Finite Group Databasebeta

← C2×#21458851 #30560982

Subgroups — C2×#21458851 #30560982

Order 15616.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840490C211yesmaximal, characteristic, complemented
2C2×#16840484C211yesmaximal, characteristic
3#21458851C2116yesmaximal, direct product factor
4C2×#16840156C211yesmaximal, characteristic
5C2×#16840155C211yesmaximal, characteristic
6C2×#16840140C211yesmaximal, characteristic, complemented
7C2×#16839987C211yesmaximal, characteristic
8C2×#16839984C211yesmaximal, characteristic
9C2×#16839972C211yesmaximal, characteristic, complemented
10C2×#16839971C211yesmaximal, characteristic, complemented
11C2×#16839971C211yesmaximal, characteristic, complemented
12C2×#16839966C211yesmaximal, characteristic
13C2×#16839890C211yesmaximal, characteristic, complemented
14C2×#16839868C211yesmaximal, characteristic, complemented
15C2×#16839849C211yesmaximal, characteristic
16C2×C61×#441C211yesmaximal, characteristic, complemented
17C22×Dic244C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758190C2211yescharacteristic
24C22×#11758201C2211yescharacteristic
25#16840490—24no—
26#16840490C2218yescomplemented
27#16840484—24no—
28#16840484C2218yes—
29C2×#14519777C2211yescharacteristic
30C2×#14519775C2211yescharacteristic
31C2×#14519775C2211yescharacteristic
32C2×#14519775C2211yescharacteristic
33C2×#14519772—21no—
34C2×#14519771—21no—
35C2×#14519769—21no—
36C2×#14519767—21no—
37C2×#14519767—21no—
38C2×#14519766C2211yescharacteristic
39C2×#14519765C2211yescharacteristic
40C2×#14519755—21no—
41C2×C4×Dic122—21no—
42C2×C4×Dic122C2211yescharacteristic
43C2×#14519742C2211yescharacteristic
44C2×#14519742C2211yescharacteristic
45C2×#14519742C2211yescharacteristic
46C2×#14519739C2211yescharacteristic
47C2×#14519734—21no—
48#16840156C2218yes—
49#16840155C2218yes—
50#16840140C2218yescomplemented
51#16839987C2218yes—
52#16839984C2218yes—
53#16839972C2218yescomplemented
54#16839971C2218yescomplemented
55#16839971C2218yescomplemented
56#16839966C2218yes—
57#16839890C2218yescomplemented
58#16839868C2218yescomplemented
59#16839849C2218yes—
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×Q8×C61C2211yescharacteristic
72C61×#441C2218yescomplemented
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C2×Dic244—24no—
84C2×Dic244—42no—
85C2×Dic244C2314yes—
86C2×Dic244C2314yes—
87C2×#11758202—42no—
88C2×#11758202—42no—
89C2×#11758202—42no—
90C2×#11758202C2314yes—
91C2×#11758202C2314yes—
92C2×#11758202C2314yes—
93C2×#11758190—24no—
94C2×#11758190—42no—
95C2×#11758190C2314yes—
96C2×#11758190C2314yes—
97C2×#11758201—42no—
98C2×#11758201C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519777—22no—
102#14519777C2314yes—
103#14519775—22no—
104#14519775—22no—
105#14519775—22no—
106#14519775C2314yes—
107#14519775C2314yes—
108#14519775C2314yes—
109#14519772—28no—
110#14519771—28no—
111#14519769—28no—
112#14519767—28no—
113#14519767—28no—
114#14519766—22no—
115#14519766C2314yes—
116#14519765—22no—
117#14519765C2314yes—
118#14519755—28no—
119C4×Dic122—28no—
120C4×Dic122D414yes—
121C4×Dic122C2314yes—
122#14519742—22no—
123#14519742—22no—
124#14519742—22no—
125#14519742C2314yes—
126#14519742C2314yes—
127#14519742C2314yes—
128#14519739—22no—
129#14519739C2314yes—
130#14519734—28no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61D411yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×#11758196D411yescharacteristic
144C2×#11758196D411yescharacteristic
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61—21no—
152C2×C4×Dic61—21no—
153C2×C4×Dic61C2311yescharacteristic
154C2×C4×Dic61C2311yescharacteristic
155C4⋊#92418C2314yes—
156#14519706C2314yes—
157#14519706C2314yes—
158#14519700C2314yes—
159#14519700C2314yes—
160#14519700C2314yes—
161#14519697C2314yes—
162#14519687C2314yes—
163C8×Dic61C2314yes—
164C22×Q8×C61C2311yescharacteristic
165C22×Q8×C61C2311yescharacteristic
166C2×Q16×C61—24no—
167C2×Q16×C61C2314yes—
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170C4×Q8×C61—22no—
171C4×Q8×C61—22no—
172C4×Q8×C61C2314yes—
173C4×Q8×C61C2314yes—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C42×C61—21no—
179C2×C42×C61—21no—
180C2×C42×C61C2311yescharacteristic
181#106×C61C2314yes—
182#103×C61C2314yes—
183#103×C61C2314yes—
184#97×C61C2314yes—
185C23×D61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61C2412yes—
193C2×Q8×C61C2412yes—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—21no—
211C2×D244C2412yes—
212C2×C4×D61—24no—
213C2×C4×D61—44no—
214C2×Dic122—24no—
215C2×Dic122—22no—
216C2×Dic122—22no—
217C2×Dic122—22no—
218C2×Dic122—22no—
219C2×Dic122—22no—
220C2×Dic122—22no—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122C2×D414yes—
225C2×Dic122C2412yes—
226C2×Dic122C2412yes—
227C2×Dic122C2412yes—
228Q16×C61—28no—
229C2×C8×C61—22no—
230C2×C8×C61#4114yes—
231C2×C8×C61C2412yes—
232C2×C8×C61C2412yes—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61C2412yes—
238C4⋊C4×C61C2412yes—
239C42×C61—24no—
240C42×C61—24no—
241C42×C61C2×D412yes—
242C42×C61C2412yes—
243#11758202—44no—
244#11758202—44no—
245#11758202—44no—
246#11758201—44no—
247#11758198—24no—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198—24no—
252C4⋊Dic61—24no—
253C4⋊Dic61—24no—
254C4⋊Dic61C2×D414yes—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196C2×D414yes—
265#11758196C2×D414yes—
266C4×Dic61—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61C2×D412yes—
270C4×Dic61C2×D412yes—
271C4×Dic61C2412yes—
272C4×Dic61C2412yes—
273C2×#92418—22no—
274C2×#92418—22no—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277Dic244—28no—
278Dic244—44no—
279#11758190—28no—
280#11758190—44no—
281C23×C61C22×D411yescharacteristic
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286Q8×C61—22no—
287Q8×C61—22no—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—42no—
291Q8×C61—42no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61C22×D412yes—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4112yes—
306C2×C4×C61H(5,𝔽2)12yes—
307C2×C4×C61C2511yescharacteristic
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61#13714yes—
318C2×Dic61C22×D412yes—
319C2×Dic61C22×D412yes—
320C2×Dic61C22×D412yes—
321C2×Dic61C22×D412yes—
322D244—22no—
323D244—22no—
324D244—42no—
325C4×D61—48no—
326Dic122—28no—
327Dic122—22no—
328Dic122—22no—
329Dic122—22no—
330Dic122—22no—
331Dic122—22no—
332Dic122—22no—
333Dic122—42no—
334Dic122—42no—
335Dic122—42no—
336C8×C61—22no—
337C8×C61C2×#4114yes—
338#92418—22no—
339#92418—22no—
340C2×#3398—611nomaximal, Sylow
341C22×C61#55012yes—
342C22×C61C2×#13712yes—
343C22×C61#57812yes—
344C22×C61C23×D411yescharacteristic
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—84no—
349C4×C61—22no—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61#55012yes—
356C4×C61C22×#4111yescharacteristic
357C4×C61C2×H(5,𝔽2)11yescharacteristic
358Dic61—22no—
359Dic61—22no—
360Dic61—22no—
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364Dic61C2×#13714yes—
365C2×#557—611no—
366C2×#556—611no—
367#3398—6116no—
368C2×#497—611no—
369C2×#497—611no—
370C2×#494—611no—
371C2×#464—611no—
372C2×#464—611no—
373C2×#462—611no—
374C2×#462—611no—
375C2×#462—611no—
376C2×#461—611no—
377C2×#446—611no—
378C2×#441—611no—
379C2×#441D6111yescharacteristic, complemented
380C2×C4×SD16—611no—
381C2×C61#339814yescomplemented
382C2×C61C2×#55011yescharacteristic
383C2×C61C22×#13711yescharacteristic
384C2×C61C2×#57811yescharacteristic
385D61—82no—
386C22×Q16—611no—
387C22×Q16—611no—
388C22×Q16—611no—
389C22×Q16—611no—
390C22×Q16—611no—
391C22×Q16C2×D6111yescharacteristic
392C22×SD16—611no—
393C22×SD16—611no—
394C22×SD16—611no—
395#557—618no—
396#557—1224no—
397#556—618no—
398#556—1224no—
399C2×C4⋊Q8—611no—
400C2×C4⋊Q8—611no—
401C2×C4⋊Q8—611no—
402C2×C4⋊Q8—611no—
403C2×#126—1221no—
404C2×#126—1221no—
405C2×#125—1221no—
406C2×#125—1221no—
407C2×#125—1221no—
408C2×#124—611no—
409C2×#124—611no—
410C2×C22⋊Q8—1221no—
411C2×C4×Q8—611no—
412C2×C4×Q8—611no—
413C2×C4×Q8—611no—
414C2×C4×Q8—611no—
415C2×C4×Q8—1221no—
416C2×C4×Q8C2×D6111yescharacteristic
417C2×C4×Q8C2×D6111yescharacteristic
418C2×C4×D4—611no—
419C2×#117—1221no—
420#497—618no—
421#497—618no—
422#494—618no—
423#464—618no—
424#464—618no—
425#462—618no—
426#462—618no—
427#462—618no—
428#461—618no—
429#446—618no—
430#441—618no—
431#441C2×D6118yescomplemented
432C4×SD16—618no—
433C2×#106C2×D6111yescharacteristic
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103C2×D6111yescharacteristic
441C2×#103C2×D6111yescharacteristic
442C2×#102—611no—
443C2×#97—611no—
444C2×#97C2×D6111yescharacteristic
445C2×C4×C8—611no—
446C61C2×#339811yescharacteristic, complemented, Sylow
447C22×Q8—611no—
448C22×Q8—611no—
449C22×Q8—611no—
450C22×Q8—611no—
451C22×Q8C22×D6111yescharacteristic
452C22×Q8C22×D6111yescharacteristic
453C22×D4—611no—
454C23×C4—1221no—
455C2×Q16—24no—
456C2×Q16—614no—
457C2×Q16—614no—
458C2×Q16—614no—
459C2×Q16—614no—
460C2×Q16—614no—
461C2×Q16—1224no—
462C2×Q16—2442no—
463C2×Q16—2442no—
464C2×Q16—2442no—
465C2×Q16—2442no—
466C2×Q16C22×D6114yes—
467C2×SD16—614no—
468C2×SD16—614no—
469C2×SD16—614no—
470C2×SD16—1224no—
471C2×SD16—2442no—
472C2×SD16—2442no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8C22×D6111yescharacteristic
476C22×C8C22×D6111yescharacteristic
477C4⋊Q8—614no—
478C4⋊Q8—614no—
479C4⋊Q8—614no—
480C4⋊Q8—614no—
481C4⋊Q8—1222no—
482C4⋊Q8—1222no—
483C4⋊Q8—1222no—
484C4⋊Q8—1222no—
485#126—1228no—
486#126—1228no—
487#125—1228no—
488#125—1228no—
489#125—1228no—
490#124—614no—
491#124—614no—
492#124—1222no—
493#124—1222no—
494C22⋊Q8—1228no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×Q8—614no—
498C4×Q8—614no—
499C4×Q8—614no—
500C4×Q8—614no—
501C4×Q8—614no—
502C4×Q8—1228no—
503C4×Q8—1222no—
504C4×Q8—1222no—
505C4×Q8—1222no—
506C4×Q8C22×D6114yes—
507C4×Q8C22×D6114yes—
508C4×D4—614no—
509C4×D4—1222no—
510#117—1228no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C42—21no—
535C2×C42—21no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—1221no—
539C2×C42—1221no—
540C2×C42—1221no—
541C2×C42C22×D6111yescharacteristic
542#106C22×D6114yes—
543C4⋊C8—614no—
544C4⋊C8—614no—
545C4⋊C8—614no—
546#103—614no—
547#103—614no—
548#103—614no—
549#103C22×D6114yes—
550#103C22×D6114yes—
551#102—614no—
552#97—614no—
553#97C22×D6114yes—
554C4×C8—614no—
555C24—1221no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—614no—
563C2×Q8—612no—
564C2×Q8—612no—
565C2×Q8—612no—
566C2×Q8—1224no—
567C2×Q8—1221no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1222no—
571C2×Q8—1222no—
572C2×Q8—1222no—
573C2×Q8—1222no—
574C2×Q8—1222no—
575C2×Q8—1222no—
576C2×Q8C23×D6112yes—
577C2×Q8C23×D6112yes—
578C2×D4—612no—
579C2×D4—1221no—
580C2×D4—1222no—
581C2×D4—1222no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—1224no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—2444no—
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598Q16—28no—
599Q16—1228no—
600Q16—2444no—
601Q16—2444no—
602Q16—2444no—
603Q16—2444no—
604SD16—1228no—
605SD16—2444no—
606SD16—2444no—
607C2×C8—22no—
608C2×C8—612no—
609C2×C8—612no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8#1175822214yes—
613C2×C8C23×D6112yes—
614C2×C8C23×D6112yes—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—614no—
620C4⋊C4—614no—
621C4⋊C4—614no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4C23×D6112yes—
634C4⋊C4C23×D6112yes—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C42—24no—
641C42—24no—
642C42—612no—
643C42—612no—
644C42—612no—
645C42—612no—
646C42—1224no—
647C42—1224no—
648C42—1224no—
649C42D4×D6112yes—
650C42C23×D6112yes—
651C23—1222no—
652C23—2442no—
653C23—2442no—
654C23—2442no—
655C23C2×D4×D6111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—1228no—
663Q8—1222no—
664Q8—1222no—
665Q8—1222no—
666Q8—1222no—
667Q8—1222no—
668Q8—1222no—
669Q8—2442no—
670Q8—2442no—
671Q8—2442no—
672D4—1222no—
673D4—1222no—
674D4—2442no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—614no—
686C2×C4—612no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—2448no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4C2×D4×D6112yes—
701C2×C4C2×D4×D6112yes—
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4C2×#1175822212yes—
704C2×C4#1451982312yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—1222no—
708C8—1222no—
709C8C2×#1175822214yes—
710C22—4884no—
711C22—2442no—
712C22—2442no—
713C22—2442no—
714C22#1684043312yes—
715C22#137×D6112yes—
716C22#1684057812yes—
717C22C22×D4×D6111yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—614no—
725C4—1222no—
726C4—1222no—
727C4—1222no—
728C4—2442no—
729C4—2442no—
730C4—2442no—
731C4#1684043312yes—
732C4C22×#1175822211yescharacteristic
733C4C2×#1451982311yescharacteristic
734C2—4882no—
735C2#2145885114yesdirect product factor
736C2C2×#1684043311yescharacteristic
737C2C2×#137×D6111yescharacteristic
738C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#441C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenterC2×#441D61
hypocenterC61C2×#3398
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×#16840490C2semidirect
3. #21458851C2direct (N × H)
6. C2×#16840140C2semidirect
9. C2×#16839972C2semidirect
10. C2×#16839971C2semidirect
11. C2×#16839971C2semidirect
13. C2×#16839890C2semidirect
14. C2×#16839868C2semidirect
16. C2×C61×#441C2semidirect
26. #16840490C22semidirect
50. #16840140C22semidirect
53. #16839972C22semidirect
54. #16839971C22semidirect
55. #16839971C22semidirect
57. #16839890C22semidirect
58. #16839868C22semidirect
72. C61×#441C22semidirect
379. C2×#441D61semidirect
381. C2×C61#3398semidirect
431. #441C2×D61semidirect
446. C61C2×#3398semidirect
735. C2#21458851direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404902
C2×#168404842
#214588512
C2×#168401562
C2×#168401552
C2×#168401402
C2×#168399872
C2×#168399842
C2×#168399722
C2×#168399712
C2×#168399662
C2×#168398902
C2×#168398682
C2×#168398492
C2×C61×#4412
C2×#339861