Finite Group Databasebeta

← #13374533

Subgroups — #13374533

Order 1792.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#104C211yesmaximal, characteristic, complemented
2#11741525C211yesmaximal, characteristic
3#11741520C211yesmaximal, characteristic, complemented
4#11741202C211yesmaximal, characteristic, complemented
5C2×#89595C211yesmaximal, characteristic, complemented
6#11729755C211yesmaximal, characteristic, complemented
7#11729286C211yesmaximal, characteristic, complemented
8#11729283C211yesmaximal, characteristic, complemented
9#11728144C211yesmaximal, characteristic, complemented
10#11728131C211yesmaximal, characteristic, complemented
11#11728130C211yesmaximal, characteristic, complemented
12#11728128C211yesmaximal, characteristic, complemented
13#11728126C211yesmaximal, characteristic, complemented
14#11728124C211yesmaximal, characteristic, complemented
15#11728121C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×M16C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C2×#6513C2211yescharacteristic
20C2×#6513C2211yescharacteristic
21C2×#6511C2211yescharacteristic
22C2×#6511C2211yescharacteristic
23#90482C2211yescharacteristic
24C2×#6470C2211yescharacteristic, complemented
25C2×C7×#104—24no—
26C2×C7×#104C2211yescharacteristic
27C2×C7×#104C2211yescharacteristic
28C2×C7×#104C2211yescharacteristic
29C2×C7×#104C2211yescharacteristic
30#90011C411yescharacteristic, complemented
31#90011C411yescharacteristic, complemented
32#90010C411yescharacteristic, complemented
33#90010C411yescharacteristic, complemented
34#90006—21no—
35#90006—21no—
36#90006C2211yescharacteristic
37#90006C2211yescharacteristic
38#90005C2211yescharacteristic
39#90005C2211yescharacteristic
40#90000C411yescharacteristic, complemented
41#89999C411yescharacteristic, complemented
42#89990C411yescharacteristic, complemented
43#89989C411yescharacteristic, complemented
44#89979—21no—
45#89979C2211yescharacteristic
46C2×C22⋊(C7⋊C8)—21no—
47C2×C22⋊(C7⋊C8)C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49#89901C2211yescharacteristic, complemented
50#89900—21no—
51#89899—21no—
52C2×#6396C2211yescharacteristic, complemented
53C2×#6396C2211yescharacteristic, complemented
54#89894C2211yescharacteristic, complemented
55#89891C2211yescharacteristic, complemented
56#89883—21no—
57C8×C22⋊D7—21no—
58C2×#6379C2211yescharacteristic, complemented
59C2×#6379C2211yescharacteristic, complemented
60C2×#6377C2211yescharacteristic, complemented
61C2×#6377C2211yescharacteristic, complemented
62#89595—24no—
63#89353C2211yescharacteristic, complemented
64#89353C2211yescharacteristic, complemented
65#89319C2211yescharacteristic, complemented
66#89319C2211yescharacteristic, complemented
67#89318C2211yescharacteristic, complemented
68#89318C2211yescharacteristic, complemented
69#22886—71nomaximal, Sylow
70C2×C7×#41—21no—
71C2×C7×#41—21no—
72C2×C7×#41—22no—
73C2×C7×#41—22no—
74C2×C7×#41—41no—
75C2×C7×#41—41no—
76C2×C7×#41C2×C411yescharacteristic
77C2×C7×#41C2×C411yescharacteristic
78C2×C7×#41C2311yescharacteristic
79C2×C7×#41C2311yescharacteristic
80C22×C7×Q8C2×C411yescharacteristic
81C22×C7×D4—21no—
82C22×C7×D4C2×C411yescharacteristic
83C23×C4×C7—21no—
84C23×C4×C7—21no—
85C23×C4×C7C2311yescharacteristic
86C2×#1157C2311yescharacteristic
87C2×C7×M16—21no—
88C2×C7×M16—22no—
89C2×C7×M16—41no—
90C2×C7×M16C2311yescharacteristic
91C2×C7×M16C2311yescharacteristic
92C22×C7×C8—21no—
93C2×C42×C7—22no—
94C2×C42×C7—21no—
95C2×C42×C7—41no—
96C2×C42×C7C2311yescharacteristic
97C2×C42×C7C2311yescharacteristic
98#6516—21no—
99#6513—22no—
100#6513—22no—
101#6513—41no—
102#6513—41no—
103#6511—22no—
104#6511—22no—
105#6511—41no—
106#6511—41no—
107C2×#1144C2×C411yescharacteristic, complemented
108C2×#1144C2×C411yescharacteristic, complemented
109C2×#1143C2×C411yescharacteristic, complemented
110C2×#1143C2×C411yescharacteristic, complemented
111C2×#1142C2×C411yescharacteristic, complemented
112C2×#1142C2×C411yescharacteristic, complemented
113C2×#1141C2×C411yescharacteristic, complemented
114C2×#1141C2×C411yescharacteristic, complemented
115#6493C2×C411yescharacteristic
116#6493C2×C411yescharacteristic
117#6492—21no—
118C4×C22⋊D7—21no—
119C4×C22⋊D7—21no—
120#6489C2311yescharacteristic
121#6487C2×C411yescharacteristic
122#6487C2×C411yescharacteristic
123C2×#1136—21no—
124C2×#1136—21no—
125C2×#1136C2311yescharacteristic
126C2×#1136C2311yescharacteristic
127C22×C7⋊C8—21no—
128C22×C7⋊C8—21no—
129C22×C7⋊C8C2311yescharacteristic
130C22×C7⋊C8C2311yescharacteristic
131C22×C7⋊C8C2311yescharacteristic
132C22×C7⋊C8C2311yescharacteristic
133#6470—22no—
134#6470—41no—
135C2×#1131—21no—
136C2×C8×D7—21no—
137C7×#104—22no—
138C7×#104—22no—
139C7×#104—22no—
140C7×#104D414yescomplemented
141#6409C2×C411yescharacteristic, complemented
142#6409C2×C411yescharacteristic, complemented
143#6409C2×C411yescharacteristic, complemented
144#6409C2×C411yescharacteristic, complemented
145#6406C2×C411yescharacteristic, complemented
146#6406C2×C411yescharacteristic, complemented
147#6406C2×C411yescharacteristic, complemented
148#6406C2×C411yescharacteristic, complemented
149C22⋊(C7⋊C8)—21no—
150C22⋊(C7⋊C8)—21no—
151C22⋊(C7⋊C8)—21no—
152C22⋊(C7⋊C8)—21no—
153C22⋊(C7⋊C8)—21no—
154C22⋊(C7⋊C8)—21no—
155C22⋊(C7⋊C8)C2×C411yescharacteristic
156C22⋊(C7⋊C8)C2×C411yescharacteristic
157C22⋊(C7⋊C8)C2×C411yescharacteristic
158C22⋊(C7⋊C8)C2×C411yescharacteristic
159C22⋊(C7⋊C8)D411yescharacteristic
160C22⋊(C7⋊C8)D411yescharacteristic
161C22⋊(C7⋊C8)D411yescharacteristic
162C22⋊(C7⋊C8)D411yescharacteristic
163#6396—22no—
164#6396—41no—
165(C2×D7)⋊C8—21no—
166(C2×D7)⋊C8—21no—
167#6389—21no—
168Dic7⋊C8—21no—
169Dic7⋊C8—21no—
170C8×Dic7—21no—
171#6379—22no—
172#6379—41no—
173#6377—22no—
174#6377—41no—
175#3002—71no—
176C2×#444—71no—
177#2933—71no—
178C22×#104D711yescharacteristic, complemented
179#2880—71no—
180#1975—71no—
181#1938—71no—
182#1929—71no—
183#1896—71no—
184#1876—71no—
185#1876—71no—
186#1866—71no—
187#1855—71no—
188#1765—71no—
189#1749—71no—
190C24×C7—21no—
191C24×C7#4111yescharacteristic
192C7×#41—21no—
193C7×#41—21no—
194C7×#41—22no—
195C7×#41—22no—
196C7×#41—21no—
197C7×#41—21no—
198C7×#41—21no—
199C7×#41—21no—
200C7×#41—42no—
201C7×#41—42no—
202C7×#41—41no—
203C7×#41—41no—
204C7×#41—42no—
205C7×#41—42no—
206C7×#41C2×D412yes—
207C7×#41#4112yes—
208C2×C7×Q8—21no—
209C2×C7×Q8—22no—
210C2×C7×Q8—41no—
211C2×C7×Q8C22×C411yescharacteristic
212C2×C7×Q8C22×C411yescharacteristic
213C2×C7×D4—21no—
214C2×C7×D4—22no—
215C2×C7×D4—21no—
216C2×C7×D4—21no—
217C2×C7×D4—21no—
218C2×C7×D4—21no—
219C2×C7×D4—41no—
220C2×C7×D4—42no—
221C2×C7×D4—42no—
222C2×C7×D4C22×C411yescharacteristic
223C2×C7×D4C22×C411yescharacteristic
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—42no—
236C22×C4×C7—42no—
237C22×C4×C7—42no—
238C22×C4×C7—42no—
239C22×C4×C7—42no—
240C22×C4×C7C22×C411yescharacteristic
241C22×C4×C7C22×C411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7#4111yescharacteristic
245C22×C4×C7C2411yescharacteristic
246C2×C22⋊D7—21no—
247C2×C22⋊D7—21no—
248C2×C22⋊D7—21no—
249#1157—21no—
250#1157—21no—
251#1157—21no—
252#1157—21no—
253C2×D28C22×C411yescharacteristic
254C2×C4×D7—21no—
255C2×Dic14C22×C411yescharacteristic
256C7×M16—21no—
257C7×M16—21no—
258C7×M16—21no—
259C7×M16—42no—
260C7×M16C2×D412yes—
261C2×C7×C8—21no—
262C2×C7×C8—21no—
263C2×C7×C8—42no—
264C42×C7—21no—
265C42×C7—21no—
266C42×C7—21no—
267C42×C7—42no—
268C42×C7C2×D412yes—
269C22⋊Dic7—21no—
270C22⋊Dic7—21no—
271C22⋊Dic7—21no—
272#1144—22no—
273#1144—41no—
274#1143—22no—
275#1143—41no—
276#1142—22no—
277#1142—41no—
278#1141—22no—
279#1141—41no—
280(C2×D7)⋊C4—21no—
281(C2×D7)⋊C4—21no—
282C4⋊Dic7C22×C411yescharacteristic
283C4⋊Dic7C22×C411yescharacteristic
284Dic7⋊C4—21no—
285Dic7⋊C4—21no—
286C4×Dic7—21no—
287#1136—21no—
288#1136—21no—
289#1136—21no—
290#1136—21no—
291#1136—42no—
292#1136—42no—
293C2×C7⋊C8—21no—
294C2×C7⋊C8—21no—
295C2×C7⋊C8—21no—
296C2×C7⋊C8—21no—
297C2×C7⋊C8—21no—
298C2×C7⋊C8—21no—
299C2×C7⋊C8—21no—
300C2×C7⋊C8—21no—
301C2×C7⋊C8—21no—
302C2×C7⋊C8—21no—
303C2×C7⋊C8—42no—
304C2×C7⋊C8—42no—
305C2×C7⋊C8C22×C411yescharacteristic
306C2×C7⋊C8C22×C411yescharacteristic
307C2×C7⋊C8C22×C411yescharacteristic
308C2×C7⋊C8C22×C411yescharacteristic
309C2×C7⋊C8C2×D411yescharacteristic
310C2×C7⋊C8C2×D411yescharacteristic
311C2×C7⋊C8C2×D411yescharacteristic
312C2×C7⋊C8C2×D411yescharacteristic
313#1131—42no—
314C8×D7—42no—
315C22×#41C2×D711yescharacteristic
316C2×#135—71no—
317C2×#135—71no—
318C2×#131—71no—
319C2×#131—71no—
320C2×#131—71no—
321C22×M16C2×D711yescharacteristic
322#525—71no—
323C22×C42C2×D711yescharacteristic
324#452—71no—
325#452—71no—
326#451—71no—
327#450—71no—
328#449—71no—
329#449—71no—
330#448—71no—
331#447—71no—
332#444—144no—
333#436—141no—
334#435—141no—
335#435—141no—
336C8×D4—141no—
337C2×#108—71no—
338C2×#108—71no—
339#424—71no—
340C2×#104—24no—
341C2×#104—71no—
342C2×#104—71no—
343C2×#104C2×D711yescharacteristic
344C2×#104C2×D711yescharacteristic
345C2×#104C2×D711yescharacteristic
346C2×#104C2×D711yescharacteristic
347#416—71no—
348#416—71no—
349#408—71no—
350#408—71no—
351#408—71no—
352#408—141no—
353#408—141no—
354#407—71no—
355#407—141no—
356C2×C22⋊C8—71no—
357C2×C22⋊C8—71no—
358C2×C22⋊C8—141no—
359#405—71no—
360C2×#97—71no—
361C2×#97—71no—
362#341—71no—
363#341—71no—
364#339—71no—
365#339—71no—
366#336—71no—
367#336—71no—
368C23×C7—21no—
369C23×C7—21no—
370C23×C7—21no—
371C23×C7—22no—
372C23×C7—21no—
373C23×C7—41no—
374C23×C7—42no—
375C23×C7—42no—
376C23×C7—81no—
377C23×C7C4×D411yescharacteristic
378C23×C7C4×D411yescharacteristic
379C23×C7C2×#4111yescharacteristic
380C22×D7—21no—
381C7×Q8—21no—
382C7×Q8—21no—
383C7×Q8—21no—
384C7×Q8—42no—
385C7×Q8C4×D412yes—
386C7×D4—22no—
387C7×D4—22no—
388C7×D4—21no—
389C7×D4—21no—
390C7×D4—21no—
391C7×D4—42no—
392C7×D4—42no—
393C7×D4—42no—
394C7×D4—41no—
395C7×D4—41no—
396C7×D4C4×D412yes—
397C2×C4×C7—21no—
398C2×C4×C7—21no—
399C2×C4×C7—21no—
400C2×C4×C7—21no—
401C2×C4×C7—21no—
402C2×C4×C7—21no—
403C2×C4×C7—21no—
404C2×C4×C7—22no—
405C2×C4×C7—21no—
406C2×C4×C7—21no—
407C2×C4×C7—22no—
408C2×C4×C7—21no—
409C2×C4×C7—21no—
410C2×C4×C7—22no—
411C2×C4×C7—21no—
412C2×C4×C7—22no—
413C2×C4×C7—42no—
414C2×C4×C7—42no—
415C2×C4×C7—42no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—48no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7C4×D411yescharacteristic
424C2×C4×C7C4×D411yescharacteristic
425C2×C4×C7C23×C411yescharacteristic
426C2×C4×C7C22×D411yescharacteristic
427C2×C4×C7C22×D411yescharacteristic
428C2×C4×C7C2×#4111yescharacteristic
429C2×C4×C7H(5,𝔽2)11yescharacteristic
430C2×C4×C7H(5,𝔽2)11yescharacteristic
431C22⋊D7—41no—
432C22⋊D7—41no—
433C22⋊D7—42no—
434C22⋊D7—81no—
435C2×Dic7—21no—
436C2×Dic7—21no—
437C2×Dic7—21no—
438D28—21no—
439D28—21no—
440C4×D7—41no—
441C4×D7—41no—
442Dic14—21no—
443Dic14—21no—
444C7×C8—22no—
445C7×C8—41no—
446C7⋊C8—21no—
447C7⋊C8—21no—
448C7⋊C8—21no—
449C7⋊C8—21no—
450C7⋊C8—21no—
451C7⋊C8—21no—
452C7⋊C8—21no—
453C7⋊C8—21no—
454C7⋊C8—41no—
455C7⋊C8—41no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—41no—
461C2×#41—41no—
462C2×#41—71no—
463C2×#41C4×D711yescharacteristic
464C2×#41C4×D711yescharacteristic
465C2×#41C22×D711yescharacteristic
466C2×#41C22×D711yescharacteristic
467C22×Q8C4×D711yescharacteristic
468C22×D4—21no—
469C22×D4C4×D711yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C22×D711yescharacteristic
473#135—142no—
474#135—142no—
475#135—281no—
476#135—281no—
477C2×Q16—71no—
478C2×Q16—71no—
479C2×SD16—71no—
480C2×SD16—71no—
481C2×SD16—71no—
482C2×SD16—71no—
483C2×D8—71no—
484C2×D8—71no—
485#131—142no—
486#131—142no—
487#131—142no—
488#131—281no—
489#131—281no—
490#131—281no—
491C2×M16—21no—
492C2×M16—22no—
493C2×M16—41no—
494C2×M16—71no—
495C2×M16—71no—
496C2×M16—141no—
497C2×M16—141no—
498C2×M16—141no—
499C2×M16C22×D711yescharacteristic
500C2×M16C22×D711yescharacteristic
501C22×C8—21no—
502C22×C8—71no—
503C22×C8—71no—
504C22×C8—71no—
505C22×C8—71no—
506C22×C8—141no—
507C22×C8—141no—
508C22×C8—141no—
509#123—141no—
510C22⋊Q8—71no—
511C22⋊Q8—71no—
512#121—71no—
513#121—71no—
514#120—141no—
515C4×D4—141no—
516C4×D4—141no—
517#117—71no—
518C2×C42—22no—
519C2×C42—21no—
520C2×C42—41no—
521C2×C42C22×D711yescharacteristic
522C2×C42C22×D711yescharacteristic
523#108—142no—
524#108—281no—
525C4⋊C8—141no—
526C4⋊C8—141no—
527#104—22no—
528#104—22no—
529#104—22no—
530#104—142no—
531#104—281no—
532#104C22⋊D714yescomplemented
533#103—71no—
534#103—71no—
535#103—71no—
536#103—71no—
537#102—71no—
538#102—71no—
539#102—71no—
540#102—71no—
541C22⋊C8—71no—
542C22⋊C8—71no—
543C22⋊C8—71no—
544C22⋊C8—71no—
545C22⋊C8—71no—
546C22⋊C8—71no—
547C22⋊C8—71no—
548C22⋊C8—71no—
549C22⋊C8—141no—
550C22⋊C8—141no—
551C22⋊C8—141no—
552C22⋊C8—141no—
553C22⋊C8—141no—
554C22⋊C8—141no—
555C22⋊C8—141no—
556C22⋊C8—141no—
557#97—141no—
558#97—142no—
559#97—281no—
560C4×C8—141no—
561C22×C7—21no—
562C22×C7—21no—
563C22×C7—21no—
564C22×C7—21no—
565C22×C7—21no—
566C22×C7—22no—
567C22×C7—21no—
568C22×C7—21no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—41no—
572C22×C7—41no—
573C22×C7—41no—
574C22×C7—41no—
575C22×C7—41no—
576C22×C7—84no—
577C22×C7#44412yescomplemented
578C22×C7C2×C4×D411yescharacteristic
579C22×C7#54611yescharacteristic
580C22×C7#55111yescharacteristic
581C2×D7—41no—
582C2×D7—41no—
583C2×D7—41no—
584C4×C7—21no—
585C4×C7—21no—
586C4×C7—22no—
587C4×C7—42no—
588C4×C7—42no—
589C4×C7—41no—
590C4×C7C2×C4×D411yescharacteristic
591C4×C7#51811yescharacteristic
592C4×C7D4211yescharacteristic
593C4×C7#54611yescharacteristic
594Dic7—41no—
595Dic7—41no—
596Dic7—41no—
597C24—21no—
598C24#115911yescharacteristic
599#41—21no—
600#41—21no—
601#41—22no—
602#41—22no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—21no—
607#41—42no—
608#41—42no—
609#41—41no—
610#41—41no—
611#41—42no—
612#41—42no—
613#41—141no—
614#41—141no—
615#41—141no—
616#41—141no—
617#41#115712yes—
618#41C2×C22⋊D712yes—
619C2×Q8—21no—
620C2×Q8—22no—
621C2×Q8—41no—
622C2×Q8—71no—
623C2×Q8C2×C4×D711yescharacteristic
624C2×Q8C2×C4×D711yescharacteristic
625C2×D4—21no—
626C2×D4—22no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—41no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—71no—
635C2×D4—141no—
636C2×D4—141no—
637C2×D4—141no—
638C2×D4C2×C4×D711yescharacteristic
639C2×D4C2×C4×D711yescharacteristic
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—141no—
657C22×C4C2×C4×D711yescharacteristic
658C22×C4C2×C4×D711yescharacteristic
659C22×C4D4×D711yescharacteristic
660C22×C4D4×D711yescharacteristic
661C22×C4#115911yescharacteristic
662C22×C4C23×D711yescharacteristic
663Q16—142no—
664Q16—281no—
665SD16—142no—
666SD16—142no—
667SD16—281no—
668SD16—281no—
669D8—142no—
670D8—281no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—42no—
675M16—141no—
676M16—141no—
677M16—141no—
678M16—141no—
679M16—282no—
680M16—282no—
681M16—282no—
682M16C2×C22⋊D712yes—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—42no—
686C2×C8—71no—
687C2×C8—71no—
688C2×C8—71no—
689C2×C8—71no—
690C2×C8—71no—
691C2×C8—71no—
692C2×C8—71no—
693C2×C8—71no—
694C2×C8—141no—
695C2×C8—141no—
696C2×C8—141no—
697C2×C8—141no—
698C2×C8—141no—
699C2×C8—141no—
700C2×C8—141no—
701C2×C8—141no—
702C2×C8—141no—
703C2×C8—141no—
704C2×C8—282no—
705C2×C8—282no—
706C2×C8—282no—
707C4⋊C4—71no—
708C4⋊C4—71no—
709C4⋊C4—141no—
710C4⋊C4—141no—
711C22⋊C4—141no—
712C22⋊C4—141no—
713C22⋊C4—141no—
714C22⋊C4—141no—
715C22⋊C4—141no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—42no—
720C42—141no—
721C42C2×C22⋊D712yes—
722C2×C7—21no—
723C2×C7—22no—
724C2×C7—21no—
725C2×C7—41no—
726C2×C7—42no—
727C2×C7—81no—
728C2×C7#235811yescharacteristic
729C2×C7C2×#44411yescharacteristic
730C2×C7#295611yescharacteristic
731D7—81no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—81no—
741C23—141no—
742C23(C22⋊D7)⋊C411yescharacteristic
743C23(C22⋊D7)⋊C411yescharacteristic
744C23C2×#115911yescharacteristic
745Q8—21no—
746Q8—21no—
747Q8—21no—
748Q8—42no—
749Q8—141no—
750Q8—141no—
751Q8C4×C22⋊D712yes—
752D4—22no—
753D4—22no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—41no—
761D4—41no—
762D4—141no—
763D4—141no—
764D4—281no—
765D4—281no—
766D4—282no—
767D4—561no—
768D4C4×C22⋊D712yes—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—141no—
796C2×C4—141no—
797C2×C4—141no—
798C2×C4—281no—
799C2×C4—281no—
800C2×C4(C22⋊D7)⋊C411yescharacteristic
801C2×C4(C22⋊D7)⋊C411yescharacteristic
802C2×C4C22×C4×D711yescharacteristic
803C2×C4C2×#115711yescharacteristic
804C2×C4C2×D4×D711yescharacteristic
805C2×C4#654811yescharacteristic
806C2×C4#654811yescharacteristic
807C2×C4C22×C22⋊D711yescharacteristic
808C8—22no—
809C8—41no—
810C8—141no—
811C8—141no—
812C8—141no—
813C8—141no—
814C8—141no—
815C8—141no—
816C8—141no—
817C8—141no—
818C8—281no—
819C8—281no—
820C7#2288611yescharacteristic, complemented, Sylow
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—22no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22—281no—
838C22—281no—
839C22—281no—
840C22#8959512yescomplemented
841C22C2×(C22⋊D7)⋊C411yescharacteristic
842C22#9018611yescharacteristic
843C22#9049711yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—281no—
851C4—281no—
852C4—281no—
853C4#9017711yescharacteristic
854C4#9018111yescharacteristic
855C4C2×C4×C22⋊D711yescharacteristic
856C4D4×C22⋊D711yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—561no—
864C2C2×#8959511yescharacteristic
865C2#1173642511yescharacteristic
866C2#1173954411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC22×C7×#104C2
socleC22×C7C2×C4×D4
prime radical#11741525C2
cosocleC22×C4×C7C24
hypercenterC22×#104D7
hypocenterC7#22886
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
1. C22×C7×#104C2semidirect
3. #11741520C2semidirect
4. #11741202C2semidirect
5. C2×#89595C2semidirect
6. #11729755C2semidirect
7. #11729286C2semidirect
8. #11729283C2semidirect
9. #11728144C2semidirect
10. #11728131C2semidirect
11. #11728130C2semidirect
12. #11728128C2semidirect
13. #11728126C2semidirect
14. #11728124C2semidirect
15. #11728121C2semidirect
24. C2×#6470C22semidirect
30. #90011C4semidirect
31. #90011C4semidirect
32. #90010C4semidirect
33. #90010C4semidirect
40. #90000C4semidirect
41. #89999C4semidirect
42. #89990C4semidirect
43. #89989C4semidirect
49. #89901C22semidirect
52. C2×#6396C22semidirect
53. C2×#6396C22semidirect
54. #89894C22semidirect
55. #89891C22semidirect
58. C2×#6379C22semidirect
59. C2×#6379C22semidirect
60. C2×#6377C22semidirect
61. C2×#6377C22semidirect
63. #89353C22semidirect
64. #89353C22semidirect
65. #89319C22semidirect
66. #89319C22semidirect
67. #89318C22semidirect
68. #89318C22semidirect
107. C2×#1144C2×C4semidirect
108. C2×#1144C2×C4semidirect
109. C2×#1143C2×C4semidirect
110. C2×#1143C2×C4semidirect
111. C2×#1142C2×C4semidirect
112. C2×#1142C2×C4semidirect
113. C2×#1141C2×C4semidirect
114. C2×#1141C2×C4semidirect
140. C7×#104D4semidirect
141. #6409C2×C4semidirect
142. #6409C2×C4semidirect
143. #6409C2×C4semidirect
144. #6409C2×C4semidirect
145. #6406C2×C4semidirect
146. #6406C2×C4semidirect
147. #6406C2×C4semidirect
148. #6406C2×C4semidirect
178. C22×#104D7semidirect
532. #104C22⋊D7semidirect
577. C22×C7#444semidirect
820. C7#22886semidirect
840. C22#89595semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1042
#117415252
#117415202
#117412022
C2×#895952
#117297552
#117292862
#117292832
#117281442
#117281312
#117281302
#117281282
#117281262
#117281242
#117281212
#228867