Finite Group Databasebeta

← #30624868

Subgroups — #30624868

Order 15616.

2960 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840831C211yesmaximal, characteristic, complemented
2C2×#16840830C211yesmaximal, characteristic, complemented
3#21462350C213yesmaximal, complemented
4#21462346C213yesmaximal, complemented
5#21462343C213yesmaximal, complemented
6#21462335C213yesmaximal, complemented
7#21462334C211yesmaximal, characteristic, complemented
8#21462324C211yesmaximal, characteristic, complemented
9Q8×C22⋊#6923C211yesmaximal, characteristic, complemented
10#21462307C213yesmaximal, complemented
11#21462306C213yesmaximal, complemented
12#124×#6923C213yesmaximal, complemented
13#21462276C213yesmaximal, complemented
14C4×Q8×#6923C211yesmaximal, characteristic, complemented
15#548×D61C211yesmaximal, characteristic
16#16840831—28no—
17#16840830—28no—
18C2×Q8×#6923C2213yes—
19C2×Q8×#6923C2211yescharacteristic
20C2×Q8×#6923C2213yes—
21C2×Q8×#6923C2211yescharacteristic
22C2×Q8×#6923C2211yescharacteristic
23C2×Q8×#6923C2211yescharacteristic
24C2×D4×#6923C2213yes—
25C2×D4×#6923C2213yes—
26C2×#14519856C2213yes—
27C2×#14519856C2213yes—
28C2×#14519856C2213yes—
29C22×C4⋊#6923C2213yes—
30(C2×#6923)⋊Q8C2213yes—
31(C2×#6923)⋊Q8C2213yes—
32#16840714C2213yes—
33#16840714C2213yes—
34#16840714C2213yes—
35#16840714C2213yes—
36#16840713C2213yes—
37#16840713C2213yes—
38#16840713C2213yes—
39#16840713C2213yes—
40#16840712C2211yescharacteristic
41#16840712C2213yes—
42#16840712C2213yes—
43#16840712C2213yes—
44#16840712C2216yes—
45#16840712C2216yes—
46#16840711C2216yes—
47#16840710C2216yes—
48#16840709C2216yes—
49#16840706C2213yes—
50#16840704C2213yes—
51#16840704C2213yes—
52C4⋊C4×#6923C2213yes—
53C4⋊C4×#6923C2213yes—
54C4×C4⋊#6923C2213yes—
55C4×C4⋊#6923C2213yes—
56C22⋊C4×#6923C2216yes—
57C22⋊C4×#6923C2216yes—
58C4×C22⋊#6923C2213yes—
59C4×C22⋊#6923C2213yes—
60C42×#6923C2213yes—
61C2×#41×D61C2211yescharacteristic
62C22×Q8×D61C2211yescharacteristic
63#16840424C411yescharacteristic, complemented
64#16840423C411yescharacteristic, complemented
65#16840422C413yescomplemented
66#16840421C413yescomplemented
67#16840420C413yescomplemented
68#16840419C411yescharacteristic, complemented
69#16840418C413yescomplemented
70#124×D61C2213yes—
71C22⋊Q8×D61C2213yes—
72#121×D61C2213yes—
73C4×Q8×D61C2211yescharacteristic
74C4×D4×D61C2213yes—
75C61×#548C411yescharacteristic, complemented
76C23×#6923C2316yes—
77Q8×#6923—24no—
78Q8×#6923—24no—
79Q8×#6923—24no—
80Q8×#6923—212no—
81Q8×#6923—212no—
82Q8×#6923D418yescomplemented
83D4×#6923—212no—
84D4×#6923—212no—
85#14519856—212no—
86#14519856—212no—
87#14519856—212no—
88C2×C4⋊#6923—212no—
89C2×C4⋊#6923C2313yes—
90C2×C4⋊#6923C2313yes—
91C2×C4⋊#6923C2313yes—
92C2×C4⋊#6923C2313yes—
93C2×C4⋊#6923C2313yes—
94C2×C4⋊#6923C2313yes—
95C2×C4⋊#6923C2311yescharacteristic
96C2×C4⋊#6923C2313yes—
97C2×C4⋊#6923C2313yes—
98C2×C4⋊#6923C2313yes—
99C2×C22⋊#6923C2313yes—
100C2×C22⋊#6923C2313yes—
101C2×C22⋊#6923C2313yes—
102C2×C22⋊#6923C2311yescharacteristic
103C2×C22⋊#6923C2311yescharacteristic
104C2×C22⋊#6923C2313yes—
105C2×C22⋊#6923C2313yes—
106C2×C22⋊#6923C2316yes—
107C2×C22⋊#6923C2313yes—
108C2×C4×#6923C2316yes—
109C2×C4×#6923C2311yescharacteristic
110C2×C4×#6923C2313yes—
111C2×C4×#6923C2313yes—
112C2×C4×#6923C2313yes—
113C2×C4×#6923C2313yes—
114C2×C4×#6923C2313yes—
115C2×C4×#6923C2313yes—
116C2×C4×#6923C2313yes—
117(C2×#6923)⋊C4C2313yes—
118(C2×#6923)⋊C4C2316yes—
119(C2×#6923)⋊C4C2313yes—
120(C2×#6923)⋊C4C2316yes—
121(C2×#6923)⋊C4C2316yes—
122(C2×#6923)⋊C4C2311yescharacteristic
123(C2×#6923)⋊C4C2313yes—
124(C2×#6923)⋊C4C2311yescharacteristic
125(C2×#6923)⋊C4C2313yes—
126C2×#11758226C2×C411yescharacteristic
127C2×#11758222C2×C413yes—
128C2×#11758224C2×C413yes—
129#41×D61—24no—
130#41×D61—24no—
131C22×Dic122C2×C413yescomplemented
132C2×Q8×D61—24no—
133C2×Q8×D61—24no—
134C2×Q8×D61C2×C411yescharacteristic, complemented
135C2×Q8×D61C2×C413yescomplemented
136C2×Q8×D61C2313yes—
137C2×Q8×D61C2311yescharacteristic
138C2×D4×D61C2313yes—
139C2×D4×D61C2313yes—
140C22×C4×D61C2313yes—
141C22×C4×D61C2313yes—
142#14519766C2×C413yescomplemented
143#14519765C2×C413yescomplemented
144#14519764C2×C413yescomplemented
145#14519763C2×C416yescomplemented
146#14519763C2×C416yescomplemented
147#14519757C2×C413yescomplemented
148#14519756C2×C413yescomplemented
149#14519755C2×C416yescomplemented
150#14519754C2×C416yescomplemented
151#14519753C2×C413yescomplemented
152#14519752C2×C413yescomplemented
153#14519751C2×C413yescomplemented
154#14519750C2×C416yescomplemented
155#14519749C2×C416yescomplemented
156#14519748C2×C413yescomplemented
157Q8×Dic61C2×C411yescharacteristic, complemented
158C4×Dic122C2×C413yescomplemented
159#14519742C2×C413yescomplemented
160C4×D244C2×C413yescomplemented
161D4×Dic61C2×C413yescomplemented
162#14519739C2×C413yescomplemented
163C4×C22⋊D61C2×C413yescomplemented
164C4×C22⋊D61C2×C413yescomplemented
165#14519737C2×C413yescomplemented
166#14519737C2×C413yescomplemented
167C4⋊C4×D61C2313yes—
168C4⋊C4×D61C2313yes—
169C22⋊C4×D61C2316yes—
170C22⋊C4×D61C2311yescharacteristic
171C22⋊C4×D61C2313yes—
172C42×D61C2313yes—
173C2×#41×C61C2×C411yescharacteristic
174C22×Q8×C61C2×C411yescharacteristic, complemented
175#124×C61C2×C413yescomplemented
176C22⋊Q8×C61C2×C413yescomplemented
177#121×C61C2×C413yescomplemented
178C4×Q8×C61C2×C411yescharacteristic, complemented
179C4×D4×C61C2×C413yescomplemented
180C23×D61C2411yescharacteristic
181C23×D61C2413yes—
182C22×#6923—212no—
183C22×#6923—46no—
184C22×#6923—46no—
185C22×#6923C2413yes—
186C22×#6923C2413yes—
187C22×#6923C2413yes—
188C22×#6923C2411yescharacteristic
189C22×#6923C2411yescharacteristic
190C22×#6923C2413yes—
191C22×#6923C2411yescharacteristic
192C22×#6923C2411yescharacteristic
193#41×C61—24no—
194C2×Q8×C61—24no—
195C2×Q8×C61C22×C413yes—
196C2×Q8×C61C22×C411yescharacteristic
197C2×D4×C61C22×C413yes—
198C2×D4×C61C22×C413yes—
199C22×C4×C61C22×C413yes—
200C22×C4×C61C22×C413yes—
201C2×C22⋊D61C22×C416yes—
202C2×C22⋊D61C22×C413yes—
203C2×C22⋊D61C22×C413yes—
204C22×Dic61C22×C413yes—
205C22×Dic61C22×C413yes—
206#11758226—24no—
207Q8×D61—24no—
208Q8×D61—26no—
209Q8×D61—26no—
210Q8×D61—212no—
211Q8×D61C2×D414yes—
212Q8×D61#4114yes—
213#11758224—212no—
214D4×D61—26no—
215D4×D61—26no—
216D4×D61—43no—
217D4×D61—43no—
218#11758222—212no—
219C2×D244C22×C413yes—
220C2×D244C22×C413yes—
221C2×C4×D61—26no—
222C2×C4×D61—26no—
223C2×C4×D61—26no—
224C2×C4×D61—26no—
225C2×C4×D61C22×C413yes—
226C2×C4×D61C22×C413yes—
227C2×C4×D61C22×C413yes—
228C2×C4×D61C22×C413yes—
229C2×C4×D61C2411yescharacteristic
230C2×C4×D61C2413yes—
231C2×C4×D61C2413yes—
232C2×C4×D61C2411yescharacteristic
233C2×C4×D61C2413yes—
234C2×Dic122—212no—
235C2×Dic122C22×C416yes—
236C2×Dic122C22×C413yes—
237C2×Dic122C22×C413yes—
238C22⋊#6923—26no—
239C22⋊#6923—22no—
240C22⋊#6923—26no—
241C22⋊#6923—26no—
242C22⋊#6923—22no—
243C22⋊#6923—26no—
244C22⋊#6923—46no—
245C22⋊#6923—43no—
246C22⋊#6923—43no—
247C4⋊#6923—26no—
248C4⋊#6923—22no—
249C4⋊#6923—26no—
250C4⋊#6923—26no—
251C4⋊#6923—26no—
252C4⋊#6923—26no—
253C4⋊#6923—26no—
254C4⋊#6923—43no—
255C4⋊#6923—43no—
256C4⋊#6923C2×D4112yes—
257C4×#6923—212no—
258C4×#6923—22no—
259C4×#6923—26no—
260C4×#6923—26no—
261C4×#6923—26no—
262C4×#6923—43no—
263C4×#6923—43no—
264C4×#6923—43no—
265C4×#6923C2×D4112yes—
266C4⋊C4×C61C22×C413yes—
267C4⋊C4×C61C22×C413yes—
268C22⋊C4×C61C22×C411yescharacteristic
269C22⋊C4×C61C22×C413yes—
270C22⋊C4×C61C22×C416yes—
271C42×C61C22×C413yes—
272C22⋊Dic61C22×C411yescharacteristic
273C22⋊Dic61C22×C413yes—
274C22⋊Dic61C22×C416yes—
275#11758198C22×C411yescharacteristic
276#11758198C22×C413yes—
277#11758198C22×C411yescharacteristic
278#11758198C22×C413yes—
279#11758198C22×C416yes—
280#11758198C22×C416yes—
281C4⋊Dic61C22×C413yes—
282C4⋊Dic61C22×C413yes—
283#11758196C22×C413yes—
284#11758196C22×C413yes—
285#11758196C22×C416yes—
286C4×Dic61C22×C413yes—
287C4×Dic61C22×C413yes—
288C4×Dic61C22×C413yes—
289C23×C61C23×C413yes—
290C23×C61C23×C411yescharacteristic
291C22×D61—21no—
292C22×D61—23no—
293C22×D61—21no—
294C22×D61—23no—
295C22×D61—21no—
296C22×D61—23no—
297C22×D61—21no—
298C22×D61—23no—
299C22×D61—23no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—23no—
303C22×D61C23×C413yes—
304C22×D61C23×C411yescharacteristic
305C22×D61C2511yescharacteristic
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—21no—
310C2×#6923—23no—
311C2×#6923—23no—
312C2×#6923—23no—
313C2×#6923—21no—
314C2×#6923—21no—
315C2×#6923—23no—
316C2×#6923—23no—
317C2×#6923—23no—
318C2×#6923—21no—
319C2×#6923—23no—
320C2×#6923—23no—
321C2×#6923—21no—
322C2×#6923—21no—
323C2×#6923—23no—
324C2×#6923—23no—
325C2×#6923—21no—
326C2×#6923—23no—
327C2×#6923—812no—
328C2×#6923C22×D416yes—
329C2×#6923C22×D412yes—
330C2×#69232−1+412yes—
331Q8×C61—26no—
332Q8×C61C4×D414yes—
333D4×C61—26no—
334D4×C61—43no—
335C2×C4×C61—26no—
336C2×C4×C61—26no—
337C2×C4×C61C23×C411yescharacteristic
338C2×C4×C61C23×C413yes—
339C2×C4×C61C23×C411yescharacteristic
340C2×C4×C61C23×C413yes—
341C2×C4×C61C23×C413yes—
342C22⋊D61—212no—
343C22⋊D61—43no—
344C22⋊D61—43no—
345C2×Dic61—26no—
346C2×Dic61—26no—
347C2×Dic61C23×C411yescharacteristic
348C2×Dic61C23×C413yes—
349C2×Dic61C23×C411yescharacteristic
350C2×Dic61C23×C413yes—
351C2×Dic61C23×C413yes—
352D244—26no—
353D244—43no—
354C4×D61—23no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—23no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—23no—
361C4×D61—23no—
362C4×D61—26no—
363C4×D61—26no—
364C4×D61—26no—
365C4×D61—26no—
366C4×D61C22×D416yes—
367C4×D61C2×#4116yes—
368Dic122—26no—
369Dic122—212no—
370Dic122C4×D4112yes—
371#34312—611nomaximal, Sylow
372C22×C61—21no—
373C22×C61—23no—
374C22×C61—21no—
375C22×C61—23no—
376C22×C61—21no—
377C22×C61—23no—
378C22×C61C24×C411yescharacteristic
379C2×D61—21no—
380C2×D61—23no—
381C2×D61—21no—
382C2×D61—23no—
383C2×D61—21no—
384C2×D61—23no—
385C2×D61—41no—
386C2×D61—43no—
387C2×D61—43no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—43no—
391C2×D61—41no—
392C2×D61—43no—
393C2×D61C23×D411yescharacteristic
394C2×D61C22×#4111yescharacteristic
395C2×D61C2×2−1+411yescharacteristic
396C2×D61#58511yescharacteristic
397C2×D61#58511yescharacteristic
398C2×D61#58511yescharacteristic
399#6923—22no—
400#6923—26no—
401#6923—22no—
402#6923—43no—
403#6923—41no—
404#6923—41no—
405#6923—43no—
406#6923—43no—
407C4×C61—23no—
408C4×C61—21no—
409C4×C61—23no—
410C4×C61—21no—
411C4×C61C2×C4×D416yes—
412Dic61—23no—
413Dic61—21no—
414Dic61—23no—
415Dic61—21no—
416Dic61C2×C4×D416yes—
417C2×#548—611no—
418C2×#520—611no—
419C2×#519—611no—
420#2367—613no—
421#2363—613no—
422#2360—613no—
423#2352—613no—
424#2351—611no—
425#2341—611no—
426Q8×C22⋊C4—611no—
427#2324—613no—
428#2323—613no—
429C4×#124—613no—
430#2293—613no—
431C42×Q8—611no—
432C2×C61—43no—
433C2×C61—41no—
434C2×C61C22×C4×D411yescharacteristic
435C2×C61#342811yescharacteristic
436C2×C61C4×2−1+411yescharacteristic
437D61—41no—
438D61—43no—
439D61#349711yescharacteristic
440D61#350011yescharacteristic
441D61#351611yescharacteristic
442D61#352411yescharacteristic
443C22×#41—611no—
444C23×Q8—611no—
445#548—611no—
446#548—611no—
447#548—613no—
448#548—613no—
449#548—613no—
450#548—611no—
451#548—613no—
452#548#692311yescharacteristic, complemented
453C2×#124—613no—
454C2×C22⋊Q8—613no—
455C2×#121—613no—
456#520—1228no—
457#519—1228no—
458C2×C4×Q8—611no—
459C2×C4×Q8—611no—
460C2×C4×Q8—613no—
461C2×C4×Q8—611no—
462C2×C4×Q8—611no—
463C2×C4×Q8—611no—
464C2×C4×Q8—613no—
465C2×C4×D4—613no—
466C2×C4×D4—613no—
467C2×C4×D4—613no—
468C2×#117—613no—
469C2×#117—613no—
470C2×#117—613no—
471C22×C4⋊C4—613no—
472#391—613no—
473#391—613no—
474#390—613no—
475#390—613no—
476#390—613no—
477#390—613no—
478#389—613no—
479#389—613no—
480#389—613no—
481#389—613no—
482#388—616no—
483#388—616no—
484#388—613no—
485#388—613no—
486#388—611no—
487#388—613no—
488#387—616no—
489#386—616no—
490#385—616no—
491#382—613no—
492#380—613no—
493#380—613no—
494C4×C4⋊C4—613no—
495C4×C4⋊C4—613no—
496C4×C4⋊C4—613no—
497C4×C4⋊C4—613no—
498C4×C22⋊C4—613no—
499C4×C22⋊C4—613no—
500C4×C22⋊C4—616no—
501C4×C22⋊C4—616no—
502C43—613no—
503C61#3431211yescharacteristic, complemented, Sylow
504C2×#41—611no—
505C2×#41—613no—
506C2×#41—613no—
507C2×#41—1224no—
508C2×#41—1224no—
509C2×#41C2×#692311yescharacteristic
510C22×Q8—611no—
511C22×Q8—613no—
512C22×Q8—613no—
513C22×Q8—611no—
514C22×Q8—613no—
515C22×Q8—1224no—
516C22×Q8—1224no—
517C22×Q8C2×#692311yescharacteristic, complemented
518C22×D4—613no—
519C22×D4—613no—
520C23×C4—613no—
521C23×C4—613no—
522C23×C4—616no—
523#124—613no—
524#124—613no—
525#124—616no—
526#124—616no—
527#124—613no—
528#124C2×#692313yescomplemented
529C22⋊Q8—613no—
530C22⋊Q8—613no—
531C22⋊Q8—616no—
532C22⋊Q8—613no—
533C22⋊Q8—616no—
534C22⋊Q8C2×#692313yescomplemented
535#121—613no—
536#121—616no—
537#121—613no—
538#121—613no—
539#121—616no—
540#121C2×#692313yescomplemented
541C4×Q8—618no—
542C4×Q8—611no—
543C4×Q8—613no—
544C4×Q8—613no—
545C4×Q8—12212no—
546C4×Q8—12212no—
547C4×Q8—1224no—
548C4×Q8—1224no—
549C4×Q8—1224no—
550C4×Q8C2×#692311yescharacteristic, complemented
551C4×D4—613no—
552C4×D4—613no—
553C4×D4—613no—
554C4×D4—613no—
555C4×D4—613no—
556C4×D4—613no—
557C4×D4—613no—
558C4×D4—12212no—
559C4×D4—12212no—
560C4×D4C2×#692313yescomplemented
561#117—12212no—
562#117—12212no—
563#117—12212no—
564C2×C4⋊C4—613no—
565C2×C4⋊C4—613no—
566C2×C4⋊C4—613no—
567C2×C4⋊C4—613no—
568C2×C4⋊C4—613no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—613no—
571C2×C4⋊C4—613no—
572C2×C4⋊C4—613no—
573C2×C4⋊C4—613no—
574C2×C4⋊C4—613no—
575C2×C4⋊C4—613no—
576C2×C4⋊C4—12212no—
577C2×C22⋊C4—611no—
578C2×C22⋊C4—613no—
579C2×C22⋊C4—616no—
580C2×C22⋊C4—613no—
581C2×C22⋊C4—611no—
582C2×C22⋊C4—613no—
583C2×C22⋊C4—613no—
584C2×C22⋊C4—611no—
585C2×C22⋊C4—613no—
586C2×C22⋊C4—613no—
587C2×C22⋊C4—616no—
588C2×C22⋊C4—613no—
589C2×C42—613no—
590C2×C42—613no—
591C2×C42—613no—
592C2×C42—616no—
593C2×C42—613no—
594C2×C42—613no—
595C2×C42—611no—
596C2×C42—613no—
597C2×C42—613no—
598C2×C42—613no—
599#95—611no—
600#95—613no—
601#95—613no—
602#95—613no—
603#95—616no—
604#95—616no—
605#95—613no—
606#95—616no—
607#95—611no—
608C24—613no—
609C24—611no—
610#41—24no—
611#41—12212no—
612#41—12212no—
613#41—1224no—
614C2×Q8—24no—
615C2×Q8—614no—
616C2×Q8—614no—
617C2×Q8—613no—
618C2×Q8—616no—
619C2×Q8—613no—
620C2×Q8—12212no—
621C2×Q8—1226no—
622C2×Q8—1226no—
623C2×Q8—12212no—
624C2×Q8—1224no—
625C2×Q8C22×#692313yes—
626C2×Q8C22×#692311yescharacteristic
627C2×D4—616no—
628C2×D4—613no—
629C2×D4—613no—
630C2×D4—613no—
631C2×D4—613no—
632C2×D4—1226no—
633C2×D4—1226no—
634C2×D4—2443no—
635C2×D4—2443no—
636C2×D4C22×#692313yes—
637C2×D4C22×#692313yes—
638C22×C4—613no—
639C22×C4—611no—
640C22×C4—613no—
641C22×C4—611no—
642C22×C4—613no—
643C22×C4—613no—
644C22×C4—611no—
645C22×C4—613no—
646C22×C4—613no—
647C22×C4—611no—
648C22×C4—613no—
649C22×C4—613no—
650C22×C4—613no—
651C22×C4—613no—
652C22×C4—613no—
653C22×C4—613no—
654C22×C4—611no—
655C22×C4—613no—
656C22×C4—611no—
657C22×C4—1226no—
658C22×C4—1226no—
659C22×C4—1226no—
660C22×C4—1226no—
661C22×C4—12212no—
662C22×C4—2446no—
663C22×C4—2446no—
664C22×C4C22×#692313yes—
665C22×C4C22×#692313yes—
666C4⋊C4—6112no—
667C4⋊C4—613no—
668C4⋊C4—613no—
669C4⋊C4—616no—
670C4⋊C4—613no—
671C4⋊C4—613no—
672C4⋊C4—1226no—
673C4⋊C4—1226no—
674C4⋊C4—1222no—
675C4⋊C4—1226no—
676C4⋊C4—1226no—
677C4⋊C4—1226no—
678C4⋊C4—1226no—
679C4⋊C4—2443no—
680C4⋊C4—2443no—
681C4⋊C4C22×#692313yes—
682C4⋊C4C22×#692313yes—
683C22⋊C4—611no—
684C22⋊C4—613no—
685C22⋊C4—616no—
686C22⋊C4—611no—
687C22⋊C4—611no—
688C22⋊C4—613no—
689C22⋊C4—613no—
690C22⋊C4—616no—
691C22⋊C4—616no—
692C22⋊C4—1222no—
693C22⋊C4—1226no—
694C22⋊C4—1226no—
695C22⋊C4—1226no—
696C22⋊C4—1222no—
697C22⋊C4—1226no—
698C22⋊C4—2443no—
699C22⋊C4—2446no—
700C22⋊C4—2443no—
701C22⋊C4C22×#692311yescharacteristic
702C22⋊C4C22×#692313yes—
703C22⋊C4C22×#692316yes—
704C42—6112no—
705C42—613no—
706C42—613no—
707C42—613no—
708C42—1226no—
709C42—1226no—
710C42—12212no—
711C42—1226no—
712C42—1222no—
713C42—2443no—
714C42—2443no—
715C42—2443no—
716C42C22×#692313yes—
717C23—611no—
718C23—613no—
719C23—611no—
720C23—1221no—
721C23—1223no—
722C23—1221no—
723C23—1223no—
724C23—1221no—
725C23—1223no—
726C23—1223no—
727C23—1221no—
728C23—1223no—
729C23—1223no—
730C23—1221no—
731C23—1221no—
732C23C23×#692313yes—
733C23C23×#692311yescharacteristic
734Q8—26no—
735Q8—6112no—
736Q8—12212no—
737Q8—1226no—
738Q8D4×#692314yes—
739D4—26no—
740D4—43no—
741D4—12212no—
742D4—1226no—
743D4—2443no—
744D4—2443no—
745D4—2443no—
746C2×C4—26no—
747C2×C4—26no—
748C2×C4—613no—
749C2×C4—616no—
750C2×C4—616no—
751C2×C4—612no—
752C2×C4—616no—
753C2×C4—612no—
754C2×C4—611no—
755C2×C4—613no—
756C2×C4—613no—
757C2×C4—611no—
758C2×C4—1226no—
759C2×C4—1226no—
760C2×C4—1223no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1223no—
764C2×C4—1223no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1223no—
768C2×C4—1226no—
769C2×C4—1226no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1223no—
775C2×C4—1223no—
776C2×C4—1226no—
777C2×C4—1226no—
778C2×C4—1221no—
779C2×C4—1223no—
780C2×C4—1221no—
781C2×C4—1223no—
782C2×C4—1223no—
783C2×C4—1223no—
784C2×C4—1223no—
785C2×C4—1221no—
786C2×C4—1223no—
787C2×C4—1221no—
788C2×C4—1223no—
789C2×C4—1223no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1223no—
793C2×C4—48812no—
794C2×C4C23×#692311yescharacteristic
795C2×C4C23×#692313yes—
796C2×C4C23×#692313yes—
797C2×C4C23×#692311yescharacteristic
798C2×C4C23×#692313yes—
799C22—21no—
800C22—23no—
801C22—21no—
802C22—23no—
803C22—21no—
804C22—23no—
805C22—611no—
806C22—611no—
807C22—611no—
808C22—611no—
809C22—611no—
810C22—611no—
811C22—1221no—
812C22—1223no—
813C22—1221no—
814C22—1223no—
815C22—1223no—
816C22—1221no—
817C22—2443no—
818C22—2441no—
819C22—2441no—
820C22—2443no—
821C22—2441no—
822C22—2443no—
823C22—2441no—
824C22—2443no—
825C22C24×#692311yescharacteristic
826C4—21no—
827C4—23no—
828C4—23no—
829C4—21no—
830C4—616no—
831C4—1226no—
832C4—1222no—
833C4—1222no—
834C4—1221no—
835C4—1223no—
836C4—1223no—
837C4—1221no—
838C4—2443no—
839C4—2441no—
840C4—2441no—
841C4—2443no—
842C4—2443no—
843C4C2×D4×#692316yes—
844C2—41no—
845C2—43no—
846C2—611no—
847C2—611no—
848C2—611no—
849C2—611no—
850C2—2441no—
851C2—2443no—
852C2C22×D4×#692311yescharacteristic
853C2#2146279911yescharacteristic
854C22−1+4×#692311yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6923
commutator, socleC22×C61C24×C4
FittingC61×#548C4
prime radical#548×D61C2
cosocleC22×D61C25
hypercenter#548#6923
hypocenterC61#34312
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#16840831C2semidirect
2. C2×#16840830C2semidirect
3. #21462350C2semidirect
4. #21462346C2semidirect
5. #21462343C2semidirect
6. #21462335C2semidirect
7. #21462334C2semidirect
8. #21462324C2semidirect
9. Q8×C22⋊#6923C2semidirect
10. #21462307C2semidirect
11. #21462306C2semidirect
12. #124×#6923C2semidirect
13. #21462276C2semidirect
14. C4×Q8×#6923C2semidirect
63. #16840424C4semidirect
64. #16840423C4semidirect
65. #16840422C4semidirect
66. #16840421C4semidirect
67. #16840420C4semidirect
68. #16840419C4semidirect
69. #16840418C4semidirect
75. C61×#548C4semidirect
82. Q8×#6923D4semidirect
131. C22×Dic122C2×C4semidirect
134. C2×Q8×D61C2×C4semidirect
135. C2×Q8×D61C2×C4semidirect
142. #14519766C2×C4semidirect
143. #14519765C2×C4semidirect
144. #14519764C2×C4semidirect
145. #14519763C2×C4semidirect
146. #14519763C2×C4semidirect
147. #14519757C2×C4semidirect
148. #14519756C2×C4semidirect
149. #14519755C2×C4semidirect
150. #14519754C2×C4semidirect
151. #14519753C2×C4semidirect
152. #14519752C2×C4semidirect
153. #14519751C2×C4semidirect
154. #14519750C2×C4semidirect
155. #14519749C2×C4semidirect
156. #14519748C2×C4semidirect
157. Q8×Dic61C2×C4semidirect
158. C4×Dic122C2×C4semidirect
159. #14519742C2×C4semidirect
160. C4×D244C2×C4semidirect
161. D4×Dic61C2×C4semidirect
162. #14519739C2×C4semidirect
163. C4×C22⋊D61C2×C4semidirect
164. C4×C22⋊D61C2×C4semidirect
165. #14519737C2×C4semidirect
166. #14519737C2×C4semidirect
174. C22×Q8×C61C2×C4semidirect
175. #124×C61C2×C4semidirect
176. C22⋊Q8×C61C2×C4semidirect
177. #121×C61C2×C4semidirect
178. C4×Q8×C61C2×C4semidirect
179. C4×D4×C61C2×C4semidirect
452. #548#6923semidirect
503. C61#34312semidirect
517. C22×Q8C2×#6923semidirect
528. #124C2×#6923semidirect
534. C22⋊Q8C2×#6923semidirect
540. #121C2×#6923semidirect
550. C4×Q8C2×#6923semidirect
560. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408312
C2×#168408302
#214623502
#214623462
#214623432
#214623352
#214623342
#214623242
Q8×C22⋊#69232
#214623072
#214623062
#124×#69232
#214622762
C4×Q8×#69232
#548×D612
#3431261