𝔽2)11yescharacteristic
444C2×C3⋊D3—22no—
445C2×C3⋊D3—22no—
446C2×C3⋊D3—22no—
447C2×C3⋊D3—22no—
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3C2×C4⋊C414yes—
451C32×C4—22no—
452C32×C4—41no—
453C3⋊Dic3—41no—
454C3⋊Dic3—41no—
455C3⋊Dic3C2×C4⋊C414yes—
456C3×Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—22no—
460C3×Dic3—22no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C22×D4—91no—
465C23×C4—31no—
466C23×C4—31no—
467C23×C4—91no—
468C23×C4—91no—
469C23×C4—91no—
470C23×C4D3211yescharacteristic
471C4×D4—98no—
472C4×D4—184no—
473C4×D4—184no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—31no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C4⋊C4—91no—
479C2×C4⋊C4—91no—
480C2×C4⋊C4—91no—
481C2×C4⋊C4—91no—
482C2×C4⋊C4—91no—
483C2×C22⋊C4—31no—
484C2×C22⋊C4—31no—
485C2×C22⋊C4—91no—
486C2×C22⋊C4—91no—
487C2×C22⋊C4—91no—
488C2×C22⋊C4—91no—
489C2×C42—91no—
490C2×C42—91no—
491C2×C42—91no—
492#95—31no—
493#95—31no—
494#95—31no—
495#95—31no—
496#95—31no—
497#95—31no—
498#95—91no—
499#95—91no—
500#95—91no—
501#95—91no—
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—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3C2×C4×D312yes—
519C23×C3C2×C4×D312yes—
520C23×C3D3×D412yes—
521C23×C3D3×D412yes—
522C23×C3D3×Q812yes—
523C23×C3D3×Q812yes—
524C23×C3C23×D311yescharacteristic
525C23×C3C23×D311yescharacteristic
526C22×D3—32no—
527C22×D3—32no—
528C22×D3—32no—
529C22×D3—32no—
530C22×D3—32no—
531C22×D3—32no—
532C22×D3—62no—
533C22×D3—62no—
534C22×D3—62no—
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—121no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3—121no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—22no—
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—22no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—32no—
565C2×C3×C4—32no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—44no—
569C2×C3×C4—44no—
570C2×C3×C4—48no—
571C2×C3×C4—61no—
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—61no—
589C2×C3×C4—61no—
590C2×C3×C4—124no—
591C2×C3×C4—124no—
592C2×C3×C4#23512yes—
593C2×C3×C4#23712yes—
594#67—316no—
595#67—316no—
596#67—616no—
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—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—44no—
623C2×Dic3—44no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—62no—
628C2×Dic3—62no—
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—61no—
640C2×Dic3—61no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3C2×C4×D312yes—
646C2×Dic3C2×C4×D312yes—
647C2×Dic3C2×C4×D312yes—
648C2×Dic3C2×C4×D312yes—
649C2×Dic3#23512yes—
650C4×D3—124no—
651C4×D3—124no—
652C4×D3—124no—
653C4×D3—124no—
654C4×D3—124no—
655C4×D3—124no—
656C4×D3—128no—
657C2×C32—24no—
658C2×C32C22×C4⋊C411yescharacteristic
659C2×C32C4×#4111yescharacteristic
660C2×C32#51811yescharacteristic
661C2×C32#54611yescharacteristic
662C2×C32#54611yescharacteristic
663C2×C32#55411yescharacteristic
664C2×C32#55411yescharacteristic
665C3⋊D3—24no—
666C24—91no—
667C24C2×D3211yescharacteristic
668C2×D4—94no—
669C2×D4—94no—
670C2×D4—94no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—34no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—41no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—94no—
686C22×C4—91no—
687C22×C4—91no—
688C22×C4—91no—
689C22×C4—121no—
690C22×C4—121no—
691C22×C4—121no—
692C22×C4—182no—
693C22×C4—182no—
694C22×C4—182no—
695C22×C4—182no—
696C22×C4—361no—
697C22×C4—361no—
698C22×C4—361no—
699C22×C4—361no—
700C22×C4C2×D3211yescharacteristic
701C22×C4C2×D3211yescharacteristic
702C4⋊C4—62no—
703C4⋊C4—94no—
704C4⋊C4—121no—
705C4⋊C4—182no—
706C4⋊C4—182no—
707C4⋊C4—182no—
708C4⋊C4—361no—
709C4⋊C4—361no—
710C4⋊C4—361no—
711C22⋊C4—34no—
712C22⋊C4—62no—
713C22⋊C4—94no—
714C22⋊C4—182no—
715C22⋊C4—182no—
716C22⋊C4—182no—
717C42—94no—
718C42—182no—
719C42—182no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—24no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—42no—
746C22×C3D3×C4⋊C414yes—
747C22×C3D3×C4⋊C414yes—
748C22×C3C22×C4×D311yescharacteristic
749C22×C3C22×C4×D311yescharacteristic
750C22×C3C2×#23511yescharacteristic
751C22×C3C2×#23511yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C22×C3C2×D3×D411yescharacteristic
754C22×C3C2×#23711yescharacteristic
755C22×C3#100411yescharacteristic
756C22×C3#100411yescharacteristic
757C22×C3#100411yescharacteristic
758C22×C3C2×D3×Q811yescharacteristic
759C22×C3C2×D3×Q811yescharacteristic
760C22×C3D3×#4111yescharacteristic
761C22×C3#100911yescharacteristic
762C2×D3—34no—
763C2×D3—34no—
764C2×D3—64no—
765C2×D3—62no—
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—122no—
778C2×D3—122no—
779C2×D3—122no—
780C2×D3—122no—
781C2×D3—122no—
782C2×D3—122no—
783C3×C4—24no—
784C3×C4—22no—
785C3×C4—22no—
786C3×C4—42no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—62no—
790C3×C4—62no—
791C3×C4—62no—
792C3×C4—62no—
793C3×C4—62no—
794C3×C4—121no—
795C3×C4—121no—
796C3×C4—121no—
797Dic3—22no—
798Dic3—22no—
799Dic3—22no—
800Dic3—22no—
801Dic3—22no—
802Dic3—34no—
803Dic3—34no—
804Dic3—41no—
805Dic3—41no—
806Dic3—41no—
807Dic3—64no—
808Dic3—122no—
809Dic3—122no—
810Dic3—121no—
811Dic3—121no—
812Dic3—121no—
813Dic3—121no—
814C32#234911yescharacteristic, complemented, Sylow
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—92no—
820C23—92no—
821C23—92no—
822C23—181no—
823C23—181no—
824C23—181no—
825C23—181no—
826C23#379712yes—
827C23C4×D3212yes—
828C23#381112yes—
829C23C22×D3211yescharacteristic
830D4—916no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—44no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
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—92no—
862C2×C4—92no—
863C2×C4—92no—
864C2×C4—124no—
865C2×C4—124no—
866C2×C4—181no—
867C2×C4—181no—
868C2×C4—181no—
869C2×C4—181no—
870C2×C4—181no—
871C2×C4—181no—
872C2×C4—364no—
873C2×C4—364no—
874C2×C4—364no—
875C2×C4#380412yes—
876C2×C3—24no—
877C2×C3—24no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—44no—
886C2×C3C4×#23511yescharacteristic
887C2×C3#548611yescharacteristic
888C2×C3#549011yescharacteristic
889C2×C3#549011yescharacteristic
890C2×C3C2×D3×C4⋊C411yescharacteristic
891C2×C3C2×D3×C4⋊C411yescharacteristic
892C2×C3#551111yescharacteristic
893C2×C3#551111yescharacteristic
894C2×C3C4×#23711yescharacteristic
895C2×C3#554511yescharacteristic
896C2×C3#559111yescharacteristic
897C2×C3#563511yescharacteristic
898C2×C3#563611yescharacteristic
899C2×C3#565411yescharacteristic
900D3—64no—
901D3—64no—
902D3—124no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—94no—
910C22—182no—
911C22—182no—
912C22—182no—
913C22—182no—
914C22—182no—
915C22—182no—
916C22#6388314yes—
917C22C2×#379711yescharacteristic
918C22C2×C4×D3211yescharacteristic
919C22D3×#23511yescharacteristic
920C22#6430711yescharacteristic
921C22C2×#380411yescharacteristic
922C22C2×#381111yescharacteristic
923C22#6433011yescharacteristic
924C4—22no—
925C4—41no—
926C4—62no—
927C4—62no—
928C4—62no—
929C4—62no—
930C4—62no—
931C4—94no—
932C4—121no—
933C4—121no—
934C4—121no—
935C4—361no—
936C4—361no—
937C3—21no—
938C3#7336911yescharacteristic, complemented
939C3#7439411yescharacteristic, complemented
940C2—24no—
941C2—184no—
942C2C4×#380411yescharacteristic
943C2C2×#6388311yescharacteristic
944C2#1059495611yescharacteristic
945C2#1059499111yescharacteristic
946C2#1059505611yescharacteristic
947C2#1059507711yescharacteristic
948C2#1059550011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C3×#5210C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. #10591718C2semidirect
7. #10591716C2semidirect
8. #10591375C2semidirect
9. #10591370C2semidirect
10. #10591367C2semidirect
11. #10591328C2semidirect
12. #10591290C2semidirect
13. #10591256C2semidirect
14. #10591247C2semidirect
15. #10591241C2semidirect
45. #63952C4semidirect
67. #5210D3semidirect
68. C2×C3⋊#95D3semidirect
108. C22×C3×Dic3C2×C4semidirect
122. C2×#624C2×C4semidirect
128. C3×#217C2×C4semidirect
132. #3724C2×C4semidirect
138. #3722C2×C4semidirect
140. Dic32C2×C4semidirect
248. #638C4⋊C4semidirect
360. C22×Dic3C4×D3semidirect
398. #217C4×D3semidirect
814. C32#2349semidirect
938. C3#73369semidirect
939. C3#74394semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×#639522
C3×#52102
C2×C3×C3⋊#952
#105917182
#105917162
#105913752
#105913702
#105913672
#105913282
#105912902
#105912562
#105912472
#105912412
#743943
#733693