Finite Group Databasebeta

← #33104079

Subgroups — #33104079

Order 18688.

1126 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988650C211yesmaximal, characteristic
2C22×#14556522C211yesmaximal, characteristic, complemented
3C2×#106×D73C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D73C211yesmaximal, characteristic
5#22612827C211yesmaximal, characteristic
6#22610693C211yesmaximal, characteristic, complemented
7#22610691C211yesmaximal, characteristic, complemented
8#22610126C211yesmaximal, characteristic, complemented
9#22610125C211yesmaximal, characteristic, complemented
10#22610122C211yesmaximal, characteristic, complemented
11#22610086C211yesmaximal, characteristic, complemented
12#22609955C211yesmaximal, characteristic, complemented
13#22609954C211yesmaximal, characteristic, complemented
14#22609819C211yesmaximal, characteristic, complemented
15C73×#1853C211yesmaximal, characteristic, complemented
16C23×#10596831C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×C4×C22⋊D73—21no—
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×#14556551—21no—
21C22×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊C4×D73C2211yescharacteristic
23C2×C4⋊C4×D73C2211yescharacteristic
24#17988650C418yescomplemented
25C2×#14556523C2211yescharacteristic
26C2×#14556523C2211yescharacteristic
27C2×#14556522—24no—
28C2×#14556522C2211yescharacteristic
29C2×#14556522C2211yescharacteristic
30C2×#14556522C2211yescharacteristic
31C2×#14556522C2211yescharacteristic
32C2×#14556522C2211yescharacteristic
33C2×#14556522C2211yescharacteristic
34#106×D73—24no—
35C2×#14556520C2211yescharacteristic
36C2×#14556503C2211yescharacteristic
37C2×C8×Dic73C2211yescharacteristic
38#17988484—21no—
39#17988482—21no—
40#17988461—21no—
41#17988460—21no—
42#17988459—21no—
43#17988458—21no—
44#17988456C2211yescharacteristic
45#17988456C2211yescharacteristic
46#17988447C2211yescharacteristic
47#17988444C2211yescharacteristic
48#17988444C2211yescharacteristic
49C4⋊C4×Dic73C2211yescharacteristic
50C4⋊C4×Dic73C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55C22×C4⋊C4×C73C2211yescharacteristic
56C2×#106×C73C2211yescharacteristic
57C2×#106×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59#380×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×C22⋊D73D411yescharacteristic
63C23×Dic73—21no—
64C22×C4×D73—21no—
65C22×C4×D73—21no—
66C22×C4×D73C2311yescharacteristic
67C22×#10596831—22no—
68C22×#10596831—22no—
69C22×#10596831C2×C414yescomplemented
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C2×C8×D73—22no—
73C2×C8×D73—22no—
74C2×C8×D73C2×C414yescomplemented
75C4×C22⋊D73—44no—
76C4×C22⋊D73C2×C414yes—
77C4×C22⋊D73Q814yes—
78#14556551—44no—
79C2×C4⋊Dic73—22no—
80C2×C4⋊Dic73—21no—
81C2×C4⋊Dic73—41no—
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C4⋊Dic73C2311yescharacteristic
85C2×C4⋊Dic73C2311yescharacteristic
86C2×#11924007—21no—
87C2×#11924007—21no—
88C2×#11924007—21no—
89C2×#11924007—21no—
90C2×#11924007—21no—
91C2×#11924007—21no—
92C2×#11924007D411yescharacteristic
93C4⋊C4×D73—22no—
94C4⋊C4×D73—22no—
95C4⋊C4×D73—41no—
96C4⋊C4×D73—41no—
97C2×C22⋊Dic73—21no—
98C2×C22⋊Dic73D411yescharacteristic
99C2×#11924005—21no—
100C2×#11924005—21no—
101C2×#11924005D411yescharacteristic
102C2×C4×Dic73—21no—
103C2×C4×Dic73—21no—
104C2×C4×Dic73C2311yescharacteristic
105#14556523—22no—
106#14556523—41no—
107#14556522—22no—
108#14556522—22no—
109#14556522—22no—
110#14556522—22no—
111#14556522—22no—
112#14556522D414yescomplemented
113#14556520C2×C414yescomplemented
114#14556503C2×C414yescomplemented
115C8×Dic73C2×C414yescomplemented
116#14556498—21no—
117#14556498—21no—
118#14556498—21no—
119#14556498—21no—
120#14556498—21no—
121C23×C4×C73—21no—
122C23×C4×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C2×C4⋊C4×C73—22no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73—41no—
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C4⋊C4×C73C2311yescharacteristic
130C2×C4⋊C4×C73C2311yescharacteristic
131C2×C4⋊C4×C73C2311yescharacteristic
132C2×C22⋊C4×C73—21no—
133#106×C73—22no—
134#106×C73—41no—
135C22⋊C8×C73C2×C414yescomplemented
136#95×C73—21no—
137C23×D73C2×D411yescharacteristic
138C2×C22⋊D73C4⋊C414yes—
139C2×C22⋊D73SD1614yes—
140C2×C22⋊D73SD1614yes—
141C22×Dic73—21no—
142C22×Dic73—21no—
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—42no—
146C22×Dic73—42no—
147C22×Dic73—81no—
148C22×Dic73C2×D411yescharacteristic
149C22×Dic73C2×D411yescharacteristic
150C22×Dic73C2×D411yescharacteristic
151C2×C4×D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—42no—
156C2×C4×D73—42no—
157C2×C4×D73—42no—
158C2×C4×D73—42no—
159C2×C4×D73—81no—
160C2×C4×D73—81no—
161C2×C4×D73C22×C412yes—
162C2×C4×D73C2×Q812yes—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—28no—
166C2×#10596831C22×C412yes—
167C2×#10596831C22×C412yes—
168C2×#10596831C2×D412yes—
169C2×#10596831#4112yes—
170C8×D73—28no—
171C4⋊Dic73—21no—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73—21no—
177C4⋊Dic73—21no—
178C4⋊Dic73—42no—
179C4⋊Dic73C2×D412yes—
180#11924007—42no—
181#11924007—42no—
182#11924007—42no—
183#11924007—42no—
184#11924007—81no—
185#11924007—81no—
186#11924007C4⋊C414yes—
187C22⋊Dic73—42no—
188C22⋊Dic73C4⋊C414yes—
189#11924005—42no—
190#11924005—42no—
191#11924005C4⋊C414yes—
192C4×Dic73—42no—
193C4×Dic73—42no—
194C4×Dic73C22×C412yes—
195C4×Dic73C2×Q812yes—
196C24×C73C2×D411yescharacteristic
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—42no—
206C22×C4×C73—42no—
207C22×C4×C73—81no—
208C22×C4×C73C22×C412yes—
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2×Q812yes—
211C22×C4×C73C2411yescharacteristic
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73C22×C412yes—
217C2×C8×C73C22×C412yes—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—42no—
226C4⋊C4×C73C2×D412yes—
227C22⋊C4×C73—42no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73C2×C4⋊C412yes—
233C23×C73C2×SD1612yes—
234C23×C73C2×SD1612yes—
235C23×C73C22×D411yescharacteristic
236C22×D73—21no—
237C22×D73—21no—
238C22×D73—21no—
239C22×D73—21no—
240C22×D73C2×C4⋊C412yes—
241C22×D73C2×SD1612yes—
242C22×D73C2×SD1612yes—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—22no—
248C2×C4×C73—22no—
249C2×C4×C73—22no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—84no—
262C2×C4×C73C2×C4⋊C412yes—
263C2×C4×C73C23×C411yescharacteristic
264C2×C4×C73C22×D411yescharacteristic
265C2×C4×C73C22×Q811yescharacteristic
266C2×C4×C73C2×#4111yescharacteristic
267C2×C4×C73H(5,𝔽2)11yescharacteristic
268C2×C4×C732−1+411yescharacteristic
269C22⋊D73#106116yescomplemented
270C2×Dic73—21no—
271C2×Dic73—21no—
272C2×Dic73—21no—
273C2×Dic73—21no—
274C2×Dic73—22no—
275C2×Dic73—41no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278C2×Dic73—41no—
279C2×Dic73—41no—
280C2×Dic73—41no—
281C2×Dic73—41no—
282C2×Dic73—41no—
283C2×Dic73—41no—
284C2×Dic73—41no—
285C2×Dic73—41no—
286C2×Dic73—84no—
287C2×Dic73C2×C4⋊C412yes—
288C2×Dic73C2×C4⋊C412yes—
289C2×Dic73C2×C4⋊C412yes—
290C2×Dic73C2×SD1612yes—
291C2×Dic73C2×SD1612yes—
292C4×D73—22no—
293C4×D73—22no—
294C4×D73—22no—
295C4×D73—22no—
296C4×D73—84no—
297C4×D73—84no—
298C8×C73—22no—
299C8×C73—22no—
300#10596831—22no—
301#10596831C4×D414yescomplemented
302C22×C73—22no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73C2×#10614yescomplemented
309C22×C73C22×C4⋊C411yescharacteristic
310C22×C73D4211yescharacteristic
311C22×C73#54711yescharacteristic
312C22×C73C22×SD1611yescharacteristic
313C22×C73C22×SD1611yescharacteristic
314C22×C73#57711yescharacteristic
315C22×C73#57711yescharacteristic
316C2×D73—22no—
317C2×D73—22no—
318C2×D73—22no—
319C2×D73—22no—
320C2×D73—22no—
321C2×D73—22no—
322C2×D73C2×#10614yescomplemented
323C4×C73—22no—
324C4×C73—42no—
325C4×C73—81no—
326C4×C73—81no—
327C4×C73—81no—
328C4×C73C2×C4×D411yescharacteristic
329C4×C73#52011yescharacteristic
330C4×C73D4×Q811yescharacteristic
331C4×C73#55411yescharacteristic
332Dic73—22no—
333Dic73—22no—
334Dic73—42no—
335Dic73—81no—
336Dic73—81no—
337Dic73—81no—
338Dic73C2×#10614yescomplemented
339D4×#106—731nomaximal, Sylow
340C2×C73—24no—
341C2×C73D4×C4⋊C411yescharacteristic
342C2×C73C22×#10611yescharacteristic
343C2×C73#291211yescharacteristic
344C2×C73D4×SD1611yescharacteristic
345C2×C73D4×SD1611yescharacteristic
346C2×C73#333511yescharacteristic
347C2×C73#333511yescharacteristic
348D73—24no—
349C2×C8×D4—731no—
350C22×#106—731no—
351C22×#106—731no—
352D4×C4⋊C4—731no—
353D4×C4⋊C4—731no—
354#1948—731no—
355#1948—731no—
356#1853—731no—
357#1853—731no—
358#1853—731no—
359#1853D7311yescharacteristic, complemented
360#1844—731no—
361#1807—731no—
362#1807—731no—
363C4×#106—731no—
364C73D4×#10611yescharacteristic, complemented, Sylow
365C23×C8—731no—
366C23×C8—731no—
367C2×C4×D4—731no—
368C2×C4×D4—1461no—
369C2×C4×D4—1461no—
370C22×C4⋊C4—731no—
371C22×C4⋊C4—731no—
372C22×C4⋊C4—731no—
373C22×C4⋊C4C2×D7311yescharacteristic
374C8×D4—738no—
375C2×#106—731no—
376C2×#106—731no—
377C2×#106—731no—
378C2×#106—731no—
379C2×#106—731no—
380C2×#106—731no—
381C2×#106—731no—
382C2×#106—731no—
383C2×#106—1464no—
384C2×#106—1464no—
385C2×#106C2×D7311yescharacteristic
386C2×#106C2×D7311yescharacteristic
387C2×C4⋊C8—731no—
388C2×C22⋊C8—731no—
389C2×C22⋊C8C2×D7311yescharacteristic
390C2×C4×C8—731no—
391#389—1461no—
392#389—1461no—
393#385—1461no—
394#385—1461no—
395#385—1461no—
396#385—1461no—
397#384—731no—
398#384—731no—
399#380—731no—
400#380—731no—
401#380—731no—
402#380C2×D7311yescharacteristic
403C4×C4⋊C4—731no—
404C4×C4⋊C4—731no—
405#340—731no—
406#340—731no—
407#340—731no—
408#340—731no—
409#340C2×D7311yescharacteristic
410#340C2×D7311yescharacteristic
411C22×D4—731no—
412C23×C4—21no—
413C23×C4—731no—
414C23×C4—1461no—
415C23×C4—1461no—
416C23×C4—1461no—
417C23×C4C22×D7311yescharacteristic
418C22×C8—731no—
419C22×C8—734no—
420C22×C8—731no—
421C22×C8—734no—
422C22×C8—1462no—
423C22×C8—1462no—
424C22×C8—1462no—
425C22×C8—1462no—
426C22×C8C22×D7311yescharacteristic
427C22×C8C22×D7311yescharacteristic
428C4×D4—2924no—
429C4×D4—2924no—
430C4×D4—734no—
431C4×D4—734no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—2921no—
436C2×C4⋊C4—2921no—
437C2×C4⋊C4—2921no—
438C2×C4⋊C4—731no—
439C2×C4⋊C4—731no—
440C2×C4⋊C4—731no—
441C2×C4⋊C4—731no—
442C2×C4⋊C4—731no—
443C2×C4⋊C4—1462no—
444C2×C4⋊C4—1461no—
445C2×C4⋊C4—1461no—
446C2×C4⋊C4—1461no—
447C2×C4⋊C4—1461no—
448C2×C4⋊C4—1461no—
449C2×C4⋊C4—1462no—
450C2×C4⋊C4—1462no—
451C2×C4⋊C4—1461no—
452C2×C4⋊C4—1461no—
453C2×C4⋊C4C22×D7311yescharacteristic
454C2×C4⋊C4C22×D7311yescharacteristic
455C2×C4⋊C4C22×D7311yescharacteristic
456C2×C4⋊C4C22×D7311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—731no—
459C2×C22⋊C4—731no—
460C2×C22⋊C4—1461no—
461C2×C22⋊C4—1461no—
462C2×C22⋊C4—1461no—
463C2×C42—731no—
464C2×C42—1461no—
465C2×C42—1461no—
466#106—22no—
467#106—41no—
468#106—2921no—
469#106—734no—
470#106—1462no—
471#106—1462no—
472#106—1462no—
473#106—1462no—
474#106—1462no—
475#106—1462no—
476C4⋊C8—734no—
477C22⋊C8—734no—
478C22⋊C8C4×D7314yescomplemented
479C4×C8—734no—
480#95—21no—
481#95—1461no—
482#95—1461no—
483#95—1461no—
484#95—1461no—
485#95—1461no—
486C24—731no—
487C24D4×D7311yescharacteristic
488C2×D4—734no—
489C2×D4—734no—
490C2×D4—734no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—2922no—
503C22×C4—2922no—
504C22×C4—2922no—
505C22×C4—2922no—
506C22×C4—2922no—
507C22×C4—2922no—
508C22×C4—5841no—
509C22×C4—5841no—
510C22×C4—5841no—
511C22×C4—731no—
512C22×C4—731no—
513C22×C4—731no—
514C22×C4—732no—
515C22×C4—732no—
516C22×C4—1461no—
517C22×C4—1461no—
518C22×C4—1461no—
519C22×C4—1461no—
520C22×C4—1461no—
521C22×C4—1461no—
522C22×C4—1461no—
523C22×C4—1461no—
524C22×C4C2×C4×D7312yes—
525C22×C4D4×D7311yescharacteristic
526C22×C4Q8×D7312yes—
527C22×C4C23×D7311yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—732no—
533C2×C8—732no—
534C2×C8—732no—
535C2×C8—732no—
536C2×C8—1468no—
537C2×C8—1468no—
538C2×C8—1461no—
539C2×C8—1461no—
540C2×C8C2×C4×D7312yes—
541C2×C8C2×C4×D7312yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—2922no—
551C4⋊C4—2922no—
552C4⋊C4—2922no—
553C4⋊C4—2922no—
554C4⋊C4—2922no—
555C4⋊C4—5841no—
556C4⋊C4—5841no—
557C4⋊C4—734no—
558C4⋊C4—732no—
559C4⋊C4—1461no—
560C4⋊C4—1461no—
561C4⋊C4—1461no—
562C4⋊C4—1461no—
563C4⋊C4—1461no—
564C4⋊C4—1461no—
565C4⋊C4—1461no—
566C4⋊C4D4×D7312yes—
567C22⋊C4—42no—
568C22⋊C4—2922no—
569C22⋊C4—2922no—
570C22⋊C4—2922no—
571C22⋊C4—734no—
572C22⋊C4—734no—
573C42—2922no—
574C42—2922no—
575C42—732no—
576C42—732no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—732no—
582C23—732no—
583C23—732no—
584C23—1461no—
585C23—1461no—
586C23—1461no—
587C23—1461no—
588C23C4⋊C4×D7312yes—
589C23SD16×D7312yes—
590C23SD16×D7312yes—
591C23C2×D4×D7311yescharacteristic
592D4—7316no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—84no—
612C2×C4—2921no—
613C2×C4—2921no—
614C2×C4—2921no—
615C2×C4—2921no—
616C2×C4—2921no—
617C2×C4—2921no—
618C2×C4—2921no—
619C2×C4—2921no—
620C2×C4—2921no—
621C2×C4—2921no—
622C2×C4—2921no—
623C2×C4—5844no—
624C2×C4—5844no—
625C2×C4—5844no—
626C2×C4—732no—
627C2×C4—732no—
628C2×C4—732no—
629C2×C4—732no—
630C2×C4—732no—
631C2×C4—1462no—
632C2×C4—1461no—
633C2×C4—1461no—
634C2×C4—1461no—
635C2×C4—1461no—
636C2×C4—1462no—
637C2×C4—1462no—
638C2×C4—1462no—
639C2×C4—1462no—
640C2×C4C4⋊C4×D7312yes—
641C2×C4C22×C4×D7311yescharacteristic
642C2×C4C2×D4×D7311yescharacteristic
643C2×C4C2×Q8×D7311yescharacteristic
644C2×C4#41×D7311yescharacteristic
645C2×C4#1455663611yescharacteristic
646C2×C4#1455663811yescharacteristic
647C8—22no—
648C8—22no—
649C8—734no—
650C8—1462no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—734no—
658C22—1462no—
659C22—1462no—
660C22—1462no—
661C22—1462no—
662C22—1462no—
663C22—1462no—
664C22#106×D7314yescomplemented
665C22C2×C4⋊C4×D7311yescharacteristic
666C22#1798921911yescharacteristic
667C22#1798923511yescharacteristic
668C22C2×SD16×D7311yescharacteristic
669C22C2×SD16×D7311yescharacteristic
670C22#1798939611yescharacteristic
671C22#1798939711yescharacteristic
672C4—22no—
673C4—42no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—2922no—
678C4—5841no—
679C4—5841no—
680C4—5841no—
681C4—734no—
682C4—1462no—
683C4—1462no—
684C4C4×D4×D7311yescharacteristic
685C4#1798906611yescharacteristic
686C4#1798925011yescharacteristic
687C4#1798929111yescharacteristic
688C2—24no—
689C2—1464no—
690C2#2261282911yescharacteristic
691C2C2×#106×D7311yescharacteristic
692C2#2261852511yescharacteristic
693C2#2262162011yescharacteristic
694C2#2262162511yescharacteristic
695C2#2262228111yescharacteristic
696C2#2262228611yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1853C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
cosocleC22×C4×C73C24
hypercenter#1853D73
hypocenterC73D4×#106
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C22×#14556522C2semidirect
3. C2×#106×D73C2semidirect
6. #22610693C2semidirect
7. #22610691C2semidirect
8. #22610126C2semidirect
9. #22610125C2semidirect
10. #22610122C2semidirect
11. #22610086C2semidirect
12. #22609955C2semidirect
13. #22609954C2semidirect
14. #22609819C2semidirect
15. C73×#1853C2semidirect
24. #17988650C4semidirect
69. C22×#10596831C2×C4semidirect
74. C2×C8×D73C2×C4semidirect
112. #14556522D4semidirect
113. #14556520C2×C4semidirect
114. #14556503C2×C4semidirect
115. C8×Dic73C2×C4semidirect
135. C22⋊C8×C73C2×C4semidirect
269. C22⋊D73#106semidirect
301. #10596831C4×D4semidirect
308. C22×C73C2×#106semidirect
322. C2×D73C2×#106semidirect
338. Dic73C2×#106semidirect
359. #1853D73semidirect
364. C73D4×#106semidirect
478. C22⋊C8C4×D73semidirect
664. C22#106×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886502
C22×#145565222
C2×#106×D732
C4⋊C4×C22⋊D732
#226128272
#226106932
#226106912
#226101262
#226101252
#226101222
#226100862
#226099552
#226099542
#226098192
C73×#18532
D4×#10673