Finite Group Databasebeta

← C73×#23978 #32933382

Subgroups — C73×#23978 #32933382

Order 18688.

1262 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552×C73C211yesmaximal, characteristic, complemented
2C2×#452×C73C211yesmaximal, characteristic, complemented
3C2×#417×C73C211yesmaximal, characteristic, complemented
4C73×#2407C211yesmaximal, characteristic
5C73×#2026C211yesmaximal, characteristic, complemented
6C73×#2025C211yesmaximal, characteristic, complemented
7C73×#2001C211yesmaximal, characteristic, complemented
8C73×#2000C211yesmaximal, characteristic, complemented
9C73×#1894C211yesmaximal, characteristic, complemented
10C73×#1880C211yesmaximal, characteristic, complemented
11C73×#1878C211yesmaximal, characteristic, complemented
12C73×#1875C211yesmaximal, characteristic, complemented
13C73×#1873C211yesmaximal, characteristic, complemented
14C73×#1870C211yesmaximal, characteristic, complemented
15C73×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×Q16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic
20#552×C73—24no—
21#552×C73—24no—
22C2×#126×C73—21no—
23C2×#125×C73—21no—
24C2×#125×C73C2211yescharacteristic
25C2×#123×C73—21no—
26C2×C22⋊Q8×C73C2211yescharacteristic
27C2×C22⋊Q8×C73C2211yescharacteristic
28C2×C22⋊Q8×C73C2211yescharacteristic
29C2×#121×C73C2211yescharacteristic
30C2×C4×Q8×C73C2211yescharacteristic
31C2×C4×D4×C73C2211yescharacteristic
32C2×#117×C73—21no—
33C2×#117×C73C2211yescharacteristic
34C22×C4⋊C4×C73C2211yescharacteristic
35#452×C73—24no—
36#417×C73—24no—
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#103×C73C2211yescharacteristic
41C2×#103×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48#394×C73—21no—
49#392×C73—21no—
50#391×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#386×C73—21no—
53#385×C73—21no—
54#380×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
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×Q8×C73C2311yescharacteristic
71C22×D4×C73—21no—
72C22×D4×C73—21no—
73C22×D4×C73D411yescharacteristic
74C22×D4×C73C2311yescharacteristic
75C23×C4×C73—21no—
76C23×C4×C73—21no—
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C2×Q16×C73—22no—
80C2×Q16×C73—22no—
81C2×Q16×C73—41no—
82C2×SD16×C73—22no—
83C2×SD16×C73—22no—
84C2×SD16×C73—41no—
85C2×M16×C73—22no—
86C2×M16×C73—41no—
87C2×M16×C73—41no—
88C22×C8×C73C2311yescharacteristic
89C22×C8×C73C2311yescharacteristic
90C22×C8×C73C2311yescharacteristic
91C22×C8×C73C2311yescharacteristic
92#126×C73—28no—
93#125×C73—28no—
94#125×C73—22no—
95#125×C73—22no—
96#123×C73—28no—
97C22⋊Q8×C73—22no—
98C22⋊Q8×C73—22no—
99C22⋊Q8×C73—22no—
100C22⋊Q8×C73—22no—
101C22⋊Q8×C73—41no—
102C22⋊Q8×C73D414yescomplemented
103#121×C73—22no—
104#121×C73—41no—
105C4×Q8×C73—22no—
106C4×Q8×C73—22no—
107C4×D4×C73—22no—
108C4×D4×C73—22no—
109#117×C73—28no—
110#117×C73—22no—
111#117×C73—22no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73—22no—
114C2×C4⋊C4×C73—21no—
115C2×C4⋊C4×C73—21no—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73—21no—
118C2×C4⋊C4×C73—21no—
119C2×C4⋊C4×C73—21no—
120C2×C4⋊C4×C73D411yescharacteristic
121C2×C4⋊C4×C73D414yescomplemented
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73D411yescharacteristic
136C2×C22⋊C4×C73D411yescharacteristic
137C2×C42×C73—21no—
138C2×C42×C73—21no—
139C2×C42×C73C2311yescharacteristic
140#103×C73—22no—
141#103×C73—22no—
142#103×C73—22no—
143#103×C73—41no—
144#103×C73—41no—
145#102×C73—22no—
146#102×C73—22no—
147#102×C73—22no—
148C22⋊C8×C73—22no—
149C22⋊C8×C73—41no—
150C22⋊C8×C73—41no—
151#95×C73—21no—
152#95×C73—21no—
153#95×C73—21no—
154C24×C73—21no—
155C24×C73C2×D411yescharacteristic
156C24×C73C2×D411yescharacteristic
157#41×C73—28no—
158#41×C73—44no—
159#41×C73—44no—
160#41×C73—44no—
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73C2×D412yes—
172C2×Q8×C73#4112yes—
173C2×D4×C73—22no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—41no—
180C2×D4×C73—41no—
181C2×D4×C73—42no—
182C2×D4×C73—42no—
183C2×D4×C73—42no—
184C2×D4×C73—42no—
185C2×D4×C73—42no—
186C2×D4×C73—81no—
187C2×D4×C73#4112yes—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—24no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
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—21no—
206C22×C4×C73—42no—
207C22×C4×C73—42no—
208C22×C4×C73—42no—
209C22×C4×C73—42no—
210C22×C4×C73—42no—
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D412yes—
216C22×C4×C73C2×D412yes—
217C22×C4×C73C2411yescharacteristic
218Q16×C73—44no—
219SD16×C73—44no—
220M16×C73—44no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C4⋊C4×C73—24no—
234C4⋊C4×C73—24no—
235C4⋊C4×C73—24no—
236C4⋊C4×C73—24no—
237C4⋊C4×C73—24no—
238C4⋊C4×C73—24no—
239C4⋊C4×C73—22no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—42no—
248C4⋊C4×C73C2×D412yes—
249C4⋊C4×C73C2×D412yes—
250C4⋊C4×C73C2×D412yes—
251C22⋊C4×C73—24no—
252C22⋊C4×C73—24no—
253C22⋊C4×C73—24no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—42no—
258C22⋊C4×C73—42no—
259C22⋊C4×C73—81no—
260C22⋊C4×C73—81no—
261C42×C73—24no—
262C42×C73—24no—
263C42×C73—21no—
264C42×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—22no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73#12012yes—
286C23×C73C22×D411yescharacteristic
287Q8×C73—22no—
288Q8×C73—22no—
289Q8×C73—22no—
290Q8×C73—22no—
291Q8×C73—41no—
292Q8×C73—41no—
293Q8×C73—41no—
294Q8×C73—41no—
295D4×C73—22no—
296D4×C73—22no—
297D4×C73—44no—
298D4×C73—48no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—84no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—21no—
314C2×C4×C73—22no—
315C2×C4×C73—21no—
316C2×C4×C73—22no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—48no—
323C2×C4×C73—48no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
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#12012yes—
345C2×C4×C73C22×D411yescharacteristic
346C2×C4×C73C22×D411yescharacteristic
347C2×C4×C73C2×#4111yescharacteristic
348C2×C4×C73C2×#4111yescharacteristic
349C2×C4×C73H(5,𝔽2)11yescharacteristic
350C2×C4×C73H(5,𝔽2)11yescharacteristic
351C8×C73—41no—
352C8×C73—41no—
353C8×C73—41no—
354C8×C73—41no—
355C22×C73—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—42no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—42no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—42no—
371C22×C73—41no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73C2×#12011yescharacteristic
377C22×C73#54611yescharacteristic
378C22×C73#54611yescharacteristic
379C22×C73#57511yescharacteristic
380C22×C73#57511yescharacteristic
381C22×C73#57711yescharacteristic
382C22×C73#57811yescharacteristic
383C4×C73—22no—
384C4×C73—41no—
385C4×C73—42no—
386C4×C73—42no—
387C4×C73—41no—
388C4×C73—42no—
389C4×C73—42no—
390C4×C73—41no—
391C4×C73—42no—
392C4×C73—81no—
393C4×C73—81no—
394C4×C73#52511yescharacteristic
395C4×C73#53511yescharacteristic
396C4×C73#54611yescharacteristic
397C4×C73#54611yescharacteristic
398#23978C7311yesmaximal, characteristic, direct product factor, Sylow
399C2×C73—42no—
400C2×C73—81no—
401C2×C73—82no—
402C2×C73#240411yescharacteristic
403C2×C73#300511yescharacteristic
404C2×C73#301311yescharacteristic
405C2×C73#331511yescharacteristic
406C2×C73#331711yescharacteristic
407C2×C73#332311yescharacteristic
408C2×C73#332711yescharacteristic
409C2×#552C2×C7311yescharacteristic, complemented
410C2×#452C2×C7311yescharacteristic, complemented
411C2×#417C2×C7311yescharacteristic, complemented
412#2407C2×C7311yescharacteristic
413#2026C2×C7311yescharacteristic, complemented
414#2025C2×C7311yescharacteristic, complemented
415#2001C2×C7311yescharacteristic, complemented
416#2000C2×C7311yescharacteristic, complemented
417#1894C2×C7311yescharacteristic, complemented
418#1880C2×C7311yescharacteristic, complemented
419#1878C2×C7311yescharacteristic, complemented
420#1875C2×C7311yescharacteristic, complemented
421#1873C2×C7311yescharacteristic, complemented
422#1870C2×C7311yescharacteristic, complemented
423#1824C2×C7311yescharacteristic, complemented
424C73#2397811yescharacteristic, direct product factor, Sylow
425C22×#41C22×C7311yescharacteristic
426C22×Q16C22×C7311yescharacteristic
427C22×SD16C22×C7311yescharacteristic
428C22×M16C22×C7311yescharacteristic
429#552—24no—
430#552—24no—
431C2×#126—21no—
432C2×#125—21no—
433C2×#125C22×C7311yescharacteristic
434C2×#123—21no—
435C2×C22⋊Q8C22×C7311yescharacteristic
436C2×C22⋊Q8C22×C7311yescharacteristic
437C2×C22⋊Q8C22×C7311yescharacteristic
438C2×#121C22×C7311yescharacteristic
439C2×C4×Q8C22×C7311yescharacteristic
440C2×C4×D4C22×C7311yescharacteristic
441C2×#117—21no—
442C2×#117C22×C7311yescharacteristic
443C22×C4⋊C4C22×C7311yescharacteristic
444#452—24no—
445#417—24no—
446C2×#103C22×C7311yescharacteristic
447C2×#103C22×C7311yescharacteristic
448C2×#103C22×C7311yescharacteristic
449C2×#103C22×C7311yescharacteristic
450C2×#103C22×C7311yescharacteristic
451C2×#102C22×C7311yescharacteristic
452C2×#102C22×C7311yescharacteristic
453C2×#102C22×C7311yescharacteristic
454C2×C22⋊C8C22×C7311yescharacteristic
455C2×C22⋊C8C22×C7311yescharacteristic
456C2×C22⋊C8C22×C7311yescharacteristic
457#394—21no—
458#392—21no—
459#391C22×C7311yescharacteristic
460#390C22×C7311yescharacteristic
461#386—21no—
462#385—21no—
463#380C22×C7311yescharacteristic
464#340C22×C7311yescharacteristic
465#340C22×C7311yescharacteristic
466#340C22×C7311yescharacteristic
467#340C22×C7311yescharacteristic
468#340C22×C7311yescharacteristic
469#340C22×C7311yescharacteristic
470#336C22×C7311yescharacteristic
471#336C22×C7311yescharacteristic
472C2×#41—22no—
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C22×Q8C23×C7311yescharacteristic
479C22×Q8C23×C7311yescharacteristic
480C22×D4—21no—
481C22×D4—21no—
482C22×D4D4×C7311yescharacteristic
483C22×D4C23×C7311yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4C23×C7311yescharacteristic
487C23×C4C23×C7311yescharacteristic
488C2×Q16—22no—
489C2×Q16—22no—
490C2×Q16—41no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—41no—
494C2×M16—22no—
495C2×M16—41no—
496C2×M16—41no—
497C22×C8C23×C7311yescharacteristic
498C22×C8C23×C7311yescharacteristic
499C22×C8C23×C7311yescharacteristic
500C22×C8C23×C7311yescharacteristic
501#126—28no—
502#125—28no—
503#125—22no—
504#125—22no—
505#123—28no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—41no—
511C22⋊Q8D4×C7314yescomplemented
512#121—22no—
513#121—41no—
514C4×Q8—22no—
515C4×Q8—22no—
516C4×D4—22no—
517C4×D4—22no—
518#117—28no—
519#117—22no—
520#117—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4D4×C7311yescharacteristic
530C2×C4⋊C4D4×C7314yescomplemented
531C2×C4⋊C4C23×C7311yescharacteristic
532C2×C4⋊C4C23×C7311yescharacteristic
533C2×C4⋊C4C23×C7311yescharacteristic
534C2×C4⋊C4C23×C7311yescharacteristic
535C2×C4⋊C4C23×C7311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4D4×C7311yescharacteristic
545C2×C22⋊C4D4×C7311yescharacteristic
546C2×C42—21no—
547C2×C42—21no—
548C2×C42C23×C7311yescharacteristic
549#103—22no—
550#103—22no—
551#103—22no—
552#103—41no—
553#103—41no—
554#102—22no—
555#102—22no—
556#102—22no—
557C22⋊C8—22no—
558C22⋊C8—41no—
559C22⋊C8—41no—
560#95—21no—
561#95—21no—
562#95—21no—
563C24—21no—
564C24C2×D4×C7311yescharacteristic
565C24C2×D4×C7311yescharacteristic
566#41—28no—
567#41—44no—
568#41—44no—
569#41—44no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8C2×D4×C7312yes—
581C2×Q8#41×C7312yes—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—81no—
596C2×D4#41×C7312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4C2×D4×C7311yescharacteristic
621C22×C4C2×D4×C7311yescharacteristic
622C22×C4C2×D4×C7311yescharacteristic
623C22×C4C2×D4×C7311yescharacteristic
624C22×C4C2×D4×C7312yes—
625C22×C4C2×D4×C7312yes—
626C22×C4C24×C7311yescharacteristic
627Q16—44no—
628SD16—44no—
629M16—44no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4C2×D4×C7312yes—
658C4⋊C4C2×D4×C7312yes—
659C4⋊C4C2×D4×C7312yes—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C42—24no—
671C42—24no—
672C42—21no—
673C42—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—22no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23#120×C7312yes—
695C23C22×D4×C7311yescharacteristic
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703Q8—41no—
704D4—22no—
705D4—22no—
706D4—44no—
707D4—48no—
708D4—41no—
709D4—41no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4#120×C7312yes—
754C2×C4C22×D4×C7311yescharacteristic
755C2×C4C22×D4×C7311yescharacteristic
756C2×C4C2×#41×C7311yescharacteristic
757C2×C4C2×#41×C7311yescharacteristic
758C2×C4H(5,𝔽2)×C7311yescharacteristic
759C2×C4H(5,𝔽2)×C7311yescharacteristic
760C8—41no—
761C8—41no—
762C8—41no—
763C8—41no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—41no—
779C22—42no—
780C22—41no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×#120×C7311yescharacteristic
786C22#546×C7311yescharacteristic
787C22#546×C7311yescharacteristic
788C22#575×C7311yescharacteristic
789C22#575×C7311yescharacteristic
790C22#577×C7311yescharacteristic
791C22#578×C7311yescharacteristic
792C4—22no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—41no—
797C4—42no—
798C4—41no—
799C4—42no—
800C4—42no—
801C4—81no—
802C4—81no—
803C4#525×C7311yescharacteristic
804C4#535×C7311yescharacteristic
805C4#546×C7311yescharacteristic
806C4#546×C7311yescharacteristic
807C2—42no—
808C2—81no—
809C2—82no—
810C2C73×#240411yescharacteristic
811C2C73×#300511yescharacteristic
812C2C73×#301311yescharacteristic
813C2C73×#331511yescharacteristic
814C2C73×#331711yescharacteristic
815C2C73×#332311yescharacteristic
816C2C73×#332711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2407C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#552×C73C2semidirect
2. C2×#452×C73C2semidirect
3. C2×#417×C73C2semidirect
5. C73×#2026C2semidirect
6. C73×#2025C2semidirect
7. C73×#2001C2semidirect
8. C73×#2000C2semidirect
9. C73×#1894C2semidirect
10. C73×#1880C2semidirect
11. C73×#1878C2semidirect
12. C73×#1875C2semidirect
13. C73×#1873C2semidirect
14. C73×#1870C2semidirect
15. C73×#1824C2semidirect
102. C22⋊Q8×C73D4semidirect
121. C2×C4⋊C4×C73D4semidirect
398. #23978C73direct (N × H)
409. C2×#552C2×C73semidirect
410. C2×#452C2×C73semidirect
411. C2×#417C2×C73semidirect
413. #2026C2×C73semidirect
414. #2025C2×C73semidirect
415. #2001C2×C73semidirect
416. #2000C2×C73semidirect
417. #1894C2×C73semidirect
418. #1880C2×C73semidirect
419. #1878C2×C73semidirect
420. #1875C2×C73semidirect
421. #1873C2×C73semidirect
422. #1870C2×C73semidirect
423. #1824C2×C73semidirect
424. C73#23978direct (N × H)
511. C22⋊Q8D4×C73semidirect
530. C2×C4⋊C4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#552×C732
C2×#452×C732
C2×#417×C732
C73×#24072
C73×#20262
C73×#20252
C73×#20012
C73×#20002
C73×#18942
C73×#18802
C73×#18782
C73×#18752
C73×#18732
C73×#18702
C73×#18242
#2397873