Finite Group Databasebeta

← C73×#24124 #32933528

Subgroups — C73×#24124 #32933528

Order 18688.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C73C211yesmaximal, characteristic, complemented
2C2×#478×C73C211yesmaximal, characteristic, complemented
3C2×C4×D8×C73C211yesmaximal, characteristic, complemented
4C73×#2535C211yesmaximal, characteristic, complemented
5C73×#2034C211yesmaximal, characteristic, complemented
6C73×#2033C211yesmaximal, characteristic, complemented
7C73×#1999C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic, complemented
9C73×#1991C211yesmaximal, characteristic, complemented
10C73×#1954C211yesmaximal, characteristic, complemented
11C73×#1875C211yesmaximal, characteristic, complemented
12C73×#1874C211yesmaximal, characteristic, complemented
13C73×#1854C211yesmaximal, characteristic, complemented
14C73×#1852C211yesmaximal, characteristic, complemented
15C73×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17#553×C73—24no—
18#553×C73—24no—
19C2×#126×C73—21no—
20C2×#125×C73C2211yescharacteristic
21C2×#123×C73—21no—
22C2×#121×C73—21no—
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×#121×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×C4×D4×C73—21no—
28C2×C4×D4×C73C2211yescharacteristic
29C2×C4×D4×C73C2211yescharacteristic
30C2×C4×D4×C73C2211yescharacteristic
31C2×#117×C73C2211yescharacteristic
32C22×C4⋊C4×C73C2211yescharacteristic
33#478×C73—24no—
34C4×D8×C73—24no—
35C2×#107×C73C2211yescharacteristic
36C2×#107×C73C2211yescharacteristic
37C2×#106×C73C2211yescharacteristic
38C2×C4⋊C8×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48C2×C22⋊C8×C73C2211yescharacteristic
49C2×C4×C8×C73C2211yescharacteristic
50#397×C73—21no—
51#392×C73—21no—
52#386×C73—21no—
53#386×C73—21no—
54#382×C73C2211yescharacteristic
55#380×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73D411yescharacteristic
68C22×D4×C73C2311yescharacteristic
69C22×D4×C73C2311yescharacteristic
70C23×C4×C73—21no—
71C23×C4×C73—21no—
72C23×C4×C73—21no—
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C2×D8×C73—22no—
76C2×D8×C73—22no—
77C2×D8×C73—22no—
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82#126×C73—28no—
83#125×C73—22no—
84#125×C73D414yescomplemented
85#123×C73—28no—
86#121×C73—28no—
87#121×C73—22no—
88#121×C73—22no—
89#121×C73—22no—
90#121×C73—22no—
91#121×C73—22no—
92#121×C73—22no—
93#121×C73—41no—
94#121×C73—41no—
95C4×D4×C73—28no—
96C4×D4×C73—22no—
97C4×D4×C73—22no—
98C4×D4×C73—22no—
99C4×D4×C73—22no—
100C4×D4×C73—22no—
101C4×D4×C73D414yescomplemented
102#117×C73—22no—
103#117×C73—22no—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—22no—
108C2×C4⋊C4×C73—22no—
109C2×C4⋊C4×C73D411yescharacteristic
110C2×C4⋊C4×C73C2311yescharacteristic
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C22⋊C4×C73—21no—
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×C73—21no—
128C2×C42×C73C2311yescharacteristic
129#107×C73—22no—
130#107×C73—22no—
131#106×C73—22no—
132C4⋊C8×C73—22no—
133#102×C73—22no—
134#102×C73—22no—
135#102×C73—22no—
136#102×C73—22no—
137#102×C73—41no—
138#102×C73—41no—
139C22⋊C8×C73—22no—
140C22⋊C8×C73—22no—
141C22⋊C8×C73—41no—
142C22⋊C8×C73—41no—
143C4×C8×C73—22no—
144#95×C73—21no—
145#95×C73—21no—
146#95×C73—21no—
147#95×C73—21no—
148C24×C73—21no—
149C24×C73—21no—
150C24×C73C2×D411yescharacteristic
151C24×C73C2×D411yescharacteristic
152C2×D4×C73—24no—
153C2×D4×C73—22no—
154C2×D4×C73—24no—
155C2×D4×C73—22no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—21no—
166C2×D4×C73—41no—
167C2×D4×C73—42no—
168C2×D4×C73—42no—
169C2×D4×C73—42no—
170C2×D4×C73—42no—
171C2×D4×C73—42no—
172C2×D4×C73—42no—
173C2×D4×C73—81no—
174C2×D4×C73—81no—
175C2×D4×C73—81no—
176C2×D4×C73—81no—
177C2×D4×C73C2×D412yes—
178C2×D4×C73#4112yes—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—24no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—24no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—42no—
200C22×C4×C73—81no—
201C22×C4×C73—81no—
202C22×C4×C73—81no—
203C22×C4×C73—81no—
204C22×C4×C73—81no—
205C22×C4×C73—81no—
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2411yescharacteristic
211D8×C73—28no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73#4112yes—
224C4⋊C4×C73—24no—
225C4⋊C4×C73—24no—
226C4⋊C4×C73—24no—
227C4⋊C4×C73—22no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73C2×D412yes—
238C4⋊C4×C73C2×D412yes—
239C4⋊C4×C73C2×D412yes—
240C22⋊C4×C73—24no—
241C22⋊C4×C73—24no—
242C22⋊C4×C73—24no—
243C22⋊C4×C73—24no—
244C22⋊C4×C73—22no—
245C22⋊C4×C73—22no—
246C22⋊C4×C73—42no—
247C22⋊C4×C73—42no—
248C22⋊C4×C73—42no—
249C22⋊C4×C73—81no—
250C22⋊C4×C73—81no—
251C42×C73—24no—
252C42×C73C2×D412yes—
253C42×C73C2×D412yes—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—22no—
262C23×C73—22no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73#13512yes—
282C23×C73C22×D411yescharacteristic
283D4×C73—22no—
284D4×C73—22no—
285D4×C73—22no—
286D4×C73—22no—
287D4×C73—44no—
288D4×C73—48no—
289D4×C73—41no—
290D4×C73—41no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—84no—
294D4×C73—84no—
295D4×C73—84no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—21no—
304C2×C4×C73—22no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
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—84no—
333C2×C4×C73—84no—
334C2×C4×C73—84no—
335C2×C4×C73#12012yes—
336C2×C4×C73#12012yes—
337C2×C4×C73C22×D411yescharacteristic
338C2×C4×C73C22×D411yescharacteristic
339C2×C4×C73C2×#4111yescharacteristic
340C2×C4×C73C2×#4111yescharacteristic
341C2×C4×C73H(5,𝔽2)11yescharacteristic
342C2×C4×C732−1+411yescharacteristic
343C8×C73—22no—
344C8×C73—41no—
345C8×C73—41no—
346C8×C73—41no—
347C22×C73—22no—
348C22×C73—22no—
349C22×C73—22no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—42no—
358C22×C73—42no—
359C22×C73—41no—
360C22×C73—42no—
361C22×C73—42no—
362C22×C73—41no—
363C22×C73—42no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—42no—
367C22×C73—81no—
368C22×C73—81no—
369C22×C73—81no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73C2×#12011yescharacteristic
376C22×C73#54611yescharacteristic
377C22×C73#54711yescharacteristic
378C22×C73C2×#13511yescharacteristic
379C22×C73#57511yescharacteristic
380C22×C73#57611yescharacteristic
381C22×C73#57611yescharacteristic
382C4×C73—22no—
383C4×C73—22no—
384C4×C73—41no—
385C4×C73—41no—
386C4×C73—42no—
387C4×C73—42no—
388C4×C73—42no—
389C4×C73—81no—
390C4×C73—81no—
391C4×C73—81no—
392C4×C73#52511yescharacteristic
393C4×C73#53711yescharacteristic
394C4×C73#54811yescharacteristic
395C4×C73#55011yescharacteristic
396#24124C7311yesmaximal, characteristic, direct product factor, Sylow
397C2×C73—42no—
398C2×C73—81no—
399C2×C73—82no—
400C2×C73—82no—
401C2×C73#240711yescharacteristic
402C2×C73#300211yescharacteristic
403C2×C73#300811yescharacteristic
404C2×C73#329711yescharacteristic
405C2×C73#332211yescharacteristic
406C2×C73#333911yescharacteristic
407C2×C73#335511yescharacteristic
408C2×#553C2×C7311yescharacteristic, complemented
409C2×#478C2×C7311yescharacteristic, complemented
410C2×C4×D8C2×C7311yescharacteristic, complemented
411#2535C2×C7311yescharacteristic, complemented
412#2034C2×C7311yescharacteristic, complemented
413#2033C2×C7311yescharacteristic, complemented
414#1999C2×C7311yescharacteristic, complemented
415#1999C2×C7311yescharacteristic, complemented
416#1991C2×C7311yescharacteristic, complemented
417#1954C2×C7311yescharacteristic, complemented
418#1875C2×C7311yescharacteristic, complemented
419#1874C2×C7311yescharacteristic, complemented
420#1854C2×C7311yescharacteristic, complemented
421#1852C2×C7311yescharacteristic, complemented
422#1804C2×C7311yescharacteristic, complemented
423C73#2412411yescharacteristic, direct product factor, Sylow
424C22×D8C22×C7311yescharacteristic
425#553—24no—
426#553—24no—
427C2×#126—21no—
428C2×#125C22×C7311yescharacteristic
429C2×#123—21no—
430C2×#121—21no—
431C2×#121C22×C7311yescharacteristic
432C2×#121C22×C7311yescharacteristic
433C2×#121C22×C7311yescharacteristic
434C2×#121C22×C7311yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C7311yescharacteristic
437C2×C4×D4C22×C7311yescharacteristic
438C2×C4×D4C22×C7311yescharacteristic
439C2×#117C22×C7311yescharacteristic
440C22×C4⋊C4C22×C7311yescharacteristic
441#478—24no—
442C4×D8—24no—
443C2×#107C22×C7311yescharacteristic
444C2×#107C22×C7311yescharacteristic
445C2×#106C22×C7311yescharacteristic
446C2×C4⋊C8C22×C7311yescharacteristic
447C2×#102C22×C7311yescharacteristic
448C2×#102C22×C7311yescharacteristic
449C2×#102C22×C7311yescharacteristic
450C2×#102C22×C7311yescharacteristic
451C2×#102C22×C7311yescharacteristic
452C2×#102C22×C7311yescharacteristic
453C2×C22⋊C8C22×C7311yescharacteristic
454C2×C22⋊C8C22×C7311yescharacteristic
455C2×C22⋊C8C22×C7311yescharacteristic
456C2×C22⋊C8C22×C7311yescharacteristic
457C2×C4×C8C22×C7311yescharacteristic
458#397—21no—
459#392—21no—
460#386—21no—
461#386—21no—
462#382C22×C7311yescharacteristic
463#380C22×C7311yescharacteristic
464#380C22×C7311yescharacteristic
465#340C22×C7311yescharacteristic
466#340C22×C7311yescharacteristic
467#340C22×C7311yescharacteristic
468#340C22×C7311yescharacteristic
469#340C22×C7311yescharacteristic
470#340C22×C7311yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C7311yescharacteristic
476C22×D4C23×C7311yescharacteristic
477C22×D4C23×C7311yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C7311yescharacteristic
482C23×C4C23×C7311yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C7311yescharacteristic
487C22×C8C23×C7311yescharacteristic
488C22×C8C23×C7311yescharacteristic
489C22×C8C23×C7311yescharacteristic
490#126—28no—
491#125—22no—
492#125D4×C7314yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C7314yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4D4×C7311yescharacteristic
518C2×C4⋊C4C23×C7311yescharacteristic
519C2×C4⋊C4C23×C7311yescharacteristic
520C2×C4⋊C4C23×C7311yescharacteristic
521C2×C4⋊C4C23×C7311yescharacteristic
522C2×C4⋊C4C23×C7311yescharacteristic
523C2×C4⋊C4C23×C7311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4D4×C7311yescharacteristic
534C2×C22⋊C4D4×C7311yescharacteristic
535C2×C42—21no—
536C2×C42C23×C7311yescharacteristic
537#107—22no—
538#107—22no—
539#106—22no—
540C4⋊C8—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C7311yescharacteristic
559C24C2×D4×C7311yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C2×D4×C7312yes—
586C2×D4#41×C7312yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C7311yescharacteristic
615C22×C4C2×D4×C7311yescharacteristic
616C22×C4C2×D4×C7311yescharacteristic
617C22×C4C2×D4×C7311yescharacteristic
618C22×C4C24×C7311yescharacteristic
619D8—28no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8#41×C7312yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4C2×D4×C7312yes—
646C4⋊C4C2×D4×C7312yes—
647C4⋊C4C2×D4×C7312yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C7312yes—
661C42C2×D4×C7312yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#135×C7312yes—
690C23C22×D4×C7311yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#120×C7312yes—
744C2×C4#120×C7312yes—
745C2×C4C22×D4×C7311yescharacteristic
746C2×C4C22×D4×C7311yescharacteristic
747C2×C4C2×#41×C7311yescharacteristic
748C2×C4C2×#41×C7311yescharacteristic
749C2×C4H(5,𝔽2)×C7311yescharacteristic
750C2×C42−1+4×C7311yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C7311yescharacteristic
784C22#546×C7311yescharacteristic
785C22#547×C7311yescharacteristic
786C22C2×#135×C7311yescharacteristic
787C22#575×C7311yescharacteristic
788C22#576×C7311yescharacteristic
789C22#576×C7311yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4#525×C7311yescharacteristic
801C4#537×C7311yescharacteristic
802C4#548×C7311yescharacteristic
803C4#550×C7311yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2C73×#240711yescharacteristic
809C2C73×#300211yescharacteristic
810C2C73×#300811yescharacteristic
811C2C73×#329711yescharacteristic
812C2C73×#332211yescharacteristic
813C2C73×#333911yescharacteristic
814C2C73×#335511yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
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×#553×C73C2semidirect
2. C2×#478×C73C2semidirect
3. C2×C4×D8×C73C2semidirect
4. C73×#2535C2semidirect
5. C73×#2034C2semidirect
6. C73×#2033C2semidirect
7. C73×#1999C2semidirect
8. C73×#1999C2semidirect
9. C73×#1991C2semidirect
10. C73×#1954C2semidirect
11. C73×#1875C2semidirect
12. C73×#1874C2semidirect
13. C73×#1854C2semidirect
14. C73×#1852C2semidirect
15. C73×#1804C2semidirect
84. #125×C73D4semidirect
101. C4×D4×C73D4semidirect
396. #24124C73direct (N × H)
408. C2×#553C2×C73semidirect
409. C2×#478C2×C73semidirect
410. C2×C4×D8C2×C73semidirect
411. #2535C2×C73semidirect
412. #2034C2×C73semidirect
413. #2033C2×C73semidirect
414. #1999C2×C73semidirect
415. #1999C2×C73semidirect
416. #1991C2×C73semidirect
417. #1954C2×C73semidirect
418. #1875C2×C73semidirect
419. #1874C2×C73semidirect
420. #1854C2×C73semidirect
421. #1852C2×C73semidirect
422. #1804C2×C73semidirect
423. C73#24124direct (N × H)
492. #125D4×C73semidirect
509. C4×D4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C732
C2×#478×C732
C2×C4×D8×C732
C73×#25352
C73×#20342
C73×#20332
C73×#19992
C73×#19912
C73×#19542
C73×#18752
C73×#18742
C73×#18542
C73×#18522
C73×#18042
#2412473