Finite Group Databasebeta

← #10812196

Subgroups — #10812196

Order 768.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#433C211yesmaximal, characteristic, complemented
2#82267C211yesmaximal, characteristic
3C2×#4726C211yesmaximal, characteristic
4#71584C211yesmaximal, characteristic, complemented
5#70478C211yesmaximal, characteristic, complemented
6#70478C211yesmaximal, characteristic, complemented
7#70450C211yesmaximal, characteristic, complemented
8#70449C211yesmaximal, characteristic, complemented
9#69955C211yesmaximal, characteristic
10#69909C211yesmaximal, characteristic, complemented
11#69907C211yesmaximal, characteristic, complemented
12#69835C211yesmaximal, characteristic, complemented
13#69808C211yesmaximal, characteristic, complemented
14#69785C211yesmaximal, characteristic, complemented
15#69781C211yesmaximal, characteristic, complemented
16#22559—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C2×C3×#117C2211yescharacteristic
19C2×#926C2211yescharacteristic
20C22×ΓL(1,𝔽25)C2211yescharacteristic
21C22×ΓL(1,𝔽25)C2211yescharacteristic
22C3×#433—24no—
23C2×C3×C4⋊C8C2211yescharacteristic, complemented
24C2×C3×C4⋊C8C2211yescharacteristic, complemented
25C2×C3×C22⋊C8C2211yescharacteristic
26C2×C3×C22⋊C8C2211yescharacteristic
27C2×C3×#97C2211yescharacteristic, complemented
28C2×C3×C4×C8C2211yescharacteristic, complemented
29C2×#830C2211yescharacteristic
30C2×#830C2211yescharacteristic
31C2×(C2×D3)⋊C8C2211yescharacteristic
32C2×(C2×D3)⋊C8C2211yescharacteristic
33C2×(C2×D3)⋊C8C2211yescharacteristic
34C2×(C2×D3)⋊C8C2211yescharacteristic
35C2×(C2×D3)⋊C8C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×#815C2211yescharacteristic, complemented
38C2×Dic3⋊C8C2211yescharacteristic, complemented
39C2×Dic3⋊C8C2211yescharacteristic, complemented
40C2×C8×Dic3C2211yescharacteristic, complemented
41#4987C411yescharacteristic
42#4987C411yescharacteristic
43#4987C411yescharacteristic
44#4987C411yescharacteristic
45#4955C411yescharacteristic
46#4955C411yescharacteristic
47#4943C411yescharacteristic
48#4943C411yescharacteristic
49C4×(C2×D3)⋊C4C2211yescharacteristic
50C4×(C2×D3)⋊C4C2211yescharacteristic
51C4×(C2×D3)⋊C4C2211yescharacteristic
52C4×(C2×D3)⋊C4C2211yescharacteristic
53#4726—24no—
54#4550C2211yescharacteristic, complemented
55#4550C2211yescharacteristic, complemented
56#4550C2211yescharacteristic, complemented
57#4550C2211yescharacteristic, complemented
58#4524C2211yescharacteristic, complemented
59#4524C2211yescharacteristic, complemented
60#4524C2211yescharacteristic, complemented
61#4524C2211yescharacteristic, complemented
62C2×#433D311yescharacteristic, complemented
63C2×#407—31no—
64#2280—31no—
65#1924—31no—
66#1924—31no—
67#1923—31no—
68#1923—31no—
69#1851—31no—
70#1851—31no—
71#1818—31no—
72#1798—31no—
73#1779—31no—
74#1753—31no—
75#1753—31no—
76#1750—31no—
77C24×D3C2×C411yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×Dic3C2×C411yescharacteristic
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3—22no—
84C22×C4×D3—41no—
85C22×C4×D3—41no—
86C22×C4×D3C2×C411yescharacteristic
87C22×C4×D3C2×C411yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×#117—22no—
95C3×#117—22no—
96C2×C3×C4⋊C4C2×C411yescharacteristic
97C2×C3×C4⋊C4C2×C411yescharacteristic
98C2×C3×C22⋊C4C2×C411yescharacteristic
99C2×C3×C22⋊C4C2×C411yescharacteristic
100C2×C3×C42C2311yescharacteristic
101C2×C3×C42C2311yescharacteristic
102C2×#217C2×C411yescharacteristic
103C2×#217C2×C411yescharacteristic
104C2×(C2×D3)⋊C4C2×C411yescharacteristic
105C2×(C2×D3)⋊C4C2×C411yescharacteristic
106C2×(C2×D3)⋊C4C2×C411yescharacteristic
107C2×(C2×D3)⋊C4C2×C411yescharacteristic
108C2×(C2×D3)⋊C4C2×C411yescharacteristic
109C2×(C2×D3)⋊C4C2×C411yescharacteristic
110C2×(C2×D3)⋊C4C2×C411yescharacteristic
111C2×(C2×D3)⋊C4C2×C411yescharacteristic
112#926—41no—
113#926—41no—
114C2×C4⋊Dic3C2×C411yescharacteristic
115C2×C4⋊Dic3C2×C411yescharacteristic
116C2×C4×Dic3C2311yescharacteristic
117C2×C4×Dic3C2311yescharacteristic
118C22×C3⋊C8C2311yescharacteristic
119C22×C3⋊C8C2311yescharacteristic
120C22×C3⋊C8C2311yescharacteristic
121C22×C3⋊C8C2311yescharacteristic
122C2×ΓL(1,𝔽25)—22no—
123C2×ΓL(1,𝔽25)—22no—
124C2×ΓL(1,𝔽25)—22no—
125C2×ΓL(1,𝔽25)—22no—
126C2×ΓL(1,𝔽25)—41no—
127C2×ΓL(1,𝔽25)—41no—
128C3×C4⋊C8—22no—
129C3×C4⋊C8—22no—
130C3×C22⋊C8—22no—
131C3×C22⋊C8D414yes—
132C3×#97—22no—
133C3×C4×C8—22no—
134C3⋊#95C2×C411yescharacteristic
135C3⋊#95C2×C411yescharacteristic
136C3⋊#95C2×C411yescharacteristic
137C3⋊#95C2×C411yescharacteristic
138C3⋊#95C2×C411yescharacteristic
139C3⋊#95C2×C411yescharacteristic
140C3⋊#95C2×C411yescharacteristic
141C3⋊#95C2×C411yescharacteristic
142#830—22no—
143#830—22no—
144(C2×D3)⋊C8—22no—
145(C2×D3)⋊C8—22no—
146(C2×D3)⋊C8—22no—
147(C2×D3)⋊C8—22no—
148(C2×D3)⋊C8—41no—
149(C2×D3)⋊C8—41no—
150#815—41no—
151Dic3⋊C8—41no—
152Dic3⋊C8—41no—
153C8×Dic3—41no—
154C24×C4—31no—
155C22×M16—31no—
156C22×M16—31no—
157C2×#117—31no—
158C2×#117C2×D311yescharacteristic
159#433—24no—
160C2×C4⋊C8—31no—
161C2×C4⋊C8—31no—
162C2×C4⋊C8C2×D311yescharacteristic, complemented
163C2×C4⋊C8C2×D311yescharacteristic, complemented
164#407—64no—
165C2×C22⋊C8—31no—
166C2×C22⋊C8—31no—
167C2×C22⋊C8—31no—
168C2×C22⋊C8—31no—
169C2×C22⋊C8—31no—
170C2×C22⋊C8—31no—
171C2×C22⋊C8—31no—
172C2×C22⋊C8—31no—
173C2×C22⋊C8C2×D311yescharacteristic
174C2×C22⋊C8C2×D311yescharacteristic
175C2×#97—31no—
176C2×#97C2×D311yescharacteristic, complemented
177C2×C4×C8—31no—
178C2×C4×C8C2×D311yescharacteristic, complemented
179#381—31no—
180#381—31no—
181#380—31no—
182#380—31no—
183#380—31no—
184#380—31no—
185#379—31no—
186#379—31no—
187C4×C22⋊C4—31no—
188C4×C22⋊C4—31no—
189C4×C22⋊C4—31no—
190C4×C22⋊C4—31no—
191#336—31no—
192#336—31no—
193#336—31no—
194#336—31no—
195#336—31no—
196#336—31no—
197#336—31no—
198#336—31no—
199C24×C3C22×C411yescharacteristic
200C23×D3—22no—
201C23×D3—22no—
202C23×D3—22no—
203C23×D3—41no—
204C23×D3—41no—
205C23×D3—41no—
206C23×D3—41no—
207C23×D3C22×C411yescharacteristic
208C23×D3C22×C411yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4C22×C411yescharacteristic
214C22×C3×C4C22×C411yescharacteristic
215C22×C3×C4C22×C411yescharacteristic
216C22×C3×C4C22×C411yescharacteristic
217C22×C3×C4C22×C411yescharacteristic
218C22×C3×C4C2×D412yes—
219C22×C3×C4#4112yes—
220C22×C3×C4C2411yescharacteristic
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—41no—
224C22×Dic3C22×C411yescharacteristic
225C22×Dic3C22×C411yescharacteristic
226C22×Dic3C22×C411yescharacteristic
227C22×Dic3C22×C411yescharacteristic
228C22×Dic3C22×C411yescharacteristic
229C22×Dic3C22×C411yescharacteristic
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—22no—
235C2×C4×D3—22no—
236C2×C4×D3—22no—
237C2×C4×D3—21no—
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—22no—
244C2×C4×D3—44no—
245C2×C4×D3—44no—
246C2×C4×D3—44no—
247C2×C4×D3—44no—
248C2×C4×D3—41no—
249C2×C4×D3—41no—
250C2×C4×D3#4112yes—
251C2×C4×D3#4112yes—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8C2×D412yes—
263C2×C3×C8C2×D412yes—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—22no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—22no—
268C3×C42—21no—
269C3×C42—21no—
270C3×C42—21no—
271C3×C42—21no—
272#217—41no—
273#217—41no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—41no—
277(C2×D3)⋊C4—41no—
278(C2×D3)⋊C4—41no—
279(C2×D3)⋊C4—41no—
280(C2×D3)⋊C4—41no—
281(C2×D3)⋊C4—41no—
282C4⋊Dic3—41no—
283C4⋊Dic3—41no—
284C4×Dic3—21no—
285C4×Dic3—21no—
286C4×Dic3—21no—
287C4×Dic3—21no—
288C2×C3⋊C8—21no—
289C2×C3⋊C8—21no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—21no—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300ΓL(1,𝔽25)—44no—
301ΓL(1,𝔽25)—44no—
302C25—31no—
303C23×C4—31no—
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—62no—
309C23×C4—62no—
310C23×C4—62no—
311C23×C4—62no—
312C23×C4—121no—
313C23×C4—121no—
314C23×C4C22×D311yescharacteristic
315C2×M16—62no—
316C2×M16—62no—
317C2×M16—62no—
318C2×M16—62no—
319C2×M16—121no—
320C2×M16—121no—
321C22×C8—31no—
322C22×C8—31no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8C22×D311yescharacteristic
326C22×C8C22×D311yescharacteristic
327C22×C8C22×D311yescharacteristic
328C22×C8C22×D311yescharacteristic
329#117—22no—
330#117—22no—
331#117—121no—
332#117—121no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4C4×D311yescharacteristic
336C2×C4⋊C4C4×D311yescharacteristic
337C2×C22⋊C4—31no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—31no—
340C2×C22⋊C4—31no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—31no—
343C2×C22⋊C4—31no—
344C2×C22⋊C4—31no—
345C2×C22⋊C4—31no—
346C2×C22⋊C4—31no—
347C2×C22⋊C4C4×D311yescharacteristic
348C2×C22⋊C4C4×D311yescharacteristic
349C2×C42—31no—
350C2×C42—31no—
351C2×C42C22×D311yescharacteristic
352C2×C42C22×D311yescharacteristic
353C4⋊C8—22no—
354C4⋊C8—22no—
355C4⋊C8—121no—
356C4⋊C8—121no—
357C22⋊C8—22no—
358C22⋊C8—62no—
359C22⋊C8—62no—
360C22⋊C8—62no—
361C22⋊C8—62no—
362C22⋊C8—62no—
363C22⋊C8—62no—
364C22⋊C8—121no—
365C22⋊C8—121no—
366C22⋊C8#6714yes—
367#97—22no—
368#97—121no—
369C4×C8—22no—
370C4×C8—121no—
371#95—31no—
372#95—31no—
373#95—31no—
374#95—31no—
375#95—31no—
376#95—31no—
377#95—31no—
378#95—31no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3C4×D412yes—
386C23×C3C23×C411yescharacteristic
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—44no—
400C22×D3—44no—
401C22×D3—44no—
402C22×D3—44no—
403C22×D3—44no—
404C22×D3—44no—
405C22×D3—44no—
406C22×D3#11712yes—
407C22×D3#13112yes—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4C4×D412yes—
427C2×C3×C4C22×D411yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430C2×C3×C4C2×#4111yescharacteristic
431C2×C3×C4H(5,𝔽2)11yescharacteristic
432C2×C3×C4H(5,𝔽2)11yescharacteristic
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—44no—
451C2×Dic3#11712yes—
452C4×D3—22no—
453C4×D3—22no—
454C4×D3—22no—
455C4×D3—22no—
456C4×D3—44no—
457C4×D3—44no—
458C4×D3—41no—
459C4×D3—41no—
460C4×D3—41no—
461C4×D3—41no—
462C3×C8—22no—
463C3×C8—22no—
464C3×C8—41no—
465C3×C8—41no—
466C3⋊C8—41no—
467C3⋊C8—41no—
468C3⋊C8—41no—
469C3⋊C8—41no—
470C24—31no—
471C24—31no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—121no—
476C24—121no—
477C24—121no—
478C24—121no—
479C24C2×C4×D311yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—31no—
485C22×C4—32no—
486C22×C4—32no—
487C22×C4—31no—
488C22×C4—31no—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4—31no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—121no—
509C22×C4—121no—
510C22×C4—124no—
511C22×C4—124no—
512C22×C4—124no—
513C22×C4—124no—
514C22×C4—121no—
515C22×C4C2×C4×D311yescharacteristic
516C22×C4C2×C4×D311yescharacteristic
517C22×C4C2×C4×D311yescharacteristic
518C22×C4C2×C4×D311yescharacteristic
519C22×C4C2×C4×D311yescharacteristic
520C22×C4#23512yes—
521C22×C4C2×#6712yes—
522C22×C4C23×D311yescharacteristic
523M16—124no—
524M16—124no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—61no—
547C2×C8C2×#6712yes—
548C2×C8C2×#6712yes—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—121no—
552C4⋊C4—121no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—62no—
556C22⋊C4—62no—
557C22⋊C4—121no—
558C22⋊C4—121no—
559C22⋊C4—121no—
560C22⋊C4—121no—
561C22⋊C4—121no—
562C22⋊C4—121no—
563C22⋊C4—121no—
564C22⋊C4—121no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—61no—
570C42—61no—
571C42—61no—
572C42—61no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3C2×#11711yescharacteristic
581C22×C3C2×C4×D411yescharacteristic
582C22×C3#51811yescharacteristic
583C22×C3C2×#13111yescharacteristic
584C22×C3#56811yescharacteristic
585C22×C3#56811yescharacteristic
586C22×C3#56811yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—22no—
592C2×D3—22no—
593C2×D3—416no—
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C3×C4—22no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4#54611yescharacteristic
608C3×C4#54611yescharacteristic
609C3×C4#55111yescharacteristic
610C3×C4#55111yescharacteristic
611Dic3—22no—
612Dic3—41no—
613Dic3—41no—
614Dic3—41no—
615Dic3—41no—
616Dic3—41no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—32no—
624C23—32no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—61no—
635C23—61no—
636C23—61no—
637C23—124no—
638C23—124no—
639C23—124no—
640C23—124no—
641C23—124no—
642C23—124no—
643C23—124no—
644C23C4×#6712yes—
645C23C22×C4×D311yescharacteristic
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—32no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—124no—
687C2×C4—124no—
688C2×C4—124no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4C4×#6712yes—
694C2×C4C2×#23511yescharacteristic
695C2×C4D3×#4111yescharacteristic
696C2×C4D3×#4111yescharacteristic
697C2×C4#100911yescharacteristic
698C2×C4#100911yescharacteristic
699C2×C4C22×#6711yescharacteristic
700C8—22no—
701C8—22no—
702C8—41no—
703C8—41no—
704C8—121no—
705C8—121no—
706C8—121no—
707C8—121no—
708C2×C3—42no—
709C2×C3#234211yescharacteristic
710C2×C3#292111yescharacteristic
711C2×C3#292411yescharacteristic
712C2×C3#293011yescharacteristic
713C2×C3#293311yescharacteristic
714C2×C3#297611yescharacteristic
715C2×C3#297811yescharacteristic
716D3—42no—
717D3—42no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—62no—
726C22—62no—
727C22—62no—
728C22—62no—
729C22—62no—
730C22—62no—
731C22—1216no—
732C22—121no—
733C22—121no—
734C22—121no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22D3×#11711yescharacteristic
741C22#552111yescharacteristic
742C22D3×#13111yescharacteristic
743C22#575011yescharacteristic
744C22#575011yescharacteristic
745C22#575011yescharacteristic
746C22C2×C4×#6711yescharacteristic
747C4—22no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—62no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4#552711yescharacteristic
759C4#552711yescharacteristic
760C4#582911yescharacteristic
761C4#582911yescharacteristic
762C3#2255911yescharacteristic, complemented, Sylow
763C2—42no—
764C2—122no—
765C2—122no—
766C2#7937111yescharacteristic
767C2#7937411yescharacteristic
768C2#7937611yescharacteristic
769C2#7937811yescharacteristic
770C2#8227111yescharacteristic
771C2#8379511yescharacteristic
772C2#8379611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC2×C3×#433C2
prime radicalC24×D3C2×C4
cosocleC22×C3×C4C24
hypercenterC2×#433D3
hypocenterC3#22559
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×C3×#433C2semidirect
4. #71584C2semidirect
5. #70478C2semidirect
6. #70478C2semidirect
7. #70450C2semidirect
8. #70449C2semidirect
10. #69909C2semidirect
11. #69907C2semidirect
12. #69835C2semidirect
13. #69808C2semidirect
14. #69785C2semidirect
15. #69781C2semidirect
23. C2×C3×C4⋊C8C22semidirect
24. C2×C3×C4⋊C8C22semidirect
27. C2×C3×#97C22semidirect
28. C2×C3×C4×C8C22semidirect
37. C2×#815C22semidirect
38. C2×Dic3⋊C8C22semidirect
39. C2×Dic3⋊C8C22semidirect
40. C2×C8×Dic3C22semidirect
54. #4550C22semidirect
55. #4550C22semidirect
56. #4550C22semidirect
57. #4550C22semidirect
58. #4524C22semidirect
59. #4524C22semidirect
60. #4524C22semidirect
61. #4524C22semidirect
62. C2×#433D3semidirect
162. C2×C4⋊C8C2×D3semidirect
163. C2×C4⋊C8C2×D3semidirect
176. C2×#97C2×D3semidirect
178. C2×C4×C8C2×D3semidirect
762. C3#22559semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4332
#822672
C2×#47262
#715842
#704782
#704502
#704492
#699552
#699092
#699072
#698352
#698082
#697852
#697812
#225593