Finite Group Databasebeta

← C73×#25559 #32934963

Subgroups — C73×#25559 #32934963

Order 18688.

1174 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C73C211yesmaximal, characteristic, complemented
2C2×#480×C73C211yesmaximal, characteristic, complemented
3C2×#468×C73C211yesmaximal, characteristic, complemented
4C73×#2414C211yesmaximal, characteristic
5C73×#2057C211yesmaximal, characteristic, complemented
6C73×#2036C211yesmaximal, characteristic, complemented
7C73×#2023C211yesmaximal, characteristic, complemented
8C73×#2000C211yesmaximal, characteristic, complemented
9C73×#1880C211yesmaximal, characteristic, complemented
10C73×#1874C211yesmaximal, characteristic, complemented
11C73×#1873C211yesmaximal, characteristic, complemented
12C73×#1870C211yesmaximal, characteristic, complemented
13C73×#1863C211yesmaximal, characteristic, complemented
14C73×#1852C211yesmaximal, characteristic, complemented
15C73×#1736C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18#554×C73—24no—
19#554×C73—24no—
20C2×C4⋊Q8×C73C2211yescharacteristic
21C2×#125×C73—21no—
22C2×C22⋊Q8×C73—21no—
23C2×C22⋊Q8×C73—21no—
24C2×C22⋊Q8×C73C2211yescharacteristic
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×C4×Q8×C73C2211yescharacteristic
29C2×C4×D4×C73—21no—
30C2×C4×D4×C73C2211yescharacteristic
31C2×#117×C73C2211yescharacteristic
32C22×C4⋊C4×C73C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34#480×C73—24no—
35#468×C73—24no—
36C2×#107×C73C2211yescharacteristic
37C2×#107×C73C2211yescharacteristic
38C2×#107×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#390×C73—21no—
51#390×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#388×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
63C22×Q8×C73—21no—
64C22×Q8×C73C2311yescharacteristic
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73D411yescharacteristic
68C22×D4×C73C2311yescharacteristic
69C23×C4×C73—21no—
70C23×C4×C73—21no—
71C23×C4×C73C2311yescharacteristic
72C23×C4×C73C2311yescharacteristic
73C2×SD16×C73—22no—
74C2×SD16×C73—22no—
75C2×SD16×C73—41no—
76C2×M16×C73—22no—
77C2×M16×C73—22no—
78C2×M16×C73—41no—
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C4⋊Q8×C73—22no—
84C4⋊Q8×C73—22no—
85#125×C73—28no—
86C22⋊Q8×C73—28no—
87C22⋊Q8×C73—28no—
88C22⋊Q8×C73—22no—
89C22⋊Q8×C73—22no—
90C22⋊Q8×C73—22no—
91C22⋊Q8×C73D414yescomplemented
92#121×C73—22no—
93#121×C73—22no—
94#121×C73—22no—
95#121×C73—41no—
96C4×Q8×C73—22no—
97C4×Q8×C73—22no—
98C4×D4×C73—28no—
99C4×D4×C73—22no—
100C4×D4×C73—22no—
101#117×C73—22no—
102#117×C73—41no—
103C2×C4⋊C4×C73—21no—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—22no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—22no—
111C2×C4⋊C4×C73—22no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73D411yescharacteristic
114C2×C4⋊C4×C73D414yescomplemented
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C22⋊C4×C73D411yescharacteristic
131C2×C42×C73—21no—
132C2×C42×C73—21no—
133C2×C42×C73C2311yescharacteristic
134#107×C73—22no—
135#107×C73—22no—
136#107×C73—22no—
137#103×C73—22no—
138#103×C73—22no—
139#103×C73—41no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—22no—
143C22⋊C8×C73—22no—
144C22⋊C8×C73—22no—
145C22⋊C8×C73—41no—
146#95×C73—21no—
147#95×C73—21no—
148C24×C73—21no—
149C24×C73C2×D411yescharacteristic
150C24×C73C2×D411yescharacteristic
151C2×Q8×C73—24no—
152C2×Q8×C73—21no—
153C2×Q8×C73—21no—
154C2×Q8×C73—21no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—81no—
158C2×Q8×C73—81no—
159C2×Q8×C73C2×D412yes—
160C2×D4×C73—22no—
161C2×D4×C73—22no—
162C2×D4×C73—22no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—42no—
170C2×D4×C73—42no—
171C2×D4×C73—42no—
172C2×D4×C73—81no—
173C2×D4×C73—81no—
174C2×D4×C73—81no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—24no—
185C22×C4×C73—24no—
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—81no—
195C22×C4×C73—81no—
196C22×C4×C73—81no—
197C22×C4×C73—81no—
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D412yes—
202C22×C4×C73C2×D412yes—
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2411yescharacteristic
205SD16×C73—44no—
206M16×C73—44no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
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#4112yes—
219C4⋊C4×C73—24no—
220C4⋊C4×C73—24no—
221C4⋊C4×C73—24no—
222C4⋊C4×C73—24no—
223C4⋊C4×C73—24no—
224C4⋊C4×C73—24no—
225C4⋊C4×C73—22no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—21no—
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—81no—
235C4⋊C4×C73C2×D412yes—
236C4⋊C4×C73C2×D412yes—
237C4⋊C4×C73C2×D412yes—
238C4⋊C4×C73#4112yes—
239C22⋊C4×C73—24no—
240C22⋊C4×C73—24no—
241C22⋊C4×C73—22no—
242C22⋊C4×C73—22no—
243C22⋊C4×C73—42no—
244C22⋊C4×C73—42no—
245C22⋊C4×C73—42no—
246C22⋊C4×C73—42no—
247C22⋊C4×C73—81no—
248C22⋊C4×C73—81no—
249C42×C73—24no—
250C42×C73—21no—
251C42×C73—21no—
252C42×C73—42no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73#12012yes—
273C23×C73#13712yes—
274C23×C73C22×D411yescharacteristic
275Q8×C73—22no—
276Q8×C73—22no—
277Q8×C73—41no—
278Q8×C73—41no—
279Q8×C73—84no—
280D4×C73—28no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—41no—
284D4×C73—41no—
285D4×C73—84no—
286D4×C73—84no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—21no—
297C2×C4×C73—22no—
298C2×C4×C73—21no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
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—84no—
327C2×C4×C73—84no—
328C2×C4×C73#12012yes—
329C2×C4×C73#13712yes—
330C2×C4×C73C22×D411yescharacteristic
331C2×C4×C73C22×D411yescharacteristic
332C2×C4×C73C2×#4111yescharacteristic
333C2×C4×C73C2×#4111yescharacteristic
334C2×C4×C73H(5,𝔽2)11yescharacteristic
335C2×C4×C732−1+411yescharacteristic
336C8×C73—22no—
337C8×C73—41no—
338C8×C73—41no—
339C8×C73—41no—
340C22×C73—22no—
341C22×C73—22no—
342C22×C73—22no—
343C22×C73—22no—
344C22×C73—22no—
345C22×C73—22no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—81no—
355C22×C73—81no—
356C22×C73—81no—
357C22×C73—81no—
358C22×C73—81no—
359C22×C73—81no—
360C22×C73—81no—
361C22×C73C2×#12011yescharacteristic
362C22×C73#54611yescharacteristic
363C22×C73#54711yescharacteristic
364C22×C73C2×#13711yescharacteristic
365C22×C73C2×#13711yescharacteristic
366C22×C73#57611yescharacteristic
367C22×C73#57611yescharacteristic
368C4×C73—22no—
369C4×C73—22no—
370C4×C73—41no—
371C4×C73—42no—
372C4×C73—41no—
373C4×C73—42no—
374C4×C73—42no—
375C4×C73—42no—
376C4×C73—42no—
377C4×C73—81no—
378C4×C73—81no—
379C4×C73#53211yescharacteristic
380C4×C73#53711yescharacteristic
381C4×C73#54611yescharacteristic
382C4×C73#54711yescharacteristic
383#25559C7311yesmaximal, characteristic, direct product factor, Sylow
384C2×C73—42no—
385C2×C73—42no—
386C2×C73—161no—
387C2×C73#243011yescharacteristic
388C2×C73#300411yescharacteristic
389C2×C73#300811yescharacteristic
390C2×C73#331411yescharacteristic
391C2×C73#333311yescharacteristic
392C2×C73#334611yescharacteristic
393C2×C73#335711yescharacteristic
394C2×#554C2×C7311yescharacteristic, complemented
395C2×#480C2×C7311yescharacteristic, complemented
396C2×#468C2×C7311yescharacteristic, complemented
397#2414C2×C7311yescharacteristic
398#2057C2×C7311yescharacteristic, complemented
399#2036C2×C7311yescharacteristic, complemented
400#2023C2×C7311yescharacteristic, complemented
401#2000C2×C7311yescharacteristic, complemented
402#1880C2×C7311yescharacteristic, complemented
403#1874C2×C7311yescharacteristic, complemented
404#1873C2×C7311yescharacteristic, complemented
405#1870C2×C7311yescharacteristic, complemented
406#1863C2×C7311yescharacteristic, complemented
407#1852C2×C7311yescharacteristic, complemented
408#1736C2×C7311yescharacteristic, complemented
409C73#2555911yescharacteristic, direct product factor, Sylow
410C22×SD16C22×C7311yescharacteristic
411C22×M16C22×C7311yescharacteristic
412#554—24no—
413#554—24no—
414C2×C4⋊Q8C22×C7311yescharacteristic
415C2×#125—21no—
416C2×C22⋊Q8—21no—
417C2×C22⋊Q8—21no—
418C2×C22⋊Q8C22×C7311yescharacteristic
419C2×C22⋊Q8C22×C7311yescharacteristic
420C2×#121C22×C7311yescharacteristic
421C2×#121C22×C7311yescharacteristic
422C2×C4×Q8C22×C7311yescharacteristic
423C2×C4×D4—21no—
424C2×C4×D4C22×C7311yescharacteristic
425C2×#117C22×C7311yescharacteristic
426C22×C4⋊C4C22×C7311yescharacteristic
427C22×C4⋊C4C22×C7311yescharacteristic
428#480—24no—
429#468—24no—
430C2×#107C22×C7311yescharacteristic
431C2×#107C22×C7311yescharacteristic
432C2×#107C22×C7311yescharacteristic
433C2×#103C22×C7311yescharacteristic
434C2×#103C22×C7311yescharacteristic
435C2×#103C22×C7311yescharacteristic
436C2×#102C22×C7311yescharacteristic
437C2×#102C22×C7311yescharacteristic
438C2×#102C22×C7311yescharacteristic
439C2×C22⋊C8C22×C7311yescharacteristic
440C2×C22⋊C8C22×C7311yescharacteristic
441C2×C22⋊C8C22×C7311yescharacteristic
442#394—21no—
443#392—21no—
444#390—21no—
445#390C22×C7311yescharacteristic
446#389C22×C7311yescharacteristic
447#388—21no—
448#380C22×C7311yescharacteristic
449#340C22×C7311yescharacteristic
450#340C22×C7311yescharacteristic
451#340C22×C7311yescharacteristic
452#340C22×C7311yescharacteristic
453#340C22×C7311yescharacteristic
454#340C22×C7311yescharacteristic
455#336C22×C7311yescharacteristic
456#336C22×C7311yescharacteristic
457C22×Q8—21no—
458C22×Q8C23×C7311yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4D4×C7311yescharacteristic
462C22×D4C23×C7311yescharacteristic
463C23×C4—21no—
464C23×C4—21no—
465C23×C4C23×C7311yescharacteristic
466C23×C4C23×C7311yescharacteristic
467C2×SD16—22no—
468C2×SD16—22no—
469C2×SD16—41no—
470C2×M16—22no—
471C2×M16—22no—
472C2×M16—41no—
473C22×C8C23×C7311yescharacteristic
474C22×C8C23×C7311yescharacteristic
475C22×C8C23×C7311yescharacteristic
476C22×C8C23×C7311yescharacteristic
477C4⋊Q8—22no—
478C4⋊Q8—22no—
479#125—28no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8—22no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8D4×C7314yescomplemented
486#121—22no—
487#121—22no—
488#121—22no—
489#121—41no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×D4—28no—
493C4×D4—22no—
494C4×D4—22no—
495#117—22no—
496#117—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4D4×C7311yescharacteristic
508C2×C4⋊C4D4×C7314yescomplemented
509C2×C4⋊C4C23×C7311yescharacteristic
510C2×C4⋊C4C23×C7311yescharacteristic
511C2×C4⋊C4C23×C7311yescharacteristic
512C2×C4⋊C4C23×C7311yescharacteristic
513C2×C4⋊C4C23×C7311yescharacteristic
514C2×C4⋊C4C23×C7311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4D4×C7311yescharacteristic
524C2×C22⋊C4D4×C7311yescharacteristic
525C2×C42—21no—
526C2×C42—21no—
527C2×C42C23×C7311yescharacteristic
528#107—22no—
529#107—22no—
530#107—22no—
531#103—22no—
532#103—22no—
533#103—41no—
534#102—22no—
535#102—22no—
536#102—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—41no—
540#95—21no—
541#95—21no—
542C24—21no—
543C24C2×D4×C7311yescharacteristic
544C24C2×D4×C7311yescharacteristic
545C2×Q8—24no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—81no—
552C2×Q8—81no—
553C2×Q8C2×D4×C7312yes—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C2×D4×C7311yescharacteristic
593C22×C4C2×D4×C7311yescharacteristic
594C22×C4C2×D4×C7311yescharacteristic
595C22×C4C2×D4×C7312yes—
596C22×C4C2×D4×C7312yes—
597C22×C4C2×D4×C7311yescharacteristic
598C22×C4C24×C7311yescharacteristic
599SD16—44no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8#41×C7312yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—81no—
629C4⋊C4C2×D4×C7312yes—
630C4⋊C4C2×D4×C7312yes—
631C4⋊C4C2×D4×C7312yes—
632C4⋊C4#41×C7312yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C42—24no—
644C42—21no—
645C42—21no—
646C42—42no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#120×C7312yes—
667C23#137×C7312yes—
668C23C22×D4×C7311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673Q8—84no—
674D4—28no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—84no—
680D4—84no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4#120×C7312yes—
723C2×C4#137×C7312yes—
724C2×C4C22×D4×C7311yescharacteristic
725C2×C4C22×D4×C7311yescharacteristic
726C2×C4C2×#41×C7311yescharacteristic
727C2×C4C2×#41×C7311yescharacteristic
728C2×C4H(5,𝔽2)×C7311yescharacteristic
729C2×C42−1+4×C7311yescharacteristic
730C8—22no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×#120×C7311yescharacteristic
756C22#546×C7311yescharacteristic
757C22#547×C7311yescharacteristic
758C22C2×#137×C7311yescharacteristic
759C22C2×#137×C7311yescharacteristic
760C22#576×C7311yescharacteristic
761C22#576×C7311yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—41no—
770C4—42no—
771C4—81no—
772C4—81no—
773C4#532×C7311yescharacteristic
774C4#537×C7311yescharacteristic
775C4#546×C7311yescharacteristic
776C4#547×C7311yescharacteristic
777C2—42no—
778C2—42no—
779C2—161no—
780C2C73×#243011yescharacteristic
781C2C73×#300411yescharacteristic
782C2C73×#300811yescharacteristic
783C2C73×#331411yescharacteristic
784C2C73×#333311yescharacteristic
785C2C73×#334611yescharacteristic
786C2C73×#335711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2414C2
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×#554×C73C2semidirect
2. C2×#480×C73C2semidirect
3. C2×#468×C73C2semidirect
5. C73×#2057C2semidirect
6. C73×#2036C2semidirect
7. C73×#2023C2semidirect
8. C73×#2000C2semidirect
9. C73×#1880C2semidirect
10. C73×#1874C2semidirect
11. C73×#1873C2semidirect
12. C73×#1870C2semidirect
13. C73×#1863C2semidirect
14. C73×#1852C2semidirect
15. C73×#1736C2semidirect
91. C22⋊Q8×C73D4semidirect
114. C2×C4⋊C4×C73D4semidirect
383. #25559C73direct (N × H)
394. C2×#554C2×C73semidirect
395. C2×#480C2×C73semidirect
396. C2×#468C2×C73semidirect
398. #2057C2×C73semidirect
399. #2036C2×C73semidirect
400. #2023C2×C73semidirect
401. #2000C2×C73semidirect
402. #1880C2×C73semidirect
403. #1874C2×C73semidirect
404. #1873C2×C73semidirect
405. #1870C2×C73semidirect
406. #1863C2×C73semidirect
407. #1852C2×C73semidirect
408. #1736C2×C73semidirect
409. C73#25559direct (N × H)
485. C22⋊Q8D4×C73semidirect
508. 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×#554×C732
C2×#480×C732
C2×#468×C732
C73×#24142
C73×#20572
C73×#20362
C73×#20232
C73×#20002
C73×#18802
C73×#18742
C73×#18732
C73×#18702
C73×#18632
C73×#18522
C73×#17362
#2555973