Finite Group Databasebeta

← C73×#25951 #32935355

Subgroups — C73×#25951 #32935355

Order 18688.

966 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#475×C73C211yesmaximal, characteristic, complemented
2C2×#416×C73C211yesmaximal, characteristic
3C73×#2439C211yesmaximal, characteristic, complemented
4C73×#2341C211yesmaximal, characteristic
5C73×#2092C211yesmaximal, characteristic, complemented
6C73×#2065C211yesmaximal, characteristic, complemented
7C73×#2065C211yesmaximal, characteristic, complemented
8C73×#2023C211yesmaximal, characteristic, complemented
9C73×#1865C211yesmaximal, characteristic, complemented
10C73×#1863C211yesmaximal, characteristic, complemented
11C73×#1854C211yesmaximal, characteristic, complemented
12C73×#1850C211yesmaximal, characteristic, complemented
13C73×#1807C211yesmaximal, characteristic, complemented
14C73×#1805C211yesmaximal, characteristic, complemented
15C73×#1788C211yesmaximal, characteristic
16C22×#41×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C2×C4⋊Q8×C73C2211yescharacteristic
19C2×C4×Q8×C73C2211yescharacteristic
20C2×C4×Q8×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22#475×C73—24no—
23C2×#107×C73C2211yescharacteristic
24C2×#106×C73C2211yescharacteristic
25C2×#106×C73C2211yescharacteristic
26C2×#106×C73C2211yescharacteristic
27C2×C4⋊C8×C73C2211yescharacteristic
28C2×C4⋊C8×C73C2211yescharacteristic
29#416×C73—24no—
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39#396×C73—21no—
40#393×C73—21no—
41#391×C73—21no—
42#390×C73—21no—
43#390×C73—21no—
44#390×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic
46#389×C73C2211yescharacteristic
47#389×C73C2211yescharacteristic
48#387×C73—21no—
49#382×C73C2211yescharacteristic
50#380×C73—21no—
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53C4×C22⋊C4×C73—21no—
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C2×#41×C73—22no—
62C2×#41×C73—22no—
63C2×#41×C73—22no—
64C2×#41×C73—41no—
65C2×#41×C73—41no—
66C2×#41×C73Q814yescomplemented
67C22×Q8×C73—21no—
68C22×Q8×C73C2311yescharacteristic
69C22×D4×C73—21no—
70C22×D4×C73C2311yescharacteristic
71C23×C4×C73—21no—
72C23×C4×C73C2311yescharacteristic
73C22×C8×C73—22no—
74C22×C8×C73—22no—
75C22×C8×C73—41no—
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C4⋊Q8×C73—22no—
81C4⋊Q8×C73—41no—
82C4×Q8×C73—22no—
83C4×Q8×C73—22no—
84C4×Q8×C73—41no—
85C4×Q8×C73—41no—
86#117×C73—22no—
87#117×C73—41no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73D411yescharacteristic
107C2×C22⋊C4×C73D411yescharacteristic
108C2×C42×C73—21no—
109C2×C42×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113#107×C73—41no—
114#106×C73—22no—
115#106×C73—22no—
116#106×C73—41no—
117C4⋊C8×C73—22no—
118C4⋊C8×C73—41no—
119#103×C73—22no—
120#103×C73—22no—
121#103×C73—22no—
122#103×C73D414yes—
123#102×C73—22no—
124#102×C73—22no—
125#102×C73—41no—
126#102×C73—41no—
127C22⋊C8×C73—22no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73D411yescharacteristic
135#95×C73D411yescharacteristic
136C24×C73—21no—
137C24×C73C2×D411yescharacteristic
138#41×C73—28no—
139#41×C73—44no—
140#41×C73—44no—
141#41×C73—44no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—42no—
146C2×Q8×C73—42no—
147C2×Q8×C73—81no—
148C2×Q8×C73C2×D412yes—
149C2×Q8×C73C2×Q812yes—
150C2×Q8×C73#4112yes—
151C2×D4×C73—24no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—42no—
158C2×D4×C73—42no—
159C2×D4×C73C2×Q812yes—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—24no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—42no—
173C22×C4×C73—42no—
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×Q812yes—
180C22×C4×C73#4112yes—
181C22×C4×C73C2411yescharacteristic
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
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—44no—
194C2×C8×C73C2×D412yes—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—42no—
207C4⋊C4×C73—42no—
208C4⋊C4×C73—42no—
209C4⋊C4×C73—42no—
210C4⋊C4×C73—81no—
211C4⋊C4×C73C2×D412yes—
212C22⋊C4×C73—22no—
213C22⋊C4×C73—41no—
214C22⋊C4×C73—42no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—42no—
217C22⋊C4×C73—81no—
218C22⋊C4×C73—81no—
219C22⋊C4×C73—81no—
220C22⋊C4×C73—81no—
221C42×C73—21no—
222C42×C73—21no—
223C42×C73—21no—
224C42×C73—21no—
225C42×C73—42no—
226C42×C73—42no—
227C42×C73—42no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—22no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73C22⋊Q812yes—
242C23×C73C22×D411yescharacteristic
243Q8×C73—22no—
244Q8×C73—22no—
245Q8×C73—22no—
246Q8×C73—84no—
247Q8×C73C22⋊Q814yes—
248D4×C73—22no—
249D4×C73—22no—
250D4×C73—48no—
251D4×C73—41no—
252D4×C73—41no—
253C2×C4×C73—22no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—21no—
265C2×C4×C73—22no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—48no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
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×C73C22⋊Q812yes—
293C2×C4×C73#13512yes—
294C2×C4×C73C22×D411yescharacteristic
295C2×C4×C73C22×Q811yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×C4×C73C2×#4111yescharacteristic
298C2×C4×C73H(5,𝔽2)11yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C8×C73—22no—
301C8×C73—41no—
302C8×C73—41no—
303C8×C73—41no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—41no—
308C22×C73—41no—
309C22×C73—41no—
310C22×C73—41no—
311C22×C73—42no—
312C22×C73—42no—
313C22×C73—42no—
314C22×C73—81no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73C2×C22⋊Q811yescharacteristic
319C22×C73D4211yescharacteristic
320C22×C73#54611yescharacteristic
321C22×C73C2×#13511yescharacteristic
322C22×C73#57511yescharacteristic
323C22×C73#57711yescharacteristic
324C22×C73#57711yescharacteristic
325C4×C73—22no—
326C4×C73—24no—
327C4×C73—22no—
328C4×C73—41no—
329C4×C73—42no—
330C4×C73—41no—
331C4×C73—41no—
332C4×C73—81no—
333C4×C73—81no—
334C4×C73—81no—
335C4×C73—81no—
336C4×C73—81no—
337C4×C73C2×C22⋊Q811yescharacteristic
338C4×C73#54311yescharacteristic
339C4×C73#54611yescharacteristic
340C4×C73#55111yescharacteristic
341#25951C7311yesmaximal, characteristic, direct product factor, Sylow
342C2×C73—42no—
343C2×C73—82no—
344C2×C73#243711yescharacteristic
345C2×C73#307611yescharacteristic
346C2×C73#308411yescharacteristic
347C2×C73#327111yescharacteristic
348C2×C73#328211yescharacteristic
349C2×C73#330411yescharacteristic
350C2×C73#332111yescharacteristic
351C2×#475C2×C7311yescharacteristic, complemented
352C2×#416C2×C7311yescharacteristic
353#2439C2×C7311yescharacteristic, complemented
354#2341C2×C7311yescharacteristic
355#2092C2×C7311yescharacteristic, complemented
356#2065C2×C7311yescharacteristic, complemented
357#2065C2×C7311yescharacteristic, complemented
358#2023C2×C7311yescharacteristic, complemented
359#1865C2×C7311yescharacteristic, complemented
360#1863C2×C7311yescharacteristic, complemented
361#1854C2×C7311yescharacteristic, complemented
362#1850C2×C7311yescharacteristic, complemented
363#1807C2×C7311yescharacteristic, complemented
364#1805C2×C7311yescharacteristic, complemented
365#1788C2×C7311yescharacteristic
366C73#2595111yescharacteristic, direct product factor, Sylow
367C22×#41C22×C7311yescharacteristic
368C23×C8C22×C7311yescharacteristic
369C2×C4⋊Q8C22×C7311yescharacteristic
370C2×C4×Q8C22×C7311yescharacteristic
371C2×C4×Q8C22×C7311yescharacteristic
372C2×#117C22×C7311yescharacteristic
373#475—24no—
374C2×#107C22×C7311yescharacteristic
375C2×#106C22×C7311yescharacteristic
376C2×#106C22×C7311yescharacteristic
377C2×#106C22×C7311yescharacteristic
378C2×C4⋊C8C22×C7311yescharacteristic
379C2×C4⋊C8C22×C7311yescharacteristic
380#416—24no—
381C2×#103C22×C7311yescharacteristic
382C2×#103C22×C7311yescharacteristic
383C2×#103C22×C7311yescharacteristic
384C2×#103C22×C7311yescharacteristic
385C2×#102C22×C7311yescharacteristic
386C2×#102C22×C7311yescharacteristic
387C2×#102C22×C7311yescharacteristic
388C2×#102C22×C7311yescharacteristic
389C2×C22⋊C8C22×C7311yescharacteristic
390#396—21no—
391#393—21no—
392#391—21no—
393#390—21no—
394#390—21no—
395#390C22×C7311yescharacteristic
396#390C22×C7311yescharacteristic
397#389C22×C7311yescharacteristic
398#389C22×C7311yescharacteristic
399#387—21no—
400#382C22×C7311yescharacteristic
401#380—21no—
402#380C22×C7311yescharacteristic
403#380C22×C7311yescharacteristic
404C4×C22⋊C4—21no—
405C4×C22⋊C4C22×C7311yescharacteristic
406#340C22×C7311yescharacteristic
407#340C22×C7311yescharacteristic
408#340C22×C7311yescharacteristic
409#340C22×C7311yescharacteristic
410#336C22×C7311yescharacteristic
411#336C22×C7311yescharacteristic
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—41no—
416C2×#41—41no—
417C2×#41Q8×C7314yescomplemented
418C22×Q8—21no—
419C22×Q8C23×C7311yescharacteristic
420C22×D4—21no—
421C22×D4C23×C7311yescharacteristic
422C23×C4—21no—
423C23×C4C23×C7311yescharacteristic
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—41no—
427C22×C8C23×C7311yescharacteristic
428C22×C8C23×C7311yescharacteristic
429C22×C8C23×C7311yescharacteristic
430C22×C8C23×C7311yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8—41no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×Q8—41no—
436C4×Q8—41no—
437#117—22no—
438#117—41no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4C23×C7311yescharacteristic
445C2×C4⋊C4C23×C7311yescharacteristic
446C2×C4⋊C4C23×C7311yescharacteristic
447C2×C4⋊C4C23×C7311yescharacteristic
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C4⋊C4C23×C7311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4D4×C7311yescharacteristic
458C2×C22⋊C4D4×C7311yescharacteristic
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C7311yescharacteristic
463C2×C42C23×C7311yescharacteristic
464#107—41no—
465#106—22no—
466#106—22no—
467#106—41no—
468C4⋊C8—22no—
469C4⋊C8—41no—
470#103—22no—
471#103—22no—
472#103—22no—
473#103D4×C7314yes—
474#102—22no—
475#102—22no—
476#102—41no—
477#102—41no—
478C22⋊C8—22no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95D4×C7311yescharacteristic
486#95D4×C7311yescharacteristic
487C24—21no—
488C24C2×D4×C7311yescharacteristic
489#41—28no—
490#41—44no—
491#41—44no—
492#41—44no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—81no—
499C2×Q8C2×D4×C7312yes—
500C2×Q8C2×Q8×C7312yes—
501C2×Q8#41×C7312yes—
502C2×D4—24no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4C2×Q8×C7312yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4C2×D4×C7311yescharacteristic
526C22×C4C2×D4×C7311yescharacteristic
527C22×C4C2×D4×C7311yescharacteristic
528C22×C4C2×D4×C7311yescharacteristic
529C22×C4C2×D4×C7311yescharacteristic
530C22×C4C2×Q8×C7312yes—
531C22×C4#41×C7312yes—
532C22×C4C24×C7311yescharacteristic
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—44no—
545C2×C8C2×D4×C7312yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—81no—
562C4⋊C4C2×D4×C7312yes—
563C22⋊C4—22no—
564C22⋊C4—41no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—42no—
578C42—42no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C22⋊Q8×C7312yes—
593C23C22×D4×C7311yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—22no—
597Q8—84no—
598Q8C22⋊Q8×C7314yes—
599D4—22no—
600D4—22no—
601D4—48no—
602D4—41no—
603D4—41no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—22no—
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—48no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4C22⋊Q8×C7312yes—
644C2×C4#135×C7312yes—
645C2×C4C22×D4×C7311yescharacteristic
646C2×C4C22×Q8×C7311yescharacteristic
647C2×C4C2×#41×C7311yescharacteristic
648C2×C4C2×#41×C7311yescharacteristic
649C2×C4H(5,𝔽2)×C7311yescharacteristic
650C2×C4H(5,𝔽2)×C7311yescharacteristic
651C8—22no—
652C8—41no—
653C8—41no—
654C8—41no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22C2×C22⋊Q8×C7311yescharacteristic
670C22D42×C7311yescharacteristic
671C22#546×C7311yescharacteristic
672C22C2×#135×C7311yescharacteristic
673C22#575×C7311yescharacteristic
674C22#577×C7311yescharacteristic
675C22#577×C7311yescharacteristic
676C4—22no—
677C4—22no—
678C4—24no—
679C4—41no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—81no—
684C4—81no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4C2×C22⋊Q8×C7311yescharacteristic
689C4#543×C7311yescharacteristic
690C4#546×C7311yescharacteristic
691C4#551×C7311yescharacteristic
692C2—42no—
693C2—82no—
694C2C73×#243711yescharacteristic
695C2C73×#307611yescharacteristic
696C2C73×#308411yescharacteristic
697C2C73×#327111yescharacteristic
698C2C73×#328211yescharacteristic
699C2C73×#330411yescharacteristic
700C2C73×#332111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×#41×C73C22
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×#475×C73C2semidirect
3. C73×#2439C2semidirect
5. C73×#2092C2semidirect
6. C73×#2065C2semidirect
7. C73×#2065C2semidirect
8. C73×#2023C2semidirect
9. C73×#1865C2semidirect
10. C73×#1863C2semidirect
11. C73×#1854C2semidirect
12. C73×#1850C2semidirect
13. C73×#1807C2semidirect
14. C73×#1805C2semidirect
66. C2×#41×C73Q8semidirect
341. #25951C73direct (N × H)
351. C2×#475C2×C73semidirect
353. #2439C2×C73semidirect
355. #2092C2×C73semidirect
356. #2065C2×C73semidirect
357. #2065C2×C73semidirect
358. #2023C2×C73semidirect
359. #1865C2×C73semidirect
360. #1863C2×C73semidirect
361. #1854C2×C73semidirect
362. #1850C2×C73semidirect
363. #1807C2×C73semidirect
364. #1805C2×C73semidirect
366. C73#25951direct (N × H)
417. C2×#41Q8×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#475×C732
C2×#416×C732
C73×#24392
C73×#23412
C73×#20922
C73×#20652
C73×#20232
C73×#18652
C73×#18632
C73×#18542
C73×#18502
C73×#18072
C73×#18052
C73×#17882
#2595173