Finite Group Databasebeta

← #33108518

Subgroups — #33108518

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
1C2×#17988709C211yesmaximal, characteristic, complemented
2C2×#17988704C211yesmaximal, characteristic, complemented
3#22618675C211yesmaximal, characteristic, complemented
4#22618499C211yesmaximal, characteristic, complemented
5#22610764C211yesmaximal, characteristic, complemented
6#22610707C211yesmaximal, characteristic, complemented
7#22610644C211yesmaximal, characteristic, complemented
8#22610637C211yesmaximal, characteristic, complemented
9#22610260C211yesmaximal, characteristic, complemented
10#22610260C211yesmaximal, characteristic, complemented
11#22610208C211yesmaximal, characteristic, complemented
12#22610208C211yesmaximal, characteristic, complemented
13#22609790C211yesmaximal, characteristic, complemented
14#22609741C211yesmaximal, characteristic, complemented
15C73×#3035C211yesmaximal, characteristic
16C2×#14556598C2211yescharacteristic
17C2×#14556598C2211yescharacteristic
18C2×#14556598C2211yescharacteristic
19C2×#14556598C2211yescharacteristic
20#17988709—24no—
21#17988704—24no—
22#17988665—21no—
23#17988659—21no—
24#17988659—21no—
25D4×#10596831—21no—
26C2×#14556527C2211yescharacteristic
27C2×#14556527C2211yescharacteristic
28#17988614—21no—
29#17988614—21no—
30#17988614C2211yescharacteristic
31#17988614C2211yescharacteristic
32#17988611—21no—
33#17988611C2211yescharacteristic
34C2×C4⋊#10596831—21no—
35C2×C4⋊#10596831C2211yescharacteristic
36C2×#14556518C2211yescharacteristic
37C2×#14556518C2211yescharacteristic
38C2×#14556518C2211yescharacteristic
39C2×#14556518C2211yescharacteristic
40C2×#14556518C2211yescharacteristic
41C2×#14556518C2211yescharacteristic
42#17988554C2211yescharacteristic
43#17988554C2211yescharacteristic
44C4×#11924012C2211yescharacteristic
45C2×#14556501C2211yescharacteristic
46C2×C8×Dic73C2211yescharacteristic
47#17988433C2211yescharacteristic
48#17988352C2211yescharacteristic
49#17988352C2211yescharacteristic
50#17988346C2211yescharacteristic
51#17988346C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C2×#135×C73C2211yescharacteristic
55C2×#135×C73C2211yescharacteristic
56#532×C73C2211yescharacteristic
57C4×#41×C73C2211yescharacteristic
58#464×C73C411yescharacteristic, complemented
59#464×C73C411yescharacteristic, complemented
60#463×C73C411yescharacteristic, complemented
61#463×C73C411yescharacteristic, complemented
62#462×C73C411yescharacteristic, complemented
63#461×C73C411yescharacteristic, complemented
64#460×C73C411yescharacteristic, complemented
65#459×C73C411yescharacteristic, complemented
66C2×C4⋊C8×C73C2211yescharacteristic
67#416×C73C2211yescharacteristic
68#416×C73C2211yescharacteristic
69#14556598—22no—
70#14556598—22no—
71#14556598—22no—
72#14556598—22no—
73#14556598—41no—
74#14556598—41no—
75#14556598—41no—
76#14556598—41no—
77C2×#11924012—21no—
78C2×#11924012—21no—
79C2×#11924012—21no—
80C2×#11924012—21no—
81C2×#11924012C2311yescharacteristic
82C2×#11924012C2311yescharacteristic
83C2×#11924012C2311yescharacteristic
84C2×#11924012C2311yescharacteristic
85C22×#10596831—21no—
86C22×#10596831—21no—
87C22×#10596831—21no—
88C22×#10596831—21no—
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2311yescharacteristic
91C2×C4×Dic73C2311yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93#14556527—22no—
94#14556527—22no—
95C4⋊#10596831—21no—
96C4⋊#10596831—21no—
97C4⋊#10596831—21no—
98C4⋊#10596831—21no—
99C4⋊#10596831—21no—
100C4⋊#10596831—21no—
101C4⋊#10596831D411yescharacteristic
102C4⋊#10596831D411yescharacteristic
103C4⋊#10596831D411yescharacteristic
104C4⋊#10596831D411yescharacteristic
105#14556518—22no—
106#14556518—22no—
107#14556518—22no—
108#14556518—41no—
109#14556518—41no—
110#14556518D414yescomplemented
111C22⋊#10596831—21no—
112C22⋊#10596831—21no—
113C22⋊#10596831—21no—
114C22⋊#10596831—21no—
115#14556502—21no—
116#14556501—22no—
117C4×#10596831—21no—
118C8×Dic73—22no—
119#14556498—21no—
120#14556498—21no—
121C2×#41×C73C2311yescharacteristic
122C2×#41×C73C2311yescharacteristic
123C2×#41×C73C2311yescharacteristic
124#135×C73—22no—
125#135×C73—22no—
126#135×C73—22no—
127#135×C73—22no—
128C2×Q16×C73C2×C411yescharacteristic
129C2×Q16×C73C2×C411yescharacteristic
130C2×SD16×C73C2×C411yescharacteristic
131C2×SD16×C73C2×C411yescharacteristic
132C2×SD16×C73C2×C411yescharacteristic
133C2×SD16×C73C2×C411yescharacteristic
134C2×D8×C73C2×C411yescharacteristic
135C2×D8×C73C2×C411yescharacteristic
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C4⋊Q8×C73C2×C411yescharacteristic
139#127×C73C2×C411yescharacteristic
140#124×C73C2×C411yescharacteristic
141#124×C73C2×C411yescharacteristic
142#121×C73—21no—
143#121×C73—21no—
144C4×Q8×C73C2×C411yescharacteristic
145C4×Q8×C73C2×C411yescharacteristic
146C4×D4×C73—21no—
147C4×D4×C73—21no—
148C4×D4×C73—21no—
149C4×D4×C73—21no—
150C4×D4×C73C2×C411yescharacteristic
151C4×D4×C73C2×C411yescharacteristic
152#117×C73—21no—
153#117×C73C2311yescharacteristic
154C2×C42×C73—21no—
155C2×C42×C73C2311yescharacteristic
156C4⋊C8×C73C2×C411yescharacteristic
157C4⋊C8×C73C2×C411yescharacteristic
158C4⋊C8×C73C2×C411yescharacteristic
159C4⋊C8×C73C2×C411yescharacteristic
160#103×C73C2×C411yescharacteristic
161#103×C73C2×C411yescharacteristic
162#103×C73C2×C411yescharacteristic
163#103×C73C2×C411yescharacteristic
164#102×C73C2×C411yescharacteristic
165#102×C73C2×C411yescharacteristic
166#102×C73C2×C411yescharacteristic
167#102×C73C2×C411yescharacteristic
168C22×Dic73—21no—
169C22×Dic73—21no—
170#11924012—21no—
171#11924012—21no—
172#11924012—21no—
173#11924012—21no—
174#11924012—21no—
175#11924012—21no—
176#11924012—21no—
177#11924012—42no—
178#11924012—42no—
179#11924012—42no—
180#11924012—42no—
181#11924012C2×D412yes—
182C2×#10596831—21no—
183C2×#10596831—21no—
184C2×#10596831—21no—
185C2×#10596831—21no—
186C2×#10596831—21no—
187C2×#10596831—21no—
188C2×#10596831—21no—
189C2×#10596831—21no—
190C2×#10596831—42no—
191C2×#10596831—42no—
192C2×#10596831—42no—
193C2×#10596831—42no—
194C2×#10596831C2×D411yescharacteristic
195C2×#10596831C2×D411yescharacteristic
196C2×#10596831C2×D411yescharacteristic
197C2×#10596831C2×D411yescharacteristic
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C4×Dic73C2×D412yes—
202#41×C73—21no—
203#41×C73—21no—
204#41×C73—21no—
205#41×C73—21no—
206#41×C73—21no—
207#41×C73—21no—
208#41×C73—21no—
209#41×C73—21no—
210#41×C73—21no—
211#41×C73—21no—
212#41×C73C2×D412yes—
213#41×C73#4112yes—
214C2×Q8×C73C22×C411yescharacteristic
215C2×Q8×C73C22×C411yescharacteristic
216C2×Q8×C73C22×C411yescharacteristic
217C2×D4×C73—21no—
218C2×D4×C73—21no—
219C2×D4×C73—21no—
220C2×D4×C73—21no—
221C2×D4×C73—21no—
222C2×D4×C73C22×C411yescharacteristic
223C2×D4×C73C22×C411yescharacteristic
224C2×D4×C73C22×C411yescharacteristic
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73#4111yescharacteristic
231C22×C4×C73#4111yescharacteristic
232C22×C4×C73C2411yescharacteristic
233Q16×C73—22no—
234Q16×C73—22no—
235SD16×C73—22no—
236SD16×C73—22no—
237SD16×C73—22no—
238SD16×C73—22no—
239D8×C73—22no—
240D8×C73—22no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73C22×C411yescharacteristic
246C2×C8×C73C22×C411yescharacteristic
247C2×C8×C73C22×C411yescharacteristic
248C2×C8×C73C22×C411yescharacteristic
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73—21no—
253C4⋊C4×C73C22×C411yescharacteristic
254C4⋊C4×C73C22×C411yescharacteristic
255C22⋊C4×C73—21no—
256C22⋊C4×C73—21no—
257C22⋊C4×C73—21no—
258C22⋊C4×C73—21no—
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×C73—21no—
271C23×C73—21no—
272C23×C73C2×#4111yescharacteristic
273Q8×C73—21no—
274Q8×C73—21no—
275Q8×C73—21no—
276Q8×C73—21no—
277Q8×C73—21no—
278Q8×C73C4×D412yes—
279D4×C73—22no—
280D4×C73—22no—
281D4×C73—21no—
282D4×C73—21no—
283D4×C73—21no—
284D4×C73—21no—
285D4×C73—21no—
286D4×C73—42no—
287D4×C73—41no—
288D4×C73—41no—
289D4×C73—41no—
290D4×C73—41no—
291D4×C73—81no—
292D4×C73C4×D412yes—
293C2×C4×C73—21no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—42no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—81no—
308C2×C4×C73C4×D411yescharacteristic
309C2×C4×C73C4×D411yescharacteristic
310C2×C4×C73C4×D411yescharacteristic
311C2×C4×C73C4×D411yescharacteristic
312C2×C4×C73C23×C411yescharacteristic
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C22×D411yescharacteristic
315C2×C4×C73C2×#4111yescharacteristic
316C2×C4×C73H(5,𝔽2)11yescharacteristic
317C2×C4×C732−1+411yescharacteristic
318C2×Dic73—22no—
319C2×Dic73—41no—
320C2×Dic73—41no—
321C2×Dic73—41no—
322C2×Dic73—41no—
323C2×Dic73—41no—
324C8×C73—21no—
325C8×C73—21no—
326C8×C73—21no—
327C8×C73—21no—
328#10596831—21no—
329#10596831—21no—
330#10596831—21no—
331#10596831—21no—
332#10596831—22no—
333#10596831—41no—
334#10596831—41no—
335#10596831—41no—
336C22×C73—21no—
337C22×C73—21no—
338C22×C73—22no—
339C22×C73—41no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73C2×C4×D411yescharacteristic
348C22×C73#54711yescharacteristic
349C22×C73#55311yescharacteristic
350C4×C73—22no—
351C4×C73—21no—
352C4×C73—21no—
353C4×C73—21no—
354C4×C73—21no—
355C4×C73—41no—
356C4×C73—41no—
357C4×C73—41no—
358C4×C73—41no—
359C4×C73C2×C4×D411yescharacteristic
360C4×C73#52011yescharacteristic
361C4×C73D4211yescharacteristic
362C4×C73#54811yescharacteristic
363Dic73—42no—
364Dic73—81no—
365#23017—731nomaximal, Sylow
366C2×C73—21no—
367C2×C73—21no—
368C2×C73—42no—
369C2×C73—81no—
370C2×C73—81no—
371C2×C73#236111yescharacteristic
372C2×C73#295511yescharacteristic
373C2×C73#295711yescharacteristic
374#3035D7311yescharacteristic
375C2×#444—731no—
376C2×#443—731no—
377#2935—731no—
378#2906—731no—
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×#135C2×D7311yescharacteristic
391C2×#135C2×D7311yescharacteristic
392C2×#131—731no—
393C2×#131—731no—
394C2×#131—731no—
395C2×#131—731no—
396#532C2×D7311yescharacteristic
397C4×#41C2×D7311yescharacteristic
398#464Dic7311yescharacteristic, complemented
399#464Dic7311yescharacteristic, complemented
400#463Dic7311yescharacteristic, complemented
401#463Dic7311yescharacteristic, complemented
402#462Dic7311yescharacteristic, complemented
403#461Dic7311yescharacteristic, complemented
404#460Dic7311yescharacteristic, complemented
405#459Dic7311yescharacteristic, complemented
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—731no—
415#424—731no—
416#424—1461no—
417#424—1461no—
418#423—731no—
419#423—1461no—
420C2×C4⋊C8—731no—
421C2×C4⋊C8—1461no—
422C2×C4⋊C8C2×D7311yescharacteristic
423C2×#104—731no—
424C2×#104—731no—
425C2×#104—731no—
426C2×#104—731no—
427C2×#104—731no—
428C2×#104—731no—
429#416C2×D7311yescharacteristic
430#416C2×D7311yescharacteristic
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×#41C22×D7311yescharacteristic
444C2×#41C22×D7311yescharacteristic
445C2×#41C22×D7311yescharacteristic
446#135—22no—
447#135—22no—
448#135—22no—
449#135—22no—
450C2×Q16C2×Dic7311yescharacteristic
451C2×Q16C2×Dic7311yescharacteristic
452C2×SD16C2×Dic7311yescharacteristic
453C2×SD16C2×Dic7311yescharacteristic
454C2×SD16C2×Dic7311yescharacteristic
455C2×SD16C2×Dic7311yescharacteristic
456C2×D8C2×Dic7311yescharacteristic
457C2×D8C2×Dic7311yescharacteristic
458#131—2921no—
459#131—2921no—
460#131—2921no—
461#131—2921no—
462#131—1462no—
463#131—1462no—
464#131—1462no—
465#131—1462no—
466C2×M16—731no—
467C2×M16—731no—
468C2×M16—731no—
469C2×M16—731no—
470C2×M16—1461no—
471C2×M16—1461no—
472C2×M16—1461no—
473C2×M16—1461no—
474C22×C8—731no—
475C22×C8—731no—
476C22×C8—1461no—
477C22×C8—1461no—
478C22×C8—1461no—
479C22×C8—1461no—
480C22×C8C22×D7311yescharacteristic
481C22×C8C22×D7311yescharacteristic
482C4⋊Q8C2×Dic7311yescharacteristic
483#127C2×Dic7311yescharacteristic
484#124C2×Dic7311yescharacteristic
485#124C2×Dic7311yescharacteristic
486#121—21no—
487#121—21no—
488C4×Q8C2×Dic7311yescharacteristic
489C4×Q8C2×Dic7311yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4C2×Dic7311yescharacteristic
495C4×D4C2×Dic7311yescharacteristic
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—731no—
505C4⋊C8—731no—
506C4⋊C8—731no—
507C4⋊C8—731no—
508C4⋊C8—1461no—
509C4⋊C8—1461no—
510C4⋊C8—1461no—
511C4⋊C8—1461no—
512C4⋊C8—1461no—
513C4⋊C8—1461no—
514C4⋊C8C2×Dic7311yescharacteristic
515C4⋊C8C2×Dic7311yescharacteristic
516C4⋊C8C2×Dic7311yescharacteristic
517C4⋊C8C2×Dic7311yescharacteristic
518#104—2921no—
519#104—2921no—
520#104—734no—
521#104—1462no—
522#104—1462no—
523#104—1462no—
524#103C2×Dic7311yescharacteristic
525#103C2×Dic7311yescharacteristic
526#103C2×Dic7311yescharacteristic
527#103C2×Dic7311yescharacteristic
528#102C2×Dic7311yescharacteristic
529#102C2×Dic7311yescharacteristic
530#102C2×Dic7311yescharacteristic
531#102C2×Dic7311yescharacteristic
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—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41D4×D7312yes—
553#41#1192402712yes—
554C2×Q8C22×Dic7311yescharacteristic
555C2×Q8C22×Dic7311yescharacteristic
556C2×Q8C22×Dic7311yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4C22×Dic7311yescharacteristic
563C2×D4C22×Dic7311yescharacteristic
564C2×D4C22×Dic7311yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—1461no—
571C22×C4—1461no—
572C22×C4#1192402711yescharacteristic
573C22×C4#1192402711yescharacteristic
574C22×C4C23×D7311yescharacteristic
575Q16—22no—
576Q16—22no—
577SD16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581D8—22no—
582D8—22no—
583M16—2922no—
584M16—2922no—
585M16—2922no—
586M16—2922no—
587M16—732no—
588M16—1461no—
589M16—1461no—
590M16—1461no—
591M16—1461no—
592M16—1461no—
593M16—1461no—
594M16—1461no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—2922no—
600C2×C8—2922no—
601C2×C8—2922no—
602C2×C8—2922no—
603C2×C8—731no—
604C2×C8—731no—
605C2×C8—731no—
606C2×C8—731no—
607C2×C8—1461no—
608C2×C8—1461no—
609C2×C8—1461no—
610C2×C8—1461no—
611C2×C8—1461no—
612C2×C8—1461no—
613C2×C8—1461no—
614C2×C8—1461no—
615C2×C8C22×Dic7311yescharacteristic
616C2×C8C22×Dic7311yescharacteristic
617C2×C8C22×Dic7311yescharacteristic
618C2×C8C22×Dic7311yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C22×Dic7311yescharacteristic
624C4⋊C4C22×Dic7311yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—732no—
636C42—1461no—
637C42—1461no—
638C42—1461no—
639C42C22×Dic7311yescharacteristic
640C42C22×Dic7311yescharacteristic
641C42D4×D7311yescharacteristic
642C42D4×D7311yescharacteristic
643C23—21no—
644C23—21no—
645C23—21no—
646C23C2×#1192402711yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8D4×Dic7312yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—42no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4D4×Dic7312yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—81no—
682C2×C4—2921no—
683C2×C4—2921no—
684C2×C4—2921no—
685C2×C4—2921no—
686C2×C4—2921no—
687C2×C4—1462no—
688C2×C4D4×Dic7311yescharacteristic
689C2×C4D4×Dic7311yescharacteristic
690C2×C4D4×Dic7311yescharacteristic
691C2×C4D4×Dic7311yescharacteristic
692C2×C4C23×Dic7311yescharacteristic
693C2×C4C2×D4×D7311yescharacteristic
694C2×C4C2×D4×D7311yescharacteristic
695C2×C4C2×#1192402711yescharacteristic
696C2×C4#1455663711yescharacteristic
697C2×C4#1455663811yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—2921no—
703C8—2921no—
704C8—2921no—
705C8—1461no—
706C8—1461no—
707C8—1461no—
708C8—1462no—
709C8—1461no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22C2×D4×Dic7311yescharacteristic
722C22#1798923711yescharacteristic
723C22#1798928911yescharacteristic
724C4—21no—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—2922no—
734C4—5841no—
735C4C2×D4×Dic7311yescharacteristic
736C4#1798907011yescharacteristic
737C4#1798922111yescharacteristic
738C4#1798924311yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—81no—
743C2—81no—
744C2#2261295111yescharacteristic
745C2#2261883411yescharacteristic
746C2#2261884811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
Fitting, prime radicalC73×#3035C2
socleC22×C73C2×C4×D4
cosocleC22×C4×C73C24
hypercenter#3035D73
hypocenterC73#23017
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. C2×#17988709C2semidirect
2. C2×#17988704C2semidirect
3. #22618675C2semidirect
4. #22618499C2semidirect
5. #22610764C2semidirect
6. #22610707C2semidirect
7. #22610644C2semidirect
8. #22610637C2semidirect
9. #22610260C2semidirect
10. #22610260C2semidirect
11. #22610208C2semidirect
12. #22610208C2semidirect
13. #22609790C2semidirect
14. #22609741C2semidirect
58. #464×C73C4semidirect
59. #464×C73C4semidirect
60. #463×C73C4semidirect
61. #463×C73C4semidirect
62. #462×C73C4semidirect
63. #461×C73C4semidirect
64. #460×C73C4semidirect
65. #459×C73C4semidirect
110. #14556518D4semidirect
389. C73#23017semidirect
398. #464Dic73semidirect
399. #464Dic73semidirect
400. #463Dic73semidirect
401. #463Dic73semidirect
402. #462Dic73semidirect
403. #461Dic73semidirect
404. #460Dic73semidirect
405. #459Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179887092
C2×#179887042
#226186752
#226184992
#226107642
#226107072
#226106442
#226106372
#226102602
#226102082
#226097902
#226097412
C73×#30352
#2301773