Finite Group Databasebeta

← C73×#21397 #32930801

Subgroups — C73×#21397 #32930801

Order 18688.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#542×C73C211yesmaximal, characteristic
2C2×#433×C73C211yesmaximal, characteristic, complemented
3C73×#2274C211yesmaximal, characteristic, complemented
4C73×#1988C211yesmaximal, characteristic, complemented
5C73×#1987C211yesmaximal, characteristic, complemented
6C73×#1983C211yesmaximal, characteristic, complemented
7C73×#1983C211yesmaximal, characteristic, complemented
8C73×#1875C211yesmaximal, characteristic
9C73×#1874C211yesmaximal, characteristic
10C73×#1873C211yesmaximal, characteristic, complemented
11C73×#1872C211yesmaximal, characteristic, complemented
12C73×#1763C211yesmaximal, characteristic, complemented
13C73×#1762C211yesmaximal, characteristic, complemented
14C4×#103×C73C211yesmaximal, characteristic, complemented
15C4×#102×C73C211yesmaximal, characteristic, complemented
16#542×C73—24no—
17#542×C73C418yescomplemented
18C2×C4⋊Q8×C73C2211yescharacteristic
19C2×#126×C73—21no—
20C2×#124×C73—21no—
21C2×#124×C73C2211yescharacteristic
22C2×#123×C73—21no—
23C2×C22⋊Q8×C73—21no—
24C2×C22⋊Q8×C73C2211yescharacteristic
25C2×#121×C73C2211yescharacteristic
26C2×C4×Q8×C73C2211yescharacteristic
27C2×C4×D4×C73C2211yescharacteristic
28C2×#117×C73C2211yescharacteristic
29C2×#117×C73C2211yescharacteristic
30C22×C4⋊C4×C73C2211yescharacteristic
31#433×C73—24no—
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×C4⋊C8×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×C22⋊C8×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×#97×C73C2211yescharacteristic
45C2×C4×C8×C73C2211yescharacteristic
46C4×C4⋊C4×C73—21no—
47C4×C4⋊C4×C73—21no—
48C4×C4⋊C4×C73C2211yescharacteristic
49C4×C4⋊C4×C73C2211yescharacteristic
50C4×C4⋊C4×C73C2211yescharacteristic
51C4×C4⋊C4×C73C2211yescharacteristic
52C4×C22⋊C4×C73—21no—
53C4×C22⋊C4×C73—21no—
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×Q8×C73—21no—
63C22×Q8×C73C2311yescharacteristic
64C22×D4×C73—21no—
65C22×D4×C73C2311yescharacteristic
66C23×C4×C73—21no—
67C23×C4×C73—21no—
68C23×C4×C73C2311yescharacteristic
69C22×C8×C73C2311yescharacteristic
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C4⋊Q8×C73—22no—
74C4⋊Q8×C73C2×C414yescomplemented
75#126×C73—28no—
76#124×C73—28no—
77#124×C73—22no—
78#124×C73C2×C414yescomplemented
79#123×C73—28no—
80C22⋊Q8×C73—22no—
81C22⋊Q8×C73—28no—
82C22⋊Q8×C73C2×C414yes—
83#121×C73—22no—
84#121×C73C2×C414yes—
85C4×Q8×C73—22no—
86C4×Q8×C73C2×C414yescomplemented
87C4×D4×C73—22no—
88C4×D4×C73C2×C414yescomplemented
89#117×C73—22no—
90#117×C73—22no—
91#117×C73C2×C414yes—
92#117×C73D414yes—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—22no—
98C2×C4⋊C4×C73—22no—
99C2×C4⋊C4×C73D411yescharacteristic
100C2×C4⋊C4×C73D411yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73D411yescharacteristic
114C2×C22⋊C4×C73D411yescharacteristic
115C2×C42×C73—21no—
116C2×C42×C73—21no—
117C2×C42×C73—21no—
118C2×C42×C73—21no—
119C2×C42×C73—21no—
120C2×C42×C73—21no—
121C2×C42×C73C2311yescharacteristic
122C2×C42×C73C2311yescharacteristic
123C4⋊C8×C73—22no—
124C4⋊C8×C73—22no—
125#103×C73—22no—
126#103×C73—22no—
127#103×C73—22no—
128#103×C73—22no—
129#102×C73—22no—
130#102×C73—22no—
131#102×C73—22no—
132#102×C73—22no—
133C22⋊C8×C73—22no—
134C22⋊C8×C73—22no—
135#97×C73—22no—
136C4×C8×C73—22no—
137#95×C73—21no—
138#95×C73—21no—
139#95×C73—21no—
140#95×C73—21no—
141C24×C73—21no—
142C24×C73C2×D411yescharacteristic
143C2×Q8×C73—24no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—81no—
150C2×Q8×C73—81no—
151C2×Q8×C73C22×C412yes—
152C2×D4×C73—24no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—81no—
159C2×D4×C73—81no—
160C2×D4×C73C22×C412yes—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—24no—
173C22×C4×C73—24no—
174C22×C4×C73—81no—
175C22×C4×C73—81no—
176C22×C4×C73—81no—
177C22×C4×C73—81no—
178C22×C4×C73C22×C412yes—
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D412yes—
185C22×C4×C73C2411yescharacteristic
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C4⋊C4×C73—24no—
199C4⋊C4×C73—24no—
200C4⋊C4×C73—24no—
201C4⋊C4×C73—24no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73C22⋊C414yes—
209C4⋊C4×C73C22⋊C414yes—
210C4⋊C4×C73C22×C412yes—
211C4⋊C4×C73C22×C412yes—
212C4⋊C4×C73#4112yes—
213C4⋊C4×C73#4112yes—
214C4⋊C4×C73#4112yes—
215C4⋊C4×C73#4112yes—
216C22⋊C4×C73—24no—
217C22⋊C4×C73—24no—
218C22⋊C4×C73—24no—
219C22⋊C4×C73—24no—
220C22⋊C4×C73—24no—
221C22⋊C4×C73—24no—
222C22⋊C4×C73C22⋊C414yes—
223C22⋊C4×C73C22⋊C414yes—
224C42×C73—24no—
225C42×C73—24no—
226C42×C73—81no—
227C42×C73—81no—
228C42×C73—81no—
229C42×C73—81no—
230C42×C73C22×C412yes—
231C42×C73C22×C412yes—
232C42×C73C2×D412yes—
233C42×C73C2×D412yes—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—22no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73C2×C22⋊C412yes—
248C23×C73C22×D411yescharacteristic
249Q8×C73—22no—
250Q8×C73—22no—
251Q8×C73—41no—
252Q8×C73—41no—
253Q8×C73—84no—
254D4×C73—22no—
255D4×C73—22no—
256D4×C73—41no—
257D4×C73—41no—
258D4×C73—84no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—84no—
295C2×C4×C73—84no—
296C2×C4×C73C2×C22⋊C412yes—
297C2×C4×C73C2×C22⋊C412yes—
298C2×C4×C73C2×C22⋊C412yes—
299C2×C4×C73C2×C22⋊C412yes—
300C2×C4×C73C2×C22⋊C412yes—
301C2×C4×C73C23×C411yescharacteristic
302C2×C4×C73C22×D411yescharacteristic
303C2×C4×C73C2×#4111yescharacteristic
304C2×C4×C73C2×#4111yescharacteristic
305C2×C4×C73C2×#4111yescharacteristic
306C2×C4×C73C2×#4111yescharacteristic
307C8×C73—41no—
308C8×C73—41no—
309C8×C73—41no—
310C8×C73—41no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—42no—
319C22×C73—42no—
320C22×C73—42no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73C22×C22⋊C411yescharacteristic
326C22×C73#52511yescharacteristic
327C22×C73#52511yescharacteristic
328C22×C73#57611yescharacteristic
329C22×C73#57711yescharacteristic
330C22×C73#57711yescharacteristic
331C22×C73#57811yescharacteristic
332C4×C73—22no—
333C4×C73—22no—
334C4×C73—22no—
335C4×C73—22no—
336C4×C73—22no—
337C4×C73—42no—
338C4×C73—42no—
339C4×C73—42no—
340C4×C73—42no—
341C4×C73—42no—
342C4×C73—42no—
343C4×C73—42no—
344C4×C73C4×#4111yescharacteristic
345C4×C73C4×#4111yescharacteristic
346C4×C73#53211yescharacteristic
347C4×C73#53211yescharacteristic
348#21397C7311yesmaximal, characteristic, direct product factor, Sylow
349C2×C73—42no—
350C2×C73—82no—
351C2×C73#229711yescharacteristic
352C2×C73#289711yescharacteristic
353C2×C73#289811yescharacteristic
354C2×C73#311811yescharacteristic
355C2×C73#312111yescharacteristic
356C2×C73#312411yescharacteristic
357C2×C73#312511yescharacteristic
358C2×#542C2×C7311yescharacteristic
359C2×#433C2×C7311yescharacteristic, complemented
360#2274C2×C7311yescharacteristic, complemented
361#1988C2×C7311yescharacteristic, complemented
362#1987C2×C7311yescharacteristic, complemented
363#1983C2×C7311yescharacteristic, complemented
364#1983C2×C7311yescharacteristic, complemented
365#1875C2×C7311yescharacteristic
366#1874C2×C7311yescharacteristic
367#1873C2×C7311yescharacteristic, complemented
368#1872C2×C7311yescharacteristic, complemented
369#1763C2×C7311yescharacteristic, complemented
370#1762C2×C7311yescharacteristic, complemented
371C4×#103C2×C7311yescharacteristic, complemented
372C4×#102C2×C7311yescharacteristic, complemented
373C73#2139711yescharacteristic, direct product factor, Sylow
374#542—24no—
375#542C4×C7318yescomplemented
376C2×C4⋊Q8C22×C7311yescharacteristic
377C2×#126—21no—
378C2×#124—21no—
379C2×#124C22×C7311yescharacteristic
380C2×#123—21no—
381C2×C22⋊Q8—21no—
382C2×C22⋊Q8C22×C7311yescharacteristic
383C2×#121C22×C7311yescharacteristic
384C2×C4×Q8C22×C7311yescharacteristic
385C2×C4×D4C22×C7311yescharacteristic
386C2×#117C22×C7311yescharacteristic
387C2×#117C22×C7311yescharacteristic
388C22×C4⋊C4C22×C7311yescharacteristic
389#433—24no—
390C2×C4⋊C8C22×C7311yescharacteristic
391C2×C4⋊C8C22×C7311yescharacteristic
392C2×#103C22×C7311yescharacteristic
393C2×#103C22×C7311yescharacteristic
394C2×#103C22×C7311yescharacteristic
395C2×#103C22×C7311yescharacteristic
396C2×#102C22×C7311yescharacteristic
397C2×#102C22×C7311yescharacteristic
398C2×#102C22×C7311yescharacteristic
399C2×#102C22×C7311yescharacteristic
400C2×C22⋊C8C22×C7311yescharacteristic
401C2×C22⋊C8C22×C7311yescharacteristic
402C2×#97C22×C7311yescharacteristic
403C2×C4×C8C22×C7311yescharacteristic
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4C22×C7311yescharacteristic
407C4×C4⋊C4C22×C7311yescharacteristic
408C4×C4⋊C4C22×C7311yescharacteristic
409C4×C4⋊C4C22×C7311yescharacteristic
410C4×C22⋊C4—21no—
411C4×C22⋊C4—21no—
412#340C22×C7311yescharacteristic
413#340C22×C7311yescharacteristic
414#340C22×C7311yescharacteristic
415#340C22×C7311yescharacteristic
416#340C22×C7311yescharacteristic
417#340C22×C7311yescharacteristic
418#340C22×C7311yescharacteristic
419#340C22×C7311yescharacteristic
420C22×Q8—21no—
421C22×Q8C23×C7311yescharacteristic
422C22×D4—21no—
423C22×D4C23×C7311yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4C23×C7311yescharacteristic
427C22×C8C23×C7311yescharacteristic
428C22×C8C23×C7311yescharacteristic
429C22×C8C23×C7311yescharacteristic
430C22×C8C23×C7311yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8C2×C4×C7314yescomplemented
433#126—28no—
434#124—28no—
435#124—22no—
436#124C2×C4×C7314yescomplemented
437#123—28no—
438C22⋊Q8—22no—
439C22⋊Q8—28no—
440C22⋊Q8C2×C4×C7314yes—
441#121—22no—
442#121C2×C4×C7314yes—
443C4×Q8—22no—
444C4×Q8C2×C4×C7314yescomplemented
445C4×D4—22no—
446C4×D4C2×C4×C7314yescomplemented
447#117—22no—
448#117—22no—
449#117C2×C4×C7314yes—
450#117D4×C7314yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4D4×C7311yescharacteristic
458C2×C4⋊C4D4×C7311yescharacteristic
459C2×C4⋊C4C23×C7311yescharacteristic
460C2×C4⋊C4C23×C7311yescharacteristic
461C2×C4⋊C4C23×C7311yescharacteristic
462C2×C4⋊C4C23×C7311yescharacteristic
463C2×C4⋊C4C23×C7311yescharacteristic
464C2×C4⋊C4C23×C7311yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4D4×C7311yescharacteristic
472C2×C22⋊C4D4×C7311yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C23×C7311yescharacteristic
480C2×C42C23×C7311yescharacteristic
481C4⋊C8—22no—
482C4⋊C8—22no—
483#103—22no—
484#103—22no—
485#103—22no—
486#103—22no—
487#102—22no—
488#102—22no—
489#102—22no—
490#102—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493#97—22no—
494C4×C8—22no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—21no—
500C24C2×D4×C7311yescharacteristic
501C2×Q8—24no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×Q8C22×C4×C7312yes—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C22×C4×C7312yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4C22×C4×C7312yes—
537C22×C4C2×D4×C7311yescharacteristic
538C22×C4C2×D4×C7311yescharacteristic
539C22×C4C2×D4×C7311yescharacteristic
540C22×C4C2×D4×C7311yescharacteristic
541C22×C4C2×D4×C7311yescharacteristic
542C22×C4C2×D4×C7312yes—
543C22×C4C24×C7311yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4C22⋊C4×C7314yes—
567C4⋊C4C22⋊C4×C7314yes—
568C4⋊C4C22×C4×C7312yes—
569C4⋊C4C22×C4×C7312yes—
570C4⋊C4#41×C7312yes—
571C4⋊C4#41×C7312yes—
572C4⋊C4#41×C7312yes—
573C4⋊C4#41×C7312yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4C22⋊C4×C7314yes—
581C22⋊C4C22⋊C4×C7314yes—
582C42—24no—
583C42—24no—
584C42—81no—
585C42—81no—
586C42—81no—
587C42—81no—
588C42C22×C4×C7312yes—
589C42C22×C4×C7312yes—
590C42C2×D4×C7312yes—
591C42C2×D4×C7312yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C2×C22⋊C4×C7312yes—
606C23C22×D4×C7311yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—84no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—84no—
653C2×C4—84no—
654C2×C4C2×C22⋊C4×C7312yes—
655C2×C4C2×C22⋊C4×C7312yes—
656C2×C4C2×C22⋊C4×C7312yes—
657C2×C4C2×C22⋊C4×C7312yes—
658C2×C4C2×C22⋊C4×C7312yes—
659C2×C4C23×C4×C7311yescharacteristic
660C2×C4C22×D4×C7311yescharacteristic
661C2×C4C2×#41×C7311yescharacteristic
662C2×C4C2×#41×C7311yescharacteristic
663C2×C4C2×#41×C7311yescharacteristic
664C2×C4C2×#41×C7311yescharacteristic
665C8—41no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊C4×C7311yescharacteristic
684C22#525×C7311yescharacteristic
685C22#525×C7311yescharacteristic
686C22#576×C7311yescharacteristic
687C22#577×C7311yescharacteristic
688C22#577×C7311yescharacteristic
689C22#578×C7311yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4C4×#41×C7311yescharacteristic
703C4C4×#41×C7311yescharacteristic
704C4#532×C7311yescharacteristic
705C4#532×C7311yescharacteristic
706C2—42no—
707C2—82no—
708C2C73×#229711yescharacteristic
709C2C73×#289711yescharacteristic
710C2C73×#289811yescharacteristic
711C2C73×#311811yescharacteristic
712C2C73×#312111yescharacteristic
713C2C73×#312411yescharacteristic
714C2C73×#312511yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×#117×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#433×C73C2semidirect
3. C73×#2274C2semidirect
4. C73×#1988C2semidirect
5. C73×#1987C2semidirect
6. C73×#1983C2semidirect
7. C73×#1983C2semidirect
10. C73×#1873C2semidirect
11. C73×#1872C2semidirect
12. C73×#1763C2semidirect
13. C73×#1762C2semidirect
14. C4×#103×C73C2semidirect
15. C4×#102×C73C2semidirect
17. #542×C73C4semidirect
74. C4⋊Q8×C73C2×C4semidirect
78. #124×C73C2×C4semidirect
86. C4×Q8×C73C2×C4semidirect
88. C4×D4×C73C2×C4semidirect
348. #21397C73direct (N × H)
359. C2×#433C2×C73semidirect
360. #2274C2×C73semidirect
361. #1988C2×C73semidirect
362. #1987C2×C73semidirect
363. #1983C2×C73semidirect
364. #1983C2×C73semidirect
367. #1873C2×C73semidirect
368. #1872C2×C73semidirect
369. #1763C2×C73semidirect
370. #1762C2×C73semidirect
371. C4×#103C2×C73semidirect
372. C4×#102C2×C73semidirect
373. C73#21397direct (N × H)
375. #542C4×C73semidirect
432. C4⋊Q8C2×C4×C73semidirect
436. #124C2×C4×C73semidirect
444. C4×Q8C2×C4×C73semidirect
446. C4×D4C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#542×C732
C2×#433×C732
C73×#22742
C73×#19882
C73×#19872
C73×#19832
C73×#18752
C73×#18742
C73×#18732
C73×#18722
C73×#17632
C73×#17622
C4×#103×C732
C4×#102×C732
#2139773