Finite Group Databasebeta

← C73×#25162 #32934566

Subgroups — C73×#25162 #32934566

Order 18688.

1240 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C73C211yesmaximal, characteristic, complemented
2C2×#449×C73C211yesmaximal, characteristic, complemented
3C2×#449×C73C211yesmaximal, characteristic, complemented
4C2×C4×D8×C73C211yesmaximal, characteristic, complemented
5C73×#2428C211yesmaximal, characteristic, complemented
6C73×#2339C211yesmaximal, characteristic, complemented
7C73×#2068C211yesmaximal, characteristic, complemented
8C73×#2034C211yesmaximal, characteristic, complemented
9C73×#2033C211yesmaximal, characteristic, complemented
10C73×#2014C211yesmaximal, characteristic, complemented
11C73×#1968C211yesmaximal, characteristic, complemented
12C73×#1923C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1877C211yesmaximal, characteristic, complemented
15C73×#1864C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C22×D8×C73C2211yescharacteristic
21C2×#127×C73C2211yescharacteristic
22C2×#121×C73—21no—
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×C4×D4×C73C2211yescharacteristic
26C2×C4×D4×C73C2211yescharacteristic
27C2×C4×D4×C73C2211yescharacteristic
28#459×C73—24no—
29#449×C73—24no—
30#449×C73—24no—
31C4×D8×C73—24no—
32C2×#107×C73C2211yescharacteristic
33C2×#106×C73C2211yescharacteristic
34C2×C4⋊C8×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic
45C2×C4×C8×C73C2211yescharacteristic
46#394×C73—21no—
47#392×C73—21no—
48#391×C73C2211yescharacteristic
49#391×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#386×C73—21no—
53#386×C73—21no—
54#386×C73—21no—
55#381×C73—21no—
56#380×C73C2211yescharacteristic
57C4×C22⋊C4×C73C2211yescharacteristic
58C2×#95×C73—21no—
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C2×#41×C73—22no—
64C2×#41×C73—22no—
65C2×#41×C73—22no—
66C2×#41×C73—22no—
67C2×#41×C73—41no—
68C2×#41×C73—41no—
69C22×Q8×C73C2311yescharacteristic
70C22×D4×C73—21no—
71C22×D4×C73—21no—
72C22×D4×C73—21no—
73C22×D4×C73—21no—
74C22×D4×C73—21no—
75C22×D4×C73C2311yescharacteristic
76C22×D4×C73C2311yescharacteristic
77C22×D4×C73C2311yescharacteristic
78C23×C4×C73—21no—
79C23×C4×C73—21no—
80C23×C4×C73—21no—
81C23×C4×C73—21no—
82C23×C4×C73C2311yescharacteristic
83C2×SD16×C73—22no—
84C2×SD16×C73—22no—
85C2×SD16×C73—22no—
86C2×SD16×C73—22no—
87C2×SD16×C73—41no—
88C2×SD16×C73—41no—
89C2×D8×C73—22no—
90C2×D8×C73—22no—
91C2×D8×C73—22no—
92C2×D8×C73—22no—
93C2×D8×C73—22no—
94C2×D8×C73D414yescomplemented
95C22×C8×C73C2311yescharacteristic
96C22×C8×C73C2311yescharacteristic
97C22×C8×C73C2311yescharacteristic
98C22×C8×C73C2311yescharacteristic
99#127×C73—22no—
100#127×C73—41no—
101#121×C73—22no—
102#121×C73—22no—
103#121×C73—44no—
104#121×C73—41no—
105#121×C73—41no—
106C4×D4×C73—22no—
107C4×D4×C73—22no—
108C4×D4×C73—22no—
109C4×D4×C73—41no—
110C4×D4×C73—41no—
111C4×D4×C73—41no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73D411yescharacteristic
126C2×C22⋊C4×C73D411yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C2×C42×C73C2311yescharacteristic
129#107×C73—22no—
130#106×C73—41no—
131C4⋊C8×C73—22no—
132#103×C73—22no—
133#103×C73—22no—
134#102×C73—22no—
135#102×C73—22no—
136#102×C73—22no—
137#102×C73—22no—
138#102×C73—41no—
139#102×C73D414yescomplemented
140C22⋊C8×C73—22no—
141C22⋊C8×C73—22no—
142C4×C8×C73—22no—
143#95×C73—21no—
144#95×C73—21no—
145#95×C73—21no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73D411yescharacteristic
150#95×C73D411yescharacteristic
151C24×C73—21no—
152C24×C73—21no—
153C24×C73—21no—
154C24×C73C2×D411yescharacteristic
155#41×C73—44no—
156#41×C73—44no—
157#41×C73—44no—
158#41×C73—44no—
159C2×Q8×C73—21no—
160C2×Q8×C73—21no—
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73#4112yes—
165C2×D4×C73—24no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—42no—
181C2×D4×C73—42no—
182C2×D4×C73—42no—
183C2×D4×C73—42no—
184C2×D4×C73—42no—
185C2×D4×C73—42no—
186C2×D4×C73—42no—
187C2×D4×C73—42no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—81no—
191C2×D4×C73—81no—
192C2×D4×C73—81no—
193C2×D4×C73—81no—
194C2×D4×C73C2×D412yes—
195C2×D4×C73C2×D412yes—
196C2×D4×C73C2×D412yes—
197C2×D4×C73#4112yes—
198C22×C4×C73—24no—
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—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—42no—
211C22×C4×C73—42no—
212C22×C4×C73—42no—
213C22×C4×C73—42no—
214C22×C4×C73—42no—
215C22×C4×C73—42no—
216C22×C4×C73—42no—
217C22×C4×C73—42no—
218C22×C4×C73—81no—
219C22×C4×C73—81no—
220C22×C4×C73—81no—
221C22×C4×C73C2×D411yescharacteristic
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2×D411yescharacteristic
226C22×C4×C73C2411yescharacteristic
227SD16×C73—44no—
228SD16×C73—44no—
229D8×C73—28no—
230D8×C73—44no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73C2×D412yes—
242C2×C8×C73C2×D412yes—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—42no—
251C4⋊C4×C73C2×D412yes—
252C22⋊C4×C73—22no—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—42no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—42no—
258C22⋊C4×C73—42no—
259C22⋊C4×C73—42no—
260C22⋊C4×C73—81no—
261C22⋊C4×C73—81no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73—21no—
265C42×C73—21no—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73—21no—
270C23×C73—22no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—41no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73—41no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73C22×D411yescharacteristic
295Q8×C73—22no—
296Q8×C73—22no—
297Q8×C73—41no—
298Q8×C73—41no—
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—22no—
302D4×C73—22no—
303D4×C73—22no—
304D4×C73—48no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—41no—
310D4×C73—41no—
311D4×C73—84no—
312D4×C73—84no—
313D4×C73—84no—
314D4×C73—84no—
315D4×C73#12114yescomplemented
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—22no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—22no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—48no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—84no—
350C2×C4×C73—84no—
351C2×C4×C73—84no—
352C2×C4×C73#13512yes—
353C2×C4×C73AGL(1,ℤ/8)12yes—
354C2×C4×C73C22×D411yescharacteristic
355C2×C4×C73C22×D411yescharacteristic
356C2×C4×C73C2×#4111yescharacteristic
357C2×C4×C73C2×#4111yescharacteristic
358C2×C4×C73H(5,𝔽2)11yescharacteristic
359C2×C4×C73H(5,𝔽2)11yescharacteristic
360C8×C73—22no—
361C8×C73—22no—
362C8×C73—41no—
363C8×C73—41no—
364C22×C73—24no—
365C22×C73—42no—
366C22×C73—42no—
367C22×C73—42no—
368C22×C73—42no—
369C22×C73—42no—
370C22×C73—42no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73—41no—
374C22×C73—42no—
375C22×C73—41no—
376C22×C73—41no—
377C22×C73—42no—
378C22×C73—42no—
379C22×C73—41no—
380C22×C73—41no—
381C22×C73—81no—
382C22×C73—81no—
383C22×C73—81no—
384C22×C73—81no—
385C22×C73—81no—
386C22×C73—81no—
387C22×C73—81no—
388C22×C73—81no—
389C22×C73—81no—
390C22×C73—81no—
391C22×C73—81no—
392C22×C73#52511yescharacteristic
393C22×C73D4211yescharacteristic
394C22×C73D4211yescharacteristic
395C22×C73C2×#13511yescharacteristic
396C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
397C22×C73#57611yescharacteristic
398C22×C73#57711yescharacteristic
399C4×C73—22no—
400C4×C73—22no—
401C4×C73—41no—
402C4×C73—42no—
403C4×C73—42no—
404C4×C73—41no—
405C4×C73—41no—
406C4×C73—81no—
407C4×C73—81no—
408C4×C73—81no—
409C4×C73C2×#12111yescharacteristic
410C4×C73#53811yescharacteristic
411C4×C73#54611yescharacteristic
412C4×C73#54611yescharacteristic
413#25162C7311yesmaximal, characteristic, direct product factor, Sylow
414C2×C73—44no—
415C2×C73—81no—
416C2×C73—82no—
417C2×C73—161no—
418C2×C73#242411yescharacteristic
419C2×C73#310611yescharacteristic
420C2×C73#311911yescharacteristic
421C2×C73#326411yescharacteristic
422C2×C73#327211yescharacteristic
423C2×C73#328011yescharacteristic
424C2×C73#328411yescharacteristic
425C2×#459C2×C7311yescharacteristic, complemented
426C2×#449C2×C7311yescharacteristic, complemented
427C2×#449C2×C7311yescharacteristic, complemented
428C2×C4×D8C2×C7311yescharacteristic, complemented
429#2428C2×C7311yescharacteristic, complemented
430#2339C2×C7311yescharacteristic, complemented
431#2068C2×C7311yescharacteristic, complemented
432#2034C2×C7311yescharacteristic, complemented
433#2033C2×C7311yescharacteristic, complemented
434#2014C2×C7311yescharacteristic, complemented
435#1968C2×C7311yescharacteristic, complemented
436#1923C2×C7311yescharacteristic, complemented
437#1879C2×C7311yescharacteristic, complemented
438#1877C2×C7311yescharacteristic, complemented
439#1864C2×C7311yescharacteristic, complemented
440C73#2516211yescharacteristic, direct product factor, Sylow
441C22×#41C22×C7311yescharacteristic
442C22×SD16C22×C7311yescharacteristic
443C22×SD16C22×C7311yescharacteristic
444C22×D8C22×C7311yescharacteristic
445C22×D8C22×C7311yescharacteristic
446C2×#127C22×C7311yescharacteristic
447C2×#121—21no—
448C2×#121C22×C7311yescharacteristic
449C2×#121C22×C7311yescharacteristic
450C2×C4×D4C22×C7311yescharacteristic
451C2×C4×D4C22×C7311yescharacteristic
452C2×C4×D4C22×C7311yescharacteristic
453#459—24no—
454#449—24no—
455#449—24no—
456C4×D8—24no—
457C2×#107C22×C7311yescharacteristic
458C2×#106C22×C7311yescharacteristic
459C2×C4⋊C8C22×C7311yescharacteristic
460C2×#103C22×C7311yescharacteristic
461C2×#103C22×C7311yescharacteristic
462C2×#102C22×C7311yescharacteristic
463C2×#102C22×C7311yescharacteristic
464C2×#102C22×C7311yescharacteristic
465C2×#102C22×C7311yescharacteristic
466C2×#102C22×C7311yescharacteristic
467C2×#102C22×C7311yescharacteristic
468C2×C22⋊C8C22×C7311yescharacteristic
469C2×C22⋊C8C22×C7311yescharacteristic
470C2×C4×C8C22×C7311yescharacteristic
471#394—21no—
472#392—21no—
473#391C22×C7311yescharacteristic
474#391C22×C7311yescharacteristic
475#390C22×C7311yescharacteristic
476#389C22×C7311yescharacteristic
477#386—21no—
478#386—21no—
479#386—21no—
480#381—21no—
481#380C22×C7311yescharacteristic
482C4×C22⋊C4C22×C7311yescharacteristic
483C2×#95—21no—
484#340C22×C7311yescharacteristic
485#340C22×C7311yescharacteristic
486#336C22×C7311yescharacteristic
487#336C22×C7311yescharacteristic
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C23×C7311yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C7311yescharacteristic
501C22×D4C23×C7311yescharacteristic
502C22×D4C23×C7311yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C7311yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8D4×C7314yescomplemented
520C22×C8C23×C7311yescharacteristic
521C22×C8C23×C7311yescharacteristic
522C22×C8C23×C7311yescharacteristic
523C22×C8C23×C7311yescharacteristic
524#127—22no—
525#127—41no—
526#121—22no—
527#121—22no—
528#121—44no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C7311yescharacteristic
539C2×C4⋊C4C23×C7311yescharacteristic
540C2×C4⋊C4C23×C7311yescharacteristic
541C2×C4⋊C4C23×C7311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C7311yescharacteristic
551C2×C22⋊C4D4×C7311yescharacteristic
552C2×C42C23×C7311yescharacteristic
553C2×C42C23×C7311yescharacteristic
554#107—22no—
555#106—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C7314yescomplemented
565C22⋊C8—22no—
566C22⋊C8—22no—
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C7311yescharacteristic
575#95D4×C7311yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C7311yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C7312yes—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C7312yes—
620C2×D4C2×D4×C7312yes—
621C2×D4C2×D4×C7312yes—
622C2×D4#41×C7312yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C7311yescharacteristic
647C22×C4C2×D4×C7311yescharacteristic
648C22×C4C2×D4×C7311yescharacteristic
649C22×C4C2×D4×C7311yescharacteristic
650C22×C4C2×D4×C7311yescharacteristic
651C22×C4C24×C7311yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C7312yes—
667C2×C8C2×D4×C7312yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C7312yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23C22×D4×C7311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4#121×C7314yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4#135×C7312yes—
778C2×C4AGL(1,ℤ/8)×C7312yes—
779C2×C4C22×D4×C7311yescharacteristic
780C2×C4C22×D4×C7311yescharacteristic
781C2×C4C2×#41×C7311yescharacteristic
782C2×C4C2×#41×C7311yescharacteristic
783C2×C4H(5,𝔽2)×C7311yescharacteristic
784C2×C4H(5,𝔽2)×C7311yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—42no—
799C22—42no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22#525×C7311yescharacteristic
818C22D42×C7311yescharacteristic
819C22D42×C7311yescharacteristic
820C22C2×#135×C7311yescharacteristic
821C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
822C22#576×C7311yescharacteristic
823C22#577×C7311yescharacteristic
824C4—22no—
825C4—22no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#121×C7311yescharacteristic
835C4#538×C7311yescharacteristic
836C4#546×C7311yescharacteristic
837C4#546×C7311yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C73×#242411yescharacteristic
843C2C73×#310611yescharacteristic
844C2C73×#311911yescharacteristic
845C2C73×#326411yescharacteristic
846C2C73×#327211yescharacteristic
847C2C73×#328011yescharacteristic
848C2C73×#328411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C73C2semidirect
2. C2×#449×C73C2semidirect
3. C2×#449×C73C2semidirect
4. C2×C4×D8×C73C2semidirect
5. C73×#2428C2semidirect
6. C73×#2339C2semidirect
7. C73×#2068C2semidirect
8. C73×#2034C2semidirect
9. C73×#2033C2semidirect
10. C73×#2014C2semidirect
11. C73×#1968C2semidirect
12. C73×#1923C2semidirect
13. C73×#1879C2semidirect
14. C73×#1877C2semidirect
15. C73×#1864C2semidirect
94. C2×D8×C73D4semidirect
139. #102×C73D4semidirect
315. D4×C73#121semidirect
413. #25162C73direct (N × H)
425. C2×#459C2×C73semidirect
426. C2×#449C2×C73semidirect
427. C2×#449C2×C73semidirect
428. C2×C4×D8C2×C73semidirect
429. #2428C2×C73semidirect
430. #2339C2×C73semidirect
431. #2068C2×C73semidirect
432. #2034C2×C73semidirect
433. #2033C2×C73semidirect
434. #2014C2×C73semidirect
435. #1968C2×C73semidirect
436. #1923C2×C73semidirect
437. #1879C2×C73semidirect
438. #1877C2×C73semidirect
439. #1864C2×C73semidirect
440. C73#25162direct (N × H)
519. C2×D8D4×C73semidirect
564. #102D4×C73semidirect
740. D4#121×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C732
C2×#449×C732
C2×C4×D8×C732
C73×#24282
C73×#23392
C73×#20682
C73×#20342
C73×#20332
C73×#20142
C73×#19682
C73×#19232
C73×#18792
C73×#18772
C73×#18642
#2516273