Finite Group Databasebeta

← #33108514

Subgroups — #33108514

Order 18688.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619386C211yesmaximal, characteristic
2C2×#17988707C211yesmaximal, characteristic, complemented
3C2×#17988702C211yesmaximal, characteristic, complemented
4#22618674C211yesmaximal, characteristic, complemented
5#22610762C211yesmaximal, characteristic, complemented
6#22610704C211yesmaximal, characteristic, complemented
7#22610641C211yesmaximal, characteristic, complemented
8#22610634C211yesmaximal, characteristic, complemented
9#22610258C211yesmaximal, characteristic, complemented
10#22610258C211yesmaximal, characteristic, complemented
11#22610205C211yesmaximal, characteristic, complemented
12#22610205C211yesmaximal, characteristic, complemented
13#22609790C211yesmaximal, characteristic, complemented
14#22609741C211yesmaximal, characteristic, complemented
15C73×#2906C211yesmaximal, characteristic, complemented
16C2×#14556611C2211yescharacteristic
17C2×#14556611C2211yescharacteristic
18C2×#14556597C2211yescharacteristic
19C2×#14556597C2211yescharacteristic
20#17989137C2211yescharacteristic
21#17988809C411yescharacteristic, complemented
22#17988809C411yescharacteristic, complemented
23#17988802C411yescharacteristic, complemented
24#17988802C411yescharacteristic, complemented
25#17988797C411yescharacteristic, complemented
26#17988792C411yescharacteristic, complemented
27#17988787C411yescharacteristic, complemented
28#17988782C411yescharacteristic, complemented
29#17988707—24no—
30#17988702—24no—
31#17988664—21no—
32#17988657—21no—
33#17988657—21no—
34#17988652—21no—
35C2×#14556526C2211yescharacteristic
36C2×#14556526C2211yescharacteristic
37C2×C4⋊#10596831C2211yescharacteristic
38C2×#14556518C2211yescharacteristic
39C2×#14556518C2211yescharacteristic
40C2×#14556517C2211yescharacteristic
41C2×#14556517C2211yescharacteristic
42C2×#14556517C2211yescharacteristic
43C2×#14556517C2211yescharacteristic
44#17988581C2211yescharacteristic
45#17988581C2211yescharacteristic
46#17988553C2211yescharacteristic
47#17988553C2211yescharacteristic
48C4×#11924012C2211yescharacteristic
49C2×#14556501C2211yescharacteristic
50C2×C8×Dic73C2211yescharacteristic
51#17988433C2211yescharacteristic
52#17988351C2211yescharacteristic
53#17988351C2211yescharacteristic
54#17988346C2211yescharacteristic
55#17988346C2211yescharacteristic
56#17988341C2211yescharacteristic
57#17988341C2211yescharacteristic
58C2×#131×C73C2211yescharacteristic
59C2×#131×C73C2211yescharacteristic
60C4×#41×C73C2211yescharacteristic
61#424×C73—21no—
62#424×C73—21no—
63#424×C73C2211yescharacteristic
64#424×C73C2211yescharacteristic
65#423×C73—21no—
66#423×C73C2211yescharacteristic
67C2×C4⋊C8×C73—21no—
68C2×C4⋊C8×C73C2211yescharacteristic
69C2×#11924028C2311yescharacteristic
70C2×#11924028C2311yescharacteristic
71#14556611—22no—
72#14556611—22no—
73#14556611—22no—
74#14556611—22no—
75C2×#11924018C2×C411yescharacteristic
76C2×#11924018C2×C411yescharacteristic
77C2×#11924016C2×C411yescharacteristic
78C2×#11924016C2×C411yescharacteristic
79C2×#11924015C2×C411yescharacteristic
80C2×#11924015C2×C411yescharacteristic
81C2×#11924013C2×C411yescharacteristic
82C2×#11924013C2×C411yescharacteristic
83#14556597—22no—
84#14556597—22no—
85#14556597—41no—
86#14556597—41no—
87C2×#11924012C2311yescharacteristic
88C2×#11924012C2311yescharacteristic
89C2×#11924011—21no—
90C2×#11924011—21no—
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93C2×C8×D73—21no—
94C2×C8×D73—21no—
95#14556591C2×C411yescharacteristic
96#14556588C2×C411yescharacteristic
97#14556579C2×C411yescharacteristic
98#14556579C2×C411yescharacteristic
99#14556565—21no—
100#14556565—21no—
101C4×D292—21no—
102C4×D292—21no—
103C2×C4×Dic73C2311yescharacteristic
104C2×C4×Dic73C2311yescharacteristic
105#14556526—22no—
106#14556526—22no—
107C4⋊#10596831C2×C411yescharacteristic
108C4⋊#10596831C2×C411yescharacteristic
109C4⋊#10596831C2×C411yescharacteristic
110C4⋊#10596831C2×C411yescharacteristic
111#14556518—22no—
112#14556518D414yescomplemented
113#14556517—22no—
114#14556517—22no—
115#14556517—41no—
116#14556517—41no—
117#14556514C2×C411yescharacteristic
118#14556514C2×C411yescharacteristic
119#14556514C2×C411yescharacteristic
120#14556514C2×C411yescharacteristic
121#14556511C2×C411yescharacteristic
122#14556511C2×C411yescharacteristic
123#14556511C2×C411yescharacteristic
124#14556511C2×C411yescharacteristic
125#14556503—21no—
126#14556503—21no—
127#14556503—21no—
128#14556503—21no—
129#14556502—21no—
130#14556501—22no—
131C4×#10596831—21no—
132C8×Dic73—22no—
133#14556498—21no—
134#14556498—21no—
135C2×#41×C73C2311yescharacteristic
136#131×C73—22no—
137#131×C73—22no—
138#131×C73—41no—
139#131×C73—41no—
140C2×M16×C73—21no—
141C2×M16×C73—21no—
142C2×M16×C73C2311yescharacteristic
143C2×M16×C73C2311yescharacteristic
144C22×C8×C73—21no—
145C22×C8×C73—21no—
146C22×C8×C73C2311yescharacteristic
147C22×C8×C73C2311yescharacteristic
148C4×Q8×C73C2×C411yescharacteristic
149C4×Q8×C73C2×C411yescharacteristic
150C4×D4×C73—21no—
151C4×D4×C73—21no—
152C4×D4×C73C2×C411yescharacteristic
153C4×D4×C73C2×C411yescharacteristic
154#117×C73—21no—
155#117×C73C2311yescharacteristic
156C2×C42×C73—21no—
157C2×C42×C73C2311yescharacteristic
158C4⋊C8×C73—21no—
159C4⋊C8×C73—21no—
160C4⋊C8×C73—21no—
161C4⋊C8×C73—21no—
162C4⋊C8×C73—21no—
163C4⋊C8×C73—21no—
164C4⋊C8×C73D411yescharacteristic
165C4⋊C8×C73D411yescharacteristic
166C4⋊C8×C73D411yescharacteristic
167C4⋊C8×C73D411yescharacteristic
168#11924028—21no—
169#11924028—21no—
170#11924028—21no—
171#11924028—21no—
172#11924028—21no—
173#11924028—21no—
174#11924028—21no—
175#11924028—21no—
176C2×Dic146C22×C411yescharacteristic
177C2×Dic146C22×C411yescharacteristic
178C2×D292—21no—
179C2×D292—21no—
180C2×D292C22×C411yescharacteristic
181C2×D292C22×C411yescharacteristic
182C2×C22⋊D73—21no—
183C2×C22⋊D73—21no—
184C22×Dic73—21no—
185C22×Dic73—21no—
186C2×C4×D73—21no—
187C2×C4×D73—21no—
188#11924018—22no—
189#11924018—22no—
190#11924016—22no—
191#11924016—22no—
192#11924015—22no—
193#11924015—22no—
194#11924013—22no—
195#11924013—22no—
196#11924012—21no—
197#11924012—21no—
198#11924012—21no—
199#11924012C2×D412yes—
200#11924011—42no—
201#11924011—42no—
202C2×#10596831—21no—
203C2×#10596831—21no—
204C2×#10596831—21no—
205C2×#10596831—21no—
206C2×#10596831—21no—
207C2×#10596831—21no—
208C2×#10596831C22×C411yescharacteristic
209C2×#10596831C22×C411yescharacteristic
210C2×#10596831C22×C411yescharacteristic
211C2×#10596831C22×C411yescharacteristic
212C8×D73—42no—
213C8×D73—42no—
214C4⋊Dic73—21no—
215C4⋊Dic73—21no—
216#11924005—21no—
217#11924005—21no—
218#11924005—21no—
219#11924005—21no—
220C4×Dic73—21no—
221C4×Dic73—21no—
222C4×Dic73—21no—
223C4×Dic73C2×D412yes—
224#41×C73—21no—
225#41×C73—21no—
226#41×C73C2×D412yes—
227#41×C73#4112yes—
228C2×Q8×C73C22×C411yescharacteristic
229C2×D4×C73—21no—
230C2×D4×C73C22×C411yescharacteristic
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73#4111yescharacteristic
235C22×C4×C73#4111yescharacteristic
236C22×C4×C73C2411yescharacteristic
237M16×C73—21no—
238M16×C73—21no—
239M16×C73—21no—
240M16×C73—21no—
241M16×C73—42no—
242M16×C73—42no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73—42no—
250C2×C8×C73—42no—
251C2×C8×C73C2×D411yescharacteristic
252C2×C8×C73C2×D411yescharacteristic
253C2×C8×C73C2×D411yescharacteristic
254C2×C8×C73C2×D411yescharacteristic
255C4⋊C4×C73—21no—
256C4⋊C4×C73—21no—
257C4⋊C4×C73C22×C411yescharacteristic
258C4⋊C4×C73C22×C411yescharacteristic
259C22⋊C4×C73—21no—
260C22⋊C4×C73—21no—
261C22⋊C4×C73—21no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73—21no—
265C42×C73C22×C411yescharacteristic
266C42×C73C22×C411yescharacteristic
267C42×C73C2×D411yescharacteristic
268C42×C73C2×D411yescharacteristic
269C23×C73—21no—
270C23×C73C2×#4111yescharacteristic
271C22×D73—21no—
272C22×D73—21no—
273Q8×C73—21no—
274Q8×C73C4×D412yes—
275D4×C73—22no—
276D4×C73—22no—
277D4×C73—21no—
278D4×C73C4×D412yes—
279C2×C4×C73—21no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—42no—
287C2×C4×C73—81no—
288C2×C4×C73C4×D411yescharacteristic
289C2×C4×C73C4×D411yescharacteristic
290C2×C4×C73C4×D411yescharacteristic
291C2×C4×C73C4×D411yescharacteristic
292C2×C4×C73C23×C411yescharacteristic
293C2×C4×C73C22×D411yescharacteristic
294C2×C4×C73C22×D411yescharacteristic
295C2×C4×C73C2×#4111yescharacteristic
296C2×C4×C73H(5,𝔽2)11yescharacteristic
297C2×C4×C732−1+411yescharacteristic
298C22⋊D73—41no—
299C22⋊D73—41no—
300C22⋊D73—41no—
301C22⋊D73—41no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73—22no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310D292—21no—
311D292—21no—
312D292—21no—
313D292—21no—
314D292—42no—
315D292—81no—
316C4×D73—41no—
317C4×D73—41no—
318C4×D73—41no—
319C4×D73—41no—
320Dic146—21no—
321Dic146—21no—
322Dic146—21no—
323Dic146—21no—
324C8×C73—21no—
325C8×C73—21no—
326C8×C73—21no—
327C8×C73—21no—
328C8×C73—41no—
329C8×C73—41no—
330#10596831—21no—
331#10596831—21no—
332#10596831—21no—
333#10596831—21no—
334#10596831—22no—
335#10596831—41no—
336C22×C73—21no—
337C22×C73—21no—
338C22×C73—22no—
339C22×C73—41no—
340C22×C73—41no—
341C22×C73C2×C4×D411yescharacteristic
342C22×C73#54711yescharacteristic
343C22×C73#55311yescharacteristic
344C2×D73—41no—
345C2×D73—41no—
346C2×D73—41no—
347C2×D73—41no—
348C2×D73—41no—
349C2×D73—41no—
350C4×C73—22no—
351C4×C73—21no—
352C4×C73—21no—
353C4×C73—21no—
354C4×C73—21no—
355C4×C73—41no—
356C4×C73—41no—
357C4×C73C2×C4×D411yescharacteristic
358C4×C73#52011yescharacteristic
359C4×C73D4211yescharacteristic
360C4×C73#54811yescharacteristic
361Dic73—42no—
362Dic73—41no—
363Dic73—41no—
364Dic73—81no—
365#23017—731nomaximal, Sylow
366C2×C73—21no—
367C2×C73—21no—
368C2×C73—42no—
369C2×C73#236111yescharacteristic
370C2×C73#295511yescharacteristic
371C2×C73#295711yescharacteristic
372D73—81no—
373D73—81no—
374#3035—731no—
375C2×#444—731no—
376C2×#443—731no—
377#2935—731no—
378#2906D7311yescharacteristic, complemented
379#1963—731no—
380#1950—731no—
381#1938—731no—
382#1937—731no—
383#1876—731no—
384#1876—731no—
385#1866—731no—
386#1866—731no—
387#1768—731no—
388#1759—731no—
389C73#2301711yescharacteristic, complemented, Sylow
390C2×#135—731no—
391C2×#135—731no—
392C2×#131—731no—
393C2×#131—731no—
394C2×#131C2×D7311yescharacteristic
395C2×#131C2×D7311yescharacteristic
396#532—731no—
397C4×#41C2×D7311yescharacteristic
398#464—731no—
399#464—731no—
400#463—731no—
401#463—731no—
402#462—731no—
403#461—731no—
404#460—731no—
405#459—731no—
406#444—1464no—
407#443—1464no—
408#436—1461no—
409#435—1461no—
410#435—1461no—
411C8×D4—1461no—
412C2×#108—731no—
413C2×#108—731no—
414#424—21no—
415#424—21no—
416#424C2×D7311yescharacteristic
417#424C2×D7311yescharacteristic
418#423—21no—
419#423C2×D7311yescharacteristic
420C2×C4⋊C8—21no—
421C2×C4⋊C8—731no—
422C2×C4⋊C8C2×D7311yescharacteristic
423C2×#104—731no—
424C2×#104—731no—
425C2×#104—731no—
426C2×#104—731no—
427C2×#104—731no—
428C2×#104—731no—
429#416—731no—
430#416—731no—
431#408—731no—
432#408—731no—
433C4×M16—731no—
434C2×#97—731no—
435C2×C4×C8—731no—
436#376—731no—
437#341—731no—
438#341—731no—
439#339—731no—
440#339—731no—
441#336—731no—
442#336—731no—
443C2×#41—731no—
444C2×#41—731no—
445C2×#41C22×D7311yescharacteristic
446#135—1462no—
447#135—1462no—
448#135—1462no—
449#135—1462no—
450C2×Q16—731no—
451C2×Q16—731no—
452C2×SD16—731no—
453C2×SD16—731no—
454C2×SD16—731no—
455C2×SD16—731no—
456C2×D8—731no—
457C2×D8—731no—
458#131—22no—
459#131—22no—
460#131—41no—
461#131—41no—
462#131—2921no—
463#131—2921no—
464#131—1462no—
465#131—1462no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—731no—
469C2×M16—731no—
470C2×M16—1461no—
471C2×M16—1461no—
472C2×M16C22×D7311yescharacteristic
473C2×M16C22×D7311yescharacteristic
474C22×C8—21no—
475C22×C8—21no—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8—1461no—
479C22×C8—1461no—
480C22×C8C22×D7311yescharacteristic
481C22×C8C22×D7311yescharacteristic
482C4⋊Q8—731no—
483#127—731no—
484#124—731no—
485#124—731no—
486#121—1461no—
487#121—1461no—
488C4×Q8C4×D7311yescharacteristic
489C4×Q8C4×D7311yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—1461no—
493C4×D4—1461no—
494C4×D4C4×D7311yescharacteristic
495C4×D4C4×D7311yescharacteristic
496#117—21no—
497#117C22×D7311yescharacteristic
498C2×C42—21no—
499C2×C42—731no—
500C2×C42—731no—
501C2×C42C22×D7311yescharacteristic
502#108—1462no—
503#108—1462no—
504C4⋊C8—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8—21no—
509C4⋊C8—21no—
510C4⋊C8—731no—
511C4⋊C8—731no—
512C4⋊C8—731no—
513C4⋊C8—731no—
514C4⋊C8C22⋊D7311yescharacteristic
515C4⋊C8C22⋊D7311yescharacteristic
516C4⋊C8C22⋊D7311yescharacteristic
517C4⋊C8C22⋊D7311yescharacteristic
518#104—2921no—
519#104—2921no—
520#104—734no—
521#104—1462no—
522#104—1462no—
523#104—1462no—
524#103—731no—
525#103—731no—
526#103—731no—
527#103—731no—
528#102—731no—
529#102—731no—
530#102—731no—
531#102—731no—
532C22⋊C8—1461no—
533C22⋊C8—1461no—
534C22⋊C8—1461no—
535C22⋊C8—1461no—
536#97—1462no—
537#97—1461no—
538C4×C8—1462no—
539C4×C8—1461no—
540#95—1461no—
541#95—1461no—
542#41—21no—
543#41—21no—
544#41—1461no—
545#41—1461no—
546#41—1461no—
547#41—1461no—
548#41—1461no—
549#41—1461no—
550#41—1461no—
551#41—1461no—
552#41D4×D7312yes—
553#41#1192402912yes—
554C2×Q8—731no—
555C2×Q8—731no—
556C2×Q8C2×C4×D7311yescharacteristic
557C2×D4—21no—
558C2×D4—731no—
559C2×D4—731no—
560C2×D4—1461no—
561C2×D4—1461no—
562C2×D4—1461no—
563C2×D4—1461no—
564C2×D4C2×C4×D7311yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4#1192402811yescharacteristic
573C22×C4#1192402811yescharacteristic
574C22×C4C23×D7311yescharacteristic
575Q16—1462no—
576Q16—1462no—
577SD16—1462no—
578SD16—1462no—
579SD16—1462no—
580SD16—1462no—
581D8—1462no—
582D8—1462no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—42no—
588M16—42no—
589M16—2922no—
590M16—2922no—
591M16—732no—
592M16—1461no—
593M16—1461no—
594M16—1461no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—2922no—
604C2×C8—2922no—
605C2×C8—731no—
606C2×C8—731no—
607C2×C8—731no—
608C2×C8—731no—
609C2×C8—1461no—
610C2×C8—1461no—
611C2×C8—1461no—
612C2×C8—1461no—
613C2×C8—1461no—
614C2×C8—1461no—
615C2×C8C2×C22⋊D7311yescharacteristic
616C2×C8C2×C22⋊D7311yescharacteristic
617C2×C8C2×C22⋊D7311yescharacteristic
618C2×C8C2×C22⋊D7311yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—1461no—
622C4⋊C4—1461no—
623C4⋊C4C2×C4×D7311yescharacteristic
624C4⋊C4C2×C4×D7311yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—1461no—
629C22⋊C4—1461no—
630C22⋊C4—1461no—
631C22⋊C4—1461no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—732no—
636C42—1461no—
637C42—1461no—
638C42—1461no—
639C42C2×C4×D7311yescharacteristic
640C42C2×C4×D7311yescharacteristic
641C42C2×C22⋊D7311yescharacteristic
642C42C2×C22⋊D7311yescharacteristic
643C23—21no—
644C23—1461no—
645C23—1461no—
646C23C2×#1192402811yescharacteristic
647Q8—21no—
648Q8—1461no—
649Q8—1461no—
650Q8—1461no—
651Q8—1461no—
652Q8#1455655312yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—2922no—
657D4—2921no—
658D4—2921no—
659D4—2921no—
660D4—2921no—
661D4—5841no—
662D4—1461no—
663D4—1461no—
664D4—1461no—
665D4—1461no—
666D4#1455655312yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—81no—
676C2×C4—2921no—
677C2×C4—2921no—
678C2×C4—2921no—
679C2×C4—2921no—
680C2×C4—2921no—
681C2×C4—2921no—
682C2×C4—2921no—
683C2×C4—2921no—
684C2×C4—2921no—
685C2×C4—1462no—
686C2×C4—1461no—
687C2×C4—1461no—
688C2×C4C4×C22⋊D7311yescharacteristic
689C2×C4C4×C22⋊D7311yescharacteristic
690C2×C4C4×C22⋊D7311yescharacteristic
691C2×C4C4×C22⋊D7311yescharacteristic
692C2×C4C22×C4×D7311yescharacteristic
693C2×C4C2×D4×D7311yescharacteristic
694C2×C4C22×C22⋊D7311yescharacteristic
695C2×C4C2×#1192402911yescharacteristic
696C2×C4#1455663611yescharacteristic
697C2×C4#1455663911yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—41no—
703C8—41no—
704C8—2921no—
705C8—1462no—
706C8—1461no—
707C8—1461no—
708C8—1461no—
709C8—1461no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—2921no—
716C22—2921no—
717C22—2921no—
718C22—2921no—
719C22—2921no—
720C22—2921no—
721C22C2×C4×C22⋊D7311yescharacteristic
722C22#1798923811yescharacteristic
723C22#1798928511yescharacteristic
724C4—21no—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—2922no—
732C4—2921no—
733C4—2921no—
734C4—5841no—
735C4C2×#1455655311yescharacteristic
736C4#1798906811yescharacteristic
737C4D4×C22⋊D7311yescharacteristic
738C4#1798924811yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—5841no—
743C2—5841no—
744C2#2261294711yescharacteristic
745C2#2261883211yescharacteristic
746C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2906C2
socleC22×C73C2×C4×D4
prime radical#22619386C2
cosocleC22×C4×C73C24
hypercenter#2906D73
hypocenterC73#23017
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. C2×#17988707C2semidirect
3. C2×#17988702C2semidirect
4. #22618674C2semidirect
5. #22610762C2semidirect
6. #22610704C2semidirect
7. #22610641C2semidirect
8. #22610634C2semidirect
9. #22610258C2semidirect
10. #22610258C2semidirect
11. #22610205C2semidirect
12. #22610205C2semidirect
13. #22609790C2semidirect
14. #22609741C2semidirect
15. C73×#2906C2semidirect
21. #17988809C4semidirect
22. #17988809C4semidirect
23. #17988802C4semidirect
24. #17988802C4semidirect
25. #17988797C4semidirect
26. #17988792C4semidirect
27. #17988787C4semidirect
28. #17988782C4semidirect
112. #14556518D4semidirect
378. #2906D73semidirect
389. C73#23017semidirect

Maximal subgroups

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

subgroupindex
#226193862
C2×#179887072
C2×#179887022
#226186742
#226107622
#226107042
#226106412
#226106342
#226102582
#226102052
#226097902
#226097412
C73×#29062
#2301773